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SHITHSOSIAS IXSTITTJTIOi; 

BUREAU OF AMEEICAX ETHNOLOGY 

BULLETIH 5 7 



.\}y KTEODUCTIOX TO THE STUDY 
OF THE MAYA HIEROGLYPHS 



BY 



-YLY-^'VS GKISWOLD MORLEY 




GOVERXilEyT PBrSTTKG OFFIC; 
1915 



LETTEE OF TRANSMITTAL 



Smithsonian Institution, 
Bureau of American Ethnology, 

Washington, D. C, January 7, IQlJf.. 

Sir: I have the honor to submit the accompanying manuscript of 
a memoir bearing the title "An Introduction to the Study of the 
Maya Hieroglyphs," by Sylvanus Griswold Morley, and to recom- 
mend its publication as a bulletin of the Bureau of American Eth- 
nology. 

The hieroglyphic writing developed by the Maya of Central America 
and southern Mexico was probably the foremost intellectual achieve- 
ment of pre-Columbian times in the New World, and as such it de- 
serves equal attention with other graphic systems of antiquity. 

The earliest inscriptions now extant probably date from about 
the beginning of the Christian era, but such is the complexity of the 
glyphs and subject matter even at this early period, that in order to 
estimate the age of the system it is necessary to postulate a far greater 
antiquity for its origin. Indeed all that can be accepted safely in 
this direction is that many centuries must have elapsed before the 
Maya hieroglyphic -writing could have been developed to the highly 
complex stage where we first encounter it. 

The first student to make any progress in deciphering the Maya 
inscriptions was Prof. Ernst Forstem'ann, of the Royal Library at 
Dresden. About 1880 Professor Forstemann published a facsimile 
reproduction of the Dresden codex, and for the next twenty years 
devoted the greater part of his time to the elucidation of this manu- 
script. He it was who first discovered and worked out the ingenious 
vigesimal system of numeration used by the Maya, and who first 
pointed out how this system was utilized to record astronomical and 
chronological facts. In short, his pioneer work made possible all 
subsequent progress in deciphering Maya texts. 

Curiously eno\igh, about the same time, or a little later (in 1891), 
another student of Ihe same subject, Mr. J. T. Goodman, of Alameda, 
California, working independently and without knowledge of Pro- 
fessor Forstemann's researches, also succeeded in deciphering the 
chronological parts of the Maya texts, and in determining the values 
of the head-variant numerals. Mr. Goodman also perfected some 

in 



IV LET'i'EB OF TEANSMITTAL 



tiiblcs, "The Archaic (lironological Cnlondar'' and "The Archaic 
Annual Calendar," whicli greatly facilitate the decipherment of the 
calculations recorded in the texts. 

It must be admitted that very little progress has been made in 
deciphering the Maya glyphs except tliose relating to the calendar and 
chronology; that is, the signs for tho various time periods (days and 
months), the numerals, and a few name-glyphs; however, as these 
known signs comprise possibly two-fifths of all the glyphs, it is clear 
that the general tenor of the Maya inscriptions is no longer concealed 
from us. The remaining three-lifths probably tell tlie nature of the 
events which occurred on the corresponding dates, and it is to these 
we must turn for the subject matter of Maya history. The deci- 
phering of this textual residuum is enormously complicated by the 
character of the Maya glyphs, which for the greater part are ideo- 
graphic rather than phonetic ; that is, the various symbols represent 
ideas rather than sounds. 

In a graphic system composed largely of ideographic elements it 
is extremely difficult to determine the meanings of the different signs, 
since little or no help is to be derived fiom varying combinations of 
elements as in a phonetic system. In phonetic writing the symbols 
have fixed sounds, which are unchanging throughout, and when these 
values have once been determined, they may be substituted for the 
characters whereA'cr they occur, and thus words are formed. 

While the Maya glyphs largely represent ideas, indubitable traces 
of phoneticism and phonetic composition appear. There are per- 
haps half a dozen glyphs in all which are laiown to be constructed 
on a purely phonetic basis, and as the remaining glyphs are gradually 
deciphered this number will doubtless be increased. 

The progress which has been made in deciphering the Maya inscrip- 
tions may be sximmarized as fo'llows: The Maya calendar, chronology, 
and astronomy as recorded in the hieroglyphic texts have been care- 
fully worked out, and it is unlikely that future discoveries wiU change 
our present conception of them. There remains, however, a group of 
glyphs which are probably non-calendric, non-chronologic, and non- 
astronomic in character. These, it may be reasonably expected, 
will be found to describe the subject matter of Maya history; that is, 
they probably set forth the nature <.f the events which took place on 
tho diittw recoi'ded. An analogy would be the following: Supposing, 
in scumiin}.' a history of the United States, only the dates could be 
read. Wo would find, for example, July 4, 1776, "followed by unknown 
characters; Aprd 12, 1861, by others; and March 4, 191 2,' by others. 
This, then, is the case with tho Maya glyphs— we find dates "followed 
by glyphs ol' unknown meaning, which presumably set forth the 
nature of the corresponding events. In a word, we know now the 



LETIEB OF lEAXsMlIIAL , Y 

chronologic skeleton of Maya history; it remains to work out the 
more intimate details which alone can make it a vital force. 

The published writings on the subject of the Maya hieroglyphs have 
become so voluminous, and are so T*-ideiy :?cattered and inaccessible, 
that it is difficult for student:^ of Central Araerican archeology to 
become f amihar with what has been accomplished in tius important 
field of investigation. In the present memoir Mr. ^lorley, who hsis 
devoted a ijumber of years to the study of Maya archeology, and 
especially to the hieroglyphs, summarizes the restilts of these re- 
searches to the present timCj and it is beheved that this Introduction 
to the Study of the Maya Hieroglyphs will be the means of enabling 
ready and closer acquaintance with this interesting though intricate 
subject. 

Verv" respectfully, 

F. W. Hodge, 

Ethnologist-in-Charge. A 

Dr. Chakt.ks D. Walcott, 

Secretary of the SmWisonian Institution, 

Washington, D. C. 



PREFACE 



With the great expansion of interest in American archeology during 
the last few years there has grown to be a corresponding need and 
denaand for primary textbooks, aroheological primers so to speak, 
which will enable the general reader, without previous knowledge of 
the science, to understand its several branches. With this end in 
view, the author has prepared An Introduction to the Study of the 
Maya Hieroglyphs. 

The need for such a textbook in this particular field is suggested 
by two considerations: (1) The writings of previous investigators, 
having been designed to meet the needs of the speciaUst rather than 
those of the beginner, are for the greater part too advanced and 
technical for general comprehension; and (2) these writings are scat- 
tered through many publications, periodicals as well as books, some 
in foreign languages, and almost all difi&cult of access to the average 
reader. 

To the second of these considerations, however, the writings of 
Mr. C. P. Bowditch, of Boston, Massachusetts, offer a conspicuous 
exception, particularly his final contribution to this subject, entitled 
"The Numeration, Calendar Systems, and Astronomical Knowledge 
of the Mayas," the publication of which in 1910 marked the dawn of 
a new era in the study of the Maya hieroglyphic writing. In this 
work Mr. Bowditch exhaustively summarizes all previous knowledge 
of the subject, and also indicates the most promising lines for future 
investigation. The book is a vast storehouse of heretofore scattered 
material, now gathered" together for the first time and presented to 
the student in a readily accessible form. Indeed, so thorough is its 
treatment, the result of many years of intensive study, that the 
writer would have hesitated to bring out another work, necessarily 
covering much of the same ground, had it not been for his belief that 
Mr. Bowditch's book is too advanced for lay comprehension. The 
Maya hieroglyphic writing is exceedingly intricate; its subject matter 
is complex and its forms irregular; and in order to be understood it 
must be presented in a very elementary way. The writer believes that 
this primer method of treatment has not been followed in the publi- 
cation in question and, furthermore, that the omission of specimen 
texts, which would give the student practice in deciphering the glyphs, 
renders it too technical for use by the beginner. 



VITI PREFACE 

Acknowledgment should bo niiulo here to Mr. Bowditch fur liis 
courtesy in permitting the reproduction of a nuinher of driiwirigs 
from his book, the ((xnrnples of the period, day and jiioiitli glyphs 
figured being derived almost entirely from this source; and in.u larger 
WMise for his share in the establishment of instruction in this fi<il(l of 
reseiireh at Harvard University where the writer first took up these 
studies. 

In the limited space available it would have been impossible to 
present a detailed picture of the Maya civilization, nor indeed is (Jiis 
essential to the purpose of the book. It has been thought advisable, 
however, to precede the general discussion of the hieroglyphs with a 
brief review of the habitat, history, customs, governmeni , and religion 
of the ancient Maya, so that Uie reader may gather a general idea 
of the remarkable people whoso writing and calendar he is about to 
study. 



CONTENTS 



Pago 

Chapter I. The Maya 1 

Habitat 1 

History 2 

Manners and customs 7 

II. The Maya hieroglyphic writing 22 

III. How the Maya reckoned tiine 37 

The tonalamatl, or 260-day period 41 

The haab, or year of 365 days 44 

The Calendar Round, or 18,980-day period 51 

The Long Count 60 

Initial Series 63 

The introducing glyph 64 

The cycle glyph 68 

The katun glyph. 68 

The tun glyph 70 

The uinal glyph , 70 

The kin glyph 72 

Secondary Series 74 

Calendar-round dates 76 

Period-ending dates 77 

U kahlay katunob 79 

IV. Maya arithmetic 87 

Bar and dot numerals 87 

Head-variant numerals 96 

First method of numeration 105 

Number of cycles in a great cycle 107 

Second method of numeration 129 

First step in solving Maya numbers 134 

Second step in solving Maya numbers 135 

Third step in solving Maya numbers 136 

Fourth step in solving Maya numbers 138 

Fifth step in solving Maya numbers 151 

V. The inscriptions 156 

Texts recording Initial Series 157 

Texts recording Initial Series and Secondary Series 207 

Texts recording Period Endings 222 

Texts recording Initial Series, Secondary Series, and Period 

Endings 233 

Errors in the originals 245 

VI. Thecodices 251 

Texts recording tonalamatls 251 

Texts recording Initial Series 266 

Texts recording Serpent Numbers - 273 

Texts recording Ascending Series 276 

IX 



List of Tables 

Page 

Table I. The twentr Maya day names 37 

II. Sequence of Maya days 42 

III. The divisions of the Maya year. 45 

IV. Pfidtions of days at the end of a year 48 

V. Relati-ve positions of days beginning Maya years 53 

VI. P'Tsitions of da>-s in di-sisdons of Maya year 55 

VII. Posirions of days in di%-isions of Maya year according to Maya nota- 
tion 55 

VIII. The Maya lime-periods 62 

IX. Sequence of katuns in u kaUay kattmob SO 

X. Characteristics of head-variant ntimerals 0-19. inclusive 103 

XI . Sequence of twenty o.'nsectitive dates in the month Pop Ill . 

XII. Comparison of the two methods of mimeiarion 133 

XIII. Values of higher periods in terms of lowest, in ins'^ripxioEs 135 

XIV. Values of higher periods in terms of lowest, in ccJices 135 

XV. The 365 posirions in the Maya year 141 

Xr\"I. S-0 Calendar Rounds espresed in Arabic and Maya notarion 143 

X\"II. Inteirelationfihip of dates on Sielse E. F, and J and Zoomorph G. 

Quirigua __ 239 

X 



ILLUSTRATIONS 



Page 
Plate 1. The Maya territory, showing locations of principal cities (map)... 1 

2. Diagram showing periods of occupancy of principal southern cities . 15 

3. Page 74 of the Dresden Codex, showing the end of the world (accord- 

ing to Forstemann) '. 32 

4. Diagram showing occurrence of dates recorded in Cj'cle 9 35 

5. Tonalamatl wheel, showing sequence of the 260 differently named 

days 43 

6. Glyphs representing Initial Series, showing use of bar and dot 

numerals and normal-form period glyphs 157 

7. Glyphs representing Initial Series, showing use of bar and dot 

numerals and head- variant period glyphs 1C7 

8. Glyijhs representing Initial Series, showing use of bar and dot 

numerals and head-variant period glyphs 170 

9. Glyphs representing Initial Series, showing use of bar and dot 

numerals and head-variant period glyphs 176 

10. Glyphs representing Initial Series, showing vise of bar and dot 

numerals and head-variant period glyphs — Stela 3, Tikal 178 

11. Glyphs representing Initial Series, showing use of bar and dot 

numerals and head-variant period glyphs — Stela A (east side), 
Quirigua 179 

12. Glyphs representing Initial Series, showing use of head- variant 

numerals and period glyphs 180 

13. Oldest Initial Series at Gopan — Stela 15 187 

14. Initial Series on Stela D, Copan, showing full-figure numeral glyphs 

and period glyphs 188 

15. Initial Series on Stela J, Copan _ 191 

16. Initial Series and Secondary Series on Lintel 21, Yaxchilan 207 

17. Initial Series and Secondarj' Series on Stela 1, Piedras Xegras 210 

18. Initial Series and Secondary Series on Stela K, Quirigua 213 

19. Initial Series and Secondary Series on Stela F (west side), Quirigua. 218 

20. Initial Series on Stela F (east side), Quirigua 220 

21. Examples of Period-ending dates in Cycle 9 223 

22. Examples of Period-ending dates in cycles other than Cycle 9 227 

23. Initial Series, Secondary Series, and Period-ending dates on Stela 3, 

Piedras Negras 233 

24. Initial Series, Secondary Series, and Period-ending dates on Stela E 

(west side), Quirigua 235 

25. Calendar-round dates on Altar 5, Tikal 240 

26. Initial Series on Stela N, Copan, showing error in month coefficient. . 248 

27. Page 12 of the Dresden Codex, showing tonalamatls in all three 

divisions - 254 

28. Page 15 of the Dresden Codex, showing tonalamatls in all three 

divisions 260 

29. Middle divisions of pages 10 and 11 of the Codex Tro-Cortesiano, 

showing one tonalamatl extending across the two pages 262 

30. Page 102 of the Codex Tro-Cortesiano, showing tonalamatls in the 

lower three divisions 263 

XI 



XII ILLUSTRATIONS 

Page 

Plate 31. Page 24 of the Dresden Codex, showing Initial Series 206 

32. Page 62 of the Dresden Coflex, showing the Serpent Numbers 273 

FiGTTEE 1. Itzamna, chief deity of the Maya Pantheon 16 

2. Kukulcan, God of I>earning 17 

3. Ahpuch, God of Death 17 

4. The God of War ■ 17 

5. Ek Ahau, the Black ( 'aptaiii, war deity 18 

6. Yum Kaax, Lord of the Harvest 18 

7. XamanEk, the North Star God 10 

8. Conflict between the Gods of Life and Death (Kukulcan and Ah- 

puch) 19 

9. Outlines of the glyphs •. 22 

10. Examples of glyph elision, showing elimination of all parts except 

essential element 23 

11. Xormal-torm and head- variant glyphs, showing retention of essen- 

tial element in each 24 

12. Normal-form and head- variant glyphs, showing absence of com- 

mon essential element 25 

13. Glyphs built up on a phonetic basis 28 

14. A rebus. Aztec, and probably Maya, personal and place names 

were written in a corresponding manner 29 

15. Aztec place names 30 

16. The day signs in the inscriptions 38 

17. The day signs in the codices 39 

18. Sign for the tonalamatl (according to Goodman) 44 

19. The month signs in the inscriptions 49 

20. The month signs in the codices 50 

21. Diagram showing engagement of tonalamatl wheel of 260 days 

and haab wheel of 365 positions; the combination of the two 

giving the Calendar Round, or 52-year period 57 

22. Signs for the Calendar Round 59 

23. Diagram showing section of Calendar-round wheel 64 

24. Initial-series "introducing glyph " 65 

25. Signs for the cycle 68 

26. Full-figure variant of cycle sign 69 

27. Signs for the katun 69 

28. Full-figure variant of katun sign 70 

29 . Signs for the tun 70 

30. Full-figure variant of tun sign 70 

31. Signs for the uinal 71 

32. Full-figure variant of uinal sign on Zoomorph B, Quirigua 71 

33. Full-figure variant of iiinal sign on Stela D, Copan 71 

34. Signs for the kin 72 

35. Full-figure variant of kin sign 73 

36. Period glyphs, from widely separated sites and of different epochs, 

showing persistence of essential elements 74 

37. Ending signs and elements 78 

38. "Snake" or "knot" element as used with day sign Ahau, possibly 

indicating presence of the u kahlay katunob in the inscriptions. 83 

39. Normal forms of numerals 1 to 19, inclusive, in the codices 88 

40. Normal forms of numerals 1 to 19, inclusive, in the inscriptions. . . 89 

41. Examples of bar and dot numeral 5, showing the ornamentation 

which the bar underwent without affecting its numerical value. . 89 



ILLUSTRATIONS XIII 

Figure 42. Examples showing the way in which numerals 1, 2, 6, 7, 11, 12, 16, page 

and 17 are not used with period, day, or month signs 90 

43. Examples showing the way in which numerals 1, 2, 6, 7, 11, 12, 16, 

and 17 are used mth period , day, or month s^s 90 

44. Normal forms of numerals 1 to 13, inclusive, in the Books of Chilan 

Balam ; gi 

45. Sign for 20 in the codices 92 

46. Sign for in the codices 92 

47. Sign for in the inscriptions 93 

48. Figure showing possible derivation of the sign for in the inscrip- 

tions 93 

49. Special sign for used exclusively as a month coefficient 94 

50. Examples of the use of bar and dot numerals with period, day, or 

month signs 95 

51. Head-variant numerals 1 to 7, inclusive 97 

52. Head-variant numerals 8 to 13, inclusive 98 

53. Head-variant numerals 14 to 19, inclusive, and 99 

54. A sign for 0, used also to express the idea "ending" or "end of" 

in Period-ending dates 102 

55. Examples of the use of head-variant numerals with period, day, or 

mouth signs 104 

56. Examples of the first method of numeration, used almost exclu- 

sively in the inscriptions 105 

57. Signs for the cycle showing coefficients above 13 110 

58. Part of the inscription on Stela N, Copan, showing a number com- 

posed of six periods 115 

59. Part of the inscription in the Temple of the Inscriptions, Palenque, 

showing a number composed of seven periods 115 

60. Part of the inscription on Stela 10, Tikal (probably an Initial 

Series), showing a number composed of eight periods 115 

61. Signs for the great cycle and the great-great cycle 118 

62. Glyphs shoeing misplacement of the kin coefficient or elimination 

of a period glyph 128 

63. Examples of the second method of numeration, used exclusively 

in the codices 131 

64. Figure showing the use of the "minus "or "backward" sign in the 

codices 137 

65. Sign for the "month indicator " 153 

66. Diagram showing the method of designating particular glyphs in a 

text 156 

67. Signs representing the hotun, or 5-tun, period 166 

68. Initial Series showing bar and dot numerals and head-variant 

period glyphs 174 

69. Initial Series showing head-variant numerals and period glyphs. . . 183 

70. Initial Series showing head-variant numerals and period glyphs. . . 186 

71. Initial Series on Stela H, Quirigua 193 

72. The tun, uinal, and kin coefficients on Stela H, Quirigua 194 

73. The Initial Series on the Tuxtla Statuette, the oldest Initial Series 

known (in the early part of Cycle 8) 195 

74 The introducing glyph (?) of the Initial Series on the Tuxtla Statu- 
ette... 196 

75. Drawings of the Initial Series: A, On the Leyden Plate; B, on a 

lintel from the Temple of the Initial Series, Chichen Itza 197 



XIV ILLUSTRATIONS 



Figure 76. The Cycle-10 Initial Series from Quen Santo 200 

77. Initial Series which proceed from a date prior to 4 Ahau 8 Cumhu, 

the starting point of Maya chronology. 204 

78. The Initial Series on Stela J, Quirigua 215 

79. The Secondary Series on Stela J, Quirigua 216 

80. Glyphs which may disclose the nature of the events that happened 

at Quirigua on the dates: a, 9. 14. 13. 4. 17 12 Caban 5 Kayab; 

6,9.15.6. 14. 6 6Cimi 4Tzec 221 

81. The Initial Series, Secondary Series, and Period-ending date on 

Altar S, Copan 232 

82. The Initial Series on Stela E (east side), Quirigua 236 

83. Calendai'-round dates 241 

84. Texts showing actual errors in the originals 245 

85. Example of first method of numeration in the codices (part of page 

69 of the Dresden Codex) 275 



BIBLIOGRAPHY 



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Yucatan. Madrid. (Reprint in Anales Mm. Nac. de Mexico, vi, pp. 17-122, 

Mexico, 1900.) 
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1908 a. Explorations of the upper Usumatsintlu and adjacent roginn. Ibid., 



, No. 1, PP- 1-51- 



XVI BIBLIOGKAPHY 

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See also Bulletin 28. 
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2 vols. New York. 

1843. Incidents of travel in Yucatan. 2 vols. New York. 

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No. 3, pp. 241-270, Washington. 
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Itza, reduccion, y progresses de la de el Lacandon y otras naciones de el reyno de 

Guatimala, a las provincias de Yucatan, en la America septentrional. Madrid. 



BUREAU OF AMERICAN ETHNOLOGY 



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THE MAYA TERRITORY, SHOWING LOCATIONS OF PRINCIPAL CITIES 



AN INTRODUCTION TO THE STUDY OF THE MAYA HIEROGLYPHS 

By SYLVANUS GRISWOLD MORLEY 



Chapter I. THE MAYA 
Habitat 

Broadly speaking, the Maya were a lowland people, inhabiting the 
Atlantic coast plains of southern Mexico- and northern Central Amer- 
ica. (See pi. 1.) The southern part of this region is abundantly 
watered by a network of streams, many of which have their rise in 
the Cordillera, while the northern part, comprising the peninsula of 
Yucatan, is entirely lacking in water courses and, were it not for 
natural wells (cenotes) here and there, would be uninhabitable. This 
condition in the north is due to the geologic formation of the penin- 
sula, a vast plain underlaid by limestone through which water 
quickly percolates to subterranean channels. 

In the south the country is densely forested, though occasional 
savannas break the monotony of the tropical jungles. The rolling 
surface is traversed in places by ranges of hills, the most important 
of which are the Cockscomb Mountains of British Honduras; these 
attain an elevation of 3,700 feet. In Yucatan the nature of the soil 
and the water-supply not being favorable to the growth of a luxuriant 
vegetation, this region is covered with a smaller forest growth and a 
sparser bush than the area farther southward. 

The chmate of the region occupied by the Maya is tropical; there 
are two seasons, the rainy and the dry. The former lasts from May 
or June until January or February, there being considerable local 
variation not only in the length of this season but also in the time of 
its beginning. 

Deer, tapirs, peccaries, jaguars, and game of many other kinds 
abound throughout the entire region, and doubtless formed a large 
part of the food supply in ancient times, though formerly corn was 
the staple, as it is now. 

There are at present upward of twenty tribes speaking various 
dialects of the Maya language, perhaps half a milUon people in aU. 
These live in the same general region their ancestors occupied, but 
under greatly changed conditions. Formerly the Maya were the van 
of civihzation in the New World,' but to-day they are a dwindling 

' All things considered, the Maya may be regarded as having developed probably the highest aboriginal 
civilization in the "Western Hemisphere, although it should be borne in mind that they were surpassed in 
many lines of endeavor by other races. The Inca, for example, excelled them in the arts of weaving and 
dyeing, the Chiriqui in metal working, and the Aztec in military proficiency. 

43508°— Bull. 57—15 1 1 



2 BUEEAU OF AMKBICAN" ETHNOLOGY [bdll. 57 

race, their once remarkable civilization is a thing of the past, and its 
manners and customs are forgotten. 

History 

The ancient Maya, with whom this volume deals, emerged from bar- 
barism probably during the first or second century of the Christian 
Era; at least their earliest dated monument can not be ascribed with 
safety to a more remote period.' How long a time had been required 
for the development of their complex calendar and hieroglyphic sys- 
tem to the point of graphic record, it is impossible to say, and any 
estimate can be only conjectural. It is certain, however, that a long 
interval must have elapsed from the first crude and unrelated scratches 
of savagery to the elaborate and involved hieroglyphs found on the 
earliest monuments, which represent not only the work of highly 
skilled sculptors, but also the thought of intensivaly developed minds. 
That this period was measured by centuries rather than by decades 
seems probable; the achievement was far too great to have been per- 
formed in a single generation or even in five or ten. 

It seems safe to assume, therefore, that by the end of the second 
century of the Christian Era the Maya civilization was fairly on its 
feet. There then began an extraordinary development all along the 
Une. City after city sprang into prominence throughout the southern 
part of the Maya territory,^ each contributing its share to the general 
progress and art of the time. With accomphshment came confidence 
and a quickening of pace. All activities doubtless shared in the gen- 
eral uplift which followed, though little more than the material evi- 
dences of architecture and sculpture have survived the ravages of the 
destructive environment in which this culture flourished; and it is 
chiefly from, these remnants of ancient Maya art that the record of 
progress has been partially reconstructed. 

This period of development, which lasted upward of 400 years, 
or untfl about the close of the sixth century, may be called per- 

> The correlation ol Maya and Christian chronology herein followed is that suggested by the writer in 
"The Correlation of Maya and Christian Chronology" (Papers of the School of American Archaeology, No. 11). 
See Morley, 1910 b, cited in Bibijogkapht, pp. xv, xvi. There are at least six other systems of correla- 
tion, however, on which the student must pass judgment. Although no two of these agree, all are based 
on data derived from the same som-ce, namely, the Boolfs of Chilan Balam (see p. 3, footnote 1). The 
differences among them are due to the varying interpretations of the material therein presented. Some 
of the systems of correlation which have been proposed, besides that of the writer, are: 

1. That of Mr. C. P. Bowditch (1901 a), found in his pamphlet entitled "Memoranda on the Maya Calen- 
dars used in The Books of Chilan Balam." 

2. That of Prof. Eduard Seler (1902-1908: I, pp. 588-S99). See also Buttelin 2S, p. 330. 

3. That of Mr. J. T. Goodman (1905). 

4. That of Pio Perez, in Stephen's Incidents of Travel in Yucatan (1843: i, pp. 434-^9; n, pp. 465-469) 
and in Landa, 1864: pp. 366-429. 

As before noted, these correlations differ greatly from one another, Professor Seler assigning the most 
remote dates to the southern cities and Mr. Goodman the most recent. The correlations of Mr. Bowditch 
and the writer are within 260 years of each' other. Before accepting any one of the systems of correlation 
above mentioned, the student is strongly lurged to examine with care The Books of Chilan Balam. 

2 It is probable that at this early date Yucatan had not been discovered, or at least not colonized. 



MOKLBT] INTRODUCTION TO STUDY OP MAYA HIEKOGLYPHS 3 

haps the "Golden Age of the Maya"; at least it was the first great 
epoch in their history, and so far as sculpture is concerned, the 
one best comparable to the classic period of Greek art. While 
sculpture among the Maya never again reached so high a degree of 
perfection, architecttire steadily developed, almost to the last. 
Judging from the dates inscribed upon their monuments, all the 
great cities of the south flourished during this period : Palenque and 
Yaxchilan in what is now southern Mexico; Piedras Negras, Seibal, 
Tikal, Naranjo, and Quirigua in the present Guatemala; and Copan 
in the present Honduras. AU these cities rose to greatness and sank 
again into insignificance, if not indeed into oblivion, before the close 
of this Golden Age. 

The causes which led to the decliue of civilization in the south are 
unknown. It has been conjectured that the Maya were driven from 
their southern homes by stronger peoples pushing in from farther 
south and from the west, or again, that the Maya civilization, having 
run its natural coiu-se, collapsed through sheer lack of inherent power 
to advance. Which, if either, of these hypotheses be true, matters 
little, since in any event one all-important fact remains: Just after' 
the close of Cycle 9 of Maya chronology, toward the end of the sixth 
centvuy, there is a sudden and final cessation of dates in aU the 
southern cities, apparently indicating that they were abandoned 
about this time. 

StiU. another condition doubtless hastened the general decline if 
indeed it did no more. There is strong documentary evidence ' that 
about the middle or close of the fifth century the southern part of 
Yucatan was discovered and colonized. In the century following, 
the southern cities one by one sank into. decay; at least none of their 
monuments bear later dates, and coincidently Chichen Itza, the first 
great city of the north, was founded and rose to prominence. In 
the absence of reliable contemporaneous records it is impossible to 
estabUsh the absolute accuracy of any theory relating to times so 

1 This evidence is presented by The Books of Chilan Balam, " which were copied or compiled in Yucaten 
by natives during the sixteenth, seventeenth, and eighteenth centuries, from much older manuscripts now 
lost or destroyed. They are written in the Maya language in Latin characters, and treat, in part at least, 
of the history of the country before the Spanish Conquest. Each town seems to have had its own book of 
Chilan Balam, distinguished from others by the addition of the name of the place where it was written, as: 
The Book of Chilan Balam of Mani, The Book of Chilan Balam of Tizimin, and so on. Although much of the 
materia] presented in these manuscripts is apparently contradictory and obscure, their importance as original 
historical sources can not be overestimated, since they constitute the only native accoimts of the early 
history of the Maya race which have survived the vandalism of the Spanish Conquerors. Of the sixteen 
Books of Chilan Balam now extant, only three, those of the towns of Mani, Tizimin, and Chumayel, 
contain historical matter. These have been translated into English, and published by Dr. D. G. Brinton 
[1882 b] under the title of "The Maya Chronicles." This translation with a few corrections has been 
freely consulted in the following discussion."— Moeley, 1910 b: p. 193. 

Although The Books of Chilan Balam are in all probability authentic sources for the reconstruction of 
Maya history, they can hardly be considered contemporaneous since, as above explained, they emanate 
from post-Conquest times. The most that can be claimed for them in this connection is that the docu- 
ments from which they were copied were probably aboriginal, and contemporaneous, or approximately 
so, with the later periods of the history which they record. 



4 BTJBEAU OF AMERICAN ETHNOLOGY [bull. 57 

remote as those here under consideration; but it seems not improbable 
that after the discovery of Yucatan and the subsequent opening up 
of that vast region, the southern cities commenced to decline. As 
the new country waxed the old waned, so that by the end of the sixth 
century the rise of the one and the fall of the other had occurred. 

The occupation and colonization of Yucatan marked the dawn of 
a new era for the Maya although their Renaissance did not take place 
at once. Under pressure of the new environment, at best a parched 
and waterless land, the Maya civihzation doubtless underwent im- 
portant modification.^ The period of colonization, with the strenu- 
ous labor by which it was marked, was not conducive to progress in 
the arts. At first the struggle for bare existence must have absorbed 
in a large measure the energies of all, and not until their foothold was 
secure could much time have been available for the cultivation of the 
gentler pursuits. Then, too, at first there seems to have been a feeling 
of unrest in the new land, a shifting of homes and a testing of locahties, 
all of which retarded the development of architectm-e, sculpture, and 
other arts. Bakhalal (see pi. 1), the first settlement in the north, was 
occupied for only 60 years. Chichen Itza, the next location, although 
occupied for more than a centm-y, was finally abandoned and the search 
for a new home resumed. Moving westward from Chichen Itza, Cha- 
kanputun was seized and occupied at the beginning of the eighth cen- 
tury. Here the Maya are said to have Hved for 260 years, imtil the 
destruction of Chakanputim by fire about 960 A. D. again set them 
wandering. By this time, however, some four centuries had elapsed 
since the first colonization of the country, and they doubtless felt 
themselves fuUy competent to cope with any problems arising from 
their environment. Once more their energies had begun to find outlet 
in artistic expression. The Transitional Period was at an end, and 
The Maya Renaissance, if the term may be used, was fully imder way. 

The opening of the eleventh century witnessed important and far- 
reaching political changes in Yucatan. After the destruction of 
Chakanputua the horizon of Maya activity expanded. Some of the 
fugitives from Chakanputun reoccupied Chichen Itza while others 
estabMshed themselves at a new site called Mayapan. About this 
time also the city of Uxmal seems to have been founded. In the 
year 1000 these three cities — Chichen Itza, Uxmal, and Mayapan — 
formed a confederacy,^ in which each was to share equally in the 
government of the country. Under the peaceful conditions which 

lAs will appear later, on the calendrie side the old system of counting time and of recording events gave 
place to a more abbreviated though less accurate chronology. In architecture and art also the change of 
environment made itself felt, and In other lines as wen the new land cast a strong influence over Maya 
thought and achievement. In his work entitled "A Study of Maya Art, its Subject Matter and Historical 
Development" (1913), to which students are referred for further information. Dr. H. J. Spinden has 
treated this subject extensively. 

2 The confederation of these three Maya cities may have served as a model for the three Nahua cities, 
Tenochtitlan, Tezcuoo, and Tlacopan, when they entered into a similar alliance some four centuries later. 



MORLET] INTRODUCTION TO STUDY Of MAYA HIEROGLYPHS 5 

followed the formation of this confederacy for the next 200 years the 
arts blossomed forth anew. 

This was the second and last great Maya epoch. It was their Age 
of Architecture as the first period had been their Age of Sculpture. 
As a separate art sculpture languished; but as an adjunct, an embel- 
' Ushment to architecture, it hved again. The one had become hand- 
maiden to the other. Facades were treated with a sculptural deco- 
ration, which for iatricacy and elaboration has rarely been equaled 
by any people at any time; and yet this result was accompUshed 
without sacrifice of beauty or dignity. During this period probably 
there arose the many cities which to-day are crumbMng in decay 
throughout the length and breadth of Yucatan, their very names 
forgotten. When these were in their prime, the country must have 
been one great beehive of activity, for only a large population could 
have left remains so extensive. 

This era of universal peace was abruptly terminated about 1200 
A. D. by an event which shook the body pohtic to its foundations 
and disrupted the Triple AlUance under whose beneficent rule the 
land had grown so prosperous. The ruler of Chichen Itza, Chac Xib 
Chac, seems to have plotted against his colleague of Mayapan, one 
Hunnac Ceel, and in the disastrous war which followed, the latter, 
with the aid of Nahua allies,' utterly routed his opponent and drove 
him from his city. The conquest of Chichen Itza seems to have been 
followed during the thirteenth century by attempted reprisals on the 
part of the vanquished Itza, which plimged the country into civil 
war; and this struggle in turn paved the way for the final ecUpse of 
Maya supremacy in the fifteenth century. 

After the dissolution of the Triple AUiance a readjustment of 
power became necessary. It was only natural that the victors in the 
late war should assume the chief direction of affairs, and there is 
strong evidence that Mayapan became the most important city in 
the land. It is not improbable also that as a result of this war 
Chichen Itza was turned over to Hunnac Ceel's Nahua allies, perhaps 
in recognition of their timely assistance, or as their share in the spoils 
of war. It is certain that sometime during its history Chichen Itza 
came under a strong Nahua influence. One group of buildings in 
particular ^ shows in its architecture and bas-reUefs that it was 
undoubtedly inspired by Nahua rather than by Maya ideals. 

According to Spanish historians, the fourteenth century was char- 
acterized by increasing arrogance and oppression on the part of the 
rulers of Mayapan, who found it necessary to surround themselves 
with Nahua aUies in order to keep the rising discontent of their sub- 

1 By Nahoa is here meant the peoples who inhabited the valley of Mexico and adjacent territory at this 
time, 
s The Ball Court, a characteristically Nahua development. 



6 • BUEEAU OF AMEEICAN ETHNOLOGY [boll. 57 

jects in check.^ This unrest finally reached its culmination about 
the middle of the fifteenth century, when the Maya nobility, unable 
longer to endure such tyranny, banded themselves together under 
the leadership of the lord of Uxmal, sacked Mayapan, and slew its 
ruler. 

AH authorities, native as well as Spanish, agree that the destruc- 
tion of Mayapan marked the end of strongly centralized government 
in Yucatan. Indeed there can be but little doubt that this event 
also sounded the death knell of Maya civilization. As one of the 
native chronicles tersely puts it, "The chiefs of the country lost their 
power." With the destruction of Mayapan the country spht into a 
number of warring factions, each bent on the downfall of the others. 
Ancient jealousies and feuds, no longer held in leash by the restrain- 
ing hand of Mayapan, doubtless revived, and soon the land was rent 
with strife. Presently to the horrors of civil war were added those 
of famine and pestilence, each of which visited the peninsida in turn, 
carrying off great numbers of people. 

These several calamities, however, were but harbingers of worse 
soon to come. In 1517 Francisco de Cordoba landed the first Spanish 
expedition ^ on the shores of Yucatan. The natives were so hostile, 
however, that he returned to Cuba, having accomplished httle more 
than the discovery of the country. In the following year Juan de 
Grijalva descended on the peninsula, but he, too, met with so deter- 
mined a resistance that he sailed away, having gained httle more 
than hard knocks for his paias. In the following year (1519) Her- 
nando Cortez landed on the northeast coast but reembarked in a few 
days for Mexico, again leaving the courageous natives to themselves. 
Seven years later, however, in 1526, Francisco Montejo, having been 
granted the title of Adelantado of Yucatan, set about the conquest 
of the country in earnest. Having obtained the necessary "sinews 
of war" through his marriage to a wealthy widow of Seville, he sailed 
with 3 ships and 500 men for Yucatan. He first landed on the 
island of Cozumel, off the northeast coast, but soon proceeded to 
the mainland and took formal possession of the country in the 
name of the King of Spain. This empty ceremony soon proved to be 

1 One authority (Landa, 1864: p. 48) says in this connection: "The goyemor, Cocom— the ruler of Maya- 
pan— began to covet riches; and for this purpose he treated with the people of the garrison, which the 
kings of Mexico had in Tabasco and Xioalango, that he should deliver his city [i. e. Mayapan] to them; 
and thus he brought the Mexican people to Mayapan and he oppressed the poor and made many slaves, 
and the lords would have killed him if they had not been afraid of the Mexicans." 

2 The first appearance of the Spaniards in Yucatan was six years earlier (in 1511), when the caravel of 
Valdivia, returning from the Isthmus of Darien to Hispaniola, foundered near Jamaica. About 10 sur- 
vivors in an open boat were driven upon the coast of Yucatan near the -Island of Cozumel. Here they 
were made prisoners by the Maya and five, including Valdivia himself, were sacriflced. The remainder 
escaped only to die of starvation and hardship, with the exception of two, Geronimo de Aguilar and 
Gonzalo Guerrero. Both of these men had risen to considerable prominence in the country by the time 
Cortez arrived eight years later. Guerrero had married a chief's daughter and had himself become a chief. 
Later Aguilar became an interpreter for Cortez. This handful of Spaniards can hardly be called an expe- 
dition, however. 



MORLBT] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 7 

but the prelude to a sanguinary struggle, which broke out almost 
immediately and continued with extraordinary ferocity for many 
years, the Maya fighting desperately in defense of their homes. 
Indeed, it was not until 14 years later, on June 11, 1541 (old style), 
that, the Spaniards having defeated a coalition of Maya chieftains 
near the city of Ichcanzihoo, the conquest was finally brought to a 
close and the pacification of the country accomplished. With this 
event ends the independent history of the Maya. 

Manners and Customs 

According to Bishop Landa,^ who wrote his remarkable history of 
Yucatan in 1565, the Maya of that day were a tall race, active and 
strong. In childhood the forehead was artificially flattened and the 
ears and nose were pierced for the insertion of earrings and nose-orna- 
ments, of which the people were very fond. Squint-eye was consid- 
ered a mark of beauty, and mothers strove to disfigure their children 
in this way by suspending pellets of wax between their eyes in order 
to make them squint, thus securing the desired effect. The faces of 
the younger boys were scalded by the appUcation of hot cloths, to 
prevent the growth of the beard, which was not popular. Both men 
and women wore their hair long. The former had a large spot burned 
on the back of the head, where the hair always remained short. With 
the exception of a small queue, which hung down behind, the hair 
was gathered around the head in a braid. The women wore a more 
beautiful coiffure divided into two braids. The faces of both sexes 
were much disfigured as a result of their rehgious behefs, which led 
to the practice of scarification. Tattooing also was common to both 
sexes, and there were persons in almost every community who were 
especially proficient in this art. Both men and women painted 
themselves red, the former decorating their entire bodies, and the 
latter aU except their faces, which modesty decreed should be left 
unpainted. The women also anointed themselves very freely with 
fragrant gums and perfumes. They filed their teeth to sharp points, 
a practice which was thought to enhance their beauty. 

The clothing of the men was simple. They wore a breechclout 
wrapped several times around the loins and tied in such a way that 
one end fell in front between the legs and the other in the correspond- 

1 Diego de Landa, second bishop of Merida, wliose remaricable book entitled "Relacion de las Cosas de 
Yucatan" is the chief authority for the facts presented in the following discussion of the manners and 
customs of the Maya, was bom in Cifuentes de I'Alcarria, Spain, in 1524. At the age of 17 he joined the 
Franciscan order. He came to Yucatan during the decade foUowing the close of the Conquest, in 1549, 
where he was one of the most zealous of the early missionaries. In 1573 he was appointed bishop of Merida, 
which position he held until his death in 1579. His priceless Relacion, written about 1565, was not printed 
until three centuries later, when it was discovered by the indefatigable Abb6 Brasseur de Bourbourg in 
the library of the Royal Academy of History at Madrid, and published by him in 1864. The Relacion 
is the standard authority for the customs prevalent in Yucatan at the time of the Conquest, and is an 
invaluable aid to the student of Maya archeology. What little we know of the Maya calendar has been 
derived directly from the pages of this book, or by developing the material therein presented. 



8 BITEEAU OF AMERICAN ETHNOLOGY [boll. 57 

ing position behind. These breechclouts were carefully embroidered 
by the women and decorated with featherwork. A large square cape 
hung from the shoulders, and sandals of hemp or leather completed 
the costume. For persons of high rank the apparel was much more 
elaborate, the humble breechclout and cape of the laboring man 
giving place to panaches of gorgeously colored feathers hanging from 
wooden helmets, rich mantles of tiger skins, and finely wrought orna- 
ments of gold and jade. 

The women sometimes wore a simple petticoat, and a cloth covering 
the breasts and passing under the arms. More often their costume 
consisted of a single loose sacklike garment called the hipil, which 
reached to the feet and had slits for the arms. This garment, with 
the addition of a cloth or scarf wrapped around the shoulders, con- 
stituted the women's clothing a thousand years ago, just as it does 
to-day. 

In ancient times the women were very chaste and modest. When 
they passed men on the road they stepped to one side, turning their 
backs and hiding their faces. The age of marriage was about 20, 
although children were frequently affianced when very yoimg. When 
boys arrived at a marriageable age their fathers consulted the pro- 
fessional matchmakers of the community, to whom arrangements for 
marriage were ordinarily intrusted, it being considered vulgar for 
parents or their sons to take an active part in arranging these affairs. 
Having sought out the girl's parents, the matchmaker arranged with 
them the matter of the dowry, which the young man's father paid, 
his wife at the same time giving the necessary clothing for her son 
and prospective daughter-in-law. On the day of the wedding the 
relatives and guests assembled at the house of the yoimg man's 
parents, where a great feast had been prepared. Having satisfied 
himself that the young couple had sufficiently considered the grave 
step they were about to take, the priest gave the bride to her hus- 
band. The ceremony closed with a feast in which all participated. 
Immediately after the wedding the young husband went to the home 
of his wife's parents, where he was obliged to work five or six years 
for his board. If he refused to comply with this custom he was 
driven from the house, and the marriage presumably was annulled. 
This step seems rarely to have been necessary, however, and the 
mother-in-law on her part saw to it that her daughter fed the young 
husband regularly, a practice which betokened their recognition of 
the marriage rite. 

Widowers and widows married without ceremony, it being consid- 
ered sufficient for a widower to call on his prospective wife and eat in 
her house. Marriage between people of the same name was con- 
sidered an evil practice, possibly in deference to some former exogamic 
law. It was thought improper to marry a mother-in-law or an a]umt 



MORLEY] INTEODUCTION TO STUDY OF MAYA HlEHOGLYPHS 9 

by marriage, or a sister-in-law; otherwise a man could marry whom 
he would, even his first cousin. 

The Maya were of a very jealous nature and divorces were frequent. 
These were effected merely by the desertion of the husband or wife, 
as the case might be. The parents tried to bring the couple together 
and effect a reconciliation, but if their efforts proved imsuccessful 
both parties were at liberty to remarry. If there were yoimg children 
the mother kept them; if the children were of age the sons followed 
the father, the daughters remaining with their mother. Although 
divorce was of common occurrence, it was condemned by the more 
respectable members of the community. It is interesting to note 
that polygamy was unknown among the Maya. 

Agriculture was the chief pursuit, corn and other grains being 
extensively cultivated, and stored against time of need in well- 
appointed granaries. Labor was largely communal; all hands joined 
to do one another's work. Bands of twenty or more each, passing 
from field to field throughout the community, quickly finished sowing 
or harvesting. This communal idea was carried to the chase, fifty or 
more men frequently going out together to hunt. At the conclusion 
of these expeditions the meat was roasted and then carried back to 
town. First, the lord of the district was given his share, after which 
the remainder was distributed among the hunters and their friends. 
Conmaunal fishing parties are also mentioned. 

Another occupation in high favor was that of trade or commerce. 
Salt, cloth, and slaves were the chief articles of barter; these were 
carried as far as Tabasco. Cocoa, stone counters, and highly prized 
red shells of a pecuhar kind were the media of exchange. These were 
accepted in return for all the products of the country, even includ- 
ing the finely worked stones, jades possibly, with which the chiefs 
adorned themselves at their fetes. Credit was asked and given, all 
debts were honestly paid, and no usury was exacted. 

The sense of justice among the Maya was highly developed. If a 
man committed an offense against one of another village, the former's 
lord caused satisfaction to be rendered, otherwise the communities 
would come to blows. Troubles between men of the same village 
were taken to a judge, who having heard both sides, fixed appropriate 
damages. If the malefactor could not pay these, the obligation 
extended to his wife and relatives. Crimes which could be satisfied 
by the payment of an indemnity were accidental killings, quarrels 
between man and wife, and the accidental destruction of property by 
fire. Malicious mischief could be atoned for only by blows and the 
shedding of blood. The punishment of murder was left in the hands 
of the deceased's relatives, who were at liberty to exact an indemnity 
or the murderer's life as they pleased. The thief was obliged to make 
good whatever he had stolen, no matter how little; in event of failure 
to do so he was reduced to slavery. Adultery was punishable by 



10 BUEEAtT OF AMERICAN ETHNOLOGY [boll. 57 

death. The adulterer was led into the courtyard of the chief's house, 
where all had assembled, and after being tied to a stake, was turned 
over to the mercies of the outraged husband, who either pardoned 
him or crushed his head with a heavy rock. As for the guilty woman, 
her infamy was deemed sufficient pvmishment for her, though usually 
her husband abandoned her. 

The Maya were a very hospitable people, always offering food and 
drink to the stranger within their gates, and sharing with him to the 
last crumb. They were much given to conviviality, particularly the 
lords, who frequently entertained one another with elaborate feasts, 
accompanied by music and dancing, expending at times on a single 
occasion the proceeds of many days' accumulation. They usually 
sat down to eat by twos or fours. The meal, which consisted of 
vegetable stews, roast meats, com cakes, and cocoa (to mention only 
a few of the viands) was spread upon mats laid on the ground. After 
the repast was finished beautiful young girls acting as cupbearers 
passed among the guests, plying them industriously with wine until 
aU were drunk. Before departing each guest was presented with a 
handsome vase and pedestal, with a cloth cover therefor. At these 
orgies drinking was frequently carried to such excess that the wives 
of the guests were obliged to come for their besotted husbands and 
drag them home. Each of the guests at such a banquet was required 
to give one in return, and not even death could stay the payment of 
a debt of this kind, since the obhgation descended to the recipient's 
heirs. The poor entertained less lavishly, as became their means. 
Guests at the humbler feasts, moreover, were not obliged to. return 
them in kind. 

The chief amusements of the Maya were comedies and dances, in 
both of which they exhibited much skiU and ingenuity. There was 
a variety of musical instruments — drums of several kinds, rattles, 
reed flutes, wooden horns, and bone whistles. Their music is 
described as having been sad, owing perhaps to the melancholy sound 
of the instruments which produced it. 

The frequent wars which darken the final pages of Maya history 
doubtless developed the miUtary organization to a high degree of 
efficiency. At the head of the army stood two generals, one hereditary 
and the other elective (nacon), the latter serving for three years. In 
each village throughout the country certain men Qiolcanes) were 
chosen to act as soldiers; these constituted a kind of a standing army, 
thoroughly trained in the art of war. They were supported by the 
community, and in times of peace caused much disturbance, con- 
tinuing the tumult of war after war had ceased. In times of great 
stress when it became necessary to call on aU able-bodied men for 
military service, the holcanes mustered all those available in their 
respective districts and trained them in the use of arms. There were 
but few weapons: Wooden bows strung with hemp cords, and arrows 



MOKLET] INTEODtrCTION TO SOTUDY OP MAYA HIEROGLYPHS 11 

tipped with obsidian or bone; long lances with sharp flint points; 
and metal (probably copper) axes, provided with wooden handles. 
The defensive armor consisted of round wicker shields strengthened 
with deer hide, and quilted cotton coats, which were said to have 
extraordinary resisting power against the native weapons. The 
highest chiefs wore wooden helmets decorated with briUiant plumes, 
and cloaks of "tiger" (jaguar) skin, thrown over their shoulders. 

With a great banner at their head the troops silently stole out of 
the city, and moved against the enemy, hoping thus to surprise them. 
When the enemies' position had been ascertained, they fell on them 
suddenly with extraordinary ferocity, uttering loud cries. Barricades 
of trees, brush, and stone were used in defense, behind which archers 
stood, who endeavored to repulse the attack.^ After a battle the 
victors mutUated the bodies of the slain, cutting out the jawbones 
and cleaning them of flesh. These were worn as bracelets after the 
flesh had been removed. At the conclusion of their wars the spoils 
were offered in sacrifice. If by chance some leader or chief had been 
captured, he was sacrificed as an offering particularly acceptable to 
the gods. Other prisoners became the slaves of those who had 
captured them. 

The Maya entertained an excessive and constant fear of death, 
many of their religious practices having no other end in view than 
that of warding off the dread visitor. After death there followed a 
prolonged period of sadness in the bereaved family, the days being 
given over to fasting, and the more restrained indulgence in grief, 
and the nights to dolorous cries and lamentations, most pitiful to 
hear. Among the common people the dead were wrapped in shrouds; 
their mouths were fiUed with ground com and bits of worked stone 
so that they should not lack for food and money in the life to come. 
The Maya buried their dead inside the houses * or behind them, 
putting into the tomb idols, and objects indicating the profession of 
the deceased — if a priest, some of his sacred books; if a seer, some 
of his divinatory paraphernalia. A house was commonly abandoned 
after a death therein, unless enough remained in the household to 
dispel the fear which always followed such an occurrence. 

In the higher walks of life the mortuary customs were more elabo- 
rate. The bodies of chiefs and others of high estate were burned 
and their ashes placed in large pottery vessels. These were buried 
in the ground and teniples erected over them.^ When the deceased 

• The excavations of Mr. E. H. Thompson at Labna, Yucatan, and of Dr. Merwin at Holmul, Guatemala, 
have confirmed Bishop Landa's statement concerning the disposal of the dead. At Labna bodies were 
found buried beneath the floors of the buildings, and at Holmul not only beneath the floors but also lying 
on them. 

2 Examples of this type of burial have been found at Chichen Itza and Mayapan In Yucatan. At the 
former site Mr. E. H. Thompson found in the center of a large pyramid a stone-lined shaft running from 
the summit into the ground. This was filled with burials and funeral objects — pearls, coral, and jade, 
which from their precious nature indicated the remains of important personages. At Mayapan, burials 
were found in a shaft of similar construction and location in one of the pyramids. 



12 BURBAtr OF AMERICAN ETfiNbLOGY [bull. S? 

was of very high rank the pottery sarcophagus took the form of 
a human statue. A variant of the above procedure was to burn 
only a part of the body, inclosing the ashes in the hollow head of a 
wooden statue, and sealing them in with a piece of skin taken from 
the back of the dead man's skuU. The rest of the body was buried. 
Such statues were jealously preserved among the figures of the gods, 
being held in deep veneration. 

The lords of Mayapan had stiU another mortuary practice. After 
death the head was severed from the body and cooked in order to 
remove all flesh. It was then sawed in half from side to side, care 
beiag taken to preserve the jaw, nose, eyes, and forehead in one piece. 
Upon this as a form the features of the dead man were filled in with 
a kind of a gum. Such was their extraordinary skiU in this peculiar 
work that the finished mask is said to have appeared exactly like the 
countenance in life. The carefully prepared faces, together with the 
statues containing the ashes of the dead, were deposited with their 
idols. Every feast day meats were set before them so they should 
lack for nothing in that other world whither they had gone. 

Very little is known about the governmental organization of the 
southern Maya, and it seems best, therefore, first to examine conditions 
in the north, concerning which the early authorities, native as well 
as Spanish, have much to say. The northern Maya lived in settle- 
ments, some of very considerable extent, under the rule of hereditary 
chiefs called halach uinicil, or "real men," who were, in fact as well 
as name, the actual rulers of the country. The settlements tribu- 
tary to each Jialach uinic were doubtless connected by tribal ties, 
based on real or fancied blood relationship. 

During the period of the Triple Alliance (1000-1200 A. D.) there' 
were probably only three of these embryonic nations: Chichen Itza, 
Uxmal, and Mayapan, among which the country seems to have been 
apportioned. After the conquest of Chichen Itza, however, the 
halach tiinic of Mayapan probably attempted to establish a more 
autocratic form of government, arrogating to himself stUl greater 
power. The Spanish authorities relate that the chiefs of the country 
assembled at Mayapan, acknowledged the ruler of that city as their 
overlord, and finally agreed to live there, each binding himself at the 
same time to conduct the affairs of his own domain through a deputy. 

This attempt to unite the country under one head and bring about 
a further centralization of power ultimately failed, as has been seen, 
through the tyranny of the Cocom family, in which the office of halach 
uinic of Mayapan was vested. This tyranny led to the overthrow 
of the Cocoms and the destruction of centralized government, so that 
when the Spaniards arrived they found a number of petty chieftains, 
acknowledging no overlord, and the country in chaos. 

The powers of the halach uinic are not clearly understood. He seems 
to have stood at the apex of the governmental organization, and doubt- 



MOKLEY] INTEODUCTION TO STUDY OP MAYA HIEROGLYPHS 13 

less his will prevailed just so far as he had sufficient strength to enforce 
it. The hatdbs, or underchiefs, were obliged to visit him and render him 
their homage. They also accompanied him in his tours about the 
country, which always gave rise to feasting back and forth. Finally 
they advised him on aU important matters. The office would seem 
to have been no stronger in any case than its incumbent, since we 
hear of the halach uinic of Mayapan being obliged to surround himself 
with foreign troops in order to hold his people in check. 

Each batab governed the territory of which he was the hereditary 
ruler, instructing his heir in the duties of the position, and counseling 
that he treat the poor with benevolence and maintain peace and 
encourage industry, so that aU might live in plenty. He settled all 
lawsuits, and through trusted lieutenants ordered and adjusted the 
various affairs of his domain. When he went abroad from his city 
or even from his house a great crowd accompanied him. He often vis- 
ited his underchiefs, holding court in their houses, and meeting at night 
ia council to discuss matters touching the common good. The batabs 
frequently entertained one another with dancing, hunting, and feast- 
ing. The people as a community tilled the batab's fields, reaped his 
com, and supplied his wants in general. The underchiefs were simi- 
larly provided for, each according to his rank and needs. 

The aTikulel, the next highest official in each district, acted as the 
batab's deputy or representative; he carried a short thick baton in 
token of his office. He had charge of the localities subject to his 
master's rule as well as of the officers immediately over them. He 
kept these assistants informed as to what was needed in the batab's 
house, as birds, game, fish, corn, honey, salt, and cloth, which they 
supplied when called on. The ahkulel was, in short, a chief steward, 
and his house was the batab's busLaess office. 

Another important position was that of the nacon, or war-chief. 
In times of war this functionary was second only to the hereditary 
chief, or batab, and was greatly venerated by all. His office was 
elective, the term being three years, during which he was obliged to 
refrain from intercourse with women, and to hold himself aloof from all. 

An important civil position was that held by the ahJiolpop, in 
whose keeping was the tunkul, or wooden drum, used in summoning 
people to the dances and public meetings, or as a tocsin in case of war. 
He had charge also of the "town hall" in which all public business 
was transacted. 

The question of succession is important. Bishop Landa distinctly 
states in one passage "That when the lord died, although his oldest 
son succeeded him, the others were always loved and served and even 
regarded as lords." This would seem to indicate definitely that 
descent was by primogeniture. However, another passage suggests 
that the oldest son did not always succeed his father: "The lords 
were the governors and confirmed their sons in their offices if they 



14 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

[the sons] were acceptable." This suggests the possibility, at least, 
that primogeniture could sometimes be set aside, particularly when 
the first-born lacked the necessary qualifications for leadership. In 
a somewhat drawn-out statement the same authority discusses the 
the question of "princely succession" among the Maya: 

If the children were too young to be intrusted with the management of their own 
affairs, these were turned over to a guardian, the nearest relation. He gave the children 
to their mothers to bringup, because according to their usage the mother has no power 
of her own. When the guardian wag the brother of the deceased [the children's 
paternal uncle] they take the children from their mother. These guardians give what 
was intrusted to them to the heirs when they come of age, and not to do so was considered 
a great dishonesty and was the cause of much contention. . . . If when the lord died 
there were no sons [ready, i. e., of age] to rule and he had brothers, the oldest or most 
capable of his brothers ruled, and they [the guardians] showed the heir the customs 
and fetes of his people until he should be a man, and these brothers, although the heir 
were [ready] to rule, commanded all their Uves, and, if there were no brothers the 
priests and principal people selected a man suitable for the position.' 

The foregoing would seem to imply that the rulers were succeeded 
by their eldest sons if the latter were of age and otherwise generally 
acceptable; and that, if they were minors when their fathers died, 
their paternal uncles, if any, or otherwise some capable man selected 
by the priests, took the reins of government, instructing the heir in 
the duties of the position which he was to occupy some day; and 
finally that the regent did not lay down his authority until death, 
even thoijjgh the heir had previously attained his majority. This 
custom is sO unusual that its existence may well be doubted, and it 
is not at all improljable that Bishop Landa's statement to the con- 
trary may have arisen from some misapprehension. Primogeniture 
was not confined to the executive succession alone, since Bishop Landa 
states further that the high priest Ahau can mai was succeeded in 
his dignity by his sons, or those next of kin. 

Nepotism doubtless prevailed extensively, all the higher offices of 
the priesthood as well as the executive offices being hereditary, and 
in all probability filled with members of the halach uinic's family.. 

The priests instructed the younger sons of the ruling family as well 
as their own, in the priestly duties and learning; in the computation of 
years, months, and days; in unlucky times; in fetes and ceremonies; 
in the administration of the sacraments; in the practices of prophecy 
and divination; in treating the sick; in their ancient history; and 
finally in the art of reading and writing their hieroglyphics, which was 
taught only to those of high degree. Genealogies were carefully 
preserved, the term meaning "of noble birth" being ah Icdba, "he who 
has a name. " The elaborate attention given to the subject of lineage, 
and the exclusive right of the ah Tcala to the benefits of education, 
show that in the northern part of the Maya territory at least govern- 

1 Landa, 1864: p. 137. 



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MORMT] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 15 

ment rested on the principle of hereditary succession. The accounts 
of native as well as of Spanish writers leave the impression that a 
system not unlike a modified form of feudaUsm prevailed. 

In attempting to gain an approxunate understanding of the form 
of government which existed in the southern part of the Maya terri- 
ritory it is necessary in the absence of all documentary information 
to interpret the southern chronology, architecture, and sculpture — 
practically all that remains of the older culture — in the hght of the 
known conditions in the north. The chronology of the several 
southern cities (see pi. 2) indicates that many of them were con- 
temporaneous, and that a few, namely, Tikal, Naranjo, Palenque, 
and Copan were occupied approximately 200 years, a much longer 
period than any of the others." These four would seem to have been 
centers of population for a long time, and at least three of them, 
Tikal, Palenque, and Copan, attained considerable size. Indeed they 
may well have been, like Chichen Itza, Uxmal, and Mayapan, at a 
later epoch in the north, the seats of halach uincil, or overlords, to 
whom all the surrounding chiefs were tributary. Geographically 
considered, the country was well apportioned among these cities: 
Tikal dominating the north, Palenque, the west, and Copan, the south. 

The architecture, sculpture, and hieroglyphic writing of all the 
southern centers is practically identical, even to the borrowing of 
unessential details, a condition which indicates a homogeneity only 
to be accounted for by long-continued and frequent intercourse. 
This characteristic of the cultm-e, together with the location and 
contemporaneity of its largest centers, suggests that originally the 
southern territory was divided into several extensive political divi- 
sions, aU in close intercotu'se with one another, and possibly united 
in a league similar to that which later united the principal cities of 
the north. The unmistakable priestly or rehgious character of the 
sculptures in the southern area clearly indicates the peaceful temper 
of the people, and the conspicuous absence of warlike subjects points 
strongly to the fact that the government was a theocracy, the highest 
ofl&cial in the priesthood being at the same time, by virtue of his 
sacerdotal rank, the highest civil authority. Whether the principle 
of hereditary succession determined or even influenced the selection 
of rulers in the south is impossible to say. However, since the highest 
offices, both executive and priestly, in the north were thus filled, it 
may be assumed that similar conditions prevailed in the south, par- 
ticularly as the northern civiHzation was but an outgrowth of the 

' As the result of a trip to the Maya field in the winter of 1914, the -writer made important discoveries in 
the chronology of Tikal, Naranjo, Piedras Negras, Altar de Sacriflcios, Quirigua, and Seibal. The occu- 
pancy of Tikal and Seibal was found to have extended to 10.2.0.0.0; of Piedras Negras to 9.18.5.0.0; 
of Naranjo to 9.19.10.6.0; and of Altar de Sacriflcios to 9.14.0.0.0. (This new material is not embodied 
in pi. 2.) 




16 BUREAU OP AMERICAN ETHNOLOGY [snLL. 57 

southern. There is some ground for beheving that the highest office 
in the south may have been elective, the term being a Twtun^ (1,800 
days), and the choice restrictedto the members of a certain family. 
The existence of this restriction, which closely parallels the Aztec 
procedure in selecting rulers,^ rests on very slender evidence, how- 
ever, so far as the Maya are concerned and is mentioned here simply 
by way of suggestion. 

The reUgion of the ancient Maya was polytheistic, its pantheon 
containing about a dozen major deities and a host of lesser ones. At 
its head stood' Itzamna, the father of the gods and creator of mankind, 
the Mayan Zeus or Jupiter. He was the personification of the East, 
the rising sun, and, by association, of light, life, and 
knowledge. He was the founder of the Maya civiliza- 
tion, the first priest of the Maya rehgion, the inventor 
of writing and books, and the great healer. Whether 
Itzamna has been identified with any of the deities in 
the ancient Maya picture-writings is uncertain, though 
there are strong reasons for believing that this deity is 
the god represented in figure 1 . His characteristics 
here are: The aged face, Koman nose, and sunken 
toothless mouth. 

Fig. 1. Itzamna, Scarcely Icss important was the great god Kukulcau, 
u^J^TlntU^l or Feathered Serpent, the personification of the West. 
(note his name It is related of him that he came into Yucatan from 
glyphs, below). ^^^ ^gg^ ^^^ settled at Chichen Itza, where he ruled 
for many years and built a great temple. During his sojourn he is 
said to have founded the city of Mayapan, which later became so 
important. Finally, having brought the country out of war and dis- 
sension to peace and prosperity, he left by the same way he had 
entered, tarrying only at Chakanputiin on the west coast to build 
a splendid temple as an everlasting memorial of his residence among 
the people. After his departure he was worshipped as a god because 
of what he had done for the public good. Kukulcan was the Maya 
counterpart of the Aztec Quetzalcoatl, the Mexican god of light, 
learning, and culture. In the Maya pantheon he was regarded as 
having been the great organizer, the founder of cities, the framer of 
laws, and the teacher of their new calendar. Indeed, his attributes 

1 As will be explained in chapter V, the writer has suggested the name hotun for the 5 tun, or 1,800 day, 
period. 

2 Succession In the Aztec royal house was not determined by primogeniture, though the supreme ofSce, 
the tloMouani, as well as the other high ofRces of state, was hereditary in one family. On the death o{ 
the tlahtouani the electors (four in number) seem to have selected his successor from among his brothers, 
or, these failing, from among his nephews. Except as limiting the succession to one family, primogeniture 
does not seem to have obtained; for example, Moctezoma (Montezuma) was chosen tlahtouani over the 
heads of several of his older brothers because he was thought to have the best qualifications tor that exalted 
office. The situation may be summarized by the statement that while the supreme ruler ajnong the 
Aztec had to be of the "blood royal," his selection was determined by personal merit rather than by 
primogenJtvirei 



MORLEY] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 



17 




Fig. 2. Kukuloan, 
God of Learning 
(note his name 
glyph, helow). 



and life history are so human that it is not improbable he may have 
been an actual historical character, some great lawgiver and organ- 
izer, the memory of whose benefactions lingered long 
after death, and whose personality was eventually dei- 
fied. The episodes of his life suggest he may have been 
the recolonizer of Chichen Itza after the destruction of 
Chakanputun. Kukulcan has been identified by some 
as the "old god" of the picture-writings (fig. 2), whose 
characteristics are : Two deformed teeth, one protruding 
from the front and one from the back part of his mouth, 
and the long tapering nose. He is to be distinguished 
further by his peculiar headdress. 

The most feared and hated of all the Maya deities 
was Ahpuch, the Lord of Death, God "Barebones" as 
an early manuscript calls him, from whom evil and 
especially death were thought to come. He is frequently represented 
in the picture-writings (fig. 3), usually in connection with the idea of 
death. He is associated with human sacrifice, suicide 
by hanging, death in childbirth, and the beheaded 
captive. His characteristics are typical and unmis- 
takable. His head is the fleshless skull, showing the 
truncated nose, the grinning teeth, and fleshless lower 
jaw, sometimes even the cranial sutures are por- 
trayed. In some places the ribs and vertebrae are 
shown, in others the body is spotted black as if to 
suggest the discoloration of death. A very constant 
symbol is the stiff feather collar with small bells at- 
tached. These bells also appear as ornaments on the 
head, arms, and ankles. The to us familiar crossbones 
were also another Maya death symbol. Even the hieroglyph of this 
god (fig. 3) suggests the dread idea for which he stood. Note the 
eye closed in death. 

Closely associated with the God of Death is the God of 
War, who probably stood as well for the larger idea of 
death by violence. He is characterized (fig. 4) by a 
black line painted on his face, sometimes ciu'ving, some- 
times straight, supposed to be symbolical of war paiat, 
or, according to others, of his gaping wounds. He ap- 
pears in the picture-writings as the Death God's com- 
panion. He presides with him over the body of a sacri- 
ficial victim, and again follows him applying torch and 
knife to the habitations of man. His hieroglyph shows 
as its characteristic the line of black parat (fig. 4),. 

Another unpropitious deity was Ek Ahau, the Black Captain, also a 
war god, being represented (fig. 5) in the picture-writings as armed 
43508°— Bull. 57—15 2 




Fig. 3. Ahpuch, God 
of Death (note his 
name glyphs, below). 




Fig. 4. The God of 
War(notehis name 
glyph, below). 



18 



BUREAU OP AMERICAN ETHNOLOGY 



[nuLL. 57 




Fig. 5. EkAhau, 
the Black Cap- 
tain, war deity 



with a spear or an ax. It was said of Mm that he was a very great 
and very cruel warrior, who commanded a band of seven black- 
amoors like himself. He is characterized by his black color, his 
drooping lower lip, and the two curved lines at the right of his eye. 
His hieroglyph is a black eye (fig. 5). 

Contrasted with these gods of death, violence, and de- 
struction was the Maize God, Yum Kaax, Lord of the 
Harvest Fields (fig. 6). Here we have one of the most 
important figures in the whole Maya pantheon, the god 
of husbandry and the fruits of the earth, of fertility and 
prosperity, of growth and plenty. The Maize God was 
as well disposed toward mankind as Ahpuch and his 
companions were unpropitious. In many of the pic- 
tm-e-writings Yum Kaax is represented as engaged in 
agricultural pursuits. He is portrayed as having for 
his head-dress a sprouting ear of corn surrounded by 
(note his name leaves, symbohc of growth, for which he stands. Even 
the hieroglyph of this deity (fig. 6) embodies the same 
idea, the god's head merging into the conyentionahzed ear of com 
surrounded by leaves. 

Another important deity aljout whom httle or nothing is knoivn 
was Xaman Ek, the North Star. He is spoken of as the "guide of 
the merchants," and in keeping with that character is associated in 
the picture-writings with symbols of peace and plenty. 
His one characteristic seems to be his cm-ious head, 
which also serves as his name hieroglyph (fig. 7). 

Other Maya deities were: Ixchel, the Rainbow, 
consort of Itzamna and goddess of childbirth and 
medicine; Ixtab, patroness of hunting and hanging; 
Ixtubtun, protectress of jade cutters; Ixchebelyax, 
the inventress of painting and color designing as ap- 
plied to fabrics. 

Although the deities above described represent only 
a small fraction of the Maya pantheon, they include, 
beyond all doubt, its most important members, the 
truly great, who held the powers of life and death, 
peace and war, plenty and famine — who were, in short, the arbiters 
of human destiny. 

The Maya conceived the earth to be a cube, which supported the 
celestial vase resting on its four legs, the four cardinal points. Out 
of this grew the Tree of Life, the fiowers of which were the immortal 
principle of man, the soul. Above htmg heavy clouds, the fructi- 
fying waters upon which all growth and life depend. The religion 
was duahstic in spirit, a constant struggle between the powers of 




Fig. 6. Yum Kaax, 
Lord of the Har- 
vest (note his name 
glyph, below). 



MORLBY] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 



19 




Fig. 7. Xaman Ek, 
the North Star God 
(Bote his name 
glyph, helow). 



light and of darkness. On one side were arrayed the gods of plenty, 
peace, and life; on the other those of want, war, and destruction; 
and between these two there waged an unending strife for the control 
of man. This struggle between the powers of light and darkness is 
graphically portrayed in the picture-writings. Where 
the God of Life plants the tree. Death breaks it in 
twain (fig. 8) ; where the former offers food, the latter 
raises an empty vase symbolizing famine ; where one 
builds, the other destroys. The contrast is complete, 
the conflict eternal. 

The Maya believed in the immortality of the soul 
and in a spiritual life hereafter. As a man Uved in this 
world so he was rewarded in the next. The good and 
righteous went to a heaven of material delights, a 
place where rich foods never failed and pain and sor- 
row were unknown. The wicked were consigned to a 
hell called Mitnal, over which ruled the archdemon 
Hunhau and his minions ; and here in hunger, cold, and exhaustion they . 
suffered everlasting torment. The materiahsm of the Maya heaven 
and hell need not surprise, nor lower our estimate of their civilization. 
Similar reahstic conceptions of the hereafter have been entertained 
by peoples much higher in the cultural scale than the Maya. 

Worship doubtless was the most important feature of the Maya 
scheme of existence, and an endless succession of rites and ceremonies 

was considered necessary to retain the 
sympathies of the good gods and to pro- 
pitiate the malevolent ones. Bishop 
Landa says that the aim and object of 
all Maya ceremonies were to secure three 
things only : Health, life, and sustenance ; 
modest enough requests to ask of any 
faith. The first step in all Maya reh- 
gious rites was the expulsion of the evil 
spirits from the midst of the worshipers. This was accomphshed 
sometimes by prayers and benedictions, set formulae of proven 
efficacy, and sometimes by special sacrifices and offerings. 

It would take us too far afield to describe here even the more 
important ceremonies of the Maya rehgion. Their number was liter- 
ally legion, and they answered almost every contingency within the 
range of human experience. ■ First of aU were the ceremonies dedi- 
cated to special gods, as Itzamna, Kukulcan, and Ixchel. Probably 
every deity in the pantheon, even the most insignificant, had at least 
one rite a year addressed to it alone, and the aggregate must have 
made a very considerable number. In addition there were the annual 
feasts of the rituaHstic year brought aroimd by the ever-recurring 




Tig. 8. Conflict between the Gods of Lile 
and Death (Kukulcan and Ahpuch). 



20 BUREAU OF AMERICAN ETHNOLOGY [BnLu 57 

seasons. Here may be mentioned the numerous ceremonies incident 
to the beginning of the new year and the end of the old, as the renewal 
of household utensils and the general renovation of aU articles, which 
took place at this time; the feasts of the various trades and occupa- 
tions — the hunters, fishers, and apiarists, the farmers, carpenters, and 
potters, the stonecutters, wood carvers, and metal workers — each 
guild having its own patron deity, whose services formed another large 
group of ceremonials. A third class comprised the rites of a more 
personal nature, those connected with baptism, confession, marriage, 
setting out on journeys, and the like. Finally, there was a fourth 
group of ceremonies, held much less frequently than the others, but 
of far greater importance. Herein faU the ceremonies held on extra- 
ordinary occasions, as famine, drought, pestilence, victory, or defeat, 
which were probably solemnized by rites of human sacrifice. 

The direction of so elaborate a system of worship necessitated a 
numerous and highly organized priesthood. At the head of the 
hierarchy stood the hereditary high priest, or ahaucan mai, a func- 
tionary of very considerable power. Although he had no actual 
share in the government, his influence was none the less far-reaching, 
since the highest lords sought his advice, and deferred to his judgment 
in the administration of their affairs. They questioned him con- 
cerning the will of the gods on various points, and he in response 
framed the divine replies, a duty which gave him tremendous power 
and authority. In the ahuacan mai was vested also the exclusive 
right to fill vacancies in the priesthood. He examined candidates 
on their knowledge of the priestly services and ceremonies, and after 
their appointment directed them in the discharge of their duties. 
He rarely officiated at sacrifices except on occasions of the greatest 
importance, as at the principal feasts or in times of general need. 
His office was maintained by presents from the lords and enforced 
contributions from the priesthood throughout the country. 

The priesthood included within its ranks women as weU as men. 
The duties were highly specialized and there were many different 
ranks and grades in the hierarchy. The chilan was one of the most 
important. This priest was carried upon the shoulders of the people 
when he appeared in public. He taught their sciences, appointed 
the holy days, healed the sick, offered sacrifices, and most important 
of aU, gave the responses of the gods to petitioners. The ahyxii choc 
was a priest who brought the rains on which the prosperity of the 
country was wholly dependent. The ah maciJc conjured the winds; 
the dhpul caused sickness and induced sleep; the ahuai xibalba 
communed with the dead. At the bottom of the ladder seems to have 
stood the nacon, whose duty it was to open the breasts of the sacrificed 
victims. An important elective office in each community was that 
held by the chac, or priest's assistant. These officials, of which there 



MOKLET] INTEODUCTION" TO STUDY OF MAYA HIEEOGLYPHS 21 

were four, were elected from the nucteelob, or village wise men. 
They served for a term of one year and could never be reelected. 
They aided the priest in the various ceremonies of the year, officiating 
in minor capacities. Their duties seem to have been not unUke those 
of the sacristan in the Roman Catholic Church of to-day. 

In closing this introduction nothing could be'more appropriate than 
to call attention once more to the supreme importance of religion 
in the life of the ancient Maya. Religion was indeed the very 
fountain-head of their civiUzation, and on its rites and observances 
they lavished a devotion rarely equaled in the annals of man. To 
its great uplifting force was due the conception and evolution of the 
hieroglyphic writing and calendar, aUke the invention and the exclusive 
property of the priesthood. To its need for sanctuary may be attrib- 
uted the origin of Maya architecture; to its desire for expression, the 
rise of Maya sculpture. AU activities reflected its powerful influence 
and all were more or less dominated by its needs and teachings. 
In short, religion was the foundation upon which the structure of the 
Maya civilization was reared. 



Chapter II. THE MAYA HIEROGLYPHIC WRITING 

The inscriptions herein described are found throughout the region 
formerly occupied by the Maya people (pi. 1), though by far the 
greater number have been discovered at the southern, or older, sites. 
This is due in part, at least, to the minor rdle played by sculpture 
as an independent art among the northern Maya, for in the north 
architecture gradually absorbed in its decoration the sculptural 
activity of the people which in the south had been applied in the 
^-^ making of the hieroglyphic monuments. 

C / The materials upon which the Maya glyphs are presented 

a are stone, wood, stucco, bone, shell, metal, plaster, pottery, 

r—j and fiber-paper; the firs1>mentioned, however, occurs more 

l_y frequently than all of the others combined. Texts have been 

6 found carved on the wooden lintels of Tikal, molded in the 

stucco reliefs of Palenque, scratched on shells from Copan and 

□ Belize, etched on a bone from Wild Cane Key, British Hon- 
duras, engraved on metal from Chichen Itza, drawn on the 
J, J g g plaster-covered walls of Kabah, Ghichen Itza, and Uxmal, and 
Outlines painted in fiber-paper books. All of these, however, with the 
°[ ?! exception of the first and the last (the inscriptions on stone 
6, lu and the fiber-paper books or codices) just mentioned, occur so 
rarely that they may be dismissed from present consideration, 
the The stones bearing inscriptions are found in a variety of 
tion" ^ shapes, the commonest being the monolithic shafts or slabs 
known as stelse. Some of the shaft-stelae attain a height of 
twenty-six feet (above ground) ; these are not unlike roughly squared 
obelisks, with human figures carved on the obverse and the reverse, 
and glyphs on the other faces. Slab-stelae, on the other hand, are 
shorter and most of them bear inscriptions only on the reverse. Fre- 
quently associated with these stelae are smaller monoliths known as 
" altars," which vary greatly in size, shape, and decoration, some bear- 
ing glyphs and others being without them. 

The foregoing monuments, however, by no means exhaust the list 
of stone objects that bear hieroglyphs. As an adjunct to architecture 
inscriptions occur on wall-slabs at Palenque, on lintels at Yaxchilan 
and Piedras Negras, on steps and stairways at Copan, and on piers 
and architraves at Holactun; and these do not include the great 
number of smaller pieces, as inscribed jades and the like. Most of 
the glyphs in the inscriptions are square in outline except for rounded 
corners (fig. 9, c). Those in the codices, on the other hand, approx- 
imate more nearly in form rhomboids or even ovals (fig. 9, a, i). 
This difference in outline, however, is only superficial in significance 
and involves no corresponding difference in meaning between other- 
22 



the 
dices; 



MORLBY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 23 

wise identical glyphs ; it is due entirely to the mechanical dissimilarity 
of the two materials. Disregarding this consideration as unessential, 
we may say that the glyphs in both the inscriptions and the codices 
belong to one and the same system of writing, and if it were possible 
to read either, the other could no longer withhold its meaning from us. 
■' In Maya inscriptions the glyphs are arranged in parallel columns, 
which are to be read two columns at a time, beginning with the upper- 
most glyph in the left-hand column, and then from left to right and 
top to bottom, ending with the lowest glyph in the second column. 
Then the next two columns are read in the same order, and so on. 
In reading glyphs in a horizontal band, the order is from left to right 
in pairs.'" The writer Imows of no text in which the above order of 
reading is not followed. 

A brief examination of any Maya text, from either the inscriptions 
or the codices, reveals the presence of certain elements which occur 
repeatedly but in varying combinations. The apparent multipHcity 
of these combinations leads at first to the conclusion that a great 
number of signs were employed in Maya writing, but closer study will 





a b c d e 

Fig. 10. Examples of glyph elision, showing elimination of all parts except essential element (here, the 

crossed bands). 

show that, as compared with the composite characters or glyphs 
proper, the simple elements are few in number. Says Doctor 
Brinton (1894 b: p. 10) in this coimection: "If we positively knew the 
meaning . . of a hundred or so of these simple elements, none of 
the inscriptions could conceal any -longer from us the general tenor 
of its contents." Unfortunately, it must be admitted that but Httle 
advance has been made toward the solution of this problem, perhaps 
because later students have distrusted the highly fanciful results 
achieved by the earlier writers who "interpreted" these "simple 
elements." 

Moreover, there is encountered at the very outset in the study of 
these elements a condition which renders progress slow and results 
uncertain. In Egyptian texts of any given period the simple pho- 
netic elements or signs are unchanging under all conditions of com- 
position. Like the letters of our own alphabet, they never vary and 
may be recognized as unfailingly. On the other hand, in Maya texts 
each glyph is in itself a finished picture, dependent on no other for 
its meaning, and consequently the various elements entering into it 
undergo very considerable modifications in order that the resulting 
composite character may not only be a balanced and harmonious de- 



24 



BUBEAU OP AMERICAN ETHNOLOGY 



[BULL. 57 



sign, but also may exactly fill its allotted space. All such modifications 
probably in no way affect the meaning of the element thus mutilated. 
The element shown in figure 10, a-e is a case in point. In a and i 
we have what may be called the normal or regular forms of this 
element. In c, however, the upper arm has been omitted for the sake 
of symmetry in a composite glyph, while in d the lower arm has been 
left out for want of space. Finally in e both arms have disappeared 
^ and the element is reduced to the sign (*), which we may con- 
* elude, therefore, is the essential characteristic of this glyph, par-- 
ticularly since there is no regularity ia the treatment of the arms in the 
normal forms. This suggests another point of the utmost importance, 
namely, the determination of the essential elements of Maya glyphs. 
The importance of this point lies in the fact that great license was 
permitted in the treatment of accessory elements so long as the 
essential element or elements of a glyph could readily be recognized 
as such. In this way may be explained the use of the so-called 








m n 

Fig. 11. Normal-form and head-variant glyphs, showing retention of essential element in each. 

"head" variants, in which the outline of the glyph was represented 
as a human or a grotesque head modified in some way by the essential 
element of the intended form. The first step in the development of 
head variants is seen in figure 11, a, &, in which the entire glyph a is 
used as a headdress in glyph I, the meaning of the two forms remain- 
ing identical. The next step is shown in the same figure, c and d, in 
which the outline of the entire glyph c has been changed to form the 
grotesque head d, though in both glyphs the essential elements are 
the same. A further development was to apply the essential element 
"iP © ^**^ ^^ ^ *° ^^^ head in /, giving rise to a head variant, 
** t the meaning of which suffered no corresponding change. 
The element (f) in figure 11, g, has been reduced in size in ^, 
though the other two essential elements remain un- 
tt changed. A final step appears in i and j, where in 
j the position of one of the two essential elements of i (ft) and 
the form of the other (t) have been changed. These variants 



MOHLEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 25 

are puzzling enough when the essential characteristics and meaning 
of a glyph have been determined, but when both are unknown the 
problem is indeed knotty. For example, it would seem as a logical 
deduction from the foregoing examples, that I of figure 11 is a "head" 
variant of Tc; and similarly n might be a "head" variant of m, but 
here we are treading on uncertain ground, as the meanings of these 
forms are unknown. 

Nor is this feature of Maya writing (i. e., the presence of "head 
variants") the only pitfall which awaits the beginner who attempts 
to classify the glyphs according to their appearance. In some cases 
two entirely dissimilar forms express exactly the same idea. For 
example, no two glyphs could diflFer more in appearance than a and &, 
figure 12, yet both of these forms have the same meaning. This 
is true also of the two glyphs c and d, and e and/. The occurrence of 
forms so absolutely urJike in appearance, yet identical in meaning, 
greatly comphcates the problem of glyph identification. Indeed, 
identity in both meaning and use must be clearly estabHshed before 
we can recognize as variants of the same glyph, forms so dissimilar 
as the examples above given. Hence, because their meanings are 
unknown we are unable to identify g and li, figure 12, as synonyms. 







ah c d e f g h 

Fig. 12. Normal-form and head-variant glyphs, showing absence of common essential element. 

notwithstanding the fact that their use seems to be identical, h 
occurring in two or three texts under exactly the same conditions 
as does ^ in all the others. 

A further source of error in glyph identification is the failure to 
recognize variations due merely to individual peculiarities of style, 
which are consequently unessential. Just as handwriting differs 
in each individual, so the delineation of glyphs differed among the 
ancient Maya, though doubtless to a lesser extent. In extreme 
cases, however, the differences are so great that identification of 
variants as forms of one and the same glyph is difficult if indeed not 
impossible. Here also are to be included variations due to differences 
in the materials upon which the glyphs are delineated, as weU as those 
arising from careless drawing and actual mistakes. 

The foregoiag difficulties, as well as others which await the student 
who would classify the Maya glyphs according to form and appear- 
ance, have led the author to discard this method of classification as 
unsuited to the purposes of an elementary work. Though a problem 
of first importance, the analysis of the simple elements is far too 
complex for presentation to the beginner, particularly since the 



26 BUREAU OF AMERICAK ETHNOLOGY [bull. 57 

greatest diversity of opinion concerning them prevails among those 
who have studied the subject, scarcely any two agreeing at any one 
•point; and finally because up to the present time success in reading 
Maya writing has not come through this channel. 

The classification followed herein is based on the general meaning 
of the glyphs, and therefore has the advantage of being at least self- 
explanatory. It divides the glyphs into two groups : (1) Astronomi- 
cal, calendary, and numerical signs, that is, glyphs used in counting 
time; and (2) glyphs accompanying the preceding, which have an 
explanatory function of some sort, probably describing the nature of 
the occasions which the first group of glyphs designate. 

According to this classification, the great majority of the glyphs 
whose meanings have been determined faU into the first group, and 
those whose meanings are still unknown into the second. This is 
particularly true of the inscriptions, in which the known glyphs 
practically all belong to the first group. In the codices, on the other 
hand, some little progress. has made been in reading glyphs of the 
second group. The name-glyphs of the principal gods, the signs for 
the cardinal points and associated colors, and perhaps a very few 
others may be mentioned in this connection.^ 

Of the unknown glyphs in both the inscriptions and the codices, a 
part at least have to do with numerical calculations of some kind, a fact 
which relegates such glyphs to the first group. The author beheves 
that as the reading of the Maya glyphs progresses, more and more 
characters will be assigned to the first group and fewer and fewer to 
the second. In the end, however, there will be left what we may 
perhaps call a "textual residue," that is, those glyphs which explain 
the nature of the events that are to be associated with the correspond- 
ing chronological parts. It is here, if anywhere, that fragments of 
Maya history will be foimd recorded, and precisely here is the richest 
field for future research, since the successful interpretation of this 
"textual residue" wiU alone disclose the true meaning of the Maya 
writings. 

Three principal theories have been advanced for the interpretation 
of Maya writing : 

1. That the glyphs are phonetic, each representing some sotmd, 
and entirely dissociated from the representation of any thought oridea. 

2. That the glyphs are ideographic, each representing in itself some 
complete thought or idea. 

3. That the glyphs are both phonetic and ideographic, that is, a 
combination of 1 and 2. 

It is apparent at the outset that the first of these theories can not 
be accepted in its entirety ; for although there are undeniable traces 

I There can be no doubt that Forstemann has identified the sign for the planet Venus and possibly a 
few others. (See Forstemann, 1906: p. 116.) 



MORLBY] INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 27 

of phoneticism among the Maya glyphs, all attempts to reduce them 
to a phonetic system or alphabet, which -will interpret the writing, 
have signally failed. The first and most noteworthy of these so-called 
"Maya alphabets," because of its genuine antiquity, is that given by 
Bishop Landa in his invaluable Relacion de las cosas de Yucatan, fre- 
quently cited in Chapter I. Writing in the year 1565, within 25 
years of the Spanish Conquest, Landa was able to obtain characters 
for 27 sounds, as follows: Three a's, two h's, c, t, e, Ji, i, ca, Ic, two I's, 
m, n, two o's, pp, p, cu, leu, two x's, two v's, z. This alphabet, which 
was first published in 1864 by Abb6 Brasseur de Bourbourg (see 
Landa, 1864), was at once heralded by Americanists as the long- 
awaited key which would imlock the secrets of the Maya writing. 
Unfortunately these confident expectations have not been realized, 
and all attempts to read the glyphs by means of this alphabet or of 
any of the numerous others * which have appeared since, have com- 
pletely broken down. 

This failure to establish the exclusive phonetic character of the 
Maya glyphs has resulted ia the general acceptance of the second 
theory, that the signs are ideographic. Doctor Brinton (1894 b : p. 14), 
however, has pointed out two facts deducible from the Landa alpha- 
bet which render impossible not only the complete acceptance of this 
second theory but also the absolute rejection of the first: (1) That a 
native writer was able to give a written character for an unfamiliar 
sound, a soimd, moreover, which was without meaning to him, as, 
for example, that of a Spanish letter; and (2) that the characters 
he employed for this, purpose were also used in the native writings. 
These facts Doctor Brinton regards as proof that some sort of 
phonetic writing was not unkoown, and, indeed, both the inscrip- 
tions and the codices establish the truth of this contention. For 
example, the sign in a, figure 13, has the phonetic value Jcin, and 
the sign in i the phonetic value yax. In the latter glyph, however, 
only the upper part (reproduced in c) is to be regarded as the essen- 
tial element. It is strongly indicative of phoneticism therefore to 
find the soimd yaxkin, a combiaation of these two, expressed by the 
sign found in d. Similarly, the character representing the phonetic 
value ]cin is found also as an element in the glyphs for the words liMn 

^ Brasseur de Bourbourg, the "discoverer" of Landa's manuscript, added several signs of his own 
invention to tlie original Landa alphabet. See his introductirai to the Codex Troano published by the 
French Government. Leon de Rosny published an alphabet of 29 letters with numerous variants. 
Later Dr. F. Le Plongeon defined 23 letters with variants and made elaborate interpretations of the texts 
with this "alphabet" as his key. Another alphabet was that proposed by Dr. Hilbome T. Cresson, which 
included syllables as well as letters, and with which its originator also essayed to read the texts. Scarce 
worthy of mention are the alphabet and volume of interlinear translations from both the inscriptions 
and the codices published by F. A. de la Rochefoucauld. This is very fantastic and utterly without value 
unless, as Doctor Brinton says, it be taken "as a warning against the intellectual aberrations to which 
students of these ancient mysteries seem peculiarly prone." The late Dr. Cyrus Thomas, of the Bureau 
of American Ethnology, was the last of those who endeavored to interpret the Maya texts by means of 
alphabets; though be was perhaps the best of them all, much of his work in this particular respect will 
not stand. 



28 



BUBEAT; of AMERICAN ETHNOLOGY 



I.BULL. 'Ji 



aad cWcin (see e and/, respectively, fig. 13), each of whicli has im.as 
its last syllable. Again, the phonetic value tun is expressed by the 
glyph in g, and the sound ca (c hard) by the sign h. The sound TcaMn 
is rejpresented by the character in i, a combination of these two. 
Sometimes the glyph for this same sound takes the form of j, the fish 
element in Ic replacing the comblike element h. Far from destroy- 
ing the phonetic character of this composite glyph, however, this 
variant Ti in reality strengthens it, since in Maya the word for fish is 
cay (c hard) and consequently the variant reads caytun, a close pho- 
netic approximation of Icatun. The remaining element of this glyph 
(Z) has the value cauac, the first syllable of which is also expressed by 
either Ji or Tc, figure 13. Its use in i and / probably may be regarded 
as but a further emphasis of the phonetic character of the glyph. 

It must be remembered, however, that all of the above glyphs have 
meanings quite independent of their phonetic values, that primarily 





rcrt 
hi j Tc 

Fig. 13. Glyphs tuilt up on a phonetic hasis. 

their fimction was to convey ideas, and that only secondarily were 
they used in their phonetic senses. 

If neither the phonetic nor the ideographic character of the glyphs 
can be wholly admitted, what then is the true nature of the Maya 
writing? The theory now most generally accepted is, that while 
chiefly ideographic, the glyphs are sometimes phonetic, and that 
although the idea of a glyphic alphabet must finally be abandoned, 
the phonetic use of syllables as illustrated above must as surely be 
recognized. 

This kind of writin.g Doctor Brinton has called ilconomatic, more 
familiarly known to us under the name of rebus, or puzzle writing. 
In such writing the characters do not indicate the ideas of the objects 
which they portray, but only the soimds of their names, and are 
used purely in a phonetic sense, like the letters of the alphabet. 
For example, the rebus in figure 14 reads as follows: "I believe Aunt 
Rose can well bear all for you." The picture of the eye recalls not 
the idea "eye" but the sound of the word denoting this object, which 
is also the sound of the word for the first person singular of the per- 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



29 



sonal pronouu I. Again, the picture of a bee does not represent the 
idea of that insect, but stands for the sound of its name, which 
used with a leaf indicates the sound "beeleaf," or in other words, 
"believe."! 

It has long been known that the Aztec employed ikonomatic char- 
acters in their writing to express the names of persons and places, 
though this practice does not seem to have been extended by them 
to the representation of abstract words. The Aztec codices contain 
maaiy glyphs which are to be interpreted ikonomatically, that is, like 
our own rebus writing. For example in figure 15, a, is shown the 
Aztec hieroglyph for the town of Toltitlan, a name which means 
"near the place of the rushes." The word toUin means "place of 
the rushes," but only its first syllable tol appears in the word Toltitlan. 
This syllable is represented in a by several rushes. The word tetlan 




Fig. 14. A rebus. Aztec, and probably Maya, personal and place names were written in a corresponding 

manner. 

means "near something" audits second syllable Uan is found also 
in the word tlanili, meaning "teeth." In a therefore, the addition 
of the teeth to the rushes gives the word Toltitlan. Another example 
of this kind of writing is given in figure 15, 6, where the hieroglyph for 
the town of Acatzinco is shown. This word means "the little reed 
grass," the diminutive being represented by the syllable tzinco. 
The reed grass (acatl) is shown by the pointed leaves or spears which 
emerge from the lower part of a human figure. This part of the 
body was called by the Aztecs tzinco, and as used here expresses merely 
the sound tzinco in the diminutive acatzinco, "the little reed grass," 
the letter I of acatl being lost in composition. 

The presence of undoubted phonetic elements in these Aztec glyphs 
expressing personal names and place names would seem to indicate 
that some similar usage probably prevailed among the Maya. 

1 Thus tliewholerebusinfigm'el4reads: "Eyebeeleafantrosecanwellbearawlfourewe." Thesewords 
may be replaced by their homophones as follows: "I believe Aunt Rose can well bear aU for you." 

Rebus writing depends on the principle of homophones; that is, words or characters which sound alike 
but have different meanings. 




30 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

While admitting this restricted use of phonetic composition by the 
Maya, Professor Seler refuses to recognize its further extension : 

Certainly there existed in the Maya writing compound hieroglyphs giving the name 
of a deity, person, or a locality, whose elements vmited on the phonetic principle. 
But as yet it is not proved that they wrote texts. And without doubt the greater 
part of the Maya hieroglyphics were conventional symbols built up on the ideographic 
principle. 

Doctor Forstemann also regards the use of phonetic elements as 
restricted to little more than the above when he says, "Finally the 
graphic system of the Maya . . . never even achieved the expres- 
sion of a phrase or even a verb." 

On the other hand, Mr. Bowditch (1910: p. 255) considers the use 
of phonetic composition extended considerably beyond these limits : 

As far as I am aware, the use of this kind of writing [rebus] 
was confined, among the Aztecs, to the names of persons and 
places, while the Mayas, if they used the rebus form at all, 
used it also for expressing common nouns and possibly ab- 
stract ideas. The Mayas surely used picture writing and the 
ideographic system, but I feel confident that a large part of 
their hieroglyphs will be found to be made up of rebus forms 
and that, the true line of research will be found to lie in this 

a J) ' 

direction. 
Fig. lo. Aztec place names: 

a, The sign tor the town Doctor Briutou (1894 b: p. 13) held an opinion 

IhetoZ'I^uLo^ '"' between these two, perhaps inclining slightly 

toward the former: "The intermediate position 

which I have defended, is that while chiefly ideographic, they [the 

Maya glyphs] are occasionally phonetic, in the same manner as are 

confessedly the Aztec picture-writings." 

These quotations from the most eminent authorities on the sub- 
ject well illustrate their points of agreement and divergence. All 
admit the existence of phonetic elements in the glyphs, but disagree 
as to their extent. And here, indeed, is the crux of the whole phonetic 
question. Just how extensively do phonetic elements enter into the 
composition of the Maya glyphs ? Without attempting to dispose 
of this point definitely one way or the other, the author may say that 
he believes that as the decipherment of Maya writing progresses, 
more and more phonetic elements will be identified, though the idea 
conveyed by a glyph will always be found to overshadow its phonetic 
value. 

The various theories above described have not been presented for 
the reader's extended consideration, but only in order to acquaint 
him with the probable nature of the Maya glyphs. Success ia 
deciphering, as we shall see, has not come through any of the above 
mentioned lines of research, which will not be pursued further in this 
work. 



MOBLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 31 

In taking up the question of the meaning of Maya writing, it must 
be admitted at the outset that in so far as they have been deciphered 
both the inscriptions and the codices have been found to deal pri- 
marily, if indeed not exclusively, with the counting of time in some 
form or other. Doctor Forstemann, the first successful interpreter 
of the codices, has shown that these waitings have for their principal 
theme the passage of time in its varying relations to the Maya calen- 
dar, ritual, and astronomy. They deal in great part with the sacred 
year of 260 days, known to the Aztec also under the name of the 
tondlamatl, in connection with which various ceremonies, offerings, 
sacrifices, and domestic occupations are set forth. Doctor Forste- 
mann believed that this 260-day period was employed by the priests 
in casting horoscopes and foretelling the future of individuals, 
classes, and tribes, as well as in predicting coming political events and 
natural phenomena; or in other words, that in so far as the 260-day 
period was concerned, the codices are nothing more nor less than 
books of prophecy and divination. 

The prophetic character of some of these native books at least is 
clearly indicated in a passage from Bishop Landa's Belacion (p. 286). 
In describing a festival held in the month Ho, the Bishop relates that 
"the most learned priest opened a book, in which he examined the 
omens of the year, which he announced to all those who were present." 
Other early Spanish writers state that these books contain the ancient 
prophecies and indicate the times appointed for their fulfillment. 

Doctor Thomas regarded the codices as religious calendars, or 
rituals for the guidance of the priests in the celebration of feasts, 
ceremonies, and other duties, seemingly a natural inference from the 
character of the scenes portrayed in connection with these 260-day 
periods. 

Another very important function of the codices is the presentation 
of astronomical phenomena and calculations. The latter had for 
their immediate object in each case the determination of the lowest 
number which would exactly contain all the numbers of a certain 
group. These lowest numbers are in fact nothing more nor less than 
the least common multiple of changing combinations of numbers, 
each one of which represents the revolution of some heavenly body. 
In addition to these calculations deities are assigned to the several 
periods, and a host of mythological allusions are introduced, the 
significance of most of which is now lost. 

The most striking proof of the astronomical character of the codices 
is to be seen in, pages 46-50 of the Dresden Manuscript. Here, to 
begin with, a period of 2,920 days is represented, which exactly con- 
tains five Venus years of 584 ' days each (one on each page) as well 
as eight solar years of 365 days each. Each of the Venus years is 
divided into four parts, respectively, 236, 90, 250, and 8 days. The 

' The period of tbe synoflical revolution of Venus as computed tonlay is 683.920 days. 



32 BUREAU OF^ AMERICAN ETHNOLOGY [bull. 57 

jBrst and third of these constitute the periods when Venus was the 
morning and the evening star, respectively, and the second and 
fourth, the periods of invisibiUty after each of these manifestations. 
This Venus-solar period of 2,920 days was taken as the basis from 
which the number 37,960 was formed. This contains 13 Venus-solar 
periods, 65 Venus-years, 104 solar years, and 146 tonalamails, or 
sacred years of 260 days each. Finally, the last number (37,960) 
with aU the subdivisions above given was thrice repeated, so that 
these five pages of the manuscript record the passage of 113,880 days, 
or 312 solar years. 

Again, on pages 51-58 of the same manuscript, 405 revolutions of 
the moon are set down; and so accurate are the calculations involved 
that although they cover a period of nearly 33 years the total number 
of days recorded (11,959) is only 89/100 of a day less than the true 
time computed by the best modern method ^—certainly a remarkable 
achievement for the aboriginal mind. It is probable that the revo- 
lutions of the planets Jupiter, Mars, Mercury, and Saturn are similarly 
recorded in the same manuscript. 

Toward the end of the Dresden Codex the niunbers becojne greater 
and greater until, in the so-caUed "serpent numbers," a grand total 
of nearly twelve and a half million days (about thirty-four thousand 
years) is recorded again and again. In these well-nigh inconceivable 
periods all the smaller units may be regarded as coming at last to a 
more or less exact close. What matter a few score years one way or 
the other in this virtual eternity? Finally, on the last page of the 
manuscript, is depicted the Destruction of the World (see pi. 3), for 
which these highest numbers have paved the way. Here we see the 
rain serpent, stretching across the sky, belching forth torrents of 
water. Great streams of water gush from the sun and moon. The 
old goddess, she of the tiger claws and forbidding aspect, the malevo- 
lent patroness of floods and cloudbursts, overturns the bowl of the 
heavenly waters. The crossbones, dread emblem of death, decorate 
her skirt, and a writhing snake crowns her head. Below with 
downward-pointed spears, symbolic of the universal destruction, the . 
black god stalks abroad, a screeching bird raging on his fearsome 
head. Here, indeed, is portrayed with graphic touch the final all- 
engulfing cataclysm. 

According to the early writers, in addition to the astronomic, pro- 
phetic, and ritualistic material above described, the codices con- 
tained records of historical events. It is doubtful whether this is 

1 According to modem calculations, the period of the lunar revolution is 29.530688, or approximately 
29J days. For 406 revolutions the accumulated error would be .03X405= 12.16 days. This error the Mava 
obviated by using 29.5 in some calculations and 29.6 in others, the latter offsetting the former. Thus the 
first 17 revolutions of the sequence are divided into three groups; the first 6 revolutions being computed 
at 29.5, each giving a tot41 of 177 days; and the second 6 revolutions also being computed at 20 5 each 
giving a total of another 177 days. The third group of 5 revolutions, however, was computed at 29 6 each' 
giving a total of 148 days. The total number of days in the first 17 revolutions was thus computed to be 
177+177+147=502, which is very close to the time computed by modem calculations, 502.02, 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 3 




PAGE 74 OF THE DRESDEN CODEX, SHOWING THE END 
OF THE WORLD (ACCORDING TO FORSTEMANN) 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 33 

true of any of the three codices now extant, though there are grounds 
for believing that the Codex Peresianus may be in part at least of an 
historical nature. 

Much less progress has been made toward discovering the meaning 
of the inscriptions. Doctor Brinton (1894 b: p. 32) states: 

My own conviction is that they [the inscriptions and codices] -will prove to be 
much more astronomical than even the latter [Doctor Forstemann] believes; that 
they are primarily and essentially records of the motions of the heavenly bodies; and 
that both figures and characters are to be interpreted as referring in the first instance 
to the sun and moon, the planets, and those constellations which are most prominent 
in the nightly eky in the latitude of Yucatan. 

Mr. Bowditch (1910: p. 199) has also brought forward very cogent 
points tending to show that in part at least the inscriptions treat of the 
intercalation of days necessary to bring the dated monuments, based 
on a 365-day year, into harmony with the true solar year of 365.2421 
days.' 

While- admitting that the inscriptions may, and probably do, 
contain such astronomical matter as Doctor Brinton and Mr. Bow- 
ditch have suggested, the writer believes nevertheless that fimda- 
mentally they are historical; that the monuments upon which they 
are presented were erected and inscribed on or about the dates they 
severally record; and finally, that the great majority of these dates 
are those of contemporaneous events, and as such pertain to the 
subject-matter of history. 

The reasons which have led him to this conclusion follow: 

First. The monuments at most of the southern Maya sites show 
a certain periodicity in their sequence. This is most pronounced at 
Quirigua, where all of the large monuments faU into an orderly 
series, in which each monument is dated exactly 1,800 days later than 
the one immediately preceding it in the sequence. This is also true 
at Copan, where, in spite of the fact that there are many gaps in the 
sequence, enough monuments conforming to the plan remain to 
prove its former existence. The same may be said also of Naranjo, 
Seibal, and Piedras Negras, and in fact of almost all the other large 
cities which afford sufficient material for a chronological arrangement. 

This interval of 1,800 days quite obviously was not determined by 
the recurrence of any natural phenomenon . It has no parallel in 
nature, but is, on the contrary, a highly artificial unit. Consequently, 
monuments the erection of which was regulated by the successive 
returns of this period could not depend in the least for the fact of 
their existence on any astronomical phenomenon other than that of 
the rising and setting of eighteen hundred successive suns, an arbi- 
trary period. 

The Maya of Yucatan had a similar method of marking time, 
though their unit of enumeration was 7,200 days, or four times the 

1 This is the tropical year or the time from one equinox to its return. 
43508°— Bull. 57—15 3 



34 BUEEAU OF AMERICAN ETHNOLOGY , [boll. 57 

length of the one used for the same purpose in the older cities. The 
foUowing quotations from early Spanish chroniclers explain this 
practice and indicate that the inscriptions presented on these time- 
markers were of an historical nature : 

There were discovered in the plaza of that city [Mayapan] seven or eight stones 
each ten feet in length , round at the end, and well worked. These had some writings 
in the characters which they use, but were so worn by water that they could not be 
read. Moreover, they think them to be in memory of the foundation and destruction 
of that city. There are other similar ones, although higher, at Zilan, one of the coast 
towns. The natives when asked what these things were, replied that they were 
accustomed to erect one of these stones every twenty years, which is the number 
they use for counting their ages.' 

The other is even more explicit: 

Their lustras having reached five in niunber, which made twenty years, which 
they call a katun, they place a graven stone on another of the same kind laid in lime 
and sand in the walls of their temples and the houses of the priests, as one still sees 
to-day in the edifices in question, and in some ancient walls of our own convent at 
Merida, about which there are some cells. In a city named Tixhualatun, 'which sig- 
nifies "place where one graven stone is placed upon another," they say are their 
archives, where everybody had recourse for events of all kinds, as we do to 
Sunancas.2 

It seems almost necessary to conclude from such a parallel that 
the inscriptions of the southern cities wiU also be found to treat of 
historical matters. 

Second. When the moniunents of the southern cities are arranged 
according to their art development, that is, in stylistic sequence, they 
are found to be arranged in their chronological order as well. This 
important discovery, due largely to the researches of Dr. H. J. 
Spinden, has enabled us to determine the relative ages of various 
monuments quite independent of their respective dates. From a 
stylistic consideration alone it has been possible not only to show 
that the monuments date from different periods, but also to estabhsh 
the sequence of these periods and that of the monuments in them. 
Finally, it has demonstrated beyond aU doubt that the great 
majority of the dates on Maya monuments refer to the time of then- 
erection, so that the inscriptions which they present are historical in 
that they are the contemporaneous records of different epochs. 

TUrd. The dates on the monuments are such as to constitute a 
strong antecedent probabihty of their historical character. Like 
the records of most ancient peoples, the Maya monuments, judging 
from their dates, were at first scattered and few. Later, as new 
cities were founded and the nation waxed stronger and stronger, the 
number of monuments increased, until at the flood tide of Maya pros- 
perity they were, comparatively speaking, common. Finally, as 
decline set in, fewer and fewer monuments were erected, and eventu- 
ally effort in this field ceased altogether. The increasing number of 



1 Landa, 1864: p. 52. sCogoUudo, 1688: i, Ub. IV, v, p. 186. 



"<»• 


"0 '0 '0 '01' ■■ 


UJ 

-1 

a. 


'0 '01 -61 '6 " " 
'0 '0 '61 '6 " " 


z 


'0 'OI 'il '6 ■ " ' 


UJ 

_I 

CQ 


0-0 -0 -81 -6 ""■ 
O-O-OT'AT'6 ■■■ 




'0 '0 'iT '6 " " " 




'0 '01 'gi '6 ■ ' ■ 




0-0 -0 -91 -6 •■■ 




0-0-0T-9I-6 "" 




-0 -0 -SI -6 • ■; 




'0 'oi: 'n '6 " • • 




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o'o-o -gx'e ■■■ 




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o-o-oni-e •■■ 




0-0 -0 -IT -6 ••" 




o-om-of6 •■■ 




0-0 -0 -01 -6 •■■ 




O'O-OT-6 -6 ••■ 




O-O'O -6 -6 •"■ 




0-0 -01 -8 -6 ■•• 




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O-O-OT-9 -6 -■■ 




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>- 
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h 

UJ 


'COI '9 "6 ""■ 
0-0 -0 -Q -6 •■• 
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a: 

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Q 
LU 
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a: 
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DC 

CO 
111 
h- 
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z 

UJ 

a: 

O 
O 

o 

z 

o 

I 

CO 

< 

a: 

< 
a 



MOELBT] INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 35 

the monuments by ten-year periods is shown in plate 4, where the 
passage of time (i. e., the successive ten-year periods) is represented 
from left to right, and the number of dates in each ten-year period 
from bottom to top. Although other dated monuments will be 
found from time to time, which will necessarily change the details 
given in this diagram, such additional evidence in all probability will 
never controvert the following general conclusions, embodied in what 
has just been stated, which are deducible from it: 

1. At first there was a long period of slow growth represented by 
few monuments, which, however, increased in number toward the end. 

2. This was followed without interruption by a period of increased 
activity, the period from which the great majority of the monuments 
date. 

3. Finally this period came to rather an abrupt end, indicated by 
the sudden cessation in the erection of dated monuments. 

The consideration of these indisputable facts tends to estabhsh the 
historical rather than the astronomical character of the monuments. 
For had the erection of the monuments depended on the successive 
recurrences of some astronomical phenomenon, there would be cor- 
responding intervals between the dates of such monuments' the 
length of which would indicate the identity of the determining phe- 
nomenon; and they would hardly have presented the same logical 
increase due to the natural growth of a nation, which the accompany- 
ing diagram clearly sets forth. 

Fourth. Although no historical codices ^ are known to have sur- 
vived, history was undoubtedly recorded in these ancient Maya 
books. The statements of the early Spanish writers are very exphcit 
on this point, as the following quotations from their works will show. 
Bishop Landa (here, as always, one of the most reliable authori- 
ties) says: "And the sciences which they [the priests] taught were 
the count of the years, months and days, the feasts and ceremonies, 
the administration of their sacraments, days, and fatal times, their 
methods of divination and prophecy, and foretelling events, and the 
remedies for the sick, and their antiquities" [p. 44]. And again, " they 
[the priests] attended the service of the temples and to the teaching 
of their sciences and how to write them in their iooJcs." And again, 
[p. 316], "This people also used certain characters or letters with 
which they wrote in their iooJcs their ancient matters and sciences." 

Father Lizana says (see Landa, 1864: p. 352): "The history and 
authorities we can cite are certain ancient characters, scarcely under- 
stood by many and explained'by some old Indians, sons of the priests 

1 For example, if the revolution of Venus had been the governing phenomenon, each monument would 
be distant from some other by 584 days; if that of Mars, 780 days; if that of Mercury, 115 or 116 days, etc. 
Furthermore, the sequence, once commenced, would naturally have been more or less uninterrupted. It 
is hardly necessary to repeat that the intervals which have been found, namely, 7200 and 1800, rest on no 
known astronomical phenomena but are the direct result of the Maya vigesimal system of numeration. 

2 It is possible that the Codex Peresianus may treat of historical matter, as already explained. 



36 BTJEEAU OP AMERICAN ETHNOLOGY [boll. 57 

of their gods, who alone knew how to read and expound them and 
who were believed in and revered as much as the gods themselves." 

Father Ponce (tome Lvni, p. 392) who visited Yucatan as early as 
1588, is equally clear: "The natives of Yucatan are among all the 
inhabitants of New Spain especially deserving of praise for three 
things. First that before the Spaniards came they made use of 
characters and letters with which they wrote out their histories, their 
ceremonies, the order of sacrifices to their idols and their calendars 
in books made of the bark of a certain tree." 

Doctor Aguilar, who wrote but little later (1596), gives more details 
as to the kind of events which were recorded. " On these [the fiber 
books] they painted in color the reckoning of their years, wars, pesti- 
lences, hurricanes, inundations, famines and other events." 

Finally, as late as 1697, some of these historical codices were in the 
possession of the last great independent Maya ruler, one Canek. 
Says Villagutierre (1701: hb. vi, cap. iv) m this connection: "Because 
their king [Canek] had read it in his analtehes [fiber-books or codices] 
they had knowledge of the provinces of Yucatan, and of the fact that 
their ancestors had formerly come from them; analtehes or histories 
being one and the same thing." 

It is clear from the foregoing extracts, that the Maya of Yucatan 
recorded their history up to the time of the Spanish Conquest, in their 
hieroglyphic books, or codices. That fact is beyond dispute. It 
must be remembered also ia this connection, that the Maya of Yucatan 
were the direct inheritors of that older Maya civilization in the south, 
which had produced the hieroglyphic monuments. For this latter 
reason the writer believes that the practice of recording history in the 
hieroglyphic writing had its origin, along with many another custom, 
ia the southern area, and consequently that the inscriptions on the 
monuments of the southern cities are probably, in part at least, of an 
historical nature. 

Whatever may be the meaning of the undeciphered glyphs, enough 
has been said in this chapter about those of known meaning to indi- 
cate the extreme importance of the element of time in Maya writing. 
The very great preponderance of astronomical, calendary, and nu- 
merical signs in both the codices and the inscriptions has determined, 
so far as the beginner is concerned, the best way to approach the 
study of the glyphs. First, it is essential to understand thoroughly 
the Maya system of counting time, in other words, their calendar and 
chronology. Second, in order to make use of this knowledge, as did 
the Maya, it is necessary to f amiUarize ourselves with their arithmetic 
and its signs and symbols. Third, and last, after this has been 
accomphshed, we are ready to apply ourselves to the deciphering 
of the inscriptions and the codices. For this reason the next chapter 
will be devoted to the discussion of the Maya system of counting time. 



Chapter III. HOW THE MAYA KECKONED TIME 

Among all peoples and in aU ages the most obvious unit for the 
measurement of time has been the day; and the never-failing reap- 
pearance of light after each interval of darloiess has been the most 
constant natural phenomenon with which the mind of man has had 
to deal. From the earliest times successive returns of the sun have 
regulated the whole scheme of human existence. When it was light, 
man worked; when it was dark, he rested. Conformity to the opera- 
tion of this natural law has been practically universal. 

Indeed, as primitive man saw nature, day was the only division of 
time upon which he could absolutely rely. The waxing and waning 
of the moon, with its everchanging shape and occasional obscuration 
by clouds, as well as its periodic disappearances from the heavens 
aU combined to render that luminary of little account in measuring 
the passage of time. The romid of the seasons was even more iinsat- 
isfactory. A late spring or an early winter by hastening or retarding 
the return of a season caused the apparent lengths of succeeding 
years to vary greatly. Even where a 365-day year had been deter- 
mined, the fractional loss, amounting to a day every four years, soon 
brought about a discrepancy between the calendar and the true year. 
The day, therefore, as the most obvious period iu nature, as well as 
the most reliable, has been used the world over as the fundamental 
unit for the measurement of longer stretches of time. 

Table I. THE TWENTY MAYA DAY NAMES 



Imix 


Chuen 


Ik 


Eb 


Akbal 


Ben 


Kan 


Ix 


Chicclian 


Men 


Cimi 


Cib 


Manik 


Cabau 


Lamat 


Ezuab 


Muluc 


Cauac 


Oc 


Ahau 



In conformity with the imiversal practice just mentioned the Maya 
made the day, which they called Tcin, the primary unit of their calen- 
dar. There were twenty such units, named as in Table I; these 
followed each other in the order there shown. When Ahau, the last 
day in the list, had been reached, the count began anew with Imix, 
and thus repeated itself again and again without interruption, 
throughout time. It is important that the student should fix this 

37 



38 



BUREAU OF AMERICAN ETHNOLOGY 



[BULL. 57 



Maya conception of the rotation of days firmly in his mind at the 
outset, since all that is to follow depends upon the absolute con- 
tinuity of this twenty-day sequence in endless repetition. 




Fig. 16. The day signs in the inscriptions. 



The glyphs for these twenty days are shown ia figures 16 and 17. 
The forms in figure 16 are from the inscriptions and those in figure 
17 from the codices. In several cases variants are given to facilitate 
identification. A study of the gl3rphs in these two figures shows on 
the whole a fairly close similarity between the forms for the same 



MORLDT] INTRODUCTION TO STUDY OF MAYA HIEIiOGLYPHS 



3^ 



day in each. The sign for the first day, Imix, is practically identical 
in both. Compare figure 16, a and h, Nvith figure 17, a and h. The 
usual form for the day Ik in the iascriptions (see fig. 16, c) , however, 

Q© O© 




IMIX 



IK 



AKBAL 






/ 
KAN 



g h 

CHICCHAN 




h 
MANIK 



I m 

LA MAT 



u 

MEN 



CIB 





CIMI 





n 
MULUC 



o 
OC 




CABAN 




EZNAB CAUAC 

Fig. 17. The day signs in the codices. 



AHAU 



is unlike the glyph for the same day in the codices (fig. 17, c, d). 
The forms for Akbal and Kan are practic^ly the same in each (see fig. 
16, d, e, and/, and fig. 17, e and/, respectively) . The day Chicchan, 
figure 16, g, occm-s rarely in the inscriptions; when present, it takes the 



40 BUREAU OF AMERICAN EIHUTOlOGY [bull. 5T 

form of a grotesque head. In the codices the common form for this 
day is very different (fig. 17, g). The head variant, however (fig. 
17, h) , shows a slightly closer similarity to the form from the inscrip- 
tions. The forms in both figure 16, h, i, and figure 17, i, j, for the 
day Cimi show little, resemblance to each other. Although figure 17, 
i, represents the conmion form in the codices, the variant in j more 
closely resembles the form in figure 16, Ji, i. The day Manik is prac- 
tically the same in both (see figs. 16, j, and 17, ^), as is also lamat 
, (figs. 16, k, I, and 17, I, m) . The day Muluc occurs rarely in the 
inscriptions (fig. 16, m, n) . Of these two variants m more closely 
resembles the form from the codices (fig. 17, -ft) . The glyph for the 
day Oc (fig. 16, o, p, q) is not often foimd in the inscriptions. In the 
codices, on the other hand, this day is frequently represented as 
shown in figure 17, o. This form bears no resemblance to the forms 
in the inscriptions. There is, however, a head-variant form found 
very rarely in the codices that bears a slight resemblance to the forms 
in the inscriptions. The day Chuen occurs but once in the inscrip- 
tions where the form is clear enough to distinguish its characteristic 
(sec fig 16, r) . This form bears a general resemblance to the glyph 
for this day in the codices (fig. 17, f, q) . The forms for the day Eb 
in both figures 16, s, t, u, and 17, r, are grotesque heads showing 
but remote resemblance to one another. The essential element in 
both, however, is the same, that is, the element occupying the 
position of the ear. Although the day Ben occurs but rarely in 
the inscriptions, its form (fig. 16, v) is practically identical with 
that in the codices (see fig. 17, s). The day Ix in the inscriptions 
appears as in figure 16, w, x. The form in the codices is shown in 
figure 17, t. The essential element in each seems to be the three promi- 
nent dots or circles. The day Men occurs very rarely on the monu- 
ments. The form shown in figure 16, y, is a grotesque head not unlike 
the sign for this day in the codices (fig. 17, u) . The signs for the 
day Cib in the inscriptions and the codices (figs. 16, z, and 17, v, w) , 
respectively, are very dissimilar. Indeed, the form for Cib (fig. 17, v) 
in the codices resembles more closely the sign for the day Caban 
(fig. 16, a', b') than it does the form for Cib in the inscriptions (see 
fig. 16, z) . The only element common to both is the line paralleling the 
/jnjj upper part of the glyph (*) and the short vertical lines connecting 
* it with the outline at the top. The glyphs for the day Caban in 
both figures 16, a', h', and 17, x, y, show a satisfactory resemblance to 
each other. The forms for the day Eznab are also practically iden- 
tical (see figs. 16, c', and 17, z, a') . The forms for the day Cauac, on 
the other hand, are very dissimilar; compare figures 16, d', and 17, b'. 
The only point of resemblance between the two seems to be the 
element which appears in the eye of the former and at the lower left- 
hand side of the latter. The last of the twenty Maya days, and by 



MOBLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 41 

far the most important, since it is foxmd in both the codices and the 
inscriptions more frequently than all of the others combined, is Ahau 
(see figs. 16, e'-k', and 17, c', d') . The latter form is the only one 
foxmd in the codices, and is identical with e' , f , figure 16, the usual 
sign for this day in the inscriptions. The variants in figure 16, g'-¥, 
appear on some of the monuments, and because of the great im- 
portance of this day Ahau it is necessary to keep all of them in 
mind. 

These examples of the glyphs, which stand for the twenty Maya 
days, are in each case as typical as possible. The student must 
remember, however, that many variations occiu, which often render 
the correct identification of a form difficult. As explained in the 
preceding chapter, such variations are due not only to individual 
peculiarities of style, careless drawing, and actual error, but also to 
the physical dissimilarities of materials on which they are por- 
trayed, as the stone of the moniunents and the fiber paper of the 
codices; consequently, such differences may be regarded as unessen- 
tial. The ability to identify variants differing from those shown in 
figures 16 and 17 will come only through experience and familiarity 
with the glyphs themselves. The student should constantly bear in 
mind, however, that almost every Maya glyph, the signs for the days 
included, has an essential element peculiar to it, and the discovery of 
such elements will greatly facilitate his study of Maya writing. 

Why the named days should have been limited to twenty is diffi- 
cult to imderstand, as this number has no parallel period in nature. 
Some have conjectured that this number was chosen because it rep- 
resents the number of man's digits, the twenty fiQgers and toes. 
Mr. Bowditch has poiated out in this connection that the Maya word 
for the period composed of these twenty named days is uindl, while the 
word for 'man' is uiniJc. The parallel is iateresting and may possibly 
explain why the niunber twenty was selected as the basis of the 
Maya system of muneration, which, as we shall see later, was vigesi- 
mal, that is, increasing by twenties or multiples thereof. 

The Tonalamatl, or 260-dat Period 

Merely calling a day by one of the twenty names given in Table I, 
however, did not sufficiently describe it according to the Maya notion. 
For instance, there was no day in the Maya calendar called merely 
Imix, Ik, or Akbal, or, in fact, by any of the other names given in 
Table I. Before the name of a day was complete it was necessary 
to prefix to it a niunber ranging from 1 to 13, inclusive, as 6 Imix 
or 13 Akbal, Then and only then did a Maya day receive its com- 
plete designation and find its proper place in the calendar. 

The manner in which these thirteen numbers, 1 to 13, inclusive, 
were joined to the twenty names of Table I was as follows: Selecting 



42 BUREAU OP AMERICAN ETHNOLOGY [bull. 57 

any one of the twenty names ^ as a starting point, Kan for example, 
the niunber 1 was prefixed to it. See Table II, in which the names 
of Table I have been repeated with the nimibers prefixed to them in 
a manner to be explained hereafter. The star opposite the name 
Kan indicates the starting point above chosen. The name Chicchan 
immediately following Kan in Table II was given the next number 
in order (2), namely, 2 Chicclian. The next name, Cimi, was given 
the next niunber (3), namely, 3 Cimi, and so on as foUows: 4 Manik, 
5 Lamat, 6 Muluc, 7 Oc, 8 Clinen, 9 Eb, 10 Ben, 11 Ix, 12 Men, 13 Cib. 

Table II. SEQUENCE OF MAYA DAYS 



5 Imix 


8 Chuen 


6 Ik 


9 Eb 


7 Akbal 


10 Ben 


^1 TTru 


11 Ix 


2 CMcchan 


13 Men 


3 Cimi 


13 Cib 


4 Manik 


1 Caban 


S Xamat 


2 Ezuab 


6 Muluc 


3 Cauac 


7 Oc 


4 Ahau 



Instead of giving to the next name in Table II (Caban) the 
number 14, the number 1 was prefixed; for, as previously stated, 
the numerical coefficients of the days did not rise above the num- 
ber 13. Following the day 1 Caban, the sequence continued as 
before: 2 Eznab, 3 Cauac, 4 Ahau. After the day 4 Ahau, the last 
in Table II, the next number in order, in this case 5, was prefixed to 
the next name in order — that is, Imix, the first name in Table II — 
and the countcontinued without interruption: 5 Imix, 6 Ik, 7 Akbal, 
or back to the name Kan with which it started. There was no break 
in the sequence, however, even at this point (or at any other, for 
that matter) . The next name in Table II, Kan, selected for the 
starting point, was given the number next in order, i. e., 8, and the 
day following 7 Akbal in Table II Would be, therefore, 8 Kan, and 
the sequence would continue to be formed in the same way: 8 
Kan, 9 Chicchan, 10 Cimi, 11 Manik, 12 lamat, 13 Muluc, 1 Oc, 
2 Chuen, 3 Eb, and so on. So far as the Maya conception of time was 
concerned, this sequence of days went on without interruption, forever. 

While somewhat unusual at first sight, this sequence is in reality 
exceedingly simple, being governed by three easily remembered rules: 

Rule 1 . The sequence of the 20 day names repeats itself again and 
again without interruption. 

1 Since the sequence of the twenty day names was continuous, It is obvious that it had no beginning or end- 
ing, lUre the rim of a wheel; consequently any day name may be chosen arbitrarily as the starting point. In 
the accompanying example Kan has been chosen to begin with, though Bishop Landa (p. 236) states 
^_ with regard to the Maya: "The character or letter with which they commence their count of the 
(Jp days or calendar is caUed Hun-ymix [i. e. 1 Imix]". Agam, " Here commences the count of the cal- 

* endar of the Indians, saying in their language Hun Imix (*) [i. e. 1 ImizJ." (Ibid., p. 246.) 



BUREAU OF AMERICAN ETHNOLOGY 




i^^W'. Cie?. 



TONALAMATL WHEEL, SHOWING SEQUENCE 



BULLETIN 57 PLATE 5 






"5~«Ssv 






* O jS 



+ ^4 *2^s 









% 






«> 



felt) ' o«)* a 

S'* ,ninw| 

uenqO 

uag 
"I 

USM 

qsuzT 



(OCD 
(ICIf 

(9ei) 

<8EI) 

fee/) 
§' ^'•■•' 



85 



lis 






5^^ 












OF THE 260 DIFFERENTLY NAMED DAYS 



MORLBY] INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 43 

Rule 2. The sequence of the numerical coefficients 1 to 13, inclusive, 
repeats itself again and again without interruption, 1 following im- 
mediately 13. 

Rule 3. The 13 numerical coefficients are attached to the 20 names, 
so that after a start has been made by prefixing any one of the 13 
numbers to any one of the 20 names, the number next in order is 
given to the name next in order, and the sequence continues indefi- 
nitely in this manner. 

It is a simple question of arithmetic to determine the niunber of 
days which must elapse before a day bearing the same designation 
as a previous one in the sequence can reappear. Since there are 
13 niunbers and 20 names, and since each of the 13 numbers must 
be attached in turn to each one of the 20 names before a given number 
can return to a given name, we must find the least conmion multiple 
of 13 and 20. As these two numbers, contain no conmion factor, 
their least common multiple "is their product (260), which is the num- 
ber sought. Therefore, any given day can not reappear in the se- 
quence until after the 259 days immediately following it shall have 
elapsed. Or, in other words, the 261st day wiU have the same 
designation as the 1st, the 262d the same- as the 2d, and so on. 

This is graphically shown in the wheel figured in plate 5, where the 
sequence of the days, commencing with 1 Imix, which is indicated 
by a star, is represented as extending around the rim of the wheel. 
After the name of each day, its number in the sequence beginning with 
the starting point 1 Imix, is shown in parenthesis. Now, if the star 
opposite the day 1 Imix be conceived to be stationary and the wheel 
to revolve in a sinistral circuit, that is contra-clookwise, the days wiU 
pass the star in the order which they occupy in the 260-day sequence. 
It appears from this diagram also that the day 1 Imix can not recur 
until after 260 days shall have passed, and that it always follows the 
day 13 Ahau. This must be true since Ahau is the name immediately 
preceding Imix in the sequence of the day names and 13 is the number 
immediately preceding 1. After the day 13 Ahau (the 260th from 
"the starting point) is reached, the day 1 Imix, the 261st, recurs and 
the sequence, having entered into itself again, begins anew as before. 

This round of the 260 differently named days was called by the 
Aztec the tondlamatl, or "book of days." The Maya name for this 
period is unknown ' and students have accepted the Aztec name for 
it. The tonalamatl is frequently represented in the Maya codices, 
there being more than 200 examples in the Codex Tro-Cortesiano 
alone. It was a very useful period for the calculations of the priests 
because of the different sets of factors into which it can be resolved, 

1 Professor Seler says the Maya of Guatemala called this period the Jcin katun, or '^order of the days." 
He feils to give his authority for this statement, however, and, as will appear later, these terms have 
entirely different meanings. (See Bulletin US, p. 14.) 




44 BUEEAXJ OF AMERICAN ETHNOLOGY [B0LL. 57 

namely, 4X65, 5X52, 10X26, 13X20, and 2X130. Tonalamatls 
divided into 4, 5, and 10 equal parts of 65, 52, and 26 days, respec- 
tively, occur repeatedly throughout the codices. 

It is aU the more curious, therefore, that this period is ra,rely 

represented in the inscriptions. The writer recalls butonecity (Copan) 

in which this period is recorded to any considerable extent. 

It might almost be inferred from this fact alone that the 

inscriptions do not treat of prophecy, divinations, or ritu- 

ahstic and ceremonial matters, since these subjects in the 

codices are always found in connection with tonalamatls. 

If true this considerably restricts the field of which the 

inscriptions may treat. 

Fig. 18. Sign Mr. Goodman has identified the glyph shown in figure 

mati ^acrard- 18 as the sigu for the 260-day period, but on wholly insuffi- 

ing to Good- cieut evidence the writer believes. On the other hand, so 

important a period as the tonalamatl undoubtedly had 

its own particular glyph, but up to the present time all efl^orts to 

identify this sign have proved unsuccessful. 

The Haab, or Year of 365 Days 

Having explained the composition and nature of the tonalamatl, 
or so-called Sacred Year, let us turn to the consideration of the Solar 
Year, which was known as haxib in the Maya language. 

The Maya used in their calendar system a 365-day year, though 
they doubtless knew that the true length of the year exceeds this 
by 6 hours. Indeed, Bishop Landa very explicitly states that such 
knowledge was current among them. "They had," he says, "their 
perfect year, hke ours, of 365 days and 6 hours;" and again, "The 
entire year had 18 of these [20-day periods] and besides 5 days and 
6 hom-s." In spite of Landa's statements, however, it is equally 
clear that had the Maya attempted to take note of these 6 additional 
hours by inserting an extra day in their calendar every fourth year, 
their day sequence would have been disturbed at once. An examina- 
tion of the tonalamatl, or rotmd of days (see pi. 5), shows also that 
the interpolation of a single day at any point would have thrown 
into confusion the whole Maya calendar, not only interfering with 
the sequence but also destroying its power of reentering" itself at the 
end of 260 days. The explanation of this statement is found in the 
fact that the Maya calendar had no elastic period corresponding to 
our month of February, which is increased in length whenever the 
accumulation of fractional days necessitates the addition of an extra 
day, in order to keep the calendar year from gaining on the true year. 

If the student can be made to realize that all Maya periods, from 
the lowest to the highest known, are always in a continuous sequence, 



MOELET] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 45 

each retTirning into itself and beginning anew after completion, he 
will have grasped the most fundamental principle of Maya chronol- 
ogy — its absolute continuity throughout. 

It may be taken for granted, therefore, in the discussion to follow 
that no interpolation of iutercalary days was actually made. It is 
equally probable, however, that the priests, iu whose hands such 
matters rested, corrected the calendar by additional calculations 
which showed just how many days the recorded year was ahead of 
the true year at any given time. Mr. Bowditch (1910: Chap, xi) has 
cited several cases ia which such additional calculations exactly 
correct the inscriptions on the monument upon which they appear and 
bring their dates into harmony with the true solar year. 

So far as the calendar is concerned, then, the year consisted of 
but 365 days. It was divided into 18 periods of 20 days each, desig- 
nated ia Maya uinal, and a closing period of 5 days known as the xma 
IcabaTcin, ©r "days without name." The sum of these (18X20 + 5) 
exactly made up the calendar year. 

Table III. THE DIVISIONS OF THE MAYA YEAR 



Pop 


Zao 


TTo 


Ceh 


Zip 


Mao 


Zotz 


TfaTikin 


Tzeo 


Milan 


Xul 


Pax 


Yaxkin 


Kayab 


Mol 


Cumhu 


Chen 


TJayeb { ^A<^-> 


Yax 


•J 



The names of these 19 divisions of the year are given in Table III 
in the order in which they follow one another; the twentieth day of 
one month was succeeded by the &st day of the next month. 

The first day of the Maya year was the first day of the month Pop, 
which, according to the early Spanish authorities. Bishop Landa (1864 : 
p. 276) included, always fell on the 16th of Jtily.^ TJayeb, the last 
division of the year, contained only 5 days, the last day of TJayeb 
being at the same time the 365th day of the year. Consequently, 
when this day was completed, the next in order was the Maya New 
Year's Day, the first day of the month Pop, after which the sequence 
repeated itself as before. 

The xma kaba kin, or "days without name," were regarded as 
especially unlucky and Ul-omened. Says Pio Perez (see Landa, 1864: 
p. 384) in speaking of these closing days of the year: "Some call 
them u yail Tcin or u yail hmb, which may be translated, the sorrow- 
ful and laboriotis days or part of the year; for they [the Maya] 

I As Bishop Landa virote not later tlian 1579, this is Old Style. The corresponding day in the 
Gregorian Calendar would be July 27. 



46 BUREAU OF AMEEICAN ETHNOLOGY [boll. 57 

believed that in them occurred sudden deaths and pestilences, and 
that they were diseased by poisonous animals, or devoured by wild 
beasts, fearing that if they went out to the field to their labors, some 
tree would pierce them or some other kind of misfortune happen to 
them." The Aztec held the five closiag days of the year iu the same 
superstitious dread. Persons bom in this unlucky period were held to 
be destiaed by this fact to wretchedness and poverty for life. These 
days were, moreover, prophetic in character; what occurred during 
them contiaued to happen ever afterward. Hence, quarreling was 
avoided during this period lest it should never cease. 

Having learned the number, length, and names of the several 
periods into which the Maya divided their year, and the sequence in 
which these followed one another, the next subject which claims 
attention is the positions of the several days in these periods. In 
order properly to present this important subject, it is first necessary 
to consider briefly how we coimt and nmnber om- own units of time, 
since through an understanding of these practices we shall better 
comprehend those of the ancient Maya. 

It is well known that our methods of counting time are inconsistent 
with each other. For example, in describing the time of day, that is, 
in coimting hours, minutes, and seconds, we speak in terms of elapsed 
time. When we say it is 1 o'clock, in reality the first hour after 
noon, that is, the hour between 12 noon and 1 p. m., has passed and 
the second hour after noon is about to commence. When we say it 
is 2 o'clock, in reahty the second hour after noon is finished and the 
third hour about to commence. In other words, we count the time 
of day by referring to passed periods and not current periods. This 
is the method used in reckoning astronomical time. During the 
passage of the first hour after midnight the hours are said to be zero, 
the time being counted by the number of minutes and seconds 
elapsed. Thus, half past 12 is written: O'"- 30™''- 0^^"-, and quarter of 
1, O'"'- 45™"- 0^®"-. Indeed one hour can not be written mitil the first 
hour after midnight is completed, or until it is 1 o'clock, namely, 

1 br. Amin. Qsec. 

We use an entirely different method, however, in counting our 
days, years, and centuries, which are referred to as current periods 
of time. It is the 1st day of January immediately after midnight 
December 31. It was the first year of the Eleventh Century imme- 
diately after midnight December 31, 1000 A. D. And finally, it was 
the Twentieth Century immediately after midnight December 31, 
1900 A. D. In this category should be included also the days of 
the week and the months, since the names of these periods also refer 
to present time. In other words when we speak of our days, months, 
years, and centuries, we do not have in mind, and do not refer to 
completed periods of time, but on the contrary to current periods. 



MOHLET] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 47 

It will be seen that in the first method of counting time, in speaking 
of 1 o'clock, 1 hour, 30 minutes, we use only the cardinal forms 
of our numbers; but in the second method we say the 1st of 
January, the Twentieth Century, usmg the ordinal forms, though 
even here we permit ourselves one inconsistency. In speaking of 
our years, which are reckoned by the second method, we say "nineteen 
hundred and twelve," when, to be consistent, we should say "nineteen 
hundred and twelfth," using the ordinal' 'twelfth" instead of the car- 
dinal "twelve." 

We may then summarize our methods of counting time as follows: 
(1) AU periods less than the day, as hours, minutes, and seconds, are 
referred to in terms of past time; and (2) the day and aU greater 
periods are referred to in terms of current time. 

The Maya seem to have used only the former of these two methods 
in counting time; that is, all the different periods recorded in the 
codices and the inscriptions seemingly refer to elapsed time rather 
than to current time, to a day passed, rather than to a day present. 
Strange as this may appear to us, who speak of our calendar as current 
time, it is probably true nevertheless that the Maya, in so far as their 
writing is concerned, never designated a present day but always 
treated of a day gone by. The day recorded is yesterday because 
to-day can not be considered an entity untU, like the hour of astronom- 
ical time, it completes itself and becomes a unit, that is, a yesterday. 

This is well illustrated by the Maya method of numbering the 
positions of the days in the months, which, as we shall see, was 
identical with our own method of coimting astronomical time. For 
example, the first day of the Maya month Pop was written Zero Pop, 
(0 Pop) for not until one whole day of Pop had passed could the day 1 
Pop be written; by that time, however, the first day of the month had 
passed and the second day commenced. In other words, the second 
day of Pop was written 1 Pop ; the third day, 2 Pop ; the fourth day, 
3 Pop ; and so on through the 20 days of the Maya month. This 
method of numbering the positions of the days in the month led to 
calling the last day of a month 1 9 instead of 20. This appears in Table 
IV, in which the last 6 days of one year and the first 22 of the next 
year are referred to their corresponding positions in the divisions of 
the Maya year. It must be remembered in using this Table that the 
closing period of the Maya year, the xma kaba kin, or XJayeb, con- 
tained only 5 days, whereas all the other periods (the 18 uinals) had 
20 days each. 

Curiously enough no glyph for theJiadb, or year, has been identified 
as yet, in spite of the apparent importance of this period.^ The 

1 This is probably to be aoco anted for by tlie fact tliat in the Maya system of chronology, as we shall see 
later, the 365-day year was not used in recording time. But that so fundamental a period had therefore 
no special glyph does not necessarily follo'F, and the writer belieyes the sign for the baab will yet be dis- 
covered. 



48 



BUKEATJ OF AMBEIOAN ETHNOLOGY 



[BUlil. 57 



glyphs whicli represent the 18 different uinals and the xma kaba kin, 
however, are shown in figures 19 and 20. The forms in figure 19 are 
taken from the inscriptions and those in figure 20 from the codices. 

Table IV. POSITIONS OF DAYS AT THE END OF A YEAR 



360th day of the year 

361st day of the year 

362d day of the year 

363d day of the year 

364th day of the year 

365th day of the year 

1st day of next year 

2d day of next year 

3d day of next year 

4th day of next year 

5thday of next year 

6th day of next year 

ythday of next year 

8th day of next year 

9th day of next year 

10th day of next year 

11th day of next year 

12th day of next year 

13th day of next year 

14th day of next year 

15th day of next year 

16th day of next year 

17th day of next year 

18th day of next year 

19th day of next year 

20th day of next year 

21st day of next year 

22d day of next year 

etc. 



last day of TTayeb and of the year, 
first day of the month Pop, and of the next 
year. 



19 Cumhu last day of the month Cumhu. 

Uayeb first day of Uayeb. 

1 trayeb 

2 TTayeb 

3 Uayeb 

4 TTayeb 
OPop 
IPop 

2 Pop 

3 Pop 

4 Pop 

5 Pop 

6 Pop 

7 Pop 

8 Pop 

9 Pop 

10 Pop 

11 Pop 

12 Pop 

13 Pop 

14 Pop 

15 Pop 

16 Pop 

17 Pop 

18 Pop 

19 Pop 
OUo 
lUo 

etc. 



last day of the month Pop. 
first day of the month TTo. 



The signs for the first four months, Pop, Uo, Zip, and Zotz, show a 
convincing similarity in both the inscriptions and the codices. The 
essential elements of Pop (figs. 19, a, and 20, a) are the crossed bands 
and the Tcin sign. The latter is found in both the forms figured, though 
oiily a part of the former appears in figure 20, a. Uo has two forms 
in the inscriptions (see fig. 19, 6, c),' which are, however, very similar 
to each other as well as to the corresponding forms in the codices 
(fig. 20, h, c). The glyphs for the month Zip are identical in both 
figures 19, d, and 20, d. The grotesque heads for Zotz in figures 19, 
e, f,^ and 20, e, are also similar to each other. The essential character- 

1 Later researches of the writer (1914) have oonvinced him that figure 19, c, is not a sign for 00, but a 
very unusual variant of the sign tor Zip, found only at Copan, and there only on monuments belonging 
to the final period. 

2 The writer was able to prove during his last trip to the Maya field that figure 19, /, is not a sign 
lor the month Zotz, as suggested by Mr. Bowditch, but a very unusual form representing EanUn. 
This identification is supported by a number of examples at Piedras Negras. 



MORLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



49 



is tic seems to be the prominent upturned and flaring nose. The 
forms for Tzec (figs. 19, g, Ji, and 20, /) show only a very general simi- 
larity, and those for Xul, the next month, are even more imhke. The 




KANKIN 



MUAN 









W X 

MAC 




d' e' f g' V i' 

KAYAB CUMHU UAYEB 

Fig. 19. The month signs m the inscriptions. 

only sign for Xul in the inscriptions (fig. 19, i, j) bears very little 
resemblance to the common form for this month in the codices (fig. 
20, g), though it is not unlike the variant in h, figure 20. The essen- 
tial characteristic seems to be the familiar ear and the small mouth, 
shown in the inscription as an oval and in the codices as a hook sur- 
rounded with dots. 

43508°— Bvdl. 57—15 1 



50 



BUEEAU OF AMERIOAN ETHNOLOGY 



[BULL. 57 



The sign for the month Yaxkin is identical in both figures 19, Ic, I, 
and 20, i, j. The sign for the month Mol in figures 19, m, n, and 20, h 
exliibits the same close similarity. The forms for the month Chen 




CUMHU 

FlQ. 20. The month signs in the codices. 



UAYEB 



in figures 19, o, p, and 20, I, m, on tlic other hand, bear only a slight 
resemblance to each other. The forms for the months Yax (fio^ 19 
2, r, and 20, n), Zac (figs. 19, s, t, and 20, 0), and Ceh (figs. 19, u v and 



MOELBT] INTBODUCTIOX TO STUDY OF MAYA HIEROGLYPHS 51 

20, Tp) are again identical in each case. The signs for the next month, 
Mac, however, are entirely dissimilar, the form commonly fomid in 
the inscriptions (fig. 19, w) bearing absolutely no resemblance to that 
shown in figm« 20, g, r, the only form for this month in the codices. 
The very unusual variant (fig. 19, x), from Stela 25 at Piedras Xegras 
is perhaps a trifle nearer the form found in the codices. The flat- 
tened oval in the main part of the variant is somewhat like the upper 
part of the glyph in figure 20, g. The essential element of the glyph for 
the month Mac, so far as the inscriptions are concerned, is the element 
^QD (*) found as the superfix in both id and z, figure 19. The sign 

* for the month Kankin (figs. 19, y, z, and 20, s, t) and the signs 
for the month Muan (figs. 19, a', 6', and 20, u, r) show only a gen- 
eral similarity. The signs for the last three months of the year. Pax 
(figs. 19, c', and 20, w), Kayab (figs. 19, d'-f, and 20. x, y), and Curnhu 
(figs. 19, g', h', and 20, z, a', h') in the inscriptions and codices, 
respectively, are practically identical. The closing division of the 
year, the five days of the xma kaba kin, called Uayeb, is represented 
by essentiaUy the same glyph in both the inscriptions and the 
codices. Compare figure 19, i', with figure 20, c'. 

It will be seen from the foregoing comparison that on the whole the 
glyphs for the months in the inscriptions are similar to the corre- 
sponding forms in the codices, and that such variations as are found 
may readily be accounted for by the fact that the codices and the 
inscriptions probably not only emanate from different parts of the 
Maya territory but also date from different periods. 

The student who wishes to decipher Maya writing is strongly urged 
to memorize the signs for the days and months given in figm-es 16, 
17, 19, and 20, since his progress wiU depend largely on his abihty to 
recognize these glyphs when he encounters them in the texts. 

The Cai^ndae Rotjot), ok 18980-dat Pehiod 

Before taking up the study of the Calendar Eound let us briefly 
summarize the principal points ascertained in the preceding pages 
concerning the Maya method of counting time. In the first place 
we learned from the tonalamatl (pi. 5) three things: (1) The number 
of differently named days; (2) the names of these days; (3) the order 
in which they invariably followed one another. And in the second 
place we learned in the discussion of the Maya year, or haab, just 
concluded, four other things: (1) The length of the year; (2) the 
number, length, and names of the several periods into which it was 
divided; (3) the order in which these periods invariably followed one 
another; (4) the positions of the days in these periods. 

The proper combination of these two, the tonalamatl, or "round of 
days," and the haab, or year of uinals, and the xma kaba kin, formed 
the Calendar Round, to which the tonalamatl contributed the names 



52 BUREAU OF AMERICAN ETHNOLOGY [bcli,. 57 

of the days and the haab the positions of these days in the divisions 
of the year. The Calendar Round was the most important period in 
Maya chronology, and a comprehension of its nature and of the prin- 
ciples which governed its composition is therefore absolutely essential 
to the understanding of the Maya system of cotmtuig time. 

It has been explained (see p. 41) that the complete designation 
or name of any day in the tonalamatl consisted of two equally essen- 
tial parts: (1) The name glyph, and (2) the numerical coefficient. 
Disregardtag the latter for the present, let us first see which of the 
twenty names in Table I, that is, the name parts of the days, can 
stand at the beginning of the Maya year. 

In applying any sequence of names or numbers to another there 
are only three possibilities concerning the names or numbers which 
can stand at the head of the resulting sequence: 

1. When the sums of the imits in each of the two sequences contain 
no common factor, each one of the units in turn will stand at the 
head of the resulting sequence. 

2. When the sum of the imits in one of the two sequences is a 
multiple of the sum of the units in the other, only the first unit 
can stand at the head of the resulting sequence. 

3. When the sums of the units in the two sequences contain a 
common factor (except in those cases which fall under (2), that is, 
in which one is a multiple of the other) only certain units can stand at 
the head of the sequence. 

Now, since our two numbers (the 20 names in Table I and the 365 
days of the year) contain a common factor, and since neither is a 
mtiltiple of the other, it is clear that only the last of the three con- 
tingencies just mentioned concerns us here ; and we may therefore 
dismiss the first two from further consideration. 

The Maya year, then, could begin only with certain of the days 
in Table I, and the next task is to find out which of these twenty 
names invariably stood at the beginnings of the years. 

When there is a sequence of 20 names in endless repetition, it is 
evident that the 361st will be the same as the 1st, since 360 = 20 X 18. 
Therefore the 362d will be the same as the 2d, tho 363d as the 3d, 
the 364th as the 4th, and the 365 as the 5th. But the 365th, or 
5th, name is the name of the last day of the year, consequently the 
1st day of the following year (the 366th from the beginning) will 
have the 6th name in the sequence. Following out this same idea, 
it appears that the 361st day of the second year will have the same 
name ps that with which it began, that is, the 6th name in the 
sequence, the 362d day the 7th name, the 363d the 8th, the 364th 
the 9th, and the 365th, or last day of the second year, the 10th name. 
Therefore the 1st day of the third year (the 731st from the beginning) 
will have the 1 1th name in the sequence. Similarly it could b6 shown 



MORLEY] INTBODTJCTION TO STUDY OP MAYA HIEBOGLYPHS 53 

that the third year, beginning with the 1 1th name, would necessarily 
end with the 15th name; and the fourth year, beginning with the 16th 
name (the 1096th from the beginning) would necessarily end with 
the 20th, or last name, in the sequence. It results, therefore, from 
the foregoing progression that the fifth year will have to begin with 
the 1st name (the 1461st from the beginning), or the same name with 
which the first year also began. 

This is capable of mathematical proof, since the 1st day of the 
fifth year has the 1461st name from the beginning of the sequence, for 
1461 = 4x365+1 = 73x20+1. The 1 in the second term of this 
equation indicates that the beginning day of the fifth year has been ■ 
reached; and the 1 in the third term indicates that the name-part 
of this day is the 1st name in the sequence of twenty. In other 
words, every fifth year began with a day, the name part of which 
was the same, and consequently only four of the names in Table I 
could stand at the beginnings of the Maya years. 

The four names which successively occupied this, the most impor- 
tant position of the year, were : Ik, Manik, Eb, and Caban (see Table V, 
in which these four names are shown in their relation to the sequence 
of twenty). Beginning with any one of these, Ik for example, the 
next in order, Manik, is 5 days distant, the next, Eb, another five 
days, the next, Caban, another 5 days, and the next, Ik, the name 
with which the Table started, another 5 days. 

Table V. RELATIVE POSITIONS OF DAYS BEGINNING MAYA YEARS 



IK 


" EB 


Akbal 


Ben 


Kan 


Ix 


Chicchan 


Men 


Cimi 


Cib 


'MANIK 


-CABAH- 


Lamat 


Eznab 


MiUuc 


Cauac 


Oo 


Ahau 


Chuen 


Imix 



Since one of the four names just given invariably began the Maya 
year, it follows that in any given year, all of its nineteen divisions, the 
18 uinals and the xma kaba kin, also began with the same name, 
which was the name of the first day of the first uinal. This is neces- 
sarily true because these 1 9 divisions of the year, with the exception of 
the last, each contained 20 days, and consequently the name of the 
first day of the first diAdsion determined the names of the first days 
of all the succeeding divisions of that particular year. Furthermore, 
since the xma kaba kin, the closing division of the year, contained 
but 5 days, the name of the first day of the following year, as well as 



54 BUREAU OP AMERICAIT ETHNOLOGY [boll. 57 

the names of the first days of all of its divisions, was shifted forward 
in the sequence another 5 days, as shown above. 

This leads directly to another important conclusion : Since the first 
days of all the divisions of any given year always had the same name- 
part, il follows that the second days of all the divisions of that year 
had the same name, that is, the next succeeding in the sequence of 
twenty. The third days in each division of that year must have had 
the same name, the fourth days the same name, and so on, through- 
out the 20 days of the month. For example, if a year began with the 
day-name Ik, aU of the divisions in that year also began with the 
same name, and the second days of aU its divisions had the day-name 
Akbal, the third days the name Kan, the fourth days the name 
Chicchan, and so forth. This enables us to formulate the following — 

Rule. The 20 day-names always occupy the same positions in all 
the divisions of any given year. 

But since the year and its divisions must begin with one of four 
names, it is* clear that the second positions also must be filled with 
one of another group of four names, and the third positions with one 
of another group of four names, and so on, through all the positions 
of the month. This enables us to formulate a second — 

Rule. Only four of the twenty day-names can ever occupy any 
given position in the divisions of the years. 

But since, in the years when Ik is the 1st name, Manik will be the 
6th, Eb the 11th, and Caban the 16th, and in the years when Manik 
is the 1st, Eb will be the 6th, Caban the 11th, and Ik the 16th, and 
in the years when Eb is the 1st, Caban will be the 6th, Ik the 1 1th, and 
Manik the 16th, and in the years when Caban is the 1st, Ik wiU be 
the 6th, Manik the 11th, and Eb the 16th, it is clear that any one of 
this group which begins the year may occupy also three other positions 
in the divisions of the year, these positions being 5 days 'distant from 
each other. Consequently, it follows that Akbal, lamat, Ben, and 
Eznab in Table V, the names which occupy the second positions in 
the divisions of the year, will fill the 7th, 12th, and 17th positions as 
well. Similarly Kan, Muluc, Ix, and Cauao wOl fill the 3d, 8th, 13th, 
and 18th positions, and so on. This enables us to formulate a third — 

Rule. The 20 day-names are divided into five groups of four names 
each, any name in" any group being five days distant from the name 
next preceding it in the same group, and furthermore, the names of 
any one group wiU occupy four different positions in the divisions of 
successive years, these positions being five days apart in each case. 
This is expressed in Table VI, in which these groups are shown as 
weU as the positions in the divisions of the years which the names of 
each group may occupy. A comparison with Table V will demon- 
strate that this arrangement is inevitable. 



MoftLBT] iNTfeotouctiOisr tO- sIuDy Of Maya hIeeoglyphs 55 

Table VI. POSITIONS OP DAYS IN DIVISIONS OP MAYA YEAR 



Positions held by 
days 


/ 1st, 6th, 
\llth, 16th 


2d, 7th, 
12th, 17th 


3d, 8th, 
13th, 18th 


4th, 9th. 
14th, 19th 


5th, 10th, 
16th. 20th 


Names of days in each 
group 


Ik 

Uanlk 
lEb 
Caban 


Akbal 
Lamat 
Ben 
Eznab 


Kan 
Muluc 
Ix 
Cauac 


Chicchan 
Oc 
Hen 
Ahau 


Clmi 
Chuen 
Clb 
Imlz 



But we have seen on page 47 and in Table IV that the Maya did 
not designate the first days of the several divisions of the years ac- 
cording to our system. It was shown there that the first day of Pop 
was not written 1 Pop, but Pop, and similarly the second day of 
Pop was written not 2 Pop, but 1 Pop, and the last day, not 20 Pop, 
but 19 Pop. Consequently, before we can use the names in Table 
VI as the Maya used them, we must make this shift, keeping in mind, 
however, that Ik, Manik, Eb, and Caban (the only four of the twenty 
names which could begin the year and which were written Pop, 
5 Pop, 10 Pop, or 15 Pop) would be written in our notation 1st Pop, 
6tli Pop, 11th Pop, and 16tk Pop, respectively. This difference, as 
has been previously explained, results from the Maya method of 
counting time by elapsed periods. 

Table VII shows the positions of the days in the divisions of the 
year according to the Maya conception, that is, with the shift in the 
month coefficient made necessary by this practice of recording their 
days as elapsed time. 

The student wiU find Table VII very useful in deciphering the texts, 
since it shows at a glance the only positions which any given day can 
occupy in the divisions of the year. Therefore when the sign for a 
day has been recognized in the texts, from Table VII can be ascer- 
tained the only four positions which this day can hold in the month, 
thus reducing the number of possible month coefficients for which 
search need be made, from twenty to four. 

Table VII. POSITIONS OP DAYS IN DIVISIONS OP MAYA YEAR 
ACCORDING TO MAYA NOTATION 



Positions held by days ex- 
pressed in Maya notation. 


|o, 5, 10, 15 


1, 6, 11, 16 


2, 7, 12, 17 


3, 8, 13, 18 


4, 9, 14, 19 


Names of days in each group 


flk 

Manik 

Eb 
Icaban 


Akbal 

Ben 

Eznab 


Kan 
Uuluc 
Iz 
Cauac 


Chicchan 
Oc 
Men 
Ahau 


Cimi 
Chuen 
Clb 
Tmiir 



Now let us summarize the points which we have successively 
established as resulting from the combination of the tonalamatl and 
haab, remembering always that as yet we have been dealing only with 



56 BUEEAU OF AMEKICAN ETHNOLOGY [bcll. 57 

the name 'parts of the days and not their complete designations. Bearing 
this in mind, we may state the following facts concerning the 20 day- 
names and their positions in the divisions of the year: 

1. The Maya year and its several divisions could begin only with 
one of these four day-names : Ik, Manik, Eb, and Caban. 

2. Consequently, any particular position in the divisions of the 
year could be occupied only by one of four day-names. 

3. Consequently, every fifth year any particular day-name returned 
to the same position in the divisions of the year. 

4. Consequently, any particular day-name could occupy only one 
of four positions in the divisions of the year, each of which it held in 
successive years, returning to the same position every fifth year. 

5. Consequently, the twenty day-names were divided into five 
groups of four day-names each, any day-name of any group being 
five days distant from the day-name of the same group next pre- 
ceding it. 

6. Finally, in any given year any particular day-name occupied 
the same relative position throughout the divisions of that year. 

Up to this point, however, as above stated, we have not been deal- 
ing with the complete designations of the Maya days, but only their 
Tiame parts or name glyphs, the positions of which in the several 
divisions of the year we have ascertained. 

It now remains to join the toiialamatl, which gives the complete 
names of the 260 Maya days, to the haab, which gives the positions 
of the days in the divisions of the year, in such a way that any one 
of the days whose name-part is Ik, Manik, Eb, or Caban shall occupy 
the first position of the first division of the year; that is, Pop, 
or, as we should write it, the first day of Pop. It matters little 
which one of these four name parts we choose first, since in four 
years each one of them in succession will have appeared in the 
position Pop. 

Perhaps the easiest way to visualize the combination of the tonala- 
matl and the haab is to conceive these two periods as two cogwheels 
revolving in contact with each other. Let us imagine that the first 
of these, A (fig. 21), has 260 teeth, or cogs, each one of which is 
named after one of the 260 day^ of the tonalamatl and foUoWs the 
sequence shown in plate 5. The second wheel, B (fig. 21), is some- 
what larger, having 365 cogs. Each of the spaces or sockets between 
these represents one of the 365 positions of the days in the divisions 
of the year, beginning with Pop and ending with 4 Uayeb. See 
Table IV for the positions of the days at the end of one year and the 
commencement of the next. Finally, let us imagine that these two 
wheels are brought into contact with each other in such a way that 
the tooth or cog named 2 Ik in A shall fit into the socket named 



MORLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



57 



B 



Pop in B, after which both wheels start to revolve in the directions 
indicated by the arrows. 

The first day of the year whose beginning is shown at the point of 
contact of the two wheels in figure 21 is 2 Ik Pop, that is, the day 
2 Ik which occupies the first position in the month Pop. The next day 
in succession will be 3 Akbal 1 Pop, the next 4 Kan 2 Pop, the next 
5 Chicchan 3 Pop, the next 6 Cimi 4 Pop, and so on. As the wheels 
revolve in the directions indicated, the days of the tonalamatl succes- 
sively fall into their 
appropriate posi- 
tions in the divi- 
sions of the year. 
Since the number of 
cogs in A is smaller 
than the number in 
B, it is clear that 
the former will 
have returned to 
its starting point, 
2 Ik (that is, made 
one complete revo- 
lution) , before the 
latter will have 
made one complete 
revolution; and, 
further, that when 
the latter (B) has 
returned to its 
starting point, 
Pop, the corre- 
sponding cog in B 
will not be 2 Ik, 
but another day (3 Manik) , since by that time the smaller wheel will 
have progressed 105 cogs, or days, farther, to the cog 3 Manik. 

The question now arises, how many revolutions will each wheel 
have to make before the day 2 Ik will return to the position Pop. 
The solution of this problem depends on the application of one 
sequence to another, and the possibilities concerning the numbers or 
names which stand at the head of the resulting sequence, a subject 
already discussed on page 52. In the present case the numbers in 
question, 260 and 365, contain a common factor, therefore our prob- 
lem falls under the third contingency there presented. Consequently, 
only certain of the 260 days can occupy the position Pop, or, in 
other words, cog 2 Ik in A will return to the position Pop in B in 
fewer than 260 revolutions t)f A. The actual solution of the problem 




Fig. 21.- Diagram showing engagemeatof tonalamatl wheel of260days(A), 
and haab wheel of 365 positions (B); the combination of the two giving 
the Calendar Round, or 52-year period. 



58 BTJEEAtr OF AMERICAN ETHNOLOGY [bcll. 57 

is a simple question of arithmetic. Since the day 2 Ik can not return 
to its original position in A until after 260 days shall have passed, 
and since the day Pop can not return to its original position in B 
until after 365 days shall have passed, it is clear that the day 2 Ik 
Pop can not recur until after a number of days shall have 
passed equal to the least common multiple of these numbers, which is 

^X^X5, or 52X73X5=18,980 days. But 18,980 days = 52X 

365 = 73X260; in other words the day 2 Ik Pop can not recur 
until after 52 revolutions of B, or 52 years of 365 days each, and 73 
revolutions of A, or 73 tonalamatls of 260 days each. The Maya 
name for this 52-year period is unknown; it has been called the 
Calendar Eound by modern students because it was only after this 
interval of time had elapsed that any given day could return to the 
same position in fche year. The Aztec name for this period was 
oduhmolpilli or toxiuhmolpia.^ 

The Calendar Round was the real basis of Maya chronology, since 
its 18,980 dates included all the possible combinations of the 260 days 
with the 365 positions of the year. Although the Maya developed 
a much more elaborate system of counting time, wherein any date of 
the Calendar Round could be fixed with absolute certainty within a 
period of 374,400 years, this truly remarkable feat was accomplished 
only by using a sequence of Calendar Rounds, or 52-year periods, in 
endless repetition from a fixed point of departure. 

In the development of their chronological system the Aztec prob- 
ably never progressed beyond the Calendar Round. At least no 
greater period of time than the roun.d of 52 years has been found in 
their texts. The failure of the Aztec to develop some device which 
would distinguish any given day in one Calendar Round from a day 
of the same name in another has led to hopeless confusion in regard 
to various events of their history. Since the same date occurred 
at intervals of every 52 years, it is often difficult to determine the 
particular Calendar Round to which any given date with its corre- 
sponding event is to be referred ; consequently, the true sequence of 
events in Aztec history stiU remains uncertain. 

Professor Seler says in this connection: ^ 

Anyone who has ever taken the trouble to collect the dates in old Mexican history 
from the various sources must speedily have discovered that the chronology is very 
much awry, that it is almost hopeless to look for an exact chronology. The date of the 
fall of Mexico is definitely fixed according to both the Indian and the Christian chro- 
nology . but in regard to all that precedes this date, even to events tolerably near 
the time of the Spanish conquest, the statements differ widely. 

1 The meanings of these words in Nahuatl, the language spoken by the Aztec, are " year bundle " and " our 
years will be bound/' respectively. These doubtless refer to the fact that at the expiration of this period 
the Aztec calendar had made one complete round; that is, the years were bound up and commenced anew. 

' Bulletin B8, -p. 330. 




MOELBT] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 59 

Such confusion indeed is only to be expected from a system of count- 
ing time and recording events which was so loose as to permit the occur- 
rence of the same date twice, or even thrice, within the span of a 
single life ; and when a system so inexact was used to regulate the lapse 
of any considerable number of years, the possibilities for error and 
misunderstanding are infinite. Thus it was with Aztec chronology. 

On the other hand, by conceiving the Calendar Rounds to be in 
endless repetition from a fixed point of departure, and measuring 
time by an accurate system, the Maya were able to secure precision 
in dating their events which is not surpassed 
even by our own system of counting time. 

The glyph which stood for the Calendar 
Roimd has not been determined with any 
degree of certainty. Mr. Goodman beheves 
the form shown in figure 22, a, to be the sign 
for this period, while Professor Forstemann 
is equally sure that the form represented by « 6 

6 of this figure expressed the same idea, fig- 22. signs for the calendar 
This_ diflFerence of opinion between two au- ^Xi'^^^'^t^^T"^'' 
thorities so eminent well illustrates the pre- 
vailing doubt as to just what glyph actually represented the 52- 
year period among the Maya. The sign in figure 22, a, as the writer 
wiU endeavor to show later, is in all probability the sign for the great 
cycle. 

As will be seen in the discussion of the Long Count, the Maya, 
although they conceived time to be an endless succession of Calendar 
Rounds, did not reckon its passage by the lapse of successive Calendar 
Rounds; consequently, the need for a distinctive glyph which should 
represent this period was not acute. The contribution of the Calendar 
Round to Maya chronology was its 18,980 dates, and the glyphs 
which composed these are found repeatedly in both the codices and 
the inscriptions (see figs. 16, 17, 19, 20). No signs have been found 
as yet, however, for either the haab or the tonalamatl, probably 
because, like the Calendar Round, these periods were not used as 
units in recording long stretches of time. 

It will greatly aid the student in his comprehension of the discussion 
to follow if he will constantly bear in mind the fact that one Calendar 
Round followed another without interruption or the interpolation of 
a single day; and further, that the Calendar Round may be hkened 
to a large cogwheel having 18,980 teeth, each one of which repre- 
sented one of the dates of this period, and that this wheel revolved 
forever, each cog passing a fixed point once every 52 years. 



60 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

The Long Count 
We have seen : 

1 . How the Maya distinguished 1 day from the 259 others in the 
tonalamatl; 

2. How they distinguished the position of 1 day from the 364 
others in the haab, or year; and, finally, 

3. How by combining (1) and (2) they distiaguished 1 day from 
the other 18,979 of the Calendar Eound. 

It remains to explain how the Maya insured absolute accuracy in 
fixing a day within a period of 374,400 years, as stated above, or how 
they distinguished 1 day from 136,655,999 others. 

The Calendar Round, as we have seen, determined the position of a 
given day within a period of only 52 years. Consequently, in order 
to prevent confusion of days of the same name in successive Calendar 
Rounds or, in other words, to secure absolute accuracy in dating 
events, it was necessary to use additional data in the description of 
any date. 

In nearly all systems of chronology that presume to deal with really 
long periods the reckoning of years proceeds from fixed starting 
points. Thus in Christian chronology the starting point is the Birth 
of Christ, and our years are reckoned as B. C. or A. D. according 
as they precede or follow this event. The Greeks reckoned time 
from the earliest Olympic Festival of which the winner's name was 
known, that is, the games held in 776 B. C, which were won by 
a certain Coroebus. The Romans took as their starting point the 
supposed date of the foundation of Rome, 753 B. C. The Baby- 
lonians counted time as beginning with the Era of Nabonassar, 747 
B. C. The death of Alexander the Great, in 325 B. C, ushered in 
the Era of Alexander. With the occupation of Babylon iii 311 B. C. 
by Seleucus Nicator began the so-called Era of Seleucidse. The con- 
quest of Spain by Augustus C^sar in 38 B. C. marked the beginning 
of a chronology which endured for more than fourteen centuries. 
The Mohammedans selected as their starting point the flight of their 
prophet Mohammed from Mecca in 622 A. D., and events in this 
chronology are described as having occurred so many years after the 
Hegira (The Flight). The Persian Era began with the date 632 
A. D., in which year Yezdegird III ascended the throne of Persia. 

It will be noted that each of the above-named systems of chro- 
nology has for its starting point some actual historic event, the occur- 
rence, if not the date of which, is indubitable. Some chronologies, 
however, commence with an event of an altogether different charac- 
ter, the date of which from its very nature must always remain 
hypothetical. In this class should be mentioned such chronologies as 
reckon time from the Creation of the World. For example, the Era 
of Constantinople, the chronological system used in the Greek Church, 



MOELEY] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 61 

commences with that event, supposed to have occurred in 5509 B. C. 
The Jews reckoned the same event as having taken place in 3761 
B. C. and begin the counting of time from this point. A more familiar 
chronology, having for its starting point the Creation of the World, is 
that of Archbishop Usher, in the Old "Testament, which assigns this 
event to the year 4004 B. C. 

In common with these other civilized peoples of antiquity the 
ancient Maya had realized in the development of their chronological 
system the need for a fixed starting point, from which all subsequent 
events could be reckoned, and for this purpose they selected one of 
the dates of their Calendar Eound. This was a certain date, 4 Ahau 
8 Cumhu,' that is, a day named 4 Ahau, which occupied the 9th posi- 
tion in the month Cumhu, the next to last division of the Maya year 
(see Table III). 

While the nature of the event which took place on this date ^ is un- 
known, its selection as the point from which time was subsequently 
reckoned alone indicates that it must have been of exceedingly great 
importance to the native mind. In attempting to approximate its 
real character, however, we are not without some assistance from the 
codices and the inscriptions. For instance, it is clear that all Maya 
dates'which it is possible to regard as contemporaneous ' refer to a time 
fully ?,^00 years later than the starting point (4 Ahau 8 Cumhu) from 
which each is reckoned. In other words, Maya history is a blank 
for more than 3,000 years after the initial date of the Maya chrono- 
logical system, during which time no events were recorded. 

This iateresting condition strongly suggests that the starting 
point of Maya chronology was not an actual historical event, as the 
founding of Rome, the death of Alexander, the birth of Christ, or 
the flight of Mohammed from Mecca, but that on the contrary it was 
a purely hypothetical occurrence, as the Creation of the World or the 
birth of the gods; and further, that the date 4 Ahau 8 Cumhu was 
not chosen as the starting point until long after the time it desig- 
nates. This, or some similar assumption, is necessary to account 
satisfactorily for the observed facts: 

1. That, as stated, after the starting point of Maya chronology there 
is a silence of more than 3,000 years, unbroken by a single contem- 
poraneous record, and 

1 All Initial Series now known, with the exception of two, have the date 4 Ahau 8 Cumhu as their com- 
mon point of departure. The two exceptions, the Initial Series on the east side of Stela at Quirigua 
and the one on the tablet in the Temple of the Cross at Palenque, proceed from the date 4 Ahau 8 Zotz— 
more than 5,000 years in advance of the starting point just named. The writer has no suggestions to offer 
in explanation of these two dates other than that he believes they refer to some mythological event. For 
instance, in the belief of the Maya the gods may have been bom on the day 4 Ahau 8 Zotz, and 5,000 
years later approximately on 4 Ahau 8 Cumhu the world, including mankind, may have been created. 

2 Some writers have called the date 4 Ahau 8 Cumhu, the normal date, probably because it is the stand- 
ard date from wLich practically all Maya calculations proceed. The writer has not followed this practice, 
however. 

3 That is, dates which signified present time when they were tQCOfd^d, 



62 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

2. That after this long period had elapsed all the dated monuments* 
had their origin in the comparatively short period of four centuries. 

Consequently, it is safe to conclude that no matter what the Ma,ya 
may have believed took place on this date 4 Ahau 8 Cumhu, in reality 
when this day was present time they had, not developed their dis- 
tinctive civilization or even achieved a social organization. 

It is clear from the foregoing that in addition to the Calendar 
Round, the Maya made use of a fixed starting point in describing 
their dates. The next question is. Did they record the lapse of more 
than 3,000 years simply by using so unwieldy a unit as the 52-year 
period or its multiples? A numerical system based on 52 as its 
primary unit immediately gives rise to exceedingly awkward num- 
bers for its higher terms; that is, 52, 104, 156, 208,-260, 312, etc. 
Indeed, the expression of really large numbers in terms of 52 involves 
the use of comparatively large multipliers and hence of more or less 
intricate multiplications, since the unit of progression is not decimal 
or even a multiple thereof. The Maya were far too clever mathemar- 
ticians to have been satisfied with a numerical system which employed 
units so inconvenient as 52 or its multiples, and which involved 
processes so clumsy, and we may therefore dismiss the possibility of 
its use without further consideration. 

In order to keep an accurate account of the large jiumbers used in 
recording dates more than 3,000 years distant from the starting point, 
a numerical system was necessary whose terms could be easily 
handled, like the units, tens, hundreds, and thousands of our own 
decimal system. Whether the desire to measure accurately the 
passage of time actually gave rise to their numerical system, or vice 
versa, is not known, but the fact remains that the several periods 
of Maya chronology (except the tonalamatl, haab, and Calendar 
Round, previously discussed) are the exact terms of a vigesimal sys- 
tem of numeration, with but a single exception. (See Table VIII.) 

Table VIII. THE MAYA TIME-PERIODS 

1 kin = 1 day 

20 kina =1 uinal = 20 days 

18 uiaals =1 tun = 360 days 

20 tuns =1 katuri = 7,200 days 

20 katuns =1 cycle = 144,000 days 

202 cycles=l great cycle =2,880,000 days 

Table VIII shows the several periods of Maya chronology by means 
of which the passage of time was measured. All are the exact terms 
of a vigesimal system of numeration, except in the 2d place (uinals) , 

1 This statement does not take account ol the Tuxtla Statuette and the Holactun Initial Series, which 
extend the range of the dated monuments to ten centuries. 

'^ For the discussion of the number of cycles in a great cycle, a question concerning which there are 
two different opinions, see pp. 107 et seq. 



MOELEY] INTEODUCTION TO STUDY OF MAYA HIEEOGLYPHS 63 

in which 18 units instead of 20 make 1 unit of the 3d place, or 
order next higher (tuns) . The break in the regularity of the viges- 
imal progression in the 3d place was due probably to the desire to 
bring the unit of this order (the tun) into agreement with the solar 
year of 365 days, the number 360 being much closer to 365 than 400, 
the third term of a constant vigesimal progression. We have seen on 
page 45 that the 18 uinals of the haab were equivalent to 360 days 
or kins, precisely the number contained in the third term of the 
above table, the tun. The fact that the haab, or solar year, was 
composed of 5 days more than the tun, thus causing a discrepancy 
of 5 days as compared with the third place of the chronological sys- 
tem, may have given to these 5 closing days of the haab — that is, the 
xma kaba kin — the unlucky character they were reputed to possess. 

The periods were numbered from to 19, inclusive, 20 units of 
any order (except the 2d) always appearing as 1 unit of the order 
next higher. For example, a number involving the use of 20 kins 
was written 1 uinal instead. 

We are now in possession of all the different factors which the 
Maya utilized in recording their dates and in counting time : 

1. The names of their dates, of which there could be only 18,980 
(the number of dates in the Calendar Round) . 

2. The date, or starting point, 4 Ahau 8 Cumhu, from which time 
was reckoned. 

3. The counters, that is, the units, used in measuring the passage 
of time. 

It remains to explain how these factors were combined to express 
the various dates of Maya chronology. 

Initial Series 

The usual manner in which dates are written in both the codices and 
the inscriptions is as follows : First, there is set down a number com- 
posed of five periods, that is, a certain number of cycles, katuns, tuns, 
uinals, and kins, which generally aggregate between 1,300,000 and 
1,500,000 days; and this number is followed by one of the 18,980 
dates of the Calendar Round. As we shall see in the next chapter, 
if this large number of days expressed as above be counted forward 
from the fixed starting point of Maya chronology, 4 Ahau 8 Cumhu, 
the date invariably ^ reached will be found to be the date written 
at the end of the long number. This method of dating has been 
called the Initial Series, because when inscribed on a monument it 
invariably stands at the head of the inscription. 

The student will better comprehend this Initial-series method of 
dating if he will imagine the Calendar Round represented by a large 
cogwheel A, figure 23, having 18,980 teeth, each one of which is 

1 There are only two known exceptions to this statement, namely, the Initial Series on the Temple of 
the Cross at Palenque and that on the east side of Stela C at QuJrigua, already noted. 



64 



BUREAU OF AMEBICAN ETHNOLOGY 



[BULL. 57 



B 



named after one of the dates of the calendar. Furthermore, let him 
suppose that the arrow B in the same figure points to the tooth, or 
cog, named 4 Ahau 8 Cumhu ; and finally that from this as its original 
position the wheel commences to revolve in the direction indicated 
by the arrow in A. 

It is clear that after one complete revolution of A, 18,980 days will 
have passed the starting point B, and that after two revolutions 

37,960 days will have 
passed, and after three, 
56,940, and so on. In- 
deed, it is only a question 
of the number of revolu- 
tions of A until as many as 
1,500,000, or any number 
of days in fact, will have 
passed the starting point 
B, or, in other words, will 
have elapsed since the in- 
itial date, 4 Ahau 8 Cumliu. 
This is actually what hap- 
pened according to the 
Maya conception of time. 
For example, let us im- 
agine that a certain Initial 
Series expresses in terms 
of cycles, katuns, tuns, 
uinals, and kins, the num- 
ber 1,461,463, and that the 
date recorded by this num- 
ber of days is 7 Akbal 11 Cumhu. Eef erring to figure 23, it is evi- 
dent that 77 revolutions of the cogwheel A, that is, 77 Calendar 
Eounds, will use up 1,461,460 of the 1,461,463 days, since 77X 18,980 
= 1,461,460. Consequently, when 77 Calendar Rounds shall have 
passed we shall still have left 3 days (1,461,463-1,461,460 = 3), 
which must be carried forward into the next Calendar Round. The 
1,461,461st day will be 5 Imix 9 Cumhu, that is, the day following 4 
Ahau 8 Cumhu (see fig. 23) ; the l,461,462d day will be 6 Ik 10 Cumhu, 
and the 1,461,463d day, the last of the days in our Initial Series, 
7 Akbal 11 Cumhu, the date recorded. Examples of this method of 
dating (by Initial Series) will be given in Chapter V, where this sub- 
ject will be considered in greater detail. 




Fig. 23. Diagram showing section of Calendar-roimd wheel. 



THE INTRODUCING GLYPH 



In the inscriptions an Initial Series is invariably preceded by the 
so-called "introducing glyph," the Maya name for which is unknown. 



MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



65 



Several examples of this glyph are shown in figure 24. This sign is 
composed of four constant elements : 

1 . The trinal superfix. 

2. The pair of comblike lateral appendages. 

3. The tun sign (see fig. 29, a, h). 

4. The trinal subfix. 

In addition to these four constant elements there is one variable 
element which is always found between the pair of combHke lateral 
appendages. In figure 24, a, h, e, this is a grotesque head; in c, a 
natural head; and in d, one of the 20 day-signs, Ik. This element 
varies greatly throughout the inscriptions, and, judging from its 
central position in the "introducing glyph " (itself the most prominent 
character in every inscription in which it occurs), it must have had 
an exceedingly important meaning.' A variant of the comblike 
appendages is shown in figure 24, c, e, in which these elements are 








j))l)J 



/ 



Fig. 24. Initial-series "introducing glyph.' 



replaced by a pair of fishes. However, in such cases, all of which 
occur at Copan, the treatment of the fins and tail of the fish strongly 
suggests the elements they replace, and it is not improbable, there- 
fore,, that the combhke appendages of the "introducing glyph" are 
nothing more nor less than conventionalized fish fins or tails ; in other 
words, that they are a kind of glyphic synecdoche in which a part 
(the fin) stands for the whole (the fish). That the original form of 
this element was the fish and not its conventionahzed fin (*) seems i) 
to be indicated by several facts: (1) On Stela D at Copan, where * 
only fuU-figure glyphs are presented,^ the two combHke appendages of 
the "introducing glyph" appear unmistakably as two fishes. (2) In 
some of the earhest stelse at Copan, as Stelae 15 and P, while these 
elements are not fish forms, a head (fish ?) appears with the conven- 
tionalized comb element in each case. The writer believes the inter- 
pretation of this phenomenon to be, that at the early epoch in which 

1 Mr. Bowditch (1910: App. VIII, 310-18) discusses the possible meanings ot this element. 

2 For explanation of the term "full-figure glyphs," see p. 67, 

43508°— Bull. 57—15 5 



66 BUREAU OF AMEBICAN ETHNOLOGY [bdll. 57 

Stelse 15 and P were erected the conventionalization of the element 
in question had not been entirely accomplished, and that the head 
was added to indicate the form from which the element was derived. 
(3) If the fish was the original form of the combMke element in the 
"introducing glyph," it was also the original form of the same element 
in the katun glyph. (Compare the comb elements (t) in figures 27, g 
a, b, e, and 24, a, h, d with each other.) If this is true, a natural t 
explanation for the use of the fish in the katun sign Hes near at hand. 
As previously explained on page 28, the comblike element stands for 
the sound ca (c hard) ; while Ml in Maya means 20. Also the element 
^^^ (**) stands for the sound tun. Therefore catun or leatun means 20 
^ST tuns. But the Maya word for "fish," cay (c hard) is also a close 
phonetic approximation of the sound ca or leal. Consequently, the 
fish sign may have been the original element in the katun glyph^ 
Ij which expressed the concept' 20, and which the conventionalization 
fl of glyphic forms gradually reduced to the element (ft) without 
destroying, however, its phonetic value. 

Without pressing this point further, it seems not unhkely that the 
combhke elements in the katun glyph, as well as in the "introducing 
glyph," may well have been derived from the fish sign. 

Turning to the codices, it must be admitted that in spite of the fact 
that many Initial Series are found therein, the "introducing glyph" 
has not as yet been positively identified. It is possible, however, that 
the sign shown in figure 24,/, may be a form of the "introducing 
glyph"; at least it precedes an Initial Series in four places in the 
Dresden Codex (see pi. 32). It is composed of the trinal superfix 
and a conventionalized fish (?). 

Mr. Goodman calls this glyph (fig. 24, a-e) the sign for the great 
cycle or unit of the 6th place (see Table VIII) . He bases this identi- 
fication on the fact that in the codices units of the 6th place stand 
immediately above "^ units of the 5th place (cycles), and consequently 
since this glyph stands immediately above the units of the 5th place 
in the inscriptions it must stand for the units of the 6th place. While 
admitting that the analogy here is close, the writer nevertheless is 
inclined to reject Mr. Goodman's identification on the following 
grounds: (1) This glyph never occurs with a numerical coefficient, 
while units of all the other orders — that is, cycles, katuns, tuns, uinals, 
and kins are never without them. (2) Units of the 6th order in the 
codices invariably have a numerical coefficient, as do all the other 
orders. (3) In the only three places in the inscriptions^ in which six 
periods are seemingly recorded, though not as Initial Series, the 6th 
period has a numerical coefficient just as have the other five, and, 

1 See the discussion of Serpent numbers in Chapter VI. 

2 These three inscriptions are found on Stela N, west side, at Copan, the tablet of the Temple of the In- 
scriptions at Palenque, and Stela 10 at TUjal. For the discussion of these inscriptions, see pp. 114-127. 



MORLEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 67 

moreover, the glypli in the 6th position is unhke the forms in figure 
24. (4) Five periods, not six, in every Initial Series express the dis- 
tance from the starting point, 4 Ahau 8 Cumhu, to the date recorded 
at the end of the long numbers. 

It is probable that when the meaning of the "introducing gljrph" 
has been determined it will be found to be quite apart from the 
numerical side of the Initial Series^ at least in so far as the distance 
of the terminal date from the starting point, 4 Ahau 8 Cumhu, is 
concerned. 

While an Initial Series in the inscriptions, as has been previously 
explained, is invariably preceded by an "introducing glyph," the 
opposite does not always obtain. Some of the very earliest monu- 
ments at Copan, notably Stelae 15, 7, and P, have "introducing 
glyphs" inscribed on two or three of their four sides, although but 
one Initial Series is recorded on each of these monuments. Examples 
of this use of the "introducing glyph," that is, other than as standing 
at the head of an Initial Series, are confined to a few of the earliest 
mommients at Copan, and are so rare that the beginner will do well 
to disregard them altogether and to follow this general rule : That in 
the inscriptions a glyph of the form shown in figure 24, a-e, wiU 
invariably be followed by an Initial Series. 

Having reached the conclusion that the introducing glyph was not 
a sign for the period of the 6th order, let us next examine the signs 
for the remaining orders or periods of the chronological system 
(cycles, katuns, tuns, uinals, and kins), constantly bearing in mind 
that these five periods alone express the long numbers of an Initial 
Series.* 

Each of the above periods has two entirely different glyphs which 
may express it. These have been called (1) The normal form; (2) 
The head variant. In the inscriptions examples of both these classes 
occtir side by side in the same Initial Series, seemingly according to 
no fixed rule, some periods being expressed by their normal forms and 
others by their head variants. In the codices, on the other hand, no 
head-variant period glyphs have yet been identified, and although 
the normal forms of the period glyphs have been foimd, they do not 
occur as units in Initial Series. 

As head variants also should be classified the so-called "fuU-figiu-e 
glyphs," in which the periods given in Table VIII are represented by 
full figures iQstead of by heads. In these forms, however, only the 
heads of the figures are essential, since they alone present the deter- 
mining characteristics, by means of which in each case identification 
is possible. Moreover, the head part of any full-figure variant is 
characterized by precisely the same essential elements as the corre- 

1 The discussion of glyplis wliich may represent the great cycle or period of the 6th order will be pre- 
sented on pp. 114-127 in connection with the discussion of numbers having six or more orders of units. 



68 



BUREAU OP AMEEICAN ETHNOLOGY 



[EULIJ. 57 



spending head variant for the same period, or in other words, the 
addition of the body parts in full-figure glyphs in no way influences 
or changes their meanings. For this reason head-variant and full- 
figure forms have been treated together. These fuU-figure glyphs 
are exceedingly rare, having been foimd only in five Initial Series 
throughout the Maya area: (1) On Stela D at Copan; (2) on Zoo- 
morph B at Quirigua; (3) on east side Stela D at Quirigua; (4) on 
west side Stela D at Quirigua; (5) on Hieroglyphic Stairway at 
Copan. A few full-figure glyphs have been found also on an oblong 
altar at Copan, though not as parts of an Initial Series, and on Stela 
15 as a period glyph of an Initial Series. 

THE CYCLE GLYPH 

The Maya name for the period of the 5th order in Table VIII is 
unknown. It has been called "the cycle," however, by Maya stu- 









d e 

Fig. 25. Signs for the cycle: a-c, Normal forms; d~f, head variants. 

dents, and in default of its true designation, this name has been 
generally adopted. The normal form of the cycle glyph is shown in 
figure 25, a, i, c. It is composed of an element which appears twice 
over a knotted support. The repeated element occurs also in the signs 
for the months Chen, Yax, Zac, and Ceh (see figs. 19, o~v, 20, l~p) . 
This has been called the Cauac element because it is similar to the 
sign for the day Cauac in the codices (fig. 17, V), though on rather 
inadequate grounds the writer is inclined to believe. The head variant 
of the cycle glyph is shown in figure 25, d-f. The essential charac- 
teristic of this grotesque head with its long beak is the hand element 
s^ (*) , which forms the lower j aw, though in a very few instances even 
* this is absent. In the fuU-figure forms this same head is joined 
to the body of a bird (see fig. 26). The bird intended is clearly a 
parrot, the feet, claws, and beak being portrayed in a very realistic 
manner. No glyph for the cycle has yet been found in the codices. 

THE KATUN GLYPH 

The period of the 4th place or order was called by the Maya the 
Tcatun; that is to say, 20 tuns, since it contained 20 units of the 3d 



MOELBT] INTRODTJCTION TO STUDY OF MAYA HIEEOGLYPHS 



69 



order (see Table VIII). The normal form of the katun glyph is 
shown in figure 27, a-d. It is composed of the normal form of the tun 
sign (fig. 29, a, h) surmounted by the pair of comb- 
like appendages, which we have elsewhere seen meant 
20, and which were probably derived from the repre- 
sentation of a fish. The whole glyph thus graph- 
ically portrays the concept 20 tuns, which according 
to Table VIII is equal to 1 katun. The normal 
form of the katun glyph in the codices (fig. 27, c, d) 
is identical with the normal form in the inscriptions 
(fig. 27, a,h). Several head variants are found. The 
most easily recognized, though not the most com- 
mon, is shown in figure 27, e, in which the superfix 
is the same as in the normal form; that is, the ele- 
^©D ™^^* (t); which probably signifies 20 in this connection. To 
t be logical, therefore, the head element should be the same 
as the head variant of the tun glyph, but this is not the case (see fig. 
29, e-h) . When this superfix is present, the identification of the head 
variant of the katun glyph is an easy matter, but when it is absent 




Fig. 26. Full-figure 
variant of cycle sign. 









Fig. 27. Signs 



/ 9 

for the katun: a-d, Normal forms; e-h, head variants. 



it is difficult to fix on any essential characteristic. The general 
shape of the head is Hke the head variant of the cycle glyph. Perhaps 
the oval (**) in the top of the head in figure 27, f-Ji, and ^) cj^ 
the small curling fang (ft) represented as protruding from ** tt 
the back part of the mouth are as constant as any of the other 
elements. The head of the fuU-figm-e variant in figure 28 presents 
the same lack of essential characteristics as the head variant, though 
in this form the small curling fang is also found. Again, the body 
attached to this head is that of a bird which has been identified as 
an eagle. 



70 



BUREAU OF AMERICAN ETHNOLOGY 



[BOLL. 57 



THE TUN GLYPH 



The period of the 3d place or order was called by the Maya the 
tun, which means "stone," possibly because a stone was set up every 
360 days or each tun or some multiple thereof. Com- 
pare so-called hotun or katun stones described on page 
34. The normal sign for the tun in the inscriptions 
(see fig. 29, a, h) is identical with the form found in 
the codices (see fig. 29, c). The head variant, which 
bears a general resemblance to the head variant for 
XV oo ^ ,, the cycle and katun, has several forms. The one 
figure variant most readily recognized, because it has the normal 
of katun sign. ^^^^ ^^^ -^g superfix, is showu in figure 29, d, e. The 
detemuning characteristic of the head variant of the tun glyph, 
however, is the fleshless lower jaw (J), as shown in figure 29 
/, g, though even this is lacking in some few cases. The ^-=*© 
form shown in figure 29, )^, is found at Palenque, where it j ° 












e f 9 h 

Fig. 29. Signs lor the tun: Or-d, Normal forms; e-h, head variants. 

seems to represent the tun period in several places. The head of 
the full-figure form (fig. 30) has the same fleshless lower jaw for its 
essential characteristic as the head-variant forms in fig- 
ure 29. The body joined to this head is again that of a 
bird the identity of which has not yet been determined. 

THE UINAL GLYPH 

The period occupying the 2d place was called by the 

Maya uinal or u. This latter word means also " the 

Fig. 30. Fuii-flg- moon" in Maya, and the fact that the moon is visible 

ure variant of fgp j^g^ about 20 days in each lunation may account 

for the application of its name to the 20-day period. 

The normal form of the uinal glyph in the inscriptions (see fig. 31, 

a, h) is practically identical with the form in the codices (see fig. 31 , c) . 




MORLEY] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 



71 









Signs for the umal: a-c, Normal forms; d-f, head 
variants. 



Sometimes the subfixial element (J J) is omitted in the inscrip- 
tions, as in figm-e 31, a. The head variant of the ninal glyph (fig. ^ 
31, d-f) is the most constant of all of the head forms for the various 
periods. Its determining characteristic is the large curl emerging from 
the back part of the mouth. The sharp-pointed teeth in the upper 
jaw are also a fairly constant feature. In very rare cases both of these 
elements are wanting. In 
such cases the glyph seems 
to be without determining 
characteristics. The ani- 
mal represented in the full- 
figure variants of the uinal 
is that of a frog (fig. 32,) 
the head of which presents 
precisely the same char- 
acteristics as the head vari- 
ants of the uinal, just de- 
scribed. That the head 
vajiant of the uinal-period 
glyph was originally de- 
rived from the representation of a frog can hardly be denied in the 
face of such striking confirmatory evidence as that afforded by the 
full-figm-e form of the uinal in figure 33. Here the spotted body, 
flattened head, prominent mouth, and bulging eyes of the frog are so 

reahstically portrayed that there is no 
doubt as to the identity of the figure in- 
tended. Mr. Bowditch (1910: p. 257) has 
pointed out in this connection an inter- 
esting phonetic coincidence, which can 
hardly be other than intentional. The 
Maya word for frog is uo, which is a fairly close phonetic approxi- 
mation of u, the Maya word for "moon" or "month." Consequently, 
the Maya may have selected the figure of the frog on phonetic grounds 
to represent their 20-day period. If this point could be 
established it would indicate an unmistakable use of the 
rebus form of writing employed by the Aztec. That is, 
the figiu-e of a frog in the utnal-period glyph would not 
recall the object which it pictures, but the soimd of that 
object's name, uo, approximating the soimd of u, which 
in turn expressed the intended idea, namely, the 20-day 
period. Mr. Bowditch has suggested also that the gro- 
tesque birds which stand for the cycle, katun, and tun periods, in 
these fuU-figure forms may also have been chosen because of the 
phonetic similarity of their names to the names of these periods. 




Fig. 32. Full-figure variant ot uinal sign 
on Zoomorph B, Quirigua. 




Fig. 33. Full- 
figure variant 
of uinal sign 
on Stela D, Co- 
pan. 



V2 



BUREAU Or AMERICAN EtHlsrOLOGY 



[BULL, 



S7 



THE KIN GLYPH 

The period of the 1st, or lowest, order was called by the Maya Mn, 
which meant the "sun" and by association the "day." The kin, as 
has been explained, was the primary unit used by the Maya in count- 
ing time. The normal form of this period glyph in the inscriptions 
is shown in figure 34, a, which is practically identical with the form 
in the codices (fig. 34, 6). In addition to the normal form of the kin 
sign, however, there are several other forms representing this period 
which can not be classified either as head variants or full-figure vari- 
ants, as in figure 34, c, for example, which bears no resemblance what- 
ever to the normal form of the kin sign. It is difficult to understand 













i 3 h I 

Fig. 34. Signs for the kin: a, b, Normal forms; c, d, miscellaneous; e-k, head variants. 

how two characters as dissimilar as those shown in a and c, figure 34 
could ever be used to express the same idea, particularly since there 
seems to be no element common to both. Indeed, so dissimilar are 
they that one is almost forced to believe that they were derived from 
two entirely distinct glyphs. Still another and very unusual sign for 
the kin is shown in figure 34, d; indeed, the writer recalls but two 
places where it occurs: Stela 1 at Piedras Negras, and Stela C (north 
side) at Quirigua. It is composed of the normal form of the sign for 
the day Ahau (fig. 16, e') inverted and a subfixial element which 
varies in each of the two cases. These variants (fig. 34, c, ^) are 
found only in the inscriptions. The head variants of the kin period 
differ from each other as much as the various normal forms above 
l(^^ O S^"^^^- "^^6 form shown in figure 34, e, may be readily 
* t recognized by its subfixial element (*) and the element (f); . 




MORLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 73 

both of which appear in the normal form, figure 34, a. In some cases, 
as in figure 34, f-h, this viariant also has the square irid and the 
crooked, snag-like teeth projecting from the front of the mouth. 
Again, any one of these features, or even all, may be lacking. Another 
and usually more grotesque type of head (fig. 34, 
i, j) has as its essential element the banded head- 
dress. A very unusual head variant is that shown 
in figure 34, Ic, the essential characteristic of which 
seems to be the crossbones in the eye. Mr. Bow- 
ditch has included also in his list of kin signs the 
form shown in figure 34, I, from an inscription at. 
Tikal. While this glyph in fact does stand between 
two dates which are separated by one day from each ^"g. 35. Fuii-agure 
other, that is, 6 Eb Pop and 7 Ben 1 Pop, the ™'^*<'f'^-^'^- 
writer believes, nevertheless, that only the element (J) — an es- ^ 
sential part of the normal form for the kin — ^here represents the t 
period one day, and that the larger characters above and below have 
other meanings. In the fuU-figure variants of the kin sign the figure 
portrayed is that of a human being (fig. 35), the head of which is 
similar to the one in figm'e 34, i, j, having the same banded head- 
dress.* 

This concludes the presentation of the various forms which stand 
for the several periods of Table VIII. After an exhaustive study of 
these as found in Maya texts the writer has reached the following 
generalizations concerning them: 

1 . Prevalence. The periods in Initial Series are expressed far more 
frequently by head variants than by normal forms. The prepon- 
derance of the former over the latter in all Initial Series known is in 
the proportion of about 80 per cent of the total ^ against 12 per cent, 
the periods in the remaining 8 per cent being expressed by these two 
forms used side by side. In other words, four-fifths of all the Initial 
Series known have their periods expressed by head-variant glyphs. 

2. Antiquity. Head-variant period glyphs seem to have been used 
very much earlier than the normal forms. Indeed, the first use of 
the former preceded the first use of the latter by about 300 years, 
while in Initial Series normal-form period glyphs do not occur until 
nearly 100 years later, or about 400 years after the first use of head 
variants for the same purpose. 

3. Variation. Throughout the range of time covered by the Initial 
Series the normal forms for any given time-period differ but little 
from one another, all following very closely one fixed type. Although 

1 The figure on Zoomorpii B at Quirigua, however, has a normal human head without grotesque char- 
acteristics. 

2 The full-flgure glyphs are included with the head variants in this proportion. 



74 



BUREAU OP AMERICAN ETHNOLOGY 



[BULL. 57 




Fig. 36. 



Period glyphs, from widely separated sites and of different 
epochs, showing persistence of essential elements. 



neany 200 years apart in point of time, the early form of the tun sign 
in figure 36, a, closely resembles the late form shown in h of the same 
figure, as to its essentials. Or again, although 375 years apart, the 
early form of the katun sign in figure 36, c, is practically identical with 
the form in figure 36, d. Instances of this kind, could be multiplied 
indefinitely, but the foregoing are sufficient to demonstrate that in 
so far as the normal-form period glyphs are concerned but little varia- 
tion occurred from first to last. Similarly, it may be said, the Itead 
variants for any given period, while differing greatly in appearance at 

different epochs, re- 
tained, nevertheless, 
the same essential 
characteristic through- 
out. For example, al- 
though the uinal sign 
in figure 36, e, precedes 
the one in figure 36,/, 
by some 800 years, the 
same essential element 
— the large mouth curl 
— appears in both. 
Again, although 300 
years separate the cycle signs shown in g and Ji, figure 36, the essen- 
tial characteristic of the early form (fig. 36, .g), the hand, is still 
retained as the essential part of the late form (Ti) . 

4. Derivation. We have seen that the full-figure glyphs probably 
show the original life-forms from which the head variants were 
developed. And since from (2), above, it seems probable that the 
head variants are older than the so-called normal forms, we may 
reasonably infer that the fuU-figure glyphs represent the life-forms 
whose names the Maya originally applied to their periods, and further 
that the first signs for those periods were the heads of these life-forms. 
This develops a contradiction in our nomenclature, for if the forms 
which we have called head variants are the older signs for the periods 
and are by far the most prevalent, they should have been called the 
normal forms and not variants, and vice versa. However, the use of 
the term "normal forms" is so general that it would be unwise at 
this time to attempt to introduce any change in nomenclature. 

Secondary Series 

The Initial Series method of recording dates, although absolutely 
accurate,^ was nevertheless somewhat lengthy, since in order to 
express a single date by means of it eight distinct glyphs were 
required, namely: (1) The Introducing glyph; (2) the Cycle glyph; 

1 Any system of counting time which describes a date in such a manner that it can not recur, satisfying 
all the necessary conditions, for 37-4,400 years, must be regarded as absolutely accurate in so far as the range 
of human life on this planet is concerned. 



MOELBT] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 75 

(3) the Katun glyph; (4) the Tun glyph; (5) the Uinal glyph; (6) 
the Km glyph; (7) the Day glyph; (8) the Month glyph. Moreover, 
its use in any inscription which contained more than one date would 
have resulted in needless repetition. For example, if all the dates 
on any given monument were expressed by Initial Series, every one 
would show the long distance (more than 3,000 years) which sepa^ 
rated it from the common starting point of Maya chronology. It 
would be just like writing the legal holidays of the current year in 
this way: February 22d, 1913, A. D., May 30th, 1913, A. D., July 4th, 
1913, A. D., December 25th, 1913, A. D.; or in other words, repeating 
in each case the designation of time elapsed from the starting point 
of Christian chronology. 

The Maya obviated this needless repetition by recording but one 
Initial Series date on a monument; '■ and from this date as a new point 
of departure they proceeded to reckon the number of days to the 
next date recorded; from this date the numbers of days to the next; 
and so on throughout that inscription. By this device the position 
of any date in the Long Count (its Initial Series) could be calculated, 
since it could be referred back to a date, the Initial Series of which 
was expressed. For example, the terminal day of the Initial Series 
given on page 64 is 7 Akbal 11 Cumhu, and its position in the Long 
Count is fixed by the statement in cycles, katuns, tuns, etc., that 
1,461,463 days separate it from the starting point, 4 Ahau 8 Cumhu. 
Now let us suppose we have the date 10 Cimi 14 Cumhu, which is 
recorded as being 3 days later than the day 7 Akbal 11 Cumhu,^ the 
Initial Series of which is known to be 1,461,463. It is clear that the 
Initial Series corresponding to the date 10 Cimi 14 Cumhu, although 
not actually expressed, wiU also be known since it must equal 
1,461,463 (Initial Series of 7 Akbal 11 Cumhu) + 3 (distance from 
7 Akbal 11 Cumhu to 10 Cimi 14 Cumhu) , or 1,461,466. Therefore it 
matters not whether we count three days forward from 7 Akbal 11 
Pumhu, or whether we count 1,461,466 days forward from the start- 
ing point of Maya chronology, 4 Ahau 8 Cumhu since in each case the 
date reached wiU be the same, namely, 10 Cimi 14 Cumhu. The 
former method, however, was used more frequently than all of the 
other methods of recording dates combined, since it insured all the 
accuracy of an Initial Series without repeating for each date so great 
a number of days. 

Thus having one date on a monument the Initial Series of which 
was expressed, it was possible by referring subsequent dates to it, or 
to other dates which in turn had been referred to it, to fix accurately 

1 There are a very few monuments wMch have two Initial Series instead of one. So far as the writer 
knows, only six monuments in the entire Maya area present this feature, namely, Stelae F, D, E, and A 
at Quirigua, Stela 17 at Tikal, and Stela 11 at Yaxchilan. 

2 Refer to p . 64 and figure 23. It will be noted that the third tooth (1 . e. day ) after the one named 7 Aibal 
11 Cumhu is 10 Cimi U Cumhu. 



76 BUREAU OF AMERICAN ETHNOLOGY [bull. 5T 

the positions of any number of dates in the Long Count without the 
use of their corresponding Initial Series. Dates thus recorded are 
known as "secondary dates," and the periods which express their 
distances from other dates of known position in the Long Count, 
as "distance numbers." A secondary date with its corresponding 
distance number has been designated a Secondary Series. In the 
example above given the distance number 3 kins and the date 10 
Cimi 14 Cumhu would constitute a Secondary Series. 

Here, then, in addition to the Initial Series is a second method, the 
Secondary Series, by means of which the Maya recorded their dates. 
The earliest use of a Secondary Series with which the writer is familiar 
(that on Stela 36 at Piedras Negras) does not occur until some 280 
years after the first Initial Series. It seems to have been a later 
development, probably owing its origin to the desire to express more 
than one date on a single monument. Usually Secondary Series are 
to be counted from the dates next preceding them in the inscriptions 
in which they are found, though occasionally they are counted from 
other dates which may not even be expressed, and which can be 
ascertained only by counting backward the distance number from 
its corresponding terminal date. The accuracy of a Secondary series 
date depends entirely on the fact that it has been counted from an 
Initial Series, or at least from another Secondary series date, which 
in turn has been derived from an Initial Series. If either of these 
contingencies applies to any Secondary series date, it is as accurate 
a method of fixing a day in the Long Count as though its correspond- 
ing Initial Series were expressed in full. If, on the other hand, a Sec- 
ondary series date can not be referred ultimately to an Initial Series 
or to a date the Initial Series of which is known though it may not be 
expressed, such a Secondary series date becomes only one of the 
18,980 dates of the Calendar Round, and will recur at intervals of 
every 52 years. In other words, its position in the Long Count will 
be unlaiown. 

Calendar-round Dates 

Dates of the character just described may be called Calendar- 
round dates, since they are accurate only within the Calendar Eound, 
or range of 52 years. While accurate enough for the purpose of dis- 
tinguishing dates in the course of a single lifetime, this method breaks 
down when used to express dates covering a long period. Witness 
the chaotic condition of Aztec chronology. The Maya seem to have 
realized the limitations of this method of dating and did not employ 
it extensively. It was used chiefly at YaxchUan on the Usamacintla 
River, and for this reason the chronology of that city is very much 
awry, and it is difficult to assign its various dates to their proper 
positions in the Long Count. 



moeley] introduction to study of maya hieroglyphs 77 

Period-ending Dates 

The Maya made use of still another method of dating, which, - 
although not so exact as the Initial Series or the Secondary Series, 
is, on the other hand, far more accurate than Calendar round datiag. 
In this method a date was described as being at the end of some par- 
ticular period in the Long Count; that is, closing a certain cycle, 
katun, or tun.' It is clear also that in this method only the name 
Ahau out of the 20 given in Table I can be recorded, since it alone 
can stand at the end of periods higher than the kin. This is true, 
since : 

1. The higher periods, as the uuial, tun, katun, and cycle are exactly 
divisible by 20 in every case (see Table VIII) , and — 

2. They are all counted from a day, Ahau, that is, 4 Ahau 8 Cumhu. 
Consequently, all the periods of the Long Count, except the kia or 
primary unit, end with days the name parts of which are the sign 
Ahau. 

This method of recording dates always involves the use of at least 
two factors, and usually three: 

. 1. A particular period of the Long Count, as Cycle 9, or Katun 14, 
etc. 

2. The date which ends the particular period recorded, as 8 Ahau 
13 Ceh, or 6 Ahau 13 Muan, the closing dates respectively of Cycle 9 
and Katun 14 of Cycle 9; and 

3. A glyph or element which means "ending" or "is ended," or. 
which indicates at least that the period to which it is attached has 
come to its close. 

The first two of these factors are absolutely essential to this method 
of dating, while the third, the so-called "ending sign," is usually, 
though not invariably, present. The order iti which these factors 
are usually found is first the date composed of the day glyph and 
month glyph, next the "ending sign," and last the glyph of the period 
whose closing day has just been recorded. Very rarely the period 
glyph and its ending sign precede the date. 

The ending glyph has three distinct variants: (1) the element 
shown as the prefix or superfix in figure 37, a-h, t, all of which are 
forms of the same variant; (2) the flattened grotesque head appear- 
ing either as the prefix or superfix in i, r, u, v of the same figure ; and 
(3) the hand, which appears as the main element in the forms shown 
in figure 37, j-q. The two first of these never stand by themselves 
but always modify some other sign. The first (fig. 37, a-h, t) is always 
attached to the sign of the period whose end is recorded either as a 

1 This method of dating does not seem to have been used with either uliial or kin period endings, probably 
because of the comparative frequency with which any given date might occur at the end of either of these 
two periods. 



78 



BUREAU OF AMERICAN ETHNOLOGY 



[BOIiL. 57 



superfix (see fig. 37, a, whereby the end of Cycle 10 is indicated ') , or 
as a prefix (see t, whereby the end of Katun 14 is recorded). The 
second form is seen as a prefix in u, whereby the end of Katun 12 is 
recorded, and in i, whereby the end of Katun 11 is shown. This 
latter sign is found also as a superfix in r. 

The hand-ending sign rarely appears as modifying period glyphs, 
although a few examples of such use have been found (see fig. 37, 




r s t u V 

Fig. 37. Ending signs and elements. 

j, Tc). This ending sign usually appears as the main element in a sepa- 
rate glyph, which precedes the sign of the period whose end is recorded 
(see fig. 37, l-q). In these cases the subordinate elements differ 
somewhat, although the element (*) appears as the suflSx in I, m, 
n, 2, and the element (f) as a postfix therein, also in o and f. 
^ In a few cases the hand is combined with the other ending 
signs, sometimes with one and sometimes with the other. 

1 In Chapter IV it will be shown that two bars stand for the number 10. It will be necessary to anticipate 
the discussion of Maya numerals there presented to the extent of stating that a bar represented 5 and a 
dot or ball, 1. The varying combinations of these two elements gave the values up to 20. 



MOKLBY] INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 79 

The use of the hand as expressing the meaning "ending" is quite 
natural. The Aztec, we have seen, called their 52-year period the 
xiuhmolpilli, or "year bundle." This imphes the concomitant idea 
of "tying up." As a period closed, metaphorically speaking, it was 
"tied up" or "bundled up." The Maya use of the hand to express 
the idea "ending" may be a graphic representation of the member 
by means of which this "tying up" was effected, the clasped hand 
indicating the closed period. 

This method of describing a date may be called "dating by period 
endings." It was far less accurate than Initial-series or Secondary- 
series dating, since a date described as occurring at the end of a cer- 
tain katun could recur after an interval of about 18,000 years in round 
numbers, as against 374,400 years in the other 2 methods. For all 
practical piu-poses, however, 18,000 years was as accurate as 374,400 
years, since it far exceeds the range of time covered by the written 
records of mankind the world over. 

Period-ending dates were not used much, and, as has been stated 
above, they are found only in connection with the larger periods — 
most frequently with the katun, next with the cycle, and but very 
rarely with the tun. Mr. Bowditch (IClOipp. 176 et seq.) has re- 
viewed fuUy the use of ending signs, and students are referred to his 
work for further information on this subject. 

U Kahlay Kattjnob 

In addition to the foregoing methods of measuring time and record- 
ing dates, the Maya of Yucatan used stiU another, which, however, 
was probably derived directly from the apphcation of Period-ending 
dating to the Long Count, and consequently introduces no new ele- 
ments. This has been designated the Sequence of the Kafcuns, 
because in this method the katun, or 7,200-day period, was the unit 
used for measuring the passage of time. The Maya themselves called 
the Sequence of the Katuns u tzolan Tcatun, "the series of the katuns" ; 
or u Icahlay uxocen Tcatunoh, "the record of the count of the katuns " ; 
or even more simply, u Tcahlay Tcatunoh, "the record of the katuns." 
These names accurately describe this system, which is simply the 
record of the successive katuns, comprising in the aggregate the range 
of Maya chronology. 

Each katun of the u kahlay katunob was named after the designa- 
tion of its ending day, a practice derived no doubt from Period-ending 
dating, and the sequence of these ending days represented passed 
time, each ending day standing for the katun of which it was the 
close. The katun, as we have seen on page 77, al-ways ended with 
some day Ahau, consequently this day-name is the only one of the 
twenty which appears in the u kahlay katunob. In this method the 
katuns were distinguished from one another, not by the positions 



80 BUEEAU OF AMEEICAW ETHNOLOGY [ehll. 57 

which they occupied in the cycle, as Katun 14, for example, but by 
the different days Ahan with which they ended, as Katun 2 Ahau, 
Katim 13 Ahau, etc. See Table IX. 



Table IX.— SEQUENCE OF KAT 


UNS IN U i 


CAHLAY Kj 


Eatun 2 Ahau 


Eatun 


8 Ahau 


Eatnu 13 Ahau 


Eatun 


6 Ahau 


Eatun 11 Ahau 


Eatun 


i Ahau 


Eaton 9 Ahau 


Eatun 


2 Ahau 


Eatun 7 Ahau 


Eatun 


13 Ahau 


Eatun 5 Ahau 


Eatun 


11 Ahau 


Eatun 3 Ahau 


Eatun 


9 Ahau 


Eatun 1 Ahau 


Eatun 


7 Ahau 


Eatun 12 Ahau 


Eatun 


5 Ahau 


Eatun 10 Ahau 


Eatun 


3 Ahau, etc, 



The peculiar retrogradiug sequence of the numerical coefl&cients in 
Table IX, decreasing by 2 from katun to katun, as 2, 13, 11, 9, 7, 
5, 3, 1, 12, etc., results directly from the number of days which the 
katim contains. Since the 13 possible numerical coefficients, 1 to 
13, inclusive, succeed each other in endless repetition, 1 following 
immediately after 13, it is clear that in counting forward- any given 
number from any given numerical coefficient, the resulting numerical 
coefficient will not be affected if we first deduct all the 13s possible 
from the number to be counted forward. The mathematical dem- 
onstration of this fact follows. If we count forward 14 from any 
given coefficient, the same coefficient will be reached as if we had 
counted forward but 1. This is true because, (1) there are only 13 
mmaerical coefficients, and (2) these follow each other without inter- 
ruption, 1 following immediately after 13; hence, when 13 has 
been reached, the next coefficient is 1, not 14; therefore 13 or any 
multiple thereof may be counted forward or backward from any one 
of the 13 numerical coefficients without changing its value. This 
truth enables us to formulate the following rule for finding numerical 
coefficients: Deduct all the multiples of 13 possible from the number 
to be coimted forward, and then count forward the remainder from 
the known coefficient, subtracting 13 if the resulting number is above 
13, since 13 is the highest possible number which can be attached to 
a day sign. If we apply this rule to the sequence of the mmaerical 
coefficients iu Table IX, we shall find that it accoimts for the retro- 
grading sequence there observed. The first katim in Table IX, 
Katun 2 Ahau, is named after its ending day, 2 Ahau. Now let us 
see whether the application of this rule wiU give us 13 Ahau as the 
ending day of the next katun. The number to be counted forward 
from 2 Ahau is 7,200, the number of days in one katim; therefore we 
must first deduct from 7,200 all the 13s possible. 7,200 h- 13 = 553^^. 
In other words, after we have deducted all the 13's possible, that is. 



MOBLEY] INTEODUCTIOHr TO STUDY OF MAYA HIEROGLYPHS 81 

553 of them, there is a remainder of 11. This the rule says is to be 
added (or counted forward) from the known coefficient (in this case 
2) in order to reach the resulting coefficient. 2 + 11 = 13. Since 
this number is not above 13, 13 is not- to be deducted from it; there- 
fore the coefficient of the ending day of the second katun is 13, as 
shown in Table IX. Similarly we can prove that the coefficient of 
the ending day of the third katun in Table IX will be 11. Again, we 
have 7,200 to count forward from the known coefficient, in this case 
1 3 (the coefficient of the ending day of the second katun) . But we have 
seen above that if we deduct all the 13s possible from 7,200 there will 
be a remainder of 11; consequently this remainder 11 must be added 
to 13, the known coefficient. 13 + 11=24; but since this number is 
above 13, we miist deduct 13 from it in order to find out the resulting 
coefficient. 24 — 13 = 11, and 11 is the coefficient of the endiug day 
of the third katim in Table IX. By applying the above rule, all of 
the coefficients of the ending days of the katuns could be shown to 
follow the sequence indicated in Table IX. And since the ending 
days of the katuns determined their names, this same sequence is also 
that of the katuns themselves. 

The above table enables us to establish a constant by means of 
which we can always find the name of the next katxm. Since 7,200 
is always the number of days in any katun, after deducting aU the 
13s possible the remainder will always be 11, which has to be added 
to the known coefficient to find the vmknown. But since 13 has to 
be deducted from the resiilting number when it is above 13, sub- 
tracting 2 will always give us exactly the same coefficient as adding 
11; consequently we may formulate for determining the mmierical 
coefficients of the ending days of katuns the following simple rule: 
Subtract 2 from the coefficient of the ending day of the preceding 
katun in every case. A glance at Table IX will demonstrate the 
truth of this rule. 

In the names of the katuns given in Table IX it is noteworthy that 
the positions which the ending days occupied in the divisions of the 
haab, or 365-day year, are not mentioned. For example, the first 
katun was not called Katun 2 Ahau 8 Zac, but simply Katim 2 Ahau, 
the month part of the day, that is, its position in the year, was omitted. 
This omission of the month parts of the ending days of the katuns in 
the u kahlay katunob has rendered this method of dating far less 
accurate than any of the others previously described except Calendar- 
round Dating. For example, when a date was recorded as falling 
within a certain katun, as Katun 2 Ahau, it might occur anywhere 
-within a period of 7,200 days, or nearly 20 years, and yet fulfill the 
given conditions. In other words, no matter how accurately this 
Katun 2 Ahau itself might be fijced in a long stretch of time, there 
was always the possibility of a maximum error of about 20 years in 
43508°— Bull. 57—15 6 



82 BUEBATJ OF AMERICAN ETHNOLOGY [bull. 57 

such dating, since the statement of the katun did not fix a date any 
closer than as occurring somewhere within a certain 20-year period. 
When greater accuracy was desired the particular tun in which the 
date occurred was also given,* as Tim 13 of Katun 2 Ahau. This 
jSxed a date as falling somewhere within a certain 360 days, which 
was acctirately fixed in a much longer period of time. Very rarely, 
in the case of an extremely important event, the Calendar-round 
date was also given as 9 Imix 19 Zip of Tun 9 of Katun 13 Ahau. 
A date thus described satisfying all the given conditions cotdd not 
recur until after the lapse of at least 7,000 years. The great major- 
ity of events, however, recorded by this method are described only 
as occurring in some particular katun, as Katun 2 Ahau, for example, 
no attempt being made to refer them to any particidar division (tim) 
of this period. Such accuracy doubtless was siifficient for recording 
the events of tribal history, since in no case could an event be more 
than 20 years out of the way. 

Aside from this initial error, the acciu-acy of this method of dat- 
ing has been challenged on the ground that since there were only 
thirteen possible numerical coefficients, any given katun, as Katun 
2 Ahau, for example, in Table IX would recur in the sequence after 
the lapse of thirteen katuns, or about 256 years, thus paving the way 
for much confusion. While admitting that every thirteenth katun 
in the sequence had the same name (see Table IX), the writer 
believes, nevertheless, that when the sequence of the katims was 
carefully kept, and the record of each entered immediately after its 
completion, so that there could be no chance of confusing it with 
an earlier katun of the same name in the sequence, acctiracy in dating 
could be secm-ed for as long a period as the sequence remained 
imbroken. Indeed, the u kahlay katunob ' from which the synopsis 
of Maya history given in Chapter I was compiled, accurately fixes 
the date of events, ignoring the possible initial inaccuracy of 20 years, 
within a period of more than 1,100 years, a remarkable feat for any 
primitive chronology. 

How early this method of recording dates was developed is uncer- 
tain. It has not yet been found (surely) in the inscriptions in either 
the south or the north; on the other hand, it is so closely connected with 
the Long Count and Period-ending dating, which occurs repeatedly 
throughout the inscriptions, that it seems as though the u kahlay 
katunob must have been developed while this system was still in use. 

There should be noted here a possible exception to the above state- 
ment, namely, that the u kahlay katunob has not been found in the 
inscriptions. Mr. Bowditch (1910: pp. 192 et seq.) has pointed out 

I Theu kahlay katunob on which the historical summary given in Chapterl is based shows an absolutely 
uninterrupted sequence ol katuns for more than 1,100 years. See Brinton (1882 b: pp. 162-164). It is nec- 
essary to note here a correction on p. 153 of that work. Doctor Brinton has omitted a Katun 8 Ahau from 
this u kahlay katimob, which is present in the Berendt copy, and he has incorrectly assigned the abandon- 
ment of Chichen Itza to the preceding katun, Katun 10 Ahau, whereas the Berendt copy shows this 
event took place during the katun omitted, Kaiun 8 Ahau. 



MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



83 



what seem to be traces of another method of dating. This consists of 
some day Ahau modified by one of the two elements shown in figure 
38 {a-d and e-li, respectively) . In such cases the month part is some- 
times recorded, though as frequently the day Ahau stands by itself. 
It is to be noted that in the great majority of these cases the days 
Ahau thus modified are the ending days of katuns, which are either 
expressed or at least indicated in adjacent glyphs. In other words, 
the day Ahan thus modified is usually the ending day of the next 
even katun after the last date recorded. The writer believes that 
this modification of certain days Ahau by either of the two ele- 
ments shown in figure 38 may indicate that such days were the 
katun ending days nearest to the time when the inscriptions present- 
ing them were engraved. The snake variants shown in figure 38, 



^ 











Fig. 38. "Snake" or "knot" element as used witli day sign Ahau, possibly indicating presence of the 
u kaUay katimob in the inscriptions. 

a-d, are all from Palenque; the knot variants {e-Ti of the same figure) 
are found at both Copan and Quirigua. 

It may be objected that one katun ending day in each inscription 
is far different from a sequence of katun ending days as shown in 
Table. IX, and that one katim ending day by itself can not be con- 
strued as an u kahlay katunob, or sequence of katuns. The differ- 
ence here, however, is apparent rather than real, and restilts from the 
different character of the monimaents and the native chronicles. The 
u kahlay katunob in Table IX is but a part of a much longer sequence 
of katims, which is shown in a number of native chronicles written 
shortly after the Spanish Conquest, and which record the events of 
Maya history for more than 1,100 years. They are in fact chrono- 
logical synopses of Maya history, and from their very nature they 
have to do with long periods. This is not true of the monuments,^ 
which, as we have seen, were probably set up to mark the passage of 
certain periods, not exceeding a katun in length in any case. Conse- 
quently, each monument would have inscribed upon it only one or two 

1 There are, of course, a few exceptions to this rule— that is. there are some monuments which indicate 
an interval of more than 3,000 years between the extreme dates. In such cases, however, this interval is 
not divided into katuns, nor in fact into any regularly recurring smaller unit, with the single exception 
mentioned in footnote 1, p. 84. 



84 BUBEATJ OP AMERICAN ETHNOLOGY [bdll. 57 

katun ending days and the events which were connected more or less 
closely with it. In other words, the monuments were erected at short 
intervals ^ and probably recorded events contemporaneous with their 
erection, while the u kahlay katunob, on the other hand, were historical 
summaries reaching back to a remote time. The former were the peri- 
odicals of current events, the latter histories of the past. The former 
m the great majority of cases had no concern with the lapse of more 
than one or two katuns, while the latter measured centuries by the 
repetition of the same unit. The writer believes that from the very 
nature of the monuments — markers of current time — no u kahlay 
katunob will be found on them, but that the presence of the katun 
ending days above described indicates that the u kahlay katunob had 
been developed while the other system was still in use. If the fore- 
going be true, the signs in figure 38, a-h, would have this meaning: 
"On this day came to an end the katun in which fall the accompany- 
ing dates," or some similar significance. 

If we exclude the foregoing as indicating the u kahlay katunob, 
we have but one aboriginal source, that is one antedating the Spanish 
Conquest, which probably records a coxmt of this kind. It has been 
stated (p. 33) that the Codex Peresianus probably treats in part at 
least of historical matter. The basis for this assertion is that in this 
particular manuscript an u kahlay katimob is seemingly recorded; 
at least there is a sequence of the ending days of katuns shown, 
exactly like the one in Table IX, that is, 13 Ahau, 11 Ahau, 9 Ahau, etc. 

At the time of the Spanish Conquest the Long Count seems to 
have been recorded entirely by the ending days of its katuns, that is, 
by the u kahlay katunob, and the use of Initial-series dating seems 
to have been discontinued, and perhaps even forgotten. Native as 
well as Spanish authorities state that at the time of the Conquest the 
Maya measured time by the passage of the katuns, and no mention 
is mads of any system of dating which resembles in the least the 
Initial Series so prevalent in the southern and older cities. While the 
Spanish authorities do not mention the u kahlay katunob as do the 
native writers, they state very clearly that this was the system used in 
counting time. Says Bishop Landa (1864: p. 312) in this connection: 
"The Indians not only had a coimt by years and days . . . but they had 
a certain method of counting time and their affairs by ages, which they 
made from twenty to twenty years . . . these they call katimes." 
Cogolludo(1688:hb.iv, cap. v, p. 186) makes a similar statement: "They 
count their eras and ages, which they put in their books from twenty 
to twenty years . . . [these] they call katun." Indeed, there can 
be but little doubt that the u kahlay katimob had entirely replaced 
the Initial Series in recording the Long Coimt centuries before the 
Spanish Conquest; and if the latter method of dating were known 

• On one monument, the tablet from the Temple of the Inscriptions at Palenque, there seems to be 
recorded a kind of u kahlay katunob; at least, there is a sequence of ten consecutive katims. 



MOELEY] INTEODUCTION TO STUDY OF MAYA HIEEOGLYPHS 85 

at all, the knowledge of it came only from half-forgotten records the 
understanding of which was gradually passmg from the minds of men. 

It is clear from the foregoing that an important change in recording 
the passage of time took place sometime between the epoch of the 
great southern cities and the much later period when the northern cities 
flourished. In the former, time was reckoned and dates were recorded 
by Initial Series; in the latter, in so far as we can judge from post- 
Conquest sources, the u kahlay katunob and Calendar-round datiag 
were the only systems used. As to when this change took place, 
we are not entirely in the dark. It is certain that the use of the 
Initial Series extended to Yucatan, siace monuments presenting thip 
method of dating have been found at a few of the northern cities, 
namely, at Chichen Itza, Holactun, and Tiiluum. On the other 
hand, it is equally certain that Initial Series could not have been 
used very extensively ia the north, since they have been discovered 
in only these three cities in Yucatan up to the present time. More- 
over, the latest, that is, the most recent of these three, was probably 
contemporaneous with the rise of the Triple Alliance, a fairly early 
event of Northern Maya history. Taking these two points into con- 
sideration, the limited use of Initial Series in the north and the early 
dates recorded in the few Initial Series known, it seems likely that 
Initial-series dating did not long survive the transplanting of the 
Maya civilization in Yucatan. 

Why this change came about is uncertain. It could hardly have 
been due to the desire for greater acctiracy, since the u kahlay katunob 
was far less exact than Initial-series dating; not only cotild dates 
satisfying all given conditions recur much more frequently in the 
u kahlay katunob, but, as generally used, this method fixed a date 
merely as occurring somewhere within a period of about 20 years. 

The writer believes the change under consideration arose from a 
very different cause; that it was in fact the result of a tendency 
toward greater brevity, which was present in the glyphic writing 
from the very earliest times, and which is to be noted on some of the 
earliest monuments that have survived the ravages of the passing 
centuries. At first, when but a single date was recorded on a monu- 
ment, an Initial Series was used. Later, however, when the need or 
desire had arisen to inscribe more than one date on the same monument, 
additional dates were not expressed as Initial Series, each of which, 
as we have seen, involves the use of 8 glj^phs, but as a Secondary 
Series, which for the record of short periods necessitated the use of 
fewer glyphs than were employed in Initial Series. It would seem 
almost as though Secondary Series had been invented to avoid the 
use of Initial Series when more than one date had to be recorded on 
the same monument. But this tendency toward brevity in dating 
did not cease y^ih the invention of Secondary Series. Somewhat 
later, dating by period-endings was introduced, obviating the neces- 



86 BUEEAt: OF AMEBlCAN ETHNOLOGY [bdll. 57 

sity for the use of even one Initial Series on every monument, in 
order that one date might be fixed in the Long Coimt to which the 
others (Secondary Series) could be referred. For all practical pur- 
poses, as we have seen, Period-ending dating was as accurate as 
Initial-series dating for fixing dates in the Long Count, and its sub- 
stitution for Initial-series dating resulted in a further saving of 
glyphs and a corresponding economy of space. StiQ later, probably 
after the Maya had colonized Yucatan, the u kahlay katunob, which 
was a direct application of Period-ending dating to the Long Count, 
came into general use. At this time a rich history lay behind the 
Maya people, and to have recorded all of its events by their corre- 
sponding Initial Series would have been far too cumbersome a prac- 
tice. . The u kahlay katunob offered a convenient and facile method 
by means of which long stretches of time could be recorded and events 
approximately dated; that is, within 20 years. This, together with 
the fact that the practice of setting up dated period-markers seems to 
have languished in the north, thus eliminating the greatest medium 
of all for the presentation of Initial Series, probably gave rise to the 
change from the one method of recording time to the other. 

This concludes the discussion of the five methods by means of 
which the Maya reckoned time and recorded dates: (1) Initial-series 
dating; (2) Secondary-series dating; (3) Calendar-round dating; 
(4) Period-ending dating; (5) Katun-ending dating, or the u kahlay 
katunob. While apparently differing considerably from one another, 
in reality all are expressions of the same fundamental idea, the com- 
bination of the numbers 13 and 20 (that is, 260) with the solar year 
conceived as containing 365 days, and all were recorded by the same 
vigesimal system of numeration; that is: 

1. All used precisely the same dates, the 18,980 dates of the Cal- 
endar Round; 

2. All may be reduced to the same fundamental unit, the day; and 

3. All used the same time counters, those shown in Table VIII. 
In conclusion, the student is strongly urged constantly to bear in 

mind two vital characteristics of Maya chronology: 

1. The absolute continuity of all sequences which had to dp with 
the counting of time: The 13 numerical coefficients of the day names, 
the 20 day name's, the 260 days of the tonalamatl, the 365 positions 
of the haab, the 18,980 dates of the Calendar Round, and the kins, 
uinals, tuns, katuns, and cycles of the vigesimal system of numera- 
tion. When the conclusion of any one of these sequences had been 
reached, the sequence began anew without the interruption or omis- 
sion of a single unit and continued repeating itself for all time. 

2. All Maya periods expressed not current time, but passed time, 
as in the case of our hours, minutes, and seconds. 

On these two facts rests the whole Maya conception of time. 



Chapter IV 
MAYA ARITHMETIC 

The present chapter will be devoted to the consideration of Maya 
arithmetic in its relation to the calendar. It will be shown how the 
Maya expressed their numbers and how they used their several time 
periods. In short, their arithmetical processes will be explained, 
and the calculations resulting from their application to the calendar 
will be set forth. 

The Maya had two different ways of writing their numerals,^ namely : 
(1) With normal forms, and (2) with head variants ; that is, each of the 
numerals up to and including 19 had two distinct characters which stood 
for it, just as in the case of the time periods and more rarely, the days 
and months. The normal forms of the numerals may be compared to 
our Eoman figures, since they are built up by the combination of 
certain elements which had a fixed numerical value, like the letters 
I, V, X, L, C, D, and M, which in Roman notation stand for the 
values 1, 5, 10, 50, 100, 500, and 1,000, respectively. The head- 
variant numerals, on the other hand, more closely resemble our 
Arabic figures, since there was a special head form for each nimaber 
up to and including 13, just as there are special characters for the 
first nine figures and zero in Arabic notation. Moreover, this 
parallel between our Arabic figures and the Maya head-variant nu- 
merals extends to the formation of the higher numbers. Thus, the 
Maya formed the head-variant numerals for 14, 15, 16, 17, 18, apd 
19 by applying the essential characteristic of the head variant for 10 
to the head variants for 4, 5, 6, 7, 8, and 9, respectively, just as the 
sign for 10 — that is, one in the tens place and zero in the units place — 
is used in connection with the signs for the first nine figures in Arabic 
notation to form the numbers 11 to 19, inclusive. Both of these 
notations occur in the inscriptions, but with very few exceptions ^ no 
head-variant numerals have yet been found in the codices. 

Bar and Dot Numerals 

The Maya "Roman numerals " — that is, the normal-form numerals, 
up to and including 19 — ^were expressed by varying combinations of 
two elements, the dot (•), which represented the numeral, or numeri- 
cal value, 1, and the bar, or line (HIHHi), which represented the nu- 
meral, or numerical value, 5. By various combinations of these two 

' The word "numeral," as used here, has been restricted to the first twenty numbers, to 19, inclu- 
sire. 
« See p. 96, footnote 1. 

87 



•• • • • •• •• •• 



• • • 



88 BUBBAIT OF AMERICAN ETHNOLOGY [bull. 57 

elements alone the Maya expressed all the numerals from 1 to 19, in- 
clusive. The norrnal forms of the numerals in the codices are shown 
in figure 39, in which one dot stands for 1, two dots for 2, three dots 
for 3, four dots for 4, one bar for 5, one bar and one dot for 6, one bar 
and two dots for 7, one bar and three dots for 8, one bar and four dots 
for 9, two bars for 10, and so on up to three bars and four dots for 19. 
The normal forms of the numerals in the inscriptions (see fig. 40) are 
identical with those in the codices, excepting that they are more elabo- 
rate, the dots and bars both taking on various decorations. Some of 
the former contain a concentric circle (*) or cross-hatch- 
® O) ® ^^S (**) ; some appear as crescents (f ) or v°> CnJ vQ) 
** n t curls (ff), more rarely as (J) or (J J). The bars * t « 
show even a greater variety of treatment (see fig. 41) . All these deco- 
rations, however, in 
no way affect the 
numerical value of 
the bar and the 
dot, which remain 5 
and 1, respectively, 
throughout the 
Maya writing. Such 
embellishments as 
those just described 
are found only in 

Fig. 39. Normal forms of numerals 1 to 19, inclusive, in the codices. the inscriptions, and 

their use was proba- 
bly due to the desire to make the bar and dot serve a decorative 
as well as a numerical function. 

An important exception to this statement should be noted here in 
connection with the normal forms for the numbers 1, 2, 6, 7, 11, 12, 
16, and 17, that is, all which involve the use of one or two dots in their 
composition.' In the inscriptions, as we have seen in Chapter II, 
every glyph was a balanced picture, exactly fitting its allotted space, 
even at the cost of occasionally losing some of its elements. To have 
expressed the numbers 1, 2, 6, 7, 11, 12, 16, and 17 as in the codices, 
with just the proper number of bars and dots in each case, would 
have left unsightly gaps in the outhnes of the glyph blocks (see fig. 
42, a^h, where these numbers are shown as the coefficients of the katun 
sign). In a, c, e, and g of the same figure (the numbers 1, 6, 11, and 
16, respectively) the single dot does not fill the space on the left- 
hand ^ side of the bar, or bars, as the case may be, and consequently 

■ In one case, on the west side of Stela E at Quirigua, the number 14 is also shown with an orna- 
mental elem3nt (*). This is very unusual and, so far as the writer knows, is the only example of 
its kind. The four dots in the numbers 4, 9, 14, and 19 never appear thus separated in any other 
text known. 
2In the examples given the numerical coefficients are attached as prefixes to the katun sign. Fre- 
quently, however, they occur as superfixes. In such cases, however, the above observations apply equally 
well. 



MORLBY] INTEODUCTION TO STUDY OP MAYA HIEEOGLYFHS 



89 



the left-hand edge of the glyph block in each case is ragged. Simi- 
larly in 6, d,f, and h, the numbers 2, 7, 12, and 17, respectively, the 
two dots at the left of the bar or bars are too far apart to fill in the 



o . © 

ONE 



®© OO ©©© GOO 

TWO THREE 



©©©© OOOO c 



FOUR 



3 e 



FIVE 



< S)oga 



SIX 



I 



SEVEN 



NINE 



ELEVEN 



c 
c 



O IM 1> 



I 



I 



EIGHT 



TEN 



TWELVE 



I 



THIRTEEN 



FOURTEEN 



FIFTEEN 



SIXTEEN SEVENTEEN EIGHTEEN NINETEEN 

Fig. 40. Normal forms of numerals 1 to 19, inclusive, in the inscriptions. 

left-hand edge of the glyph blocks neatly, and consequently in these 
cases also the left edge is ragged. The Maya were quick to note this 
discordant note in glyph design, and in the great majority of the 



f 



^ 



(r\ 




Fig. 41. Examples of bar and dot nxuneral 5, showing the ornamentation which the bar underwent 
without affecting its numerical value. 

places where these numbers (1, 2, 6, 7, 11, 12, 16, and 17) had to be 
recorded, other elements of a purely ornamental character were 
introduced to fill the empty spaces. In figure 43, a, c, e, g, the spaces 
on each side of the single dot have been filled with ornamental cres- 



% 



BtrREAtJ Of AMERICAN BTHNCLOGY 



[bcll. 37 



cents about the size of the dot, and these give the glyph in each case a 
final touch of balance and harmony, which is lacking without them. 
In b, d, f, and Ji of the same figure a single crescent stands between 
the two numerical dots, and this again harmoniously fills in the 




Fig. 42. Examples showing tlie way in which the numerals 1, 2, 6, 7, 11, 12, 16, and 17 are not used with 

period, day, or month signs. 

glyph block. While the crescent (*) is the usual form taken ^ <^ 
by this purely decorative element, crossed lines (**) are * ** 
B £2 1^ f ^0"^<J ^ places, as in (f) ; or, again, a pair of dotted 
f tt f elements (ff), as in (J). These variants, however, are 
of rare, occurrence, the common form being the crescent shown in 
figure 43. 




Pig. 43. Examples showing the way in which the numerals 1, 2, 6, 7, 11, 12, 16, and 17 are used with period, 
day, or month signs. Note the filling of the otherwise vacant spaces with ornamental elements. 

The use of these purely ornamental elements, to fill the empty 
spaces in the normal forms of the numerals 1, 2, 6, 7, 11, 12, 16, and 
17, is a fruitful source of error to the student of the inscriptions. 
Slight weathering of an inscription is often sufficient to make orna- 
mental crescents look exactly like numerical dots, and consequently 
the numerals 1, 2, 3 are frequently mistaken for one another, as are 
also 6, 7, and 8; 11, 12, and 13; and 16, 17, and 18. The student 
must exercise the greatest caution at aU times in identifying these 



MohLby] lUrTEODUCTION TO STUDY OF MAYA HtEEOGLYPHS 91 

numerals in the inscriptions, or otherwise he will quickly find himself 
involved in a tangle from which there seems to be no egress. Proba- 
bly more errors in reading the inscriptions have been made 

through the incorrect identification of these numerals than ■ 

through any other one cause, and the student is urged ■ ■ 

to be continually on his guard if he would avoid making ■ ■ ■ 

this capital blunder. ■ ■ ■ ■ 

Although the early Spanish authorities make no mention 

of the fact that the Maya expressed their numbers by bars 

and dots, native testimony is not lacking on this point. 

Doctor Brinton (1882 b : p. 48) gives this extract, accom- " * 

panied by the drawing shown in figure 44, from a native ■ ■ ■ 

writer of the eighteenth century who clearly describes this ^^ ^^ 

system of writing numbers : 

They [our ancestors] used [for numerals in their calendars] dots and 

lines [i. e., bars] back of them; one dot for one year, two dots for two ■ 

years, three dots for three years, four dots for four, and so on; in ad- 

dition to these they used a hne; one line meant five years, two lines * * 

meant ten years; if one line and above it one dot, six years; it two ■ ■ ■ 

dots above the line, seven years; if three dots above, eight years; if : 

four dots above the line, nine; a dot above two lines, eleven; if two Fig.44. Nor- 

dots, twelve; if three dots, thirteen. mal forms 

This description is so clear, and the values therein as- i to is, in- 
signed to the several combinations of bars and dots have thT'soofa 
been verified so extensively throughout both the inscrip- of chiian 
tions and the codices, that we are justified in identifying s*'™- 
the bar and dot as the signs for five and one, respectively, wherever 
they occur, whether they are found by themselves or in varying 
combinations. 

In the codices, as will appear in Chapter VI, the bar and dot 
numerals were painted in two colors, black and red. These colors 
were used to distinguish one set of numerals from another, each of 
which has a different use. In such cases, however, bars of one color 
are never used with dots of the other color, each number being either 
all red or all black (see p. 93, footnote 1, for the single exception to 
this rule). 

By the development of a special character to represent the number 
5 the Maya had far surpassed the Aztec in the science of mathematics; 
indeed, the latter seem to have had but one numerical sign, the dot, 
and they were obliged to resort to the clumsy makeshift of repeating 
this in order to represent all numbers above 1. It is clearly seen 
that such a system of notation has very definite limitations, which 
must have seriously retarded mathematical progress among the Aztec. 

In the Maya system of numeration, which was vigesimal, there was 
no need for a special character to represent the number 20,' because 

I Care should be taken to distinguish the number oi- figure 20 from any period which contained 20 periods 
of the order next below it; otherwise the uinal, katun, and cycle glyphs could all be construed as signs 
for 20, since each of these periods contains 20 units of the period next lower. 



02 



BtiKBAtr 01* amemcan ethnology 



[boll. 57 



(1) as we have seen in Table VIII, 20 units of any order (except the 
2d, in which only 18 were required) were equal to 1 unit of the order 
next higher, and consequently 20 could not be attached to any period 
glyph, since this number of periods (with the above exception) was 






FiQ. 45. Sign for 20 in the codices. 

always recorded as 1 period of the order next higher; and (2) although 
there were 20 positions in each period except the uinal, as 20 kins in 
each uinal, 20 tuns in each katun, 20 katuns in each cycle, these posi- 
tions were numbered not from 1 to 20, but on the contrary from to 
19, a system which eliminated the need for a character expressing 20. 

In spite of the foregoing 
fact, however, the number 
20 has been found in the 
codices (see fig. 45) . A pe- 
culiar condition there, how- 
ever, accounts satisfactorily 
for its presence. In the cod- 
ices the sign for 20 occurs 
only in connection with to- 
nalamatls, which, as we 
shall see later, were usually 
portrayed in such a manner 
that the numbers of which 
they were composed could 
not be presented from bot- 
tom to top in the usual 
way, but had to be written horizontally from left to right. This 
destroyed the possibility of numeration by position,^ according to 
the Maya point of view, and consequently some sign was necessary 
which should stand for 20 regardless of its position or relation to 
others. The sign shown in figure 45 was used for this pin-pose. It 
has not yet been found in the inscriptions, perhaps because, as was 
pointed out in Chapter II, the inscriptions generally do not appear 
to treat of tonalamatls. 

If the Maya numerical system had no vital need for a character to 
express the number 20, a sign to represent zero was absolutely indis- 






FiG. 46. Sign tor in the codices. 



1 The Maya numbered by relative position from bottom to top, as will be presently explained. 



MOKLEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



93 





Fig. 47. Sign for in tlie inscriptions. 



pensable. Indeed, any numerical system which rises to a second 
order of units requires a character which will signify, when the need 
arises, that no units of a certain order are involved; as zero imits and 
zero tens, for example, in writing 100 in our own Arabic notation. 

The character zero seems to have played an important part in Maya 
calculations, and signs for it have been found in both the codices and 
the inscriptions. The form found in the codices (fig. 46) is lenticu- 
lar; it presents an interior dec- 
oration which does not follow 
any fixed scheme.' Only a 
very few variants occur. The 
last one in figure 46 has clearly 
as one of its elements the nor- 
mal form (lenticular). The 
remaining two are different. 
It is noteworthy, however, 
that these last three forms aU 
stand in the 2d, or uinal, place 
in the texts in which they occur, though whether this fact has 
influenced their variation is unknown. 

Both normal forms and head variants for zero, as indeed for all 
the numbers, have been found in the inscriptions. The normal 
forms for zero are shown in figure 47. They are common and are 
unmistakable. An interesting origin for this sign has been suggested 

by Mr. A. P. Maudslay. On _ 

pages 75 and 76 of the Co- :"••.''•., .•■'.••■,■ "•.'■•'•■. 

dex Tro-Cortesiano^ the 260 
days of a tonalamatl are 
graphically represented as 
for min g the outline shown 
in figure 48, a. Half of this 
(see fig. 48, 6) is the sign 
which stands for zero (com- 
pare with fig. 47). The train 
of association by which half 
of the graphic representa- 
tion of a tonalamatl could 
come to stand for zero is 
not clear. Perhaps a of figure 48 may have signified that a complete 
tonalamatl had passed with no additional days. From this the sign 
may have come to represent the idea of completeness as apart from 
the tonalamatl, and finally the general idea of completeness applica- 

1 This form of zero is always red and is used witli black bar and dot numerals as well as with red in the 
codices. 

^ It is interesting to note in this connection that the Zapotec made use of the same outline in graphic 
representations of the tonalamatl. On page 1 of the Zapotec Codex F^jerv4ry-Mayer an outline formed 
by the 260 days of the tonalamatl exactly like the one in fig. 48, a, is shown. 



■■■••••■-•;/r 




Fig. 48. Figure showing possible derivation of tlie sign for 
in the inscriptions : a, Outline of the days of the tonalamatl as 
represented graphically in the Codex Tro-Cortesiano; 6, half 
of same outline, which is also sign for Oshown in fig. 47. 






94 BXJREATJ OF AMEEICAN ETHNOLOGY [bull. 57 

ble to any period; for no period could be exactly complete without a 
fractional remainder unless all the lower periods were wanting; that 
is, represented by zero. Whether this explains the connection be- 
tween the outline of the tonalamatl and the zero sign, or whether 
indeed there be any connection between the two, is of course a 
matter of conjecture. 

There is still one more normal form for zero not included in the 
examples given above, which must be described. This form (fig. 49), 
which occurs throughout the inscriptions and in the Dresden Codex,' 
is chiefly interesting because of its highly specialized function. 
Indeed, it was iised for one purpose only, namely, to express the 
first, or zero, position in each of the 19 divisions of the haab, or year, 
and for no other. In other words, it denotes the positions Pop, 
Uo, Zip, etc., which, as we have seen (pp. 47, 48), corresponded 

with our firsfcvdays of the months. 
iT^ \^ Cn^S. /^^P '^^^ forms shown in figure 49, a-e, 
{U \(^ \'iSy ff^S ; are from the inscriptions and those 

in f-h from the Dresden Codex. 
They are all similar. The general 
outhne of the sign has suggested 
the name "the spectacle" glyph. 
Its essential characteristic seems 
to be the division into two roughly 
circular parts, one above the 
other, best seen in the Dresden 
Codex forms (fig. 49, f-h) and a 

FIG. 49. Special sign for used exclusively aa a j-q^Mj circular infix in Cach. 
montli coefficient. . 

The lower infix is quite regular 
in all of the forms, being a circle or ring. The upper infix, however, 
varies considerably. In figure 49, a, h, this ring has degenerated into 
a loop. In c and d of the same figure it has become elaborated into 
a head. A simpler form is that in / and g. Although comparatively 
rare, this glyph is so unusual in form that it can be readily recognized. 
Moreover, if the student will bear ia mind the two following points 
concerning its use,_ he will never fail to identify it in the inscriptions : 
The "spectacle" sign (1) can be attached only to the glyphs for the 
19 divisions of the haab, or year, that is, the 18 uinals and the xma 
kaba kin; in other words, it is found only with the glyphs shown in 
figures 19 and 20, the signs for the months in the inscriptions and 
codices, respectively. 

(2) It can occur only in connection with one of the four day-signs, 
Ik, Manik, Eb, and Caban (see figs. 16, c, j, s, t, u, a', b', and 17, c, d, Jc, 
r, X, y, respectively), since these four alone, as appears in Table VII, 
can occupy the (zero) positions in the several divisions of the haab. 

1 This form of zero has been found only in the Dresden Codex, Its absence from the other two codices 
is doubtless due to the fact that the month glyphs are recorded only a very few times in them— but once in 
the Codex Tro-Cortesiano and tliree times in the Codex Peresianus. 




MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



95 



Examples of the normal-form numerals as used with the day, 
month, and period glyphs in both the inscriptions and the codices 
are shown in figure 50. Under each is given its meaning in English.' 




13 Manik 5 Lamat 



2 Cib 



12 Caban 



5 Caban 



5 Eznab 




CycL 9 Cycle 9 



Katun 8 



Katun 3 



Tun 5 



Tun 1 




Uinal 1 



Kin4 



Kin 8 




KinO 



Fig. 50. Example&.of tlie use of bar and dot numerals with period, day, or month signs. The translation 
of each glyph appears below it. 

The student is advised to familiarize himself with these forms, since 
on his abihty to recognize them will largely depend his progress in 
reading the inscriptions. This figure illustrates the use of all the 
foregoing forms except the sign for 20 in figure 45 and the sign for 
zero in figure 46. As these two forms never occur with day, month, 
or period glyphs, and as they have been found only in the codices, 
examples showing their use will not be given imtil Chapter VI is 
reached, which treats of the codices exclusively. 

1 The forms shown attached to these numerals are those of the day and month signs (see figs. 16, 17, and 
19, 20, respectively), and of the period glyphs (see figs. 25-35, inclusive). Reference to these figures will 
explain the English translation in the case of any form which the student may not remember. 



96 BUEEATJ OF AMERICAST ETHNOLOGY [bull. 57 

Head-variant Numerals 

Let us next turn to the consideration of the Maya "Arabic nota- 
tion," that is, the head-variant numerals, which, Hke all other known 
head variants, are practically restricted to the ioscriptions.* It 
should be noted here before proceeding further that the fuU-figure 
numerals found in connection with full-figure period, day, and month 
glyphs ia a few inscriptions, have been classified with the head- 
variant numerals. As explained on page 67, the body-parts of such 
glyphs have no fxmction in determining their meanings, and it is only 
the head-parts which present in each case the determining character- 
istics of the form intended. 

In the "head" notation each of the numerals, 0, 1, 2, 3, 4, 5, 6, 7, 8, 
9, 10, 11, 12, 13^ is expressed by a distinctive type of head; each 
type has its own essential characteristic, by means of which it can 
be distinguished from all of the others. Above 13 and up to but not 
including 20, the head numerals are expressed by the apphcation of 
the essential characteristic of the head for 10 to the heads for 3 to 9, 
inclusive. No head forms for the niimeral 20 have yet been dis- 
covered. 

The identification of these head-variant numerals in some cases is 
not an easy matter, since their determining characteristics are not 
always presented clearly. Moreover, in the case of a few numerals, 
notably the heads for 2, 11, and 12, the essential elements have not 
yet been determined. Head forms for these numerals occur so rarely 
in the inscriptions that the comparative data are insufficient to 
enable us to fix on any particular element as the essential one. 
Another difficulty encountered in the identffication of head-variant 
numerals is the app?irent irregularity of the forms in the earlier 
inscriptions. The essential elements of these early head numerals 
in some cases, seem to differ widely from those of the later forms, 
and consequently it is sometimes difficult, indeed even impossible, to 
determine their corresponding numerical values. 

1 The following possible exceptions, however, should be noted: In the Codex Peresianus the f~gm^ 
normal form of the tun sign sometimes occurs attached to varying heads, as (*). Whether these ^^|^£g 
heads denote numerals is unknowB, but the construction of this glyph in such cases (a head ^"^^ 
attached to the sign of a time period) absolutely parallels the use of head-variant numerals with 
time-period glyphs in the inscriptions. A much stronger example of the possible use of head numerals with 

^^ period glyphs in the codices, however, is found in the Dresden Codex. Here the accompanying 
1^^ head (f) is almost surely that for the number 16, the hatchet eye denoting 6 and the fleshless lower 
^^^ jaw 10. Compare (t) with flg. 53, /-!, where the head for 16 is shown. The glyph (J) here ,_.^_^ 
T shown is the normal form for the kin sign. Compare flg. 34, b. The meaning of these two JfiSt 
forms would thus seem to be 16 kins. In the passage in which these glyphs occur the glyph 1*-'^' 
next preceding the head for 16 is "8 tuns," the numerical coefHcient 8 being expressed by one * 
bar and three dots. It seems reasonably clear here, therefore, that the form in question is a head 
numeral. However, these cases are so very rare and the context where they occur is so little understood, 
that they have been excluded in t;he general consideration of head-variant numerals presented above. 

2 It will appear presently that the number 13 could be expressed in two different ways: (1) by a 
special head meaning 13, and (2) by the essential characteristic of the head for 10 applied to the head 
fora(i.e., 10-1-3=13), 



MORLBY] INTEODUCTION TO STUDY OF MAYA HIEKOGLYPHS 



97 



The head-variant numerals are shown in figures 51-53. Taking 
these up in their numerical order, let us commence with the head 
signifjTing 1 ; see figure 51, a-e. The essential element of this head is 






s>o 







FOUR 




Fig. 51. Head-variant numerals 1 to 7, inclusive. 

its forehead ornament, which, to signify the number 1, must be ^^.^ 
j^ composed of more than one part (*),in order to distinguish it ^ 
W from the forehead ornament (**), which, as we shall see pres- 
ently, is the essential element of the head for 8 (fig. 52, a-f). 
Except for their forehead ornaments the heads for 1 and 8 are 
almost identical, and great care must be exercised in order to avoid 
mistaking one for the other. 
43508°— Bull. 57—15 7 



98 



BTJBEAU OF AMEBICAN ETHNOLOGY 



[BDLL. 57 



The head for 2 (fig. 51,/, g) has been found only twice in the inscrip- 
tions — on Lintel 2 at Piedras Negras and on the tablet in the Temple 
of the Initial Series at Holactun. The oval at the top of the head 
seems to be the only element these two forms have in common, and 
the writer therefore accepts this element as the essential character- 







NINE 






o p 

TEN 




ELEVEN 





X 

THIRTEEN 
Fig. 52. Head-variant numerals 8 to 13, inclusive. 

is tic of the head for 2, admitting at the same time that the evidence 
is insufficient. 

The head for 3 is shown in figure 51, Ti, i. Its determining charac- 
teristic is the fillet, or headdress. 

The head for 4 is shown in figure 51, j-m. It is to be distin- 

^ guished by its large prominent eye and square irid (*) (probably 

* eroded in Z), the snaghke front tooth, and the curling fang 

Ta^ protruding from the back part of the mouth (**) (wanting in 

** I and m). 



MOELEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



99 



The head for 5 (fig. 51, ji^s) is always to be identified by its 
pecuHar headdress (f), which is the normal form of the tun /^M\ 
sign. Compare figure 29, a, 6. The same element appears t 
also in the head for 15 (see fig. 53, h-e). The head for 5 is one 
of the most constant of all the head numerals. 




FOURTEEN 





FIFTEEN 






g h 

SIXTEEN 





k I 

SEVENTEEN 






p 

EIGHTEEN 





NINETEEN 







Fig. 53. Head-variant numerals 14 to 19, inclusive, and 0. 

The head for 6 (fig. 51, t-^) is similarly unmistakable. It is always 
characterized by the so-called hatchet eye (ff ), which appears ^ 
also in the head for 16 (fig. 53, f-4). tt 

The head for 7 (fig. 51, w) is found only once in the inscriptions — 
on the east side of Stela D at Quirigua. Its essential characteristic, 



100 BTJEEAU OF AMERICAN ETHNOLOGY [bull. 57 

the large ornamental scroll passing under the eye and curling up in 
•^jQ^ front of the forehead (J), is better seen in the head for 17 
X (fig. 53, j'-m). 

The head for 8 is shown in figure 52, or-f. It is very similar to the 
head for 1, as previously explained (compare figs. 51, a-e and 52, a-f), 
and is to be distinguished from it only by the character of the fore- 
head ornament, which is composed of but a single element (J J). ^ 
In figure 52, a, b, this takes the form of a large curl. In c of the « 
same figure a flaring element is added above the curl and in d and e 
this element replaces the curl. In / the tongue or tooth of a gro- 
tesque animal head forms the forehead ornament. The heads for 18 
(fig. 53, n-q) foUow the first variants (fig. 51, a, h), having the large 
curl, except g, which is similar to din having a flaring element instead. 

The head for 9 occurs more frequently than all of the others with 
the exception of the zero head, because the great majority of aU 
Initial Series record dates which fell after the completion of Cycle 9, 
but before the completion of Cycle 10. Consequently, 9 is the coeffi- 
cient attached to the cycle glyph in almost all Initial Series.^ The 
head for 9 is shown in figure 52, g-l. It has for its essential charac- 
teristic the dots on the lower cheek or around the mouth (*). "y^. 
Sometimes these occur in a circle or again irregularly. Occa- * 
sionally, as in j-l, the 9 head has a beard, though this is not a con- 
stant element as are the dots, which appear also in the head for 19. 
Compare figure 53, r. 

The head for 10 (fig. 52, m-?") is extremely important since its 
essential element, the fleshless lower jaw (*), stands for the ,^g 
numerical value 10, in composition with the heads for 3, 4, 5, * 
6, 7, 8, and 9, to form the heads for 13, 14, 15, 16, 17, 18, and 19, 
respectively. The 10 head is clearly the fleshless skuU, having the 
truncated nose and fleshless jaws (see fig. 52, m-p). The fleshless 
lower jaw is shown in profile in all cases but one — ^Zoomorph B at 
Quirigua (see r of the same figure). Here a full front view of a 10 
head is shown in which the fleshless jaw extends clear across the 
lower part of the head, an interesting confirmation of the fact that 
this characteristic is the essential element of the head for 10. 

The head for 11 (flg. 52, s) has been found only once in the inscrip- 
tions, namely, on Lintel 2 at Piedras Negras; hence comparative 
data are lacking for the determination of its essential element. This 
head has no fleshless lower jaw and consequently would seem, there- 
fore, not to be built up of the heads for 1 and 10. 

Similarly, the head for 12 (fig. 52, t-v) has no fleshless lower jaw, and 
consequently can not be composed of the heads for 10 and 2. It is to 
be noted, however, that all three of the faces are of the same type, 
even though their essential characteristic has not yet been determined. 

1 For the discussion of Initial Series in cycles other than Cycle 9, see pp. 194-207. 



MOELBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 101 

The head for 13 is shown in figure 52, w-b'. Only the first of these 
forms, w, however, is built on the 10 + 3 basis. Here we see the char- 
acteristic 3 head with its banded headdress or fillet (compare h and 
i, fig. 51), to which has been added the essential element of the 10 
head, the fleshless lower jaw, the combination of the two giving the 
head for 13. The other form for 13 seems to be a special character, 
and not a composition of the essential elements of the heads for 3 and 
10, as in the preceding example. This form of the 13 head (fig. 52, 
x—V) is grotesque. It seems to be characterized by its long pendulous 
nose surmounted by a curl (*), its large bulging eye (**), and f2 -^ 
^ ;^ a curl (t) or fang (ft) protruding from the back part * ** 
t tt of the mouth. Occurrences of the first type — the composite 
head — are very rare, there being only two examples of this kind 
known in all the inscriptions. The form given in w is from the Temple 
of the Cross at Palenque, and the other is on the Hieroglyphic Stair- 
way at Copan. The individual type, having the pendulous nose, 
bulging eye, and mouth curl is by far the more frequent. 

The head for 14 (fig. 53, a) is found but once — in the inscriptions on 
the west side of Stela F at Quirigua. It has the fieshless lower jaw 
denoting 10, while the rest of the head shows the characteristics of 
4 — the bulging eye and snaglike tooth (compare fig. 51, j'-m). The 
curl protruding from the back part of the mouth is wanting because 
the whole lower part of the 4 head has been replaced by the fleshless 
lower jaw. 

The head for 15 (fig. 53, 6-e) is composed of the essential element of 
the 5 head (the tun sign; see fig. 51, n-s) and the fleshless lower jaw 
of the head for 10. 

The head for 16 (fig. 53,/-^) is characterized by the fieshless lower 
jaw and the hatchet eye of the 6 head. Compare figures 51, t-v, and 
52, m-r, which together form 16 (10 + 6). 

The head for 17 (fig. 53, j-m) is composed of the essential element 
of the 7 head (the scroll projecting above the nose; see fig. 51, w) and 
the fieshless lower jaw of the head for 10. 

The head for 18 (fig. 53, n-q) has the characteristic forehead 
ornament of the 8 head (compare fig. 52, a-f) and the fleshless lower 
jaw denoting 10. 

Only one example (fig. 53, r) of the 19 head has been found in the 
inscriptions. This occurs on the Temple of the Cross at Palenque 
and seems to be formed regularly, both the dots of the 9 head and the 
fleshless lower jaw of the 10 head appearing. 

The head for (zero), figure 53, s-w, is always to be distinguished by 
the hand clasping the lower part of the face (*). In this sign ^^ 
for zero, the hand probably represents the idea "ending" or * 
"closing," just as it seems to have done iii the ending signs used with 



102 ETJEEAU OF AMERICAN ETHNOLOGY [bull. 57 

Period-ending dates. According to the Maya conception of time, 
when a period had ended or closed it was at zero, or at least no new 
period had commenced. Indeed, the normal form for zero in figure 
47, the head variant for zero in figure 53, s-w, and the form for zero 
shown in figure 54 are used interchangeably in the same inscription 
to express the same idea — namely, that no periods thus modified are 
involved in the calculations and that consequently the end of some 
higher period is recorded; that is, no fractional parts of it are present. 
That the hand in "ending signs" had exactly the same meaning 
as the hand in the head variants for zero (fig. 53, s^w) receives striking 
corroboration from the rather unusual sign for zero shown in figure 
54, to which attention was called above. The essential elements of 







Fig. 54. A sign for 0, used also to express the idea "ending" or "end of" in 
Period-ending dates. (See figs. 47 and 53 s-w, tor forms used Interchangeably 
in the inscriptions to express the idea of or of completion.) 

this sign are' (1) the clasped hand, identical with the hand in the 
head-variant forms for zero, and (2) the large element above it, con- 
taining a curling infix. This latter element also occurs though below 
the clasped hand, in the "ending signs" shown in figure 37, Z, m, n, 
the first two of which accompany the closing date of Katun 14, and 
the last the closing date of Cycle 13. The resemblance of these three 
" ending signs" to the last three forms in figure 54 is so close that the 
conclusion is well-nigh inevitable that they represented one and the 
same idea. The writer is of the opinion that this meaning of the 
hand (ending or completion) will be found to explain its use through- 
out the inscriptions. 

In order to f amiharize the student with the head-variant numerals, 
their several essential characteristics have been gathered together in 
Table X, where they may be readily consulted. Examples covering 
their use with period, day, and month gljrphs are given in figure 55 
with the corresponding English translations below. 

Head-variant numerals do not occur as frequently as the bar and 
dot forms, and they seem to have been developed at a much later 
period. At least, the earliest Initial Series recorded with bar and dot 
numerals antedates by nearly two hundred years the earhest Initial 
Series the numbers of which are expressed by head variants. This 
long priority in the use of the former would doubtless be considerably 
diminished if it were possible to read the earliest Initial Series which 

> The subflxial element in the first three forms of fig. 64 does not seem to be essential, since it is wanting 
in the last. 



MOBLEy] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 



103 



have head-variant numerals; but that 'the earliest of these latter 
antedate the earliest bar and dot Initial Series may well be doubted. 

Table X. CHARACTERISTICS OF HEAD-VARIANT NUMERALS TO 19, 

INCLUSIVE 



Forms 


Characteristics 


Head for 


Clasped hand across lower part of face. 


Head tor 1 


Forehead ornament composed of more than one part. 


Head for 2 


Oval in upper part of head. (?) 


Head for 3 


Banded headdress or fillet. 


Head for 4 


Bulging eye with square hid, snaglilce front tooth, curlmg fang from backofmouth. 


Head for 5 


Normal form of tun sign as headdress. 


Head for 6 


"Hatchet eye." 


Head for 7 


Large scroll passing under eye and curling up in front of forehead. 


Head for 8 


Forehead ornament composed of one part. 


Head for 9 


Dots on lower cheek or around mouth and ia some cases beard. 


Head for 10 


Fleshless lower jaw and in some cases other death's-head characteristics, trun- 




cated nose, etc. 


Head for 11 


Undetermined. 


Head for 12 


Undetermined; type ot head known, however. 


Head for 13 


(o) Long pendulous nose, bulging eye, and curling fang from back of mouth. 




(6) Head for 3 with fieshless lower jaw of head for 10. 


Head for 14 


Head for 4 with fleshless lower jaw of head for 10. 


Head for 15 


Head for 6 with fleshless lower jaw of head for 10. 


Head for 16 


Head for 6 with fleshless lower jaw of head for 10. 


Head for 17 


Head for 7 with fleshless lower jaw of head for 10. 


Head for 18 


Head tor 8 with fleshless lower jaw ot head for 10. 


Head tor 19 


Head for 9 with fleshless lower jaw ot head tor 10. 



Mention should be made here of a numerical form which can not 
be classified either as a bar and dot numeral or a head variant. 
This is the thumb (*), which has a numerical value of one. 

We have seen in the foregoing pages the different characters which 
stood for the numerals to 19, inclusive. The next point claiming 
our attention is, how were the higher numbers written, numbers 
which in the codices are in excess of 12,000,000, and in the inscrip- 
tions, in excess of 1,400,000? In short, how were numbers so large 
expressed by the foregoing twenty (0 to 19, inclusive) characters? 

The Maya expressed their higher numbers in two ways, in both of 
which the numbers rise by successive terms of the same vigesimal 
system : 

1. By using the numbers to 19, inclusive, as multiphers with the 
several periods of Table VIII (reduced in each case to units of the 
lowest order) as the multiplicands, and — 

2. By using the same numbers' in certain relative positions, each of 
which had a fixed numerical value of its own, hke the positions to the 
right and left of the decimal point in our own numerical notation. 

1 As previously explained, the number 20 is used only in the codices and there only in connection with 
tonalamatls. 



104 



BUREAU OF AMERICAN ETHNOLOGY 



[BULL. 57 



The first of thege methods is rarely found outside of the inscriptions, 
while the second is confined exclusively to the codices. Moreover, 
although the first made use of both normal-form and head-variant 




1 Ahau 





Cycle 1 



6 Ahau 




Katun 8 



Cycle 9 




Katun 9 




Ulna! 4 




8 Ahau 





Katun 14 



Tun 15 




Tun 13 




Kin 16 




13 Pop 




Katun 17 




ISTzec 




Katun 19 




Kin O 




Cycle 1 



Fig. 55. Examples of the use of head-variant numerals with period, day, or month signs. The translation 

of each glyph appears below it. 

numerals, the second could be expressed by normal forms only, that 
is, bar and dot numerals. This enables us to draw a comparison 
between these two forms of Maya numerals : 

Head-variant numerals never occur independently, but are always 
prefixed to some period, day, or month sign. Bar and dot numerals, 
on the other hand, frequently stand by themselves in the codices 
unattached to other signs. In such cases, however, some sign was 
to be supphed mentally with the bar and dot numeral. 



moelby] introduction to study of maya hieeoglyphs 
First Method of Numeration 



105 



111 the first of the above methods the numbers to 19, inclusive, 
were expressed by multiplying the kin sign by the numerals ' to 19 




m n o p q 

Fig. 56. Examples of the first method of numeration, used almost exclusively in the inscriptions. 

in turn. Thus, for example, 6 days was written as shown in figure 
56, a, 12 days as shown in I, and 17 days as shown in c of the same 

1 Whether the Maya used their numerical system in the inscriptions and codices for counting anything 
besides time is not known. As used in the texts, the numbers occur only in connection with calendric 
matters, at least in so far as they have been deciphered. It is true many numbers are found in both the 
inscriptions and codices which are attached to signs of unknown meaning, and it is possible that these 
may have nothing to do with the calendar. An enumeration of cities or towns, or of tribute rolls, for 
example, may be recorded in some of these places. Both of these subjects are treated of in the Aztec 
manuscripts and may well be present in Maya texts. 



106 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

figure. In other words, up to and including 19 the numbers were ex- 
pressed by prefixing the sign for the number desired to the kin sign, 
that is, the sign for 1 day.* 

The numbers 20 to 359, inclusive, were expressed by multiplying 
both the kin and uinal signs by the numerical forms to 19, and adding 
together the resulting products. For example, the number 257 was 
written as shown in figure 56, d. We have seen in Table VIII that 1 
uinal = 20 kins, consequently 12 uinals (the 12 being indicated by 2 bars 
and 2 dots) = 240 kins. However, as this number falls short of 257 by 
17 kins, it is necessary to express these by 17 kins, which are written 
immediately below the 1 2 uinals . The sum of these two products = 257 . 
Again, the number 300 is written as in figure 56, e. The 15 uinals 
(three bars attatihed to the uinal sign) = 15X20 = 300 kins, exactly 
the number expressed. However, since no kins are required to com- 
plete the number, it is necessary to show that none were involved, 
and consequently kins, or "no kins" is written immediately below 
the 15 uinals, and 300 + = 300. One more example will suffice to 
show how the numbers 20 to 359 were expressed. In figure 56,/, the 
number 198 is shown. The 9 uinals = 9x20 = 180 kins. But this 
number falls short of 198 by 18, which is therefore expressed by 18 
kins written immediately below the 9 uinals; and the sum of these 
two products is 198, the number to be recorded. 

The numbers 360 to 7,199, inclusive, are indicated by multiplying 
the kin, uinal, and tun signs by the nimierals to 19, and adding 
together the resulting products. For example, the number 360 is 
shown in figure 56, g. We have seen in Table VIII that 1 tim=18 
uinals; but 18 uinals = 360 kins (18X20 = 360); therefore 1 tun 
also = 360 kins. However, in order to show that no uinals and 
kins are involved in forming this number, it is necessary to 
record this fact, which was done by vmting uinals immedi- 
ately below the 1 tun, and kins immediately below the uinals. 
The sum of these three products equals 360 (360 + + = 360). 
Again, the number 3,602 is shown in figure 56, Ti. The 10 tuns = 
10 X 360 = 3,600 kins. This falls short of 3,602 by only 2 units of the 
first order (2 kins), therefore no uinals are involved in forming this 
number, a fact which is shown by the use of uinals between the 10 
tuns and 2 kins. The sum of these three products = 3,602 (3,600 + 
+ 2). Again, in figure 56, i, the number 7,100 is recorded. The 
19 tuns = 19x360 = 6,840 kins, which falls short of 7,100 kins by 
7,100-6,840 = 260 kins. But 260 kins = 13 uinals with no kins 

1 The numerals and periods given in fig. 66 ai-e expressed by- their normal forms in every case, since these 
may be more readily recognized than the corresponding head variants, and consequently entail less work 
for the student. It should be borne in mind, however, that any bar and dot numeral or any period ui 
flg. 56 could be expressed equally well by its corresponding head form without afOecting m the least the 
values of the resulting numbers. 



MOELEY] IWTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 10*7 

remaining. Consequently, the sum of these products equals 7,100 
(6,840 + 260 + 0). 

The numbers 7,200 to 143,999 were expressed by multiplying the 
kin, uiual, tun, and katun signs by the numerals to 19, inclusive, 
and adding together the resulting products. For example, figure 
56, j, shows the number 7,204. We have seen in Table VIII that 1 
katun = 20 tuns, and we have seen that 20 tuns = 7,200 kins (20 X 360) ; 
therefore 1 katun = 7,200 kins. This number falls short of the numr 
ber recorded by exactly 4 kins, or in other words, no tuns or uinals 
are involved in its composition, a fact shown by the tuns and 
uinals between the 1 katun and the 4 kins. The sum of these four 
products = 7,204 (7,200 + + + 4). The number 75,550 is shown in 
figure 56, Ic. The 10 katuns = 72,000 ; the 9 tuns, 3,240; the 15 
uinals, 300; and the 10 Mns, 10. The sum of these four products = 
75,550 (72,000 + 3,240 + 300 + 10). ^ain, the number 143,567 is 
shown in figm-e 56, Z. The 19 katuns = 136,800; the 18 tuns, 6,480; 
the 14 uinals, 280; and the 7 kius, 7. The sum of these four prod- 
ucts = 143,567 (136,800 + 6,480 + 280+7). 

The i;iumbers 144,000 to 1,872,000 (the highest number, accordiug 
to some authorities, which has been found' in the inscriptions) were 
expressed by multiplying the kin, uinal, tun, katun, and cycle signs by 
the numerals to 19, iaclusive, and adding together the resultir^ 
products. For example, the number 987,322 is shown in figure 56, m. 
We have seen in Table VIII that 1 cycle = 20 katuns, but 20 ka- 
tims = 144,000 kins; therefore 6 cycles = 864,000 kins; and 17 
katuns = 122,400 kins; and 2 tuns, 720 kins; and 10 uinals, 200 kius; 
and the 2 kins, 2 kins. The sum of these five products equals the 
number recorded, 987,322 (864,000 + 122,400 + 720 + 200 + 2). The 
highest mmiber m the inscriptions upon which all are agreed is 
1,872,000, as shown in figure 56, n. It equals 13 cycles (13 x 144,000), 
and consequently all the periods below^ — the katun, tun, uinal, and 
kin — are indicated as being used times. 



Number of Cycles in a Great Cycle 

This brings us to the consideration of an extremely important point 
concerning which Maya students entertain two widely different opin- 
ions; and although its presentation will entail a somewhat lengthy 
digression from the subject imder consideration, it is so pertinent to 
the general question of the higher niunbers and their formation, that 
the writer has thought best to discuss it at this point. 

In a vigesimal system of numeration the imit of increase is 20, and 
so far as the codices are concerned, as we shall presently see, this 

1 There may be three other numbers in the inscriptions which are considerably higher (see pp. 114-127). 



108 BUREAU OF AMERICAN ETHNOLOGY [bdll. 57 

number was in fact the only tinit of progression used, except in the 
2d order, in which 18 instead of 20 units were required to make 1 
imit of the 3d order. In other words, in the codices the Maya carried 
out their vigesimal system to six places without a break other than 
the one in the 2d place, just noted. See Table VIII. 

In the inscriptions, however, there is some ground for believing 
that only 13 units of the 5th order (cycles), not 20, were required to 
make 1 unit of the 6th order, or 1 great cycle. Both Mr. Bowditch 
(1910: App. IX, 319-321) and Mr. Goodman (1897: p. 25) iacHne to 
this opinion, and the former, in Appendix IX of his book, presents 
the evidence at some length for and against this hypothesis. 

This hypothesis rests mainly on the two following points : 

1. That the cycles in the imscriptions are numbered from 1 to 13, 
inclusive, and not from to 19, inclusive, as in the case of all the 
other periods except the uinal, which is munbered from to 17, 
inclusive. 

2. That the only two Initial Series which are not counted from the 
date 4 Ahau 8 Cumhu, the starting point of Maya chronology, are 
counted from a date 4 Ahau 8 Zotz, which is exactly 13 cycles in 
advance of the former date. 

Let us examine the passages in the inscriptions upon which these 
points rest. In three places ' in the inscriptions the date 4 Ahau 
8 Cumhu is declared to have occurred at the end of a Cycle 13; that 
is, in these three places this date is accompanied by an "ending sign" 
and a Cycle 13. In another place in the inscriptions, although the 
starting point 4 Ahau 8 Cumhu is not itself expressed, the second 
cycle thereafter is declared to have been a Cycle 2, not a Cycle 15, 
as it would have been had the cycles been numbered from to 19, 
inclusive, like all the other periods.^ In still another place the ninth 
cycle after the starting point (that is, the end of a Cycle 13) is not a 
Cycle 2 in the following great cycle, as would be the case if the cycles 
were mmibered from to 19, inclusive, but a Cycle 9, as if the cycles 
were numbered from 1 to 13. Again, the end of the tenth cycle after 
the starting point is recorded in several places, but not as Cycle 3 of 
the following great cycle, as if the cycles were numbered from to 
19, inclusive, but as Cycle 10, as would be the case if the cycles were 
numbered from 1 to 13. The above examples leave little doubt that 
the cycles were numbered from 1 to 13, inclusive, and not from to 19, 
as in the case of the other periods. Thus, there can be no question 
concerning the truth of the first of the two above points on which 
this hypothesis rests. 

1 These are: (1) The tablet from the Temple of the Cross at Palenque; (2) Altar 1 at Piedras Negras; 
and (3) The east side of Stela C at Quirigua. 

2 This case occm's on the tablet from the Temple of the Foliated Cross at Palenque. 



MORLBT] INTRODUCTION TO STUDY OF MAYA HIBEOGLYPHS 109 

But becaiise this is true it does not necessarily follow that 13 cycles 
made 1 great cycle. Before deciding this point let us examine the 
two Initial Series mentioned above, as iwt proceeding from the date 
4 Ahau 8 Cumlm, but from a date 4 Ahau 8 Zotz, exactly 13 cycles in 
advance of the former date. 

These are in the Temple of the Cross at Paienque and on the east 
side of Stela C at Quirigua. In these two cases, if the long nxunbers 
expressed in terms of cycles, katuns, tuns, uinals, and kins are 
reduced to kins, and counted forward from the date 4 Ahau 8 Cumhu, 
the starting point of Maya chronology, in neither case will the 
recorded terminal day of the Initial Series be reached; hence these 
two Initial Series could not have had the day 4 Ahau 8 Cumhu as 
their starting point. It may be noted here that these two Initial 
Series are the only ones throughout the inscriptions known at the 
present time which are not counted from the date 4 Ahau 8 Cumhu.' 
However, by counting backward each of these long numbers from 
their respective terminal days, 8 Ahau 18 Tzec, in the case of the 
Paienque Initial Series, and 4 Ahau 8 Cumhu, in the case of the 
Quirigua Initial Series, it will be found that both of them proceed 
from the same starting point, a date 4 Ahau 8 Zotz, exactly 13 cycles 
in advance of the starting point of Maya chronology. Or, in other 
words, the starting point of all Maya Initial Series save two, was 
exactly 13 cycles later than the starting point of these two. Because 
of this fact and the fact that the cycles were numbered from 1 to 13, 
inclusive, as shown above, Mr. Bowditch and Mr. Goodman have 
reached the conclusion that in the inscriptions only 13 cycles were 
required to make 1 great cycle. 

It remains to present the points against this hypothesis, which 
seem to indicate that the great cycle in the inscriptions contained 
the same number of cycles (20) as in the codices: 

1. In the codices where six orders (great cycles) are recorded it 
takes 20 of the 5th order (cycles) to make 1 of the 6th order. This 
absolute \miformity in a strict vigesimal progression in the codices, 
so similar in other respects to the inscriptions, gives presumptive 
support at least to the hypothesis that the 6th order in the inscrip- 
tions was formed in the same way. 

2. The nimierical system in both the codices and inscriptions is 
identical even to the slight irregularity in the second place, where 
only 18 instead of 20 units were required to make 1 of the third place. 
It would seem probable, therefore, that had there been any irregu- 
larity in the 5th place in the inscriptions (for such the use of 13 ia a 
vigesimal system must be called), it would have been found also in 
the codices. 

1 It seems probable that the number on the north side of Stela C at Copan was not counted from the 
date 4 Ahau 8 Cumhu, The writer has not been able to satisfy himself, however, that this number is an 
Initial Series. 




110 BUREAU OF AMERICAN ETHNOLOGY [Bni,L.57 

3. Moreover, in the inscriptions themselves the cycle glyph occurs 
at least twice (see fig. 57, a, i) "with a coefficient greater than 13, which 
would seem to imply that more than 13 cycles could be recorded, and 
consequently that it required more than 13 to make 1 of the period next 
higher. The writer knows of no place in the inscriptions where 20 
kins, 18 uinals, 20 tims, or 20 katxms are recorded, each of these being 
expressed as 1 uinal, 1 tun, 1 katun, and 1 cycle, respectively.' There- 
fore, if 13 cycles had made 1 great cycle, 14 cycles wotdd not have 
been recorded, as in figure 57, a, but as 1 great cycle and 1 cycle; 
and 17 cycles would not have been recorded, as in 6 of the same figure, 
but as 1 great cycle and 4 cycles. The fact that they were not 
recorded in this latter manner would seem to indicate, therefore, that 

more than 13 cycles were required to make 
O CrD O ^ great cycle, or unit of the 6th place, in 
i ^ the inscriptions as weU as in the codices. 

The above points are simply positive evi- 
dence in support of this hypothesis, however, 
and in no way attempt to explain or other- 
no. s?. signs fof the cycle showing wise account for the xmdoubtedly contra- 

coefflcieDtsabovel3:a,Fronithe dictory points given LQ the disCUSsioU of (1) 

Temple ol the Inscriptions, Pa- , „ _ -, nr, -r\ j.i i j -i 

lenque; b, from Stela N, copan. on pages 108-109. Furthermore, not until 
these contradictions have been cleared away 
can it be established that the great cycle in the inscriptions was of 
the same length as the great cycle in the codices. The writer 
believes the following explanation will satisfactorily dispose of these 
contradictions and make possible at the same time the acceptance of. 
the theory that the great cycle in the inscriptions and in the codices 
was of equal length, being composed in each case of 20 cycles. 

Assuming for the moment that there were .13 cycles in a great 
cycle, it is clear that if this were the case 13 cycles could never be 
recorded in the inscriptions, for the reason that, being equal to 1 
great cycle, they would have to be recorded in terms of a great cycle. 
This is true because no period in the inscriptions is ever expressed, 
so far as now known, as the full number of the periods of which 
it was composed. For example, 1 uinal never appears as 20 kins; 
1 tun Ls never written as its equivalent, 18 uinals; 1 katun is never 
recorded as 20 tuns, etc. Consequently, if a great cycle composed 
of 13 cycles had come to its end with the end of a Cycle 13, which 
fell on a day 4 Ahau 8 Cumhu, such a Cycle 13 could never have been 
expressed, since in its place would have been recorded the end of the 
great cycle which fcU on the same day. In other words, if there had 
been 13 cycles in a great cycle, the cycles would have been num- 
bered from to 12, inclusive, and the last. Cycle 13, would have been 
recorded instead as completing some great cycle. It is necessary to 

1 Mr. Bowditch (1910: pp. 41-42) notes a seeming exception to this, not in the inscription, however, 
but in the Dresden Codex, In which, in a series of numbers on pp. 71-73, the number 390 is written 19 
uinals and 10 kins, instead of 1 tun, 1 uinal, and 10 kins. 



MOELBY] INTEODUCTION TO STUDY OP MAYA HIEEOGLYPHS 111 

admit this point or repudiate the numeration of all the other periods 
in the inscriptions. The writer believes, therefore, that, when the 
starting point of Maya chronology is declared to be a date 4 Ahau 8 
Cumhu, which an "ending sign" and a Cycle 13 further declare fell at 
the close of a Cycle 13, this does not indicate that there were 13 
cycles in a great cycle, but that it is to be interpreted as a Period- 
ending date, pure and simple. Indeed, where this date is foimd in 
the inscriptions it occurs with a Cycle 13, and an "ending sign" 
which is practically identical with other tmdoubted "ending signs." 
Moreover, if we interpret these places as indicating that there were 
only 13 cycles in a great cycle, we have equal grounds for saying that 
the great cycle contained only 10 cycles. For example, on Zoomorph 
G at Quirigua the date 7 Ahau 18 Zip is accompanied by an "ending 
sign" and Cycle 10, which on this basis of interpretation would sig- 
nify that a great cycle had only 10 cycles. Similarly, it could be 
shown by such an interpretation that in some cases a cycle had 14 
katuns, that is, where the end of a Katun 14 was recorded, or 17 
katuns, where the end of a Katmi 17 was recorded. All such places, 
including the date 4 Ahau 8 Cumhu, which closed a Cycle 13 at the 
starting point of Maya chronology, are only Period-ending dates, the 
writer believes, and have no reference to the number of periods which 
any higher period contains whatsoever. They record merely the end 
of a particular period in the Long Count as the end of a certain Cycle 
13, or a certain Cycle 10, or a certain Katxm 14, or a certain Katun 
17, as the case may be, and contain no reference to the beginning or 
the end of the period next higher. 

There can be no doubt, however, as stated above, that the cycles 
were numbered from 1 to 13, inclusive, and then began again with 1. 
This sequence strikingly recalls that of the numerical coefficients of 
the days, and in the parallel which this latter sequence affords, the 
writer believes, lies the true explanation of the misconception con- 
cerning the length of the great cycle in the inscriptions. 

Table XI. SEQUENCE OF TWENTY CONSECUTIVE DATES IN THE 

MONTH POP 



1 Ik 


Pop 


11 Eb 


10 Pop 


2Akbal 


1 Pop 


12 Ben 


11 Pop 


3 Kan 


2 Pop 


13 Ix 


12 Pop 


4 Chiccliaii 


3 Pop 


1 Men 


13 Pop 


5 Cimi 


4 Pop 


2 Cib 


14 Pop 


6 Manik 


S Pop 


3 Caban 


15 Pop 


7 Lamat 


6 Pop 


4 Eznab 


16 Pop 


8 Muluc 


7 Pop 


8 Cauao 


17 Pop 


9 Oc 


8 Pop 


6 Ahau 


18 Pop 


10 Chuen 


9 Pop 


7 ImiTf 


19 Pop 



The numerical coefficients of the days, as we have seen, were num- 
bered from 1 to 13, inclusive, and then began again with 1. See 



112 BTJEEAU OF AMERICAN ETHNOLOGY [bdli,.57 

Table XI, in which the 20 days of the month Pop are enumerated. 
Now it is evident from this table that, although the coefficients of 
the days themselves do not rise above 13, the numbers showing the 
positions of these days in the month continue up through 19. In 
other words, two diflFerent sets of numerals were used in describing 
the Maya days: (1) The numerals 1 to 13, inclusive, the coefficients 
of the days, and an integral part of their names; and (2) The numerals 

to 19, inclusive, showing the positions of these days in the divisions 
of the year — the uinals, and the xma kaba kin. It is clear from the 
foregoing, moreover, that the number of possible day coefficients (13) 
has nothing whatever to do in determining the number of days in 
the period next higher. That is, although the coefficients of the days 
are numbered from 1 to 13, inclusive, it does not necessarily follow 
that the next higher period (the uinal) contained only 13 days. 
Similarly, the writer believes that while the cycles were undoubtedly 
numbered — that is, named — ^from 1 to 13, inclusive, like the coeffi- 
cients of the days, it took 20 of them to make a great cycle, just as it 
took 20 kins to make a uinal. The two cases appear to be parallel. 
Confusion seems to have arisen through mistaking the name of the 
period for its position in the period next higher — two entirely different 
things, as we have seen. 

A somewhat similar case is that of the katuns in the u kahlay 
katunob in Table IX. Assuming that a cycle commenced with the 
first katim there given, the name of this katun is Katun 2 Ahau, 
although it occupied the _^rs^ position in the cycle. Again, the name 
of the second katun in the sequence is Katun 13 Ahau, although it 
occupied the second position in the cycle. In other words, the katuns 
of the u kahlay katunob were named quite independently of their 
position in the period next higher (the cycle), and their names do not 
indicate the corresponding positions of the katun in the period next 
higher. 

Applying the foregoing explanation to those passages in the 
inscriptions which show that the enumeration of the cycles was from 

1 to 13, inclusive, we may interpret them as follows: When we find 
the date 4 Ahau 8 Cumhu in the inscriptions, accompanied by an 
"ending sign" and a Cycle 13, that "Cycle 13," even granting that 
it stands at the end of some great cycle, does not signify that there 
were only 13 cycles in the great cycle of which it was a part. On the 
contrary, it records only the end of a particular Cycle 13, being a 
Period-ending date pure and simple. Such passages no more fix the 
length of the great cycle as containing 13 cycles than does the coeffi- 
cient 13 of the day name 13 Ix in Table XI limit the number of days 
in a uinal to 13, or, again, the 13 of the katun name 13 Ahau in 
Table IX limit the number of katuns in a cycle to 13. This expla- 
nation not only accounts for the use of the 14 cycles or 17 cycles, as 



MOBLEY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 113 

shown in figure 57, a, h, but also satisfactorily provides for the enu- 
meration of the cycles from 1 to 13, inclusive. 

If the date "4 Ahau 8 Cumhu ending Cycle 13" be regarded as a 
Period-ending date, not as indicating that the number of cycles in a 
great cycle was restricted to 13, the next question is — ^Did a great 
cycla also come to an end on the date 4 Ahau 8 Cumhu — the starting 
point of Maya chronology and the closing date of a Cycle 13 ? That 
it did the writer is firmly convinced, although final proof of the point 
can not be presented imtil numerical series containing more than 5 
terms shall have been considered. (See pp. 114-127 for this discus- 
sion.) The following points, however, which may be introduced 
here, tend to prove this condition: 

1. In the natural course of affairs the Maya would have commenced 
their chronology with the beginning of some great cycle, and to have 
done this in the Maya system of coimting time — that is, by elapsed 
periods — ^it was necessary to reckon from the end of the preceding 
great cycle as the starting point. 

2. Moreover, it would seem as though the natural cycle with which 
to commence coxmting time would be a Cycle 1, and if this were done 
time would have to be counted from a Cycle 13, since a Cycle 1 could 
follow only a Cycle 13. 

On these two probabilities, together with the discussion on pages 
114^127, the writer is inclined to beheve that the Maya com- 
menced their chronology with the beginning of a great cycle, whose 
first cycle was named Cycle 1, which was reckoned from the close 
of a great cycle whose ending cycle was a Cycle 13 and whose ending 
day fell on the date 4 Ahau 8 Cumhu. 

The second point (see p. 108) on which rests the hypothesis of "13 
cycles to a great cycle" in the inscriptions admits of no such plausible 
explanation as the first point. Indeed, it will probably never be 
known why in two inscriptions the Maya reckoned time from a start- 
ing point different from that used in all the others, one, moreover, 
which was 13 cycles in advance of the other, or more than 5,000 years 
earlier than the beginning of their chronology, and more than 8,000 
years earlier than the beginning of their historic period. That this 
remoter starting point, 4 Ahau'8 Zotz, from which proceed so far as 
known only two inscriptions throughout the whole Maya area, stood 
at the end of a great cycle the writer does not beheve, in view of 
the evidence presented on pages 114-127. On the contrary, the 
material given there tends to show that although the cycle which 
ended on the day 4 Ahau 8 Zotz was also named Cycle 13,' it was the 
8th division of the grand cycle which ended on the day 4 Ahau 8 Cumhu, 

1 That it was a Cycle 13 is sHown from the fact that it was just 13 cycles in advance of Cycle 13 ending 
on the' date 4 Ahau 8 Cumhu. 

43508°— Bull. 57—15 8 



114 BUREAU OF AMEEICAN ETHNOLOGY [bull. 57 

the starting point of Maya chronology, and not the closing division 
of the preceding grand cycle. However, without attempting to settle 
this question at this time, the writer inclines to the belief, on the basis 
of the evidence at hand, that the great cycle in the inscriptions was of 
the same length as in, the codices, where it is known to have contained 
20 cycles. 



Let us return to the discussion interrupted on page 107, where the 
first method of expressing the higher numbers was being explained. 
We saw there how the higher numbers up to and including 1,872,000 
were written, and the digression just concluded had for its purpose 
ascertaining how the numbers above this were expressed; that is, 
whether 13 or 20 units of the 5th order were equal to 1 unit of the 6th 
order. It was explained also that this number, 1 ,872,000, was perhaps 
the highest which has been found in the inscriptions. Three possible 
exceptions, however, to this statement should be noted here : (1 ) On 
the east side of Stela N at Copan six periods are recorded (see fig. 58) ; 
(2) on the west panel from the Temple of the Inscriptions at Palenque 
six and probably seven periods occur (see fig. 59); and (3) on Stela 
10 at Tikal eight and perhaps nine periods are found (see fig. 60). 
If in any of these cases all of the periods belong to one and the 
same numerical series, the resulting numbers would be far higher than 
1,872,000. Indeed, such numbers wotdd exceed by many millions 
all others throughout the range of Maya writings, in either the 
codices or the inscriptions. 

Before presenting these three numbers, however, a distinction 
should be drawn between them. The first and second (figs. 58, 59) 
are clearly not Initial Series. Probably they are Secondary Series, 
although this point can not be established with certainty, since they 
can not be connected with any known date the position of which is 
definitely fixed. The third number (fig. 60), on the other hand, is an 
Initial Series, and the eight or nine periods of which it is composed 
may fix the initial date of Maya chronology (4 Ahau 8 Cumliu) in a 
much grander chronological scheme, as wUl appear presently. 

The first of these three numbers (see fig. 58), if all its six periods 
belong to the same series, equals 42,908,400. Although the order 
of the several periods is just the reverse of that in the numbers in 
figure 56, this difference is unessential, as will shortly be explained, 
and in no way affects the value of the mmiber recorded. Commencing 
at the bottom of figure 58 with the highest period involved and read- 
ing up, A6,i the 14 great cycles =40,320,000 kins (see Table VIII, in 
which 1 great cycle = 2,880,000, and consequently 14 = 14 X 2,880,000 = 

' See p. 156 and fig. 66 for method of designating tlie individual glyphs in a text. 



MOELEY] INTBODUOTIOlir TO STUDY OF MAYA HIEROGLYPHS 



115 



40,320,000) ; A5, the 17 cycles = 2,448,000 kins (17 X 144,000) ; A4, the 
19 katuns = 136,800 kms (19x7,200); A3, the 10 tuns = 3,600 kins 
(10 X 360) ; A2, the umals, kins; and the kins, kins. The sum 












Fig. 58 




Tia.SO 




OSS 



C 








Missing 



Fig. 60 



Fig. 58. Part of the inscription on Stela N, Copan, showing a number composed of six periods. 

Fig. 59. Part of the inscription in the Temple of the Inscriptions, Palenque, showing a number composed 

of seven periods. 
Fig. 60. Part oftheinscriptioh on Stela 10, Tikal (probably an Initial Series), showing a number composed 

of eight periods. 

of these products = 40,320,000 + 2,448,000 + 136,800 + 3,600 + + = 
42,908,400. 

The second of these three numbers (see fig. 59), if all of its seven 
terms belong to one and the same number, equals 455,393,401. 
Commencing at the bottom as in figure 58, the first term A4, has the co- 
efl&cient 7. Since this is the term following the sixth, or great cycle, 
we may call it the great-great cycle. But we have seen that the 



116 BUREAU OF AMEEIOAN ETHNOLOGY [bull. 57 

great cycle = 2,880,000 ; therefore the great-great cycle = twenty timies 
this number, or 57,600,000. Our text shows, however, that seven of 
these great-great cycles are used in the number in question, therefore 
our first term = 403,200,000. The rest may be reduced by means of 
Table VIII as follows : B3, 18 great cycles = 51,840,000 ; A3, 2 cycles = 
288,000; B2, 9 katuns = 64,800; A2, 1 "tun = 360; Bl, 12 uinals = 240; 
Bl, 1 kin= 1. The sum of these (403,200,000 + 51,840,000 + 288,000 + 
64,800 + 360 + 240 + 1 ) = 455,393,401 . 

The third of these numbers (see fig. 60), if all of its terms belong to 
one and the same number, equals 1,841,639,800. Commencing with 
A2, this has a coefficient of 1. Since it immediately foUowsthe 
great-great cycle, which we foimd above consisted of 57,600,000, we 
may assume that it is the great-great-great cycle, and that it con- 
sisted of 20 great-great cycles, or 1,152,000,000. Since its coefficient 
is only 1, this large number itself will be the first term in our series. 
The rest may readily be reduced as follows: A3, 11 great-great 
cycles = 633,600,000; A4, 19 great cycles = 54^20,000; A5, 9cycles = 
1,296,000; A6, 3 katuns = 21,600; A7, 6 tuns = 2,160; A8, 2 uiaals = 
40; A9, kins = 0.' The sum of these (1,152,000,000 + 633,600,000 + 
64,720,000 + 1 ,296,000 + 21,600 + 2, 160 + 40 + 0) = 1,841,639,800, the 
highest number found anywhere in the Maya writings, equivalent to 
about 5,000,000 years. 

Whether these three numbers are actually recorded in the inscrip- 
tions under discussion depends solely on the question whether or not 
the terms above the cycle in each belong to one and the same series. 
If it could be determined with certaiuty that these higher periods in 
each text were all parts of the same number, there would be no further 
doubt as to the accuracy of the figures given above; and more impor- 
tant still, the 17 cycles of the first number (see A5, fig. 58) would 
then prove conclusively that more than 13 cycles were required to 
make a great cycle in the inscriptions as well as in the codices. And 
furthermore, the 14 great cycles in A6, figure 58, the 18 in B3, figure 
59, and the 19 in A4, figure 60, would also prove that more than 13 
great cycles were required to make one of the period next higher — 
that is, the great-great cycle. It is needless to say that this point 
has not been universally admitted. Mr. Goodman (1897: p. 132) has 
suggested in the case of the Copan inscription (%. 58) that only the 
lowest four periods — the 19 katmis, the 10 tuns, the uinals, and the 
kins — A2, A3, and A4,^ here form the number; and that if this 
number is counted backward from the Initial Series of the inscription, 
it will reach a Katun 17 of the preceding cycle. Finally, Mr. Goodman 

1 The kins are missing from tliis number (see A9, fig. 60). At the maximum, however, they could in- 
crease this large number only by 19. They have been used here as at 0. 

2 As will be explained presently, the kin sign is frequently omitted and its coefficient attached to the 
uinal glyph. - See p. 127. 



MOSLey] introduction TO STUDY OF MAYA HIEROGLYPHS 117 

believes this Katun 17 is declared in the glyph following the 19 katuns 
(A5), which the writer identifies as 17 cycles, and consequently 
according to the Goodman interpretation the whole passage is a 
Period-ending date. Mr. Bowditch (1910: p. 321) also o£fers the same 
interpretation as a possible reading of this passage. Even granting 
the truth of the above, this interpretation still leaves unexplained 
the lowest glyph of the number, which has a coefficient of 14 (A6). 

The strongest proof that this passage will not bear the construction 
placed on it by Mr. Goodman is a£Forded by the very glyph upon which 
his reading depends for its verification, namely, the glyph which he 
interprets Katim 17. This glyph (A5) bears no resemblance to the 
katun sign standing immediately above it, but on the contrary has 
for its lower jaw the clasping hand (*), which, as we have seen, is fk<^ 
the determining characteristic of the cycle head. Indeed, this * 
element is so clearly portrayed in the glyph in question that its identi- 
fication as a bead variant for the cycle follows almost of necessity. 
A comparison of this glyph with the head variant of the cycle given in 
figure 25, d-f, shows that the two forms are practically identical. 
This correction deprives Mr. Goodman's reading of its chief support, 
and at the same time increases the probability that all the 6 terms 
here recorded belong to one and the same number. That is, since 
the first five are the kin, uinal, tim, katun, and cycle, respectively, it 
is probable that the sixth and last, which follows immediately the 
fifth, without a break or interiuption of anj kind, belongs to the 
same series also, in which event this glyph would be most likely to 
represent the units of the sixth order, or the so-called great cycles. 

The passages in the Palenque and Tikal texts (figs. 59 and 60, 
respectively) have never been satisfactorily 'explained. In default of 
calendric checks, as the known distance between two dates, for 
example, which may be appHed to these three numbers to test their 
accuracy, the writer knows of no better check than to study the char- 
acteristics of this possible great-cycle glyph in all three, and of the 
possible great-great-cycle glyph in the last two. 

Passing over the kins, the normal form of the uinal glyph appears 
in figures 58, A2, and 59, Bl (see fig. 31, a, 6), and the head variant 
in figure 60, A8. (See fig. 31, d-f.) Below the uirial sign in A3, fig- 
ure :58, and A2, figure 59, and above A7, in figure 60 the tuns are re- 
corded as head variants, in all three of which the fleshless lower jaw, 
the determining characteristic of the tun head, appears. Compare 
these three head variants with the head variant for the tun in figure 29, 
d~g. In the Copan inscription (fig. 58) the katun glyph, A4, appears 
as a head Variant, the essential elements of which seem to be the oval 
in the top part of the head and the curHng fang protruding from the 
back part of the mouth. Compare this head with the head variant 
for the katun in figure 27, e-h,. In the Palenque and Tikal texts (see 



118 



BUREAU OF AMERICAN ETHNOLOGY 



[BULL. 57 



figs. 59, B'2, and 60, A6, respectively), on the other hand, the katun 
is expressed by its normal form, which is identical with the normal 
form shown in figure 27, a, h. In figures 58, A5, and 59, A3, the cycle 
is expressed by its head variant, and the determining characteristic, 
the clasped hand, appears in both. Compare the cycle signs in figures 
58, A5, and 59, A3, with the head variant for the cycle shown in 
figure 25, d-f. The cycle glyph in the Tikal text (fig. 60, A5) is 
clearly the normal form. (See fig. 25, o-c.) The glyph following the 
cycle sign in these three texts (standing above the cycle sign in figure 
60 at A4) probably stands for the period of the sixth order, the 
so-called great cycle. These three glyphs are redrawn in figure 
61, a-c, respectively. In the Copan inscription this glyph (%. 
61, a) is a head variant, while in the Palenque and Tikal texts (a 
and 6 of the same figure, respectively) it is a normal form. 



^M 




1^ 




Fig. 61. Signs for the great cycle (a-c), and the great-great cycle (d, e): a, Stela N, Copan; b, d, Temple 
of the Inscriptions, Palenque; c, e. Stela 10, Tikal. 

Inasmuch as these three inscriptions are the only ones in which 
numerical series composed of 6 or more consecutive terms are 
recorded, it is imfortimate that the sixth term in all three should 
not have been expressed by the same form, since this would have 
facilitated their comparison. Notwithstanding this handicap, how- 
ever, the writer beheves it will be possible to show clearly that 
the head variant in figure 61, a, and the normal forms in 6 and c are 
only variants of one and the same sign, and that p,ll three stand for 
one and the same thing, namely, the great cycle, or unit of the sixth 
order. 

In the first place, it will be noted that each of the three glyphs just 
mentioned is composed in part of the cycle sign. For example, in 
figure 61, a, the head variant has the same clasped hand as the head- 
variant cycle sign in the same text (see fig. 58, A5), which, as 
we have seen elsetrhere, is the determining characteristic of the head 
variant for the cycle. In figure 61, 6, c, the normal forms there 
presented contain the entire normal form for the cycle sign; compare 
figure 25, a, c. Indeed, except for its superfix, the glyphs in figure 61,6, 
c, are normal forms of the cycle sign ; and the glyph in a of the same 
figure, except for its superfixial element, is similarly the head variant 
for the cycle. It would seem, therefore, that the determining charac- 
teristics of these three glyphs must be their superfixial elements. In 
the normal form in figure 61, 6, the superfix is very clear. Just 
inside the outhne and parallel to it there is a line of smaller circles. 



MOBLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 119 

and in the middle there are two infixes Uke shepherds' crooks facing 
away from the center (*). In c of the last-mentioned figure the 0g]) 
superfix is of the same size and shape, and although it is partially * 
destroyed the left-hand "shepherd's crook" can still be distinguished. 
A faint dot treatment around the edge can also still be traced. 
Although the superfix of the head variant in a is somewhat weathered, 
enough remains to show that it was similar to, if indeed not identical 
with, the superfixes of the normal forms in 6 and c. The line of circles 
defining the left side of this superfix, as well as traces of the lower 
ends of the two "shepherd's crook" infixes, appears very clearly in 
the lower part of the superfix. Moreover, in general shape and pro- 
portions this element is so similar to the corresponding elements in 
figure 61, &, c, that, taken together with the similarity of the other 
details pointed out above, it seems more than Hkely that aU three 
of these superfixes are one and the same element. The points which 
have led the writer to identify glyphs a, b, and c in figure 61 as forms 
for the great cycle, or period of the sixth order, may be summarized 
as follows: 

1. All three of these glyphs, head-variant as well as normal forms, 
are made up of the corresponding forms of the cycle sign plus 
another element, a superfix, which is probably the determining char- 
acteristic in each case. 

2. All three of these superfixes are probably identical, thus showing 
that the three glyphs in which they occur are probably variants of 
the same sign. 

3. All three of these glyphs occur in numerical series, the preceding 
term of which in each case is a cycle sign, thus showing that by posi- 
tion they are the logical "next" term (the sixth) of the series. 

Let us next examine the two texts in which great-great-cycle 
glyphs may occur. (See figs. 59, 60.) The two glyphs which may 
possibly be identified as the sign for this period are shown in figure 
61, d, e. 

A comparison of these two forms shows that both are composed of 
the same elements: (1) The cycle sign; (2) a superfix in which the 
hand is the principal element. 

The superfix in figure 61, d, consists of a hand and a tassel-hke 
postfix, not unlike the upper half of the ending signs in figure 37, 
l-q. However, in the present case, if we accept the hypothesis that 
d of figure 61 is the sign for the great-great cycle, we are obliged to 
see in its superfix alone the essential element of the great-great-cycle 
sign, since the rest of this glyph (the lower part) is quite clearly the 
normal form for the cycle. 

The superfix in figure 61, e, consists of the same two elements as 
the above, with the sUght difference that the hand in e holds a rod. 
Indeed, the similarity of the two forms is so close that in default of 



120 BUREAU OF AMERICAN ETHNOLOGY [bdll. 57 

any evidence to the contrary the writer beheves they may be accepted 
as signs for one and the same period, namely, the great-great cycle. 

The points on which this conclusion is based may be sununarized 
as follows: 

1. Both glyphs are made up of the same elements — (a) The normal 
form of the cycle sign; (&) a superfix composed of a hand with a tassel- 
Hke postfix. 

2. Both glyphs occur in numerical series the next term but one of 
which is the cycle, showing that by position they are the logical next 
term but one, the seventh or great-great cycle, of the series. 

3. Both of these glyphs stand next to glyphs which have been 
identified as great-cycle signs, that i^, the sixth terms of the series 
ia which they occur. 

By this same fine of reasoning it seems probable that A2 in figure 60 
is the sign for the great-great-great cycle, although this fact can not 
be definitely estabhshed because of the lack of comparative evidence. 

This possible sign for the great-great-great cycle, or period of the 
8th order, is composed of two parts, just Hke the signs for the great 
cycle and the great-great cycle already described. These are: (1) 
The cycle sign; (2) a superfix composed of a hand and a semicircular 
postfix, quite distinct from the superfixes of the great cycle and 
great-great cycle signs. 

However, since there is no other inscription known which presents 
a number composed of eight terms, we must lay aside this Hne of 
investigation and turn to another for further hght on this point. 

An examination of figure 60 shows that the glyphs which we have 
identified as the signs for the higher periods (A2, A3, A4, and A5,) 
contain one element common to aU — the sign for the cycle, or period 
of 144,000 days. Indeed, A6 is composed of this sign alone with 
its usual coefiicient of 9. Moreover, the next glyphs (A6, A7, A8, 
and A9 ^) are the signs for the kattm, tun, uinal, and kin, respectively, 
and, together with A5, form a regular descending series of 6 
terms, all of which are of known value. 

The next question is. How is this glyph in the sixth place formed ? 
We have seen that in the only three texts in which more than five 
periods are recorded this sign for the sixth period is composed of the 
same. elements in each: (1) The cycle sign; (2) a superfix containii^ 
two "shepherd's crook" infixes and surrounded by dots. 

Further, we have seen that in two cases in the inscriptions the 
cycle sign has a coefficient greater than 13, thus showing that in all 
probability 20, not 13, cycles made 1 great cycle. 

Therefore, since the great-cycle signs in figure 61, a-c, are composed 

^^ of the cycle sign plus a superfix (*), this superfix must have the 

* value of 20 in order to make the whole glyph have the value of 

1 Glyph A9 is missing but tindoutitedly was tlie kin sign and coeffloient. 



MORLEY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 121 

20 cycles, or 1 great cycle (that is, 20 X 144,000 = 2,880,000) . In other 
words, it may be accepted (1) that the glyphs in figure 61, a-c, are 
signs for the great cycle, or period of the sixth place; and (2) that 
the great cycle was composed of 20 cycles shown graphically by two 
elements, one being the cycle sign itself and the other a superfix 
having the value of 20. 

It has been shown that the last six glyphs in fi.gure 60 (A4, AS, A6, 
A7, As, and A9) all belong to the same series. Let us next examine 
the seventh glyph or term from the bottom (A3) and see how it is 
formed. We have seen that in the only two texts in which more than 
six periods are recorded the signs for the seventh period (see %. 61, 
d, e) are composed of the same elements in each: (1) The cycle sign; 
(2) a superfix having the hand as its principal element. We have 
seen, further, that in the only three places in which great cycles are 
recorded in the Maya writing (fig. 61, a-c) the coefficient in every case 
is greater than 13, thus showing that in aU probability 20, not 13, 
great cycles made 1 great-great cycle. 

Therefore, since the great-great cycle signs in figure &\,d,e, are com. 
posed of the cycle sign plus a superfix (*), this superfix must f^Pi 
have the value of 400 (20 X 20) in order to make the whole glyph * 
have the value of 20 great cycles, or 1 great-great cycle (20 X 2,880,000 = 
57,600,000). In other words, it seems highly probable (1) that the 
glyphs in figure 61, d, e, are signs for the great-great cycle or period 
of the seventh place, and (2) that the great-great cycle was composed 
of 20 great cycles, shown graphically by two elements, one being 
the cycle sign itself and the other a hand having the value of 400. 

It has been shown that the first seven glyphs (A3, A4, A5, A6, A7, 
A8, and A9) probably all belong to the same series. Let us next 
examine the eighth term (A2) and see how it is formed. 

As stated above, comparative evidence can help us no further, 
since the text under discussion is the only one which presents a num- 
ber composed of more than seven terms. Nevertheless, the writer 
believes it will be possible to show by the morphology of this, the 
only glyph which occupies the position of an eighth term, that it is 
20 times the glyph in the seventh position, and consequently that 
the vigesimal system was perfect to the highest known unit found 
in the Maya writing. 

We have seen (1 ) that the sixth term was composed of the fifth term 
plus a superfix which increased the fifth 20 times, and (2) that the 
seventh term was composed of the fifth term plus a superfix which 
increased the fifth 400 times, or the sixth 20 times. 

Now let us examine the only known example of a sign for the 
eighth term (A2, fig. 60). This glyph is composed of (1) the cycle 
sign; (2) a superfix of two elements, (a) the hand, and (6) a semi- 
circular element in which dots appear. 



122 BUREAU OF AMEEICAN ETHNOLOGY [boll. 57 

But this same hand in the superfix of the great-great cycle increased 
the cycle sign 400 times (20x20; see A3, fig. 60). Therefore we 
must assume the same condition obtains here. And finally, since the 
eighth term = 20 X 20 X 20 X cycle, we must recognize in the second 
^^ element of the superfix (*) a sign which means 20. 

* A close study of this element shows that it has two impor- 
tant points of resemblance to the superfix of the great-cycle glyph 
(see A4, fig. 60), which was shown to have the value 20: (1) Both ele- 
ments have the same outline, roughly semicircular; (2) both elements 
have the same chain of dots aroimd their edges. 

Compare this element in A2, figure 60, with the superfixes in figure 
61, a, b, bearing in mind that there is more than 275 years' differ- 
ence in time between the carving of A2, figure 60, and a, figure 61, 
and more than 200 years between the former and figure 61, h. The 
writer believes both are variants of the same element, and conse- 
quently A2, figure 60, is probably composed of elements which signify 
20 X 400 (20 X 20) X the cycle, which equals one great-great-great 
cycle, or term of the eighth place. 

Thus on the basis of the glyphs themselves it seems possible to 
show that all belong to one and the same numerical series, which 
progresses according to the terms of a vigesimal system of numera- 
tion. 

The several points supporting this conclusion may be summarized 
as follows: 

1. The eight periods ' in figure 60 are consecutive, their sequence 
being uninterrupted throughout. Consequently it seems probable 
that all belong to one and the same number. 

2. It has been shown that the highest three period glyphs are com- 
posed of elements which multiply the cycle sign by 20, 400, and 
8,000, respectively, which has to be the case if they are the sixth, 
seventh, and eighth terms, respectively, of the Maya vigesimal system 
of numeration., 

3. The highest three glyphs have numerical coefficients, just like 
the five lower ones; this tends to show that all eight are terms of 
the same numerical series. 

4. In the two texts which alone can furnish comparative data for 
this sixth term, the sixth-period glyph in each is identical with A4, 
figure 60, thus showing the existence of a sixth period in the inscrip- 
tions and a generally ^ accepted sign for it. 

5. In the only other text which can furnish comparative data for 
the seventh term, the period glyph in its seventh place is identical 

1 The lowest period, the Mn, is missing. See A9, flg. 60. 

2 The use of the word "generally" seems reasonable here; these three texts come from widely sepa- 
rated centers— Copan to the extreme southeast, Palenque in the extreme west, and Tikal in the central 
part of the area. 



MOELEY] INTEODUCTION TO STUDY OF MAYA HIBEOGLYPHS 123 

with A3, figure 60; thus showing the existence of a seventh period in 
the inscriptions and a generally accepted sign for it. 

6. The one term higher than the cycle in the Copan text, the two 
terms higher in the Palenque text, and the three terms higher in this 
text, are all built on the same basic element, the cycle, thus showing 
that in each case the higher term or terms is a continuation of the 
same number, not a Period-ending date, as suggested by Mr. Good- 
man for the Copan text. 

7. The other two texts, showing series composed of more than five 
terms, have all their period glyphs in an unbroken sequence in each, 
like the text under discussion, thus showing that in each of these 
other two texts aU the terms preajent probably belong to one and 
the same number. 

8. Finally, the two occurrences of the cycle sign with a coeflBcient 
above 13, and the three occurrences of the great-cycle sign with a 
coefficient above 13, indicate that 20, not 13, was the unit of progres- 
sion in the higher numbers in the inscriptions just as it was in the 
codices. 

Before closing the disciission of this unique inscription, there is one 
other important point in connection with it which must be considered, 
because of its possible bearing on the meaning of the Initial-series 
introducing glyph. 

The first five glyphs on the east side of Stela 10 at Tikal are not 
illustrated in figure 60. The sixth glyph is Al in figure 60, and 
the remaining glyphs in this figure carry the text to the bottom of 
this side of the monument. The first of these five unfigured glyphs 
is very clearly an Initial-series introducing glyph. Of this there can 
be no doubt. The second resembles the day 8 Manik, though it is 
somewhat effaced. The remaining three are unknown. The next 
glyph, Al, figure 60, is very clearly another Initial-series intro- 
ducing glyph, having all of the five elements common to that sign. 
Compare Al with the forms for the Initial series introducing glyph 
in figure 24. This certainly would seem to indicate that an Initial 
Series is to follow. Moreover, the fourth glyph of the eight-term 
number following in A2-A9, inclusive (that is, A5), records "Cycle 9," 
the cycle in which practically all Initial-series dates fall. Indeed, if 
A2, A3, and A4 were omitted and A5, A6, A7, A8, and A9 were 
recorded immediately after Al, the record would be that of a regular 
Initial-series number (9. 3. 6. 2. 0).. Can this be a matter of chance ? 
If not, what effect can A2, A3, and A4 have on the Initial-series 
dateinAl, A5-A9? 

The writer beUeves that the only possible effect they could have 
would be to fix Cycle 9 of Maya chronology in a far more compre- 
hensive and elaborate chronological conception, a conception which 



124 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

indeed staggers the imaginatioii, dealing as it does with more than*' 
five million years. 

If these eight terms all belong to one and the same ntunerical' 
series, a fact the writer believes he has established in the foregoing'^ 
pages, it means that Cycle 9, the first historic period of the Mayji'' 
civilization, was Cycle 9 of Great Cycle 19 of Great-great Cycle 1 1 of 
Great-great-great Cycle 1. In other words, the starting point of 
Maya chronology, which we have seen was the date 4 Ahau 8 Cnmlm, 
9 cycles before the close of a Cycle 9, was in reality 1. 11. 19. 0. 0. 0. 
0. 0. 4 Ahau 8 Cumhu, or simply a fixed point in a far vaster chrono- 
logical conception. 

Furthermore, it proves, as contended by the writer on page 113, 
that a great cycle came to an end on this date, 4 Ahau 8 Cumhn. 
This is true because on the above date (1. 11. 19. 0. 0. 0. 0. 0. 4 Ahaa 
8 Cumhu) all the five periods lower than the great cycle are at 0. It 
proves, fm-thermore, as the writer also contended, that the date 4 Ahau 
8 Zotz, 13 cycles in advance of the date 4 Ahau 8 Cumhu, did not end 
a great cycle — 

1. 11. 19. 0. 0. 0. 0. 0. 4 Ahau 8 Cumhu 

13. 0. 0. 0. 0. 
1. 11. 18. 7. 0. 0. 0. 0. 4 Ahau 8 Zotz 

but, on the contrary, was a Cycle 7 of Great Cycle 18, the end of 
which (19. 0. 0. 0. 0. 0. 4 Ahau 8 Cumhu) was the starting point of 
Maya chronology. 

It seems to the writer that the above construction is the only one 
that can be put on this text if we admit that the eight periods in 
A2-A9, figure 60, all belong to one and the same numerical series. 

Furthermore, it would show that the great cycle in which fell the 
first historic period of the Maya civilization (Cycle 9) was itself the 
closing great cycle of a great-great cycle, namely. Great-great Cycle 1 1 : 

1. 11. 19. 0. 0. 0. 0. 0. 

1. 0. 0. 0. 0. 0. 

1. 12. 0. 0. 0. 0. 0. 0. 

That is to say, that when Great Cycle 19 had completed itself. Great- 
great Cycle 12 would be ushered in. 

We have seen on pages 108-113 that the names of the cycles followed 
one another in this sequence: Cycle 1, Cycle 2, Cycle 3, etc., to Cycle 
13, which was followed by Cycle 1, and the sequence repeated itself. 
We saw, however, that these names probably had nothing to do with 
the positions of the cycles in the great cycle; that on the contrary 
these numbers were names and not positions in a higher term. 

Now we have seen that Maya chronology began with a Cycle 1; 
that is, it was counted from the end of a Cycle 13. Therefore, the 



MOELBY] IKTEODUCTION TO STUDY OF MAYA HIEBOGLYPHS 125 

closing cycle of Great Cycle 19 of Great-great Cycle 11 of Great-great- 
great Cycle 1 was a Cycle 13, that is to say, 1. 11. 19. 0. 0. 0. 0. 0. 
4 Ahau 13 Cumhu concluded a great cycle, the closing cycle of which 
was named Cycle 13. This large number, composed of one great- 
great-great cycle, eleven great-great cycles, and nineteen great cycles, 
contains exactly 12,780 cycles, as below: 

I great-great-great cycle = 1 X 20 X 20 X 20 cycles = 8, 000 cycles 

II great-great cycles =11 X 20x20 cycles = 4, 400 cycles 
19 great cycles = 19 X 20 cycles = 380 cycles 

12, 780 cycles 

But the closing cycle of this number was named Cycle 13, and by 
deducting all the multiples of 13 possible (983) we can jSnd the name 
of the first cycle of Great-great-great Cycle 1, the highest Maya time 
period of which we have any knowledge: 983X13 = 12,779. And 
deducting this from the number of cycles involved (12,780), we 
have — 

12, 780 

12, 779 



This covmted backward from Cycle 1, brings us again to a Cycle 13 as 
the name of the first cycle in the Maya conception of time. In 
other words, the Maya conceived time to have commenced, in so far 
as we can judge from the single record available, with a Cycle 13, 
not with the beginning of a Cycle 1, as they did their chronology. 

We have still to explain Al, figure 60. This glyph is quite clearly 
a form of the Initial-series introducing glyph, as already explained, 
in which the five components of that glyph are present in usual form: 
(1) Trinal superfix; (2) pair of comb-hke lateral appendages ; (3) the 
tun sign; (4) the trinal subfix; (5) the variable central element, here 
represented by a grotesque head. 

Of these, the first only claims our attention here. The trinal super- 
fix in Al (fig. 60), as its name signifies, is composed of three parts, 
but, unlike other forms of this element, the middle part seems to be 
nothing more nor less than a numerical dot or 1 . The question at 
once arises, can the two flanking parts be merely ornamental and^ 
the whole element stand for the number 1 ? The introducing glyph 
at the beginning of this text (not figured here) , so far as it can be 
made out, has a trinal superfix of exactly the same character — a dot 
with an ornamental scroll on each side. What can be the explanation 
of this element, and indeed of the whole glyph? Is it one great- 
great-great-great cycle — a period twenty times as great as the one 
recorded in A2, or is it not a term of the series in glyphs A2-A9 ? 



126 BUREAU OP AMEKICAN ETHNOLOGY [BUix. 57 

The writer believes that whatever it may be, it is at least Tiot a mem- 
ber of this series, and in support of his belief he suggests that if it 
were, why should it alone be retained in recording aU Initial-series 
dates, whereas the other three — the great-great-great cycle, the great- 
great cycle, and the great-cycle signs^ — have disappeared. 

The following explanation, the writer believes, satisfactorily accounts 
for all of these points, though it is advanced here only by way of sug- 
gestion as a possible solution of the meaning of the Initial-series 
introducing glyph. It is suggested that in Al we may have a sign 
representing "eternity," "this world," "time"; that is to say, a sign 
denoting the duration of the present world-epoch, the epoch of 
which the Maya civihzation occupied only a small part. The middle 
dot of the upper element, being 1, denotes that this world-epoch is 
the first, or present, one, and the whole glyph itself might mean ' ' the 
present world." The appropriateness of such a glyph ushering in 
every Initial-series date is apparent. It signified time in general, 
while the succeeding 7 glyphs denoted what particular day of time 
was designated in the inscription. 

But why, even admittiag the correctness of this interpretation of 
Al, should the great-great-great cycle, the great-great cycle, and 
the great cycle of their chronological scheme be omitted, and 
Initial-series dates always open with this glyph, which signifies 
time in general, followed by the current cycle ? The answer to this 
question, the writer believes, is that the cycle was the greatest 
period with which the Maya could have had actual experience. It 
will be shown in Chapter V that there are a few Cycle-8 dates 
actually recorded, as well as a half a dozen Cycle-10 dates. That 
is, the cycle, which changed its coefficient every 400 years, was a 
period which they could not regard as never changing within the 
range of human experience. On the other hand, it was the shortest 
period of which they were imcertain, since the great cycle could 
change its coefficient only every 8,000 years — practically eternity so 
far as the Maya were concerned. Therefore it could be onaitted as 
well as the two higher periods in a date without giving rise to con- 
fusion as to which great cycle was the current one. The cycle, on 
the contrary, had to be given, as its coefficient changed every 400 
years, and the Maya are -known to have recorded dates in at least 
three cycles — Nos. 8, 9, and 10. Hence, it was Great Cycle 19 for 
8,000 years, Great-great Cycle 11 for 160,000, and Great-great-great 
Cycle 1 for 3,200,000 years, whereas it was Cycle 9 for only 400 years. 
This, not the fact that the Maya never had a period higher than the 
cycle, the writer beheves was the reason why the three higher periods 
were omitted from Initial-series dates — they were unnecessary so far 
as accuracy was concerned, since there covdd never be any doubt 
concerning them. 



i^M 



MOELBY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 127 

It is not necessary to press this point further, though it is beHeved 
the foregoing conception of time had actually been worked out by 
the Maya. The archaic date recorded by Stela 10 at Tikal (9. 3.6.2. 0) 
makes this monument one of the very oldest in the Maya territory; 
indeed, there is only one other stela which has an earher Initial Series, 
Stela 3 at Tikal. In the archaic period from which this monument 
dates the middle dot of the trinal superfix in the Initial-series intro- 
ducing glyph may still have retained its numerical value, 1, but in 
later times this naiddle dot lost its numerical characteristics and 
frequently appears as a scroll itself. 

The early date of Stela 10 makes it not unUkely that this process 
of glyph elaboration may not have set in at the time it was erected, 
and consequently that we have in this simplified trinal element the 
genesis of the later elaborated form; and, finally, that Al, figure 60, 
may have meant "the present world-epoch" or something similar. 

In concluding the presentation of these three numbers the writer 
may express the opinion that a careful study of the period glyphs in 
figures 58-60 will lead to the foUowing conclusions: (1) That the six 
periods recorded in the first, the seven in the second, and the eight or 
nine in the third, all belong to the same series in each case ; and (2) 
that throughout the six terms of the first, the seven of the second, 
and the eight of the third, the series in each case conforms strictly 
to the vigesunal system of numeration given in Table VIII. 

As mentioned on page 116 (footnote 2), in this method of recording 
the higher numbers the kin sign may sometimes be omitted without 
affecting the nunaerical value of the series wherein the omission 
occurs. In such cases the coefiicient of the kin sign is usually pre- 
fixed to the uinal sign, the coefficient of the uinal itseK standing 
above the uinal sign. In figure 58, for example, the uinal and the 
kin coefficients are both 0. In this case, however, the on the left 
of the uinal sign is to be understood as belonging to the kin sign, 
which is omitted, while the above the uinal sign is the uinal's own 
coefficient 0. Again in figure 59, the kin sign is omitted and the kin 
coefficient 1 is prefixed to the uinal sign, while the uinal's own coeffi- 
cient 12 stands above the uinal sign. Similarly, the 12 uinals and 
17 kins recorded in figure 56, d, might as well have been written as 
in of the same figure, that is, with the kin sign omitted and its 
coefficient 17 prefixed to the uinal sign, whUe the urnal's own coeffi- 
cient 12 appears above. Or again, the 9 uinals and 18 kins recorded 
in / also might have been written as in "p, that is, with the kin sign 
omitted and the kin coefficient 18 prefixed to the uinal sign while 
the uinal's own coefficient 9 appears above. 

In aU the above examples the coefficients of the omitted kin signs 
are on the left of the uinal signs, while the uinal coefficients are above 
the uinal signs. Sometimes, however, these positions are reversed. 



128 



BtTEBATJ OF AMERICAN ETHNOLOGY 



[BULL. 57 



and the uinal coefficient stands on the left of the uinal sign, while the 
kin coefficient stands above. This interchange in certain cases prob- 
ably resulted from the needs of gljrphic balance and synametry. 
For example, in figure 62, a, had the kin coefficient 19 been placed on 
the left of the uinal sign, the uinal coefficient 4 would have been 
insufficient to fill the space above the period glyph, and consequently 
the corner of the glyph bl6ck would have appeared ragged. The 
use of the 19 above and the 4 to the left, on the other hand, properly 
fills this space, making a symmetrical glyph. Such cases, however, 
are unusual, and the customary position of the kin coefficient, when 
the kin sign is omitted, is on the left of the uinal sign, not above 
it. This practice, namely, omitting the kin sign in numerical series. 



OOOO 



,o O O 






om^) 




Fig. 62. Glyphs showing misplacement of the kin coefficient (a) or elimination of a period glyph (6, c); 
a, Stela E, Qairigua; &, Altar U, Copan; c, Stela J, Copan. 

seems to have prevailed extensively in connection with both Initial 
Series and Secondary Series; indeed, in the latter it is the rul6 to 
which there are but few exceptions. 

The omission of the kin sign, while by far the most common, is not 
the only example of glyph omission found in numerical series in the 
inscriptions. Sometimes, though very rarely, numbers occur in which 
periods other than the kin are wanting. A case in point is figure 62, h. 
Here a tun sign appears with the coefficient 13 above and 3 to the left. 
Since there are only two coefficients (13 and 3) and three time periods 
(tun, uinal, and kin), it is clear that the signs of both the lower periods 
have been omitted as well as the coefficient of one of them. In c of the 
last-mentioned figure a somewhat different practice was followed. 
Here, although three time periods are recorded — tuns,uinals and kins — 
one period (the uinal) and its coefficient have been omitted, and there 
is nothing between the kins and 10 tuns. Such cases are exceed- 
ingly rare, however, and may be disregarded by the beginner. 

We have seen that the order of the periods in the numbers in figure 
56 was just the reverse of that in the numbers shown in figures 58 
and 59 ; that in one place the kins stand at the top and in the other 
at the bottom; and finally, that this difference was not a vital one, 
since it had no effect on the values of the numbers. This is true, 
because in the first method of expressing the higher numbers, it 
matters not which end of the number comes first, the highest or the 



MOELDY] INTKODUCTION TO STUDY OF MAYA HIEEOGLYPHS 129 

lowest period, so long as its several periods always stand in the same 
relation to each other. For example, in figure 56, 2, 6 cycles, 1 7 katuns, 
2 tuns, 10 uinals, and kins represent exactly the same number as 
kins, 10 uinals, 2 tuns, 17 katuns, and 6 cycles; that is, with the 
lowest term first. 

It was explained on page 23 that the order in which the glyphs are 
to be read is from top to bottom and from left to right. Applying 
this rule to the inscriptions, the student will find that aU Initial Series 
are descending series; that in reading from top to bottom and left 
to right, the cycles will be encountered first, the katuns next, the 
tuns next, the uinals, and the kins last. Moreover, it will be found 
also that the great majority of Secondary Series are ascending series, 
that is, in reading from top to bottom and left to right, the kins will 
be encountered first, the uinals next, the tuns next, the katuns next, 
and the cycles last. The reason why Initial Series always should be 
presented as descending series, and Secondary Series usually as 
ascending series is unknown; though as stated above, the order in 
either case might have been reversed without affecting in any way 
the numerical value of either series. 

This concludes the discussion of the first method of expressing the 
higher numbers, the only method which has been found in the 
inscriptions. 

Second Method of Numeration 

The other method by means of which the Maya expressed their 
higher numbers (the second method given on p. 103) may be called 
"numeration by position," since in this method the numerical value 
of the symbols depended solely on position, just as in our own deci- 
mal system, in which the value of a figure depends on its distance 
from the decimal point, whole numbers being written to the left and 
fractions ttj the right. The ratio of increase, as the word "decimal" 
implies, is 10 throughout, and the numerical values of the consecutive 
positions increase as they recede from the decimal point in each 
direction, according to the terms of a geometrical progression. For 
example, in the number 8888.0, the second 8 from the decimal point, 
counting from right to left, has a value ten times greater than the first 
8, since it stands for 8 tens (80) ; the third 8 from the decimal point 
similarly has a value ten times greater than the second 8, since it 
stands for 8 hundreds (800); finally, the fourth 8 has a value ten 
times greater than the third 8, since it stands for 8 thousands 
(8,000). Hence, although the figures used are the same in each case, 
each has a different numerical value, depending solely upon its posi- 
tion with reference to the decimal point. 

In the second method of writing their numbers the Maya had 
devised a somewhat similar notation. Their ratio of increase was 20 in 
all positions except the third. The value of these positions increased 
43508°— Bull. 57—15 9 



130 BUEEAU OF AMERICAN ETHNOLOGY [boll. 57 

with their distance from the bottom, according to the terms of the 
vigesimal system shown in Table VIII. This second method, or 
"numeration by position," as it may be called, was a distinct advance 
over the first, since it required for its expression only the signs for 
the numerals to 19, inclusive, and did not involve the use of any 
period glyphs, as did the first method. To its greater brevity, no 
doubt, may be ascribed its use in the codices, where numerical calcu- 
lations running into numbers of 5 and 6 terms form a large part of 
the subject matter. It should be remembered that in numeration 
by position only the normal forms of the numbers — bar and dot 
numerals — are used. This probably results from the fact that head- 
variant numerals never occur independently, but are always prefixed 
to some other glyph, as period, day, or month signs (see p. 104). 
Since no period glyphs are used in numeration by position, only 
normal-form numerals, that is, bar and dot numerals, can appear. 

The numbers from 1 to 19, inclusive, are expressed in this method, as 
shown in figure 39, and the number as shown in figure 46. As all 
of these numbers are below 20, they are expressed as units of the first 
place or order, and consequently each shoiild be regarded as having 
been multiplied by 1 , the numerical value of the first or lowest position. 

The number 20 was expressed in two different ways: (1) By the 
sign shown in figure 45; and (2) by the numeral in the bottom 
place and the numeral 1 in the next place above it, as in figure 63, a. 
The first of these had only a very restricted use in connection with 
the tonalamatl, wherein numeration by position was impossible, and 
therefore a special character for 20 (see fig. 45) was necessary. 
See Chapter VI. 

The numbers from 21 to 359, inclusive, involved the use of two 
places — the kin place and the uinal place — which, according to Table 
VIII, we saw had numerical values of 1 and 20, respectively. For 
example, the number 37 was expressed as shown in figure 63, i. The 
17 in the kin place has a value of 17 (17 X 1) and the 1 in the uinal, or 
second, place a value of 20 (1 (the numeral) X 20. (the fixed numerical 
value of the second place)). The sum of these two products equals 
37. Again, 300 was written as in figure 63, c. The in the kin 
place has the value (0X1), and the 15 in the second place has the 
value of 300 (15 X 20), and the sum of these products equals 300. 

To express the numbers 360 to 7,199, inclusive, three places or 
terms were necessary — kins, uinals, and tuns — of which the last had a 
numerical value of 360. (See Table VIII.) For example, the number 
360 is shown in figure 63, d. The in the lowest place indicates that 
kins are involved, the in the second place indicates that uinals 
or 20's are involved, whUe the 1 in the third place shows that there is 1 
tun, or 360, kins recorded (1 (the numeral) X 360 (the fixed numerical 
value of the third position) ) ; the sum of these three products equals 
360. Again, the number 7,113 is expressed as shown in figure 63, e. 



MOELBY] INTE0DX7CTI0N TO STUDY OF MAYA HIEROGLYPHS 131 

The 13 in the lowest place equals 13 (13x1); the 13 in the second 
place, 260 (13X20); and the 19 in the third place, 6,840 (19x360). 
The sum of these three products equals 7,113 (13 + 260 + 6,840). 



<^ ^S ^ ^ 



^3S^ ^S!^^ ^^^BB 

<^^ a^M <:^^> 

•• sss 

/ 9 

•• •••• 



i j k 

Fig. 63. Examples of the second method of numeration, used exclusively in the codices. 

The numbers from 7,200 to 143,999, inclusive, involved the use of 
four places or terms — kins, uinals, tuns, and katuns — the last of 
which (the fourth place) had a numerical value of 7,200. (See Table 
VIII.) For example, the number 7,202 is recorded in figure 63, /. 



132 BUREAU OP AMERICAN ETHNOLOGY [boll. 57 

The 2 in the first place equals 2 (2x1); the in the second place, 
(0 X 20) ; the in the third place, (0 X 360) ; and the 1 in the fourth 
place, 7,200 (1 X 7,200). The sum of these four products equals 7,202 
(2 + + 0+ 7,200). Again, the number 100,932 is recorded in figure 
63, g. Here the 12 in the first place equals 12 (12 X 1); the 6 in the 
second place, 120 (6X20); the in the third place, (0x360); and 
the 14 in the fourth place, 100,800 (14x7,200). The sum of these 
four products equals 100,932 (12 + 120 + + 100,800). 

The immbers from 144,000 to 2,879,999, inclusive, involved the 
use of five places or terms — kins, uinals, tuns, katuns, and cycles. 
The last of these (the fifth place) had a nurnerical value of 144,000. 
(See Table VIII.) For example, the number 169,200 is recorded in 
figure 63, Ti. The in the first place equals (0x1); the in the 
second place, (0x20); the 10 in the third place, 3,600 (10x360); 
the 3 in the fourth place, 21,600 (3 X 7,200) ; and the 1 in the fifth place, 
144,000 (1 X 144,000). The sum of these five products equals 169,200 
(0 + + 3,600 + 21,600+144,000). Again, the number 2,577,301 is 
recorded in figure 63, i. The 1 in the first place equals 1 (1x1); 
the 3 in the second place, 60 (3 X 20) ; the 19 in the third place, 6,840 
(19 X 360) ; the 17 in the fourth place, 122,400 (17 X 7,200) ; and the 17 
in the fifth place, 2,448,000 (17x144,000). The sum of these five 
products equals 2,577,301 (1+60 + 6,480 + 122,400 + 2,448,000). 

The writing of numbers above 2,880,000 up to and including 
12,489,781 (the highest number found in the codices) involves the 
use of six places, or terms — kins, uinals, tuns, katuns, cycles, and 
great cycles — the last of which (the sixth place) has the numerical 
value 2,880,000. It will be remembered that some have held that 
the sixth place in the inscriptions contained only 13 units of the fifth 
place, or 1,872,000 units of the first place. In the codices, however, 
there are numerous calendric checks which prove conclusively that 
in so far as the codices are concerned the sixth place was composed of 
20 units of the fifth place. For example, the number 5,832,060 is 
expressed as in figure 63, j. The in the first place equals (0x1); 
the 3 in the second place, 60 (3 X 20) ; the in the third place, (0 X 
360) ; the 10 in the fourth place, 72,000 (10 X 7,200) ; the in the fifth 
place, (0x144,000); and the 2 in the sixth place, 5,760,000 (2X 
2,880,000). The sum of these six terms equals 5,832,060 (0 + 60 + + 
72,000 + 0+ 5,760,000). The highest number in the codices, as ex- 
plained above, is 12,489,781, which is recorded on page 61 of the 
Dresden Codex. This number is expressed as in figure 63, Tc. The 1 
in the first place equals 1 (1x1); the 15 in the second place, 300 (15 X 
20); the 13 in the third place, 4,680 (13x360); the 14 in the fourth 
place, 100,800 (14x7,200); the 6 in the fifth place, 864,000 (6x 
144,000); and the 4 in the sixth place, 11,520,000 (4x2,880,000). 
The sum of these six products equals 12,489,781 (1 + 300 + 4,680 + 
100,800 + 864,000 + 1 1,520,000) . 



MOBLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 133 

It is clear that in numeration by position the order of the units 
could not be reversed as in the &st method without seriously affecting 
their numerical values. This must be true, since in the second method 
the numerical values of the numerals depend entirely on their position — 
that is, on their distance above the bottom or first term. In the first 
method, the multiphcands — the period glyphs, each of which had a 
fixed numerical value — are always expressed * with their correspond- 
ing multipliers — the numerals to 19, inclusive; in other words, the 
period glyphs themselves show whether the series is an ascending or 
a descending one. But in the second method the multiplicands are 
not expressed. Consequently, since there is nothing about a column 
of bar and dot numerals which in itself indicates whether the series 
is an ascending or a descending one, and since in numeration by 
position a fixed starting point is absolutely essential, in their sec- 
ond method the Maya were obhged not only to fix arbitrarily the 
direction ef reading, as from bottom to top, but also to confine them- 
selves exclusively to the presentation of one kind of series only — that 
is, ascending series. Only by means of these two arbitrary rules was 
confusion obviated in numeration by position. 

However dissimilar these two methods of representing the numbers 
may appear at first sight, fundamentally they are the same, since 
both have as their basis the same vigesimal system of numeration. 
Indeed, it can not be too strongly emphasized that throughout the 
range of the Maya writings, codices, inscriptions, or Books of Chilam 
Balam^ the several methods of counting time and recording events 
found in each are all derived from the same source, and all are expres- 
sions of the same numerical system. 

That the student may better grasp the points of difference between 
the two methods they are here contrasted: 

Table XII. COMPARISON OF THE TWO METHODS OF NUMERATION 



FIRST METHOD 

1. Use confined almost exclusively to the 

inscriptions. 

2. Numerals represented by both normal 

forms and head variants. 

3. Numbers expressed by using the num- 

erals to 19, inclusive, as multipliers 
with the period glyphs as multipli- 
cands. 

4. Numbers presented as ascendiag or de- 

scending series. 

5. Direction of reading either from bot- 

tom to top, or vice versa. 

* A few exceptions to this have been noted on pp. 127, 128. 

2 The Books of Chilan Balam have been included here as they are also expressions of the native Maya 
mind. ' 



SECOND METHOD 

Use confLned exclusively to the co- 
dices. 

Numerals represented by normal forms 
exclusively. 

Numbers expressed by using the nu- 
merals to 19, inclusive, as multi- 
pliers in certain positions the fixed 
numerical values of which served as 
multiplicands. 

Numbers presented as ascendiag series 
exclusively. 

Direction of reading from bottom to top 
exclusively. 



134 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

We have seen in the foregoing pages (1 ) how the Maya wrote their 20 
numerals, and (2) how these numerals were used to express the higher 
numbers. The next question which concerns us is, How did they use 
these numbers in their calculations; or in other words, how was their 
arithmetic apphed to their calendar ? It may be said at the very 
outset in answer to this question, that in so far as known, numbers 
appear to Tw/ve had hut one use tJirougJiout the Maya texts, mt/meiy, to 
express the time elapsing between dates} In the codices and the inscrip- 
tions ahke all the numbers whose use is understood have been found 
to deal exclusively with the counting of time. 

This highly specialized use of the numbers in Maya texts has 
determined the first step to be taken in the process of deciphering 
them. Since the primary unit of the calendar was the day, all numbers 
should be reduced to terms of this unit, or in other words, to units of 
the first order, or place. ^ Hence, we may accept the following as the 
first step in ascertaining the meaning of any number: 

FmsT Step in Solving Maya Numbers 

Reduce all the units of the higher orders to units of its first, or 
lowest, order, and then add the resulting quantities together. 

The apphcation of this rule to any Maya number, no matter of 
how many terms, wiU always give the actual number of primary units 
which it contains, and in this form it can be more conveniently utihzed 
in connection with the calendar than if it were left as recorded, that is, 
in terms of its higher orders. 

The reduction of units of the higher orders to units of the first order 
has been explained on pages 105-133, but in order to provide the 
student with this same information in a more condensed and accessible 
form, it is presented in the following tables, of which Table XIII is 
to be used for reducing numbers to their primary units in the inscrip- 
tions, and Table XIV for the same purpose in the codices. 

1 This excludes, of course, the use of the numerals 1 to 13, inclusive, in the day names, and in the numer- 
ation of the cycles; also the numerals to 19, inclusive, when used to denote the positions of the days in 
the divisions of the year, and the position of any period in the division next higher. 

2 Various methods and tables have been devised to avoid the necessity of reducing the higher terms of 
Maya numbers to units of the first order. Of the former, that suggested by Mr. Bowditoh (1910: pp. 302- 
309) isprobably the most serviceable. Of tbe tables Mr. Goodman's Archaeic Annual Calendar and Archaeic 
Chronological Calendar (1897) are by far the best. By using either of the above the necessity of reducing the 
higher terms to units of the first order is obviated. On the other hand, the processes by means of which 
this is achieved in each case are far more complicated and less easy of comprehension than those of the 
method followed in this book, a method which from its simplicity might be termed perhaps the logical way, 
since it reduces all quantities to a primary unit, which is the same as the primary unit of the Maya cal- 
endar. This method was first devised by Prof. Ernst Forstemann, and has the advantage of being the most 
readily understood by the beginner, sufficient reason for its use in this book. 



MOELBY] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 



13-5 



Table XIII. VALUES OF HIGHER 
PERIODS IN TERMS OF LOWEST, 
IN INSCRIPTIONS 

1 great cycle= ' 2,880,000 





cycle 


144,000 




katun 


7,200 




tun 


360 




uinal 


20 




kin 


1 



Table XIV. VALUES OF HIGHER 
PERIODS IN TERMS OF LOWEST, 
IN CODICES 



I unit of the 6th place =2, 880, 000 
I unit of the 5th place 144,000 
1 unit of the 4th place 7,200 

1 unit of the 3d place 600 

1 unit of tTie 2d place 20 

1 unit of the 1st place 1 

It should be remembered, in using these tables, that each of the signs 
for the periods therein given has its own particular numerical value, 
and that this value in each case is a multipHcand which is to be multi- 
plied by the numeral attached to it (not shown in Table XIII) . For 
example, a 3 attached to the katun sign reduces to 21,600 units of the 
&st order (3x7,200). Again, 5 attached to the uinal sign reduces 
to 100 units of the first order (5x20). In using Table XIV, however, 
it should be remembered that the position of a numeral multiplier 
determines at the same time that multiplier's multiplicand. Thus a 
5 in the third place indicates that the 5's multiplicand is 360, the 
numerical value of the third place, and such a term reduces to 1,800 
units of the first place (5x360=1,800). Again, a 10 in the fourth 
place indicates that the lO's multiplicand is 7,200, the numerical value 
corresponding to the fourth place, and such a term reduces to 72,000 
units of the first place. 

Having reduced all the terms of a number to units of the 1st order, 
the next step in finding out its meaning is to discover the date from 
which it is counted. This operation gives rise to the second step. 

Second Step in Solving Maya Numbers 

Find the date from which the number is counted. 

This is not always an easy matter, since the dates from which Maya 
numbers are counted are frequently not expressed in the texts ; con- 
sequently, it is clear that no single rule can be formulated which will 
cover aU cases. There are, however, two general rules which will be 
found to apply to the great majority of numbers in the texts: 

Rule 1. When the starting point or date is expressed, usually, 
though not invariably, it precedes ^ the number counted from it. 

It should be noted, however, in connection with this rule, that the 
starting date hardly ever immediately precedes the number from 
which it is counted, but that several glyphs nearly always stand 

1 This number is formed on the basis of 20 cycles to a great cycle (20X144,000=2,880,000). The writer 
assumes that he has established the fact that 20 cycles were required to make 1 great cycle, in the inscrip- 
tions as well as in the codices. 

2 This is true in spite of the fact that in the codices the starting points frequently appear to follow— that 
is, they stand below — the numbers which are counted from them. In reality such cases are perfectly 
regular and conform to this rule, because there the order is not from top to bottom but from bottom to top, 
and, therefore, when read in this direction the dates come first. 



136 BUREAU OF- AMERICAN ETHNOLOGY [bpll. 57 

between.^ Certain exceptions to the above rule are by no means 
rare, and the student must be continually on the lookout for such 
reversals of the regular order. These exceptions are cases in which 
the starting date (1) follows the number counted from it, and (2) 
stands elsewhere in the text, entirely disassociated from, and unat- 
tached to, the number counted from it. 

The second of the above-mentioned general rules, covering the 
majority of cases, follows: 

Rule 2. When the starting point or date is not expressed, if the 
number is an Inital Series the date from which it should be counted 
will be found to be 4 Ahau 8 Cumliu.^ 

This rule is particularly useful in deciphering numbers in the 
inscriptions. For example, when the student finds a number which 
he can identify as an Initial Series,^ he may assume at once that such 
a number in all probability is counted from the date 4 Ahau 8 Cumhu, 
and proceed on this assumption. The exceptions to this rule, that 
is, cases in which the starting point is not expressed and the number 
is not an Initial Series, are not mmierous. No rule can be given cov- 
ering all such cases, and the starting points of such numbers can be 
determined only by means of the calculations given under the third 
and fourth steps, below. 

Having determined the starting point or date from which a given 
number is to be counted (if this is possible), the next step is to find 
out which way the count runs; that is, whether it is forward from 
the starting point to some later date, or whether it is iackward from 
the starting point to some earlier date. This process may be called 
the third step. 

Third Step in Solving Maya Numbers 

Ascertain whether the number is to be counted forward or backward 
from its starting point. 

It may be said at the very outset in this connection that the over- 
whelming majority of Maya numbers are coMnted forward from their 
starting points and not backward. In other words, they proceed from 
earlier to later dates and not vice versa. Indeed, the preponderance 
of the former is so great, and the exceptions are so rare, that the 
student should always proceed on the postulate that the count is 
forward until proved definitely to be otherwise. 

1 These intervening glyphs the writer believes, as stated in Chapter II, are those which tell the real story 
of the inscriptions. 

2 Only two exceptions to this rule have been noted throughout the Maya territory: (1) The Initial Series 
bn the east side of Stela C at Quirigua, and (2) the tablet from the Temple of the Cross at Palenque. It 
has been explained that both of these Initial Series are counted from the date 4 Ahau 8 Zotz. 

3 In the inscriptions an Initial Series may always be identified by the so-called introducing glyph (see 
flg. 24) which invariably precedes it. 




MOBLEY] IWTEODUCTIOK TO BTUDY OF MAYA HIBEOGLYPHS 137 

In the codices, moreover, when the count is backward, or contrary 
to the general practice, the fact is clearly indicated ' by a special char- 
acter. This character, although attached only to the lowest term '' 
of the number which is to be counted backward, is to be interpreted 
as applying to aU the other terms as well, its effect extending to the 
number as a whole. This "backward sign" (shown in fig. 64) is a 
circle drawn in red around the lowest term of the number which it 
affects, and is surmounted by a knot of the same color. An example 
covering the use of this sign is given in figure 64. Although the 
"backward sign" in this figure surrounds only the _ 

numeral in the first place, 0, it is to be interpreted, as 
we have seen, as applying to the 2 in the second place 
and the 6 in the third place. This number, expressed 
as 6 tuns, 2 uinals, and kins, reduces to 2,200 units 
of the first place, and in this form may be more readily 
handled (first step). Since the starting point usually 
precedes the number counted from it and since in figure 
64 the number is expressed by the second method, its 
starting point will be found standing below it. This yj^ ^^ -^-^^^^ 
foUows from the fact that in numeration by position showing the 
the order is from bottom to top. Therefore the start- "''?"^!'''^" 

x^ _ nus or back- 

ing point from which the 2,200 recorded in figure 64 is ward" signm 

counted will be found to be below it, that is, the date *»'='"i*««s- 

4 Ahau 8 Cumhu' (second step). Finally, the red circle and knot 

surrounding the lowest (0) term of this 2,200 indicates that this 

number is to be counted backward from its starting point, not 

forward (third step) . 

On the other hand, in the inscriptions no special character seems 
to have been used with a number to indicate that it was to be counted 
backward; at least no such sign has yet been discovered. In the 
inscriptions, therefore, with the single exception ^ mentioned below, 
the student can only apply the general rule given on page 136, that 
in the great majority of cases the count is forward. This rule will be 
found to apply to at least nine out of every ten numbers. The excep- 
tion above noted, that is, where the practice is so uniform as to render 
possible the formulation of an unfailing rule, has to do with Initial 
Series. This rule, to which there are no known exceptions, may be 
stated as follows: 

Rule 1. In Initial Series the count is always forward, and, in general 
throughout the inscriptions. The very few cases in which the count 
is backward, are confined chiefiy to Secondary Series, and it is in 

1 Professor FSrstemann has pointed out a few cases in the Dresden Codex in which, although the count 
is backward, the special character indicating the fact is wanting (fig. 64). (See Bulletin 28, p. 401.) 

^ There are a lew cases in which the "backward sign" includes also the numeral in the second position. 

» In the text wherein this number is found the date 4 Ahau 8 Cumliii stands below the lowest term. 

< It should be noted here that in the u Tiuhlay katunob also, from the Books of Chilan Balam, the count is 
always forward. 



138 BTJKBAU OF AMERICAN ETHNOLOGY [bull. 57 

dealing with this kind of series that the student will find the greatest 
number of exceptions to the general rule. 

Having determined the direction of the count, whether it is forward 
or backward, the next (fourth) step may be given. 

Fourth Step in Solving Maya Numbers 

To count the number from its starting point. 

We have come now to a step that involves the consideration of 
actual arithmetical processes, which it is thought can be set forth 
much more clearly by the use of specific examples than by the state- 
ment of general rules. Hence, we wiU formulate our rules after the 
processes which they govern have been fuUy explained. 

In counting any number, as 31,741, or 4.8.3.1 as it would be 
expressed in Maya notation,^ from any date, as 4 Ahau 8 Cumhu, 
there are four unloiown elements which have to be determined before 
we can write the date which the count reaches. These are: 

1. The day coefficient, which must be one of the numerals 1 to 13, 
inclusive. 

2. The day name, which must be one of the twenty given in Table I. 

3. The position of the day in some division of the year, which must 
be one of the numerals to 19, inclusive. 

4. The name of the division of the year, which must be one of the 
niaeteen given iu Table IH. 

These four unknown elements all have to be determined from (1) 
the starting date, and (2) the number which is to be counted from it. 

If the student will constantly bear in mind that all Maya sequences, 
whether the day coefficients, day signs, positions in the divisions of 
the year, or what not, are absolutely continuous, repeating themselves 
without any break or interruption whatsoever, he will better under- 
stand the calculations which follow. 

It was explaiued in the text (see pp. 41-44) and also shown graph- 
ically ia the tonalamatl wheel (pi. 5) that after the day coefficients 
had reached the number 13 they returned to 1, following each other 
indefinitely in this order without interruption. It is clear, therefore, 
that the highest multiple of 13 which the given number contains may 
be subtracted from it without affecting in any way the value of the 
day coefficient of the date which the number will reach when counted 
from the starting point. This is true, because no matter what the 
day coefficient of the starting point may be, any multiple of 13 will 
always bring the count back to the same day coefficient. 

1 For. transcribing the Maya numerical notation into the characters ol our own Arabic notation Maya 
students have adopted the practice of writing the various terms from left to right in a descending series, 
as the units of our decimal system are written. For example, 4 katuns, 8 tuns, 3 uinals, and 1 Mn are 
written 4.8.3.1; and 9 cycles, 16 katuns, 1 tun, uinal, and kins are written 9.16.1.0.0. According to this 
method, the highest term in each number is written on the left, the next lower on its right, the next lower 
on the right of that, and so on down through the units of the first, or lowest, order. This notation is very 
convenient for transcribing the Maya numbers and will be followed hereafter. 



MOBLBT] -. INTEODUCTION TO STUDY OP MAYA HIEKOGLYPHS 139 

Taking up the number, 31,741, which we have chosen for our first 
example, let us deduct from it the highest multiple of 13 which it 
contains. This will be found by dividing the number by 13, and 
multiplying the whole-number part of the resulting quotient by 13: 
31,741 H- 13 = 2,441t^. Multiplying 2,441 by 13, we have 31,733, 
which is the highest multiple of 13 that 31,741 contains; consequently 
it may be deducted from 31,741 without affecting the value of the 
resulting day coefiicient: 31,741 — 31,733 = 8. In the example under 
consideration, therefore, 8 is the number which, if counted from the 
day coefficient of the starting point, will give the day coefficient of 
the resulting date. In other words, after dividing by 13 the only 
part of the resulting quotient which is used in determining the new 
day coefficient is the numerator of the fractional part.^ Hence the 
following rule for determining the first unknown on page 138 (the day 
coefficient) : 

Buie 1. To find the new day coefficient divide the given number 
by 13, and count forward. the numerator of the fractional part of the 
resulting quotient frona the starting point if the count is forward, 
and backward if the count is backward, deducting 13 in either case 
from the resulting number if it should exceed 13. 

Applying this rule to 31,741, we have seen above that its division 
by 13 gives as the fractional part of the quotient ^. Assuming that 
the count is forward from the starting point, 4 Ahau 8 Cninlin, if 8 
(the numerator of the fractional part of the quotient) be counted 
forward from 4, the day coefficient of the starting point (4 Ahau 
8 Cnmliu), the day coefficient of the resulting date will be 12 (4 + 8). 
Since this number is below '13, the last sentence of the above rule has 
ho application in this case. In counting forward 31,741 from the 
date 4 Ahau 8 Cumhu, therefore, the day coefficient of the resulting 
date will be 12; thus we have determined our first unknown. Let 
us next find the second unknown, the day sign to which this 12 is 
prefixed. 

It was explained on page 37 that the twenty day signs given in 
Table I succeed one another in endless rotation, the first following 
immediately the twentieth no matter which one of the twenty was 
chosen as the first. Consequently, it is clear that the highest mul- 
tiple of 20 which the given number contains may be deducted from it 
without affecting in any way the name of the day sign of the date 
which the number will reach when counted from the starting point. 
This is true becatise, no matter what the day sign of the starting 
point may be, any multiple of 20 will always bring the count back to 
the same day sign. 

1 The Eeason for rejecting all parts of the quotient except the numerator of the fractional part is that this 
part alone shows the actual number of units which have to be counted either forward or backward, as the 
count may be, in order to reach the number which exactly uses up or finishes the dividend — the last unit 
of the number which has to be counted. 



140 BUEEAU OP AMERICAN ETHNOLOGY [bull. 57 

Returning to the number 31,741, let us deduct from it the highest 
multiple of 20 which it contains, found |>y dividing the number-by 
20 and multiplying the whole number part of the resulting quotisnt 
by 20; 31,741 -h20 = 1,587-^. Multiplyiiig 1,587 by 20, we have 
31,740, which is the highest multiple of 20 that 31,741 contains, and 
which maybe deducted from 31,741 without affecting the resulting 
day sign; 31,741—31,740 = 1. Therefore in the present example 1 
is the number which, if counted forward from the day sign of the 
starting point in the sequence of the 20 day signs given in Table I, 
will reach the day sign of the resulting date. In other words, after 
dividing by 20 the only part of the resulting quotient which is used 
in determining the new day sign is the numerator of the fractional 
part. Thus we may formulate the rule for determining the second 
unknown on page 138 (the day sign) : 

Rule 2. To find the new day sign, divide the given number by 20, 
and count forward the numerator of the fractional part of the result- 
ing quotient from the starting point in the sequence of the twenty 
day signs given in Table I, if the count is forward, and backward if 
the count is backward, and the sign reached will be the new day sign. 

Applying this rule to 31,741, we have geen above that its division 
by 20 gives us as the fractional part of the quotient, -^. Since the 
count was forward from the starting point, if 1 (the numerator of the 
fractional part of the quotient) be counted forward in the sequence 
of the 20 day signs in Table I from the day sign of the starting point, 
Ahan (4 Ahau 8 Cumhu), the day sign reached will be the day sign 
of the resulting date. Counting forward 1 from Ahan in Table- I, 
the day sign Imix is reached, and Imix, "therefore, will be the new 
day sign. Thus our second unknown is determined. 

By combining the above two values, the 12 for the first unknown 
and Imix for the second, we can now say that in counting forward 
31,741 from the date 4 Ahau 8 Cumhu, the day reached will be 12 Imix. 
It remains to find what position this particular day occupied in the 
365-day year, or haab, and thus to determine the third and fourth 
unknowns on page 138. Both of these may be found at one time by 
the same operation. 

It was explained on pages 44-51 that the Maya year, at least in 
so far as the calendar was concerned, contained only 365 days, divided 
into 18 uinals of 20 days each, and the xma Jcaba Mn of 5 days; and 
further, that when the last position in the last division of the year 
(4 Uayeb) was reached, it was followed without interruption by the 
first position of the first division of the next year (0 Pop); and, 
finally, that this sequence was continued indefinitely. Consequently 
it is clear that the highest multiple of 365 which the given number 
contains may be subtracted from it without affecting in any way the 
position in the year of the day which the number will reach when 



MOBLEY] INTKODUOTION TO STUDY OF MAYA HIEROGLYPHS 



141 



counted from the starting point. This is true, because no matter 
what position in the year the day of the starting point may occupy, 
any multiple of 365 will bring the count back again to the same 
position in the year. 

Returning again to the number 31,741, let us deduct from it the 
highest multiple of 365 which it contains. This will be found by 
dividing the number by 365 and multiplying the whole number part 
of the resulting quotient by 365: 31,741 X 365 = 86f|i. Multiplying 
86 by 365, we have 31,390, which is the highest multiple that 31,741 
contains. Hence it may be deducted from 31,741 without affecting 
the position in the year of the resulting day; 31,741-31,390 = 351. 
Therefore, in the present example, 351 is the number which, if 
counted forward from the year position of the starting date in the 
sequence of the 365 positions in the year, given in Table XV, will 
reach the position in the year oi the day of the resulting date. This 
enables us to formulate the rule for determining the third and fourth 
unknowns on page 138 (the position in the year of the day of the re- 
sulting date) : 

Rule 3. To find the position ia the year of the new day, divide 
the given number by 365 and count forward the numerator of the 
fractional part of the resulting quotient from the year position of 
the starting point in the sequence of the 365 positions of the year 
shown in Table XV, if the count is forward; and backward if the 
count is backward, and the position reached will be the position in 
the year which the day of the resulting date will occupy. 

Table XV. THE 365 POSITIONS IN THE MAYA YEAR 



Montti. 



g. 









I 



Position. 
Do.. 
Do.. 
Do.. 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 
Do... 



10 
11 
12 
13 
14 
15 
16 
17 
18 
19 



10 
11 
12 
13 
14 
15 
16 
17 
18 
19 





1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

14 
15 

16 
17 
18 
19 





1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

.17 

18 

19 





1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

18 

19 





1 

2 

3 

4 

5 

6 

7 

S' 

^ 
10 
11 
12 
13 
14 
15 
16 
17 
IS- 
IS.' 



142 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

Applying this rule to the number 31,741, we have seen above that 
its division by 365 gives 351 as the numerator of the fractional part of 
its quotient. Assuming that the count is forward from the starting 
point, it will be necessary, therefore, to count 351 forward in Table 
XV from the position 8 Ciimhu, the position of the day of the starting 
point, 4 Ahau 8 Cumliu. 

A glance at the month of Cumliu in Table XV shows that after the 
position 8 Cumhu there are 11 positions in that month; adding to 
these the 5 in TJayeb, the last division of the year, there will be in all 
16 more positions before the first of the next year. Subtracting 
these from 351, the total number to be counted forward, there remains 
the number 335 (351-16), which must be counted forward in Table 
XV from the beginning of the year. Since each of the months has 
20 positions, it is clear that 16 months will be used before the month 
is reached in which wiU fall the 335th position from the beginning of 
the year. In other words, 320 positions of our 335 wUl exactly use 
up all the positions of the first 16 months, namely. Pop, Uo, Zip, 
Zotz, Tzec, Xul, Taxkin, Mol, Chen, Tax, Zac, Ceh, Mac, Eankin, 
Muan, Pax, and will bring us to the beginning of the 17th month 
(Kayab) with still 15 more positions to count forward. If the student 
will refer to this month in Table XV he wiU see that 15 positions 
counted forward in this month wiU reach the position 14 Kayab, 
which is also the position reached by counting forward 31,741 posi- 
tions from the starting position 8 Cumhu. 

Having determined values for all of the unknowns on page 138, we 
can now say that if the number 31,741 be counted forward from the 
date 4 Ahau 8 Cumhu, the date 12 Imix 14 Kayab will be reached. 
To this latter date, i. e., the date reached by any count, the name "ter- 
minal date" has been given. The rules indicating the processes by 
means of which this terminal date is reached apply also to examples 
where the count is hackward, not forward, from the starting point. 
In such cases, as the rules say, the only difference is that the 
numerators of the fractional parts of the quotients resulting from the 
different divisions are to be counted backward from the starting 
points, instead of forward as in the example above given. 

Before proceeding to apply the rules by means of which our fourth 
step or process (see p. 138) may be carried out, a modification may 
sometimes be introduced which will considerably decrease the size 
of the number to be counted without affecting the values of the 
several parts of its resulting terminal date. 

We have seen on pages 51-60 that in Maya chronology there were 
possible only 18,980 different dates — that is, combinations of the 260 
days and the 365 positions of the year — and further, that any given 
day of the 260 could return to any given position of the 365 only after 
the lapse of 18,980 days, or 52 years. 



MOELDY] INTRODUCTION TO STUDY OP MAYA HIEEOGLYPHS 143 

Since the foregoing is true, it follows, that this number 18,980 or 
any multiple thereof, may be deducted from the number whioh is to 
be counted without affecting in any way the terminal date which the 
number will reach when counted from the starting point. It is 
obvious that this modification applies only to numbers which are 
above 18,980, all others being divided by 13, 20, and 365 directly, as 
indicated ia rules 1, 2, and 3, respectively. This enables us to 
formulate another rule, which should be applied to the number to 
be counted before proceeding with rules 1,2, and 3 above, if that 
number is above 18,980. 

Bule. If the number to be counted is above 18,980, first deduct 
from it the highest multiple of 18,980 which it contains. 

This rule should be applied whenever possible, since it reduces the 
size of the nmnber to be handled, and consequently involves fewer 
calculations. 

In Table XVT are given 80 Calendar Rounds, that is, 80 multiples 
of 18,980, iu terms of both the Maya notation and our own. These 
will be found sufficient to cover most numbers. 

Applying the above rule to the number 31,741, which was selected 
for our first example, it is seen by Table XVI that 1 Calendar Eound, 
or 18,980 days, may be deducted from it; 31,741-18,980 = 12,761. 
In other words, we can count the number 12,761 forward (or back- 
ward had the count been backward iu om- example) from the starting 
point 4 Ahau 8 Cumhu, and reach exactly the same terminal date as 
though we had counted forward 31,741, as iu the first case. 

Mathematical proof of this point follows : 

12,761 H- 13 = 981^ 12,7614-20 = 638^ 12,761 -^ 365 = 34||^ 

The numerators of the fractions ia these three quotients are 8, 1, 
and 351; these are identical with the numerators of the fractions in 
the quotients obtained by dividing 31,741 by the same divisors, those 
indicated iu rules 1, 2, and 3, respectively. Consequently, if these 
three numerators be counted forward from the corresponding parts 
of the starting point, 4 Ahau 8 Cumhu, the residting terms together 
will form the correspondirig parts of the same terminal date, 12 Imix 
14 Kayab. 

Similarly it could be .shown that 50,721 or 69,701 counted forward 
or backward from any starting poiut would both reach this same ter- 
minal date, since subtracting 2 Calendar Hounds, 37,960 (see Table 
XVI), from the first, and 3 Calendar Rounds, 56,940 (see Table XVI), 
from the second, there would remain in each case 12,761. The student 
will find his calculations greatly facilitated if he will apply this rule 
whenever possible. To familiarize the student with the working of 
these rules, it is thought best to give several additional examples 
involving their use. 



144 



BUREAU OF AMERICAN ETHNOLOGY 



[BULI-. 57 



Table XVI. 80 CALENDAR ROUNDS EXPRESSED IN ARABIC AND 

MAYA NOTATION 



Calendar 
Rounds 


Days 


Cycles, etc. 


Calendar 
Bounds 


Days 


Cycles, etc. 


1 


18, 980 


2. 12. 13. 


41 


778, 180 


5. 8. 1.11.0 


2 


37, 960 


5. 5. 8.0 


42 


797, 160 


5.10.14. 6.0 


3 


56, 940 


7.18. 3.0. 


43 


816, 140 


5.13. 7. 1.0 


, 4 


75, 920 


10. 10. 16. 


44 


835, 120 


5.15.19.14.0 


5 


94, 900 


13. 3.11.0 


45 


854, 100 


5.18.12. 9.0 


6 


113,880 


15.16. 6.0 


46 


873, 080 


6. 1. 5. 4.0 


7 


132, 860 


18. 9. 1.0 


47 


892,060 


6. 3.17.17.0 


8 


151, 840 


1. 1. 1.14.0 


48 


911,040 


6. 6.10.12.0 


9 


170, 820 


1. 3.14. 9.0 


49 


930, 020 


6. 9. 3. 7.0 


10 


189, 800 


1. 6. 7. 4,0 


50 


949, 000 


6.11.16. 2.0 


11 


208, 780 


1. 8.19.17.0 


51 


967, 980 


6.14. 8.15.0 


12 


227, 760 


1.11.12.12.0 


52 


986, 960 


6.17. 1.10.0 


13 


246, 740 


1. 14. 5. 7.0 ' 


53 


1,005,940 


6.19.14. 5.0 


14 


265, 720 


1.16.18. 2.0 : 


54 


1, 024, 920 


7. 2. 7. 0.0 


15 


284, 700 


1. 19. 10. 15. ' 


55 


1, 043, 900 


7. 4.19.13.0 


16 


303, 680 


2. 2. 3. 10. 


56 


1, 062, 880 


7. 7.12.. 8.0 


17 


322, 660 


2. 4. 16. 5. 


57 


1,081,860 


7.10. 5. 3.0 


18 


341, 640 


2. 7. 9. 0. 


58 


1, 100, 840 


7. 12. 17. 16. 


19 


360, 620 . 


2.10. 1.13.0 


59 


1, 119, 820 


7. 15. 10. 11. 


20 


379, 600 


2.12.14. 8.0 


60 


1, 138, 800 


7.18. 3. 6.0 


21 


398, 580 


2.15. 7. 3.0 


61 


1, 157, 780 


8. 0.16. 1.0 


22 


417, 560 


2. 17. 19. 16. 


62 


1, 176, 760 


8. 3. 8.14.0 


23 


436, 540 


3. 0.12.11.0 


63 


1, 195, 740 


8. 6. 1. 9.0 


24 


455, 520 


3. 3. 5. 6.0 


64 


1,214,720 


8. 8.14. 4.0 


25 


474, 500 


3. 5.18. 1.0 


65 


1, 233, 700 


8.11. 6.17.0 


26 


493, 480 


3. 8.10.14.0 


66 


1, 252, 680 


8. 13. 19. 12. 


27 


512, 460 


3.11. 3. 9.0 


67 


1, 271, 660 


8.16.12. 7.0 


28 


531, 440 


3.13.16. 4.0 


68 


1, 290, 640 


8.19. 5. 2.0 


29 


550, 420 


3.16. 8.17.0 


69 


1, 309, 620 


9. 1.17.15.0 


30 


569,400 


3.19. 1.12.0 


70 


1, 328, 600 


9. 4.10.10.0 


31 


588, 380 


4. 1.14. 7.0 


71 


1, 347, 580 


9. 7. 3. 5.0 


32 


607, 360 


4. 4. 7. 2.0 


72 


1, 366, 560 


9. 9.16. 0.0 


33 


626, 340 


4. 6.19.15.0 


73 


1, 385, 540 


9.12. 8.13.0 


34 


645, 320 


4. 9.12.10.0 


74 


1,404,520 


9.15. 1. 8.0 


35 


664, 300 


4.12. 5. 5.0 


75 


1,423,500 


9.17.14. 3.0 


36 


683,280 


4.14.18. 0.0 


76 


1,442,480 


10. 0. 6.16.0 


37 


702, 260 


4. 17. 10. 13. 


77 


1, 461, 460 


10. 2.19.11.0 


38 


721, 240 


5. 0. 3. 8.0 


78 


1, 480, 440 


10. 5.12. 6.0 


39 


740, 220 


5. 2.16. 3.0 


79 


1, 499, 420 


10. 8. 5. 1.0 


40 


759, 200 


5. 5. 8.16.0 


80 


1,518,400 


10. 10. 17. 14. 



MORLBY] INTBODUCTION TO STUDY OF MAYA HIBKOGLYPHS 145 

Let US count forward the number 5,799 from the starting point 
2 Kan 7 Tzec. It is apparent at the outset that, since this number 
is less than 18,980, or 1 Calendar Round, the preliminary rule given 
on page 143 does not apply in this case. Therefore we may proceed 
with the first rule given on page 139, by means of which the new day 
coefficient may be determined. Dividing the given number by 13 
we have: 5,799 -e 13 =446^15-. Counting forward the numerator of the 
fractional part of the resulting quotient (1) from the day coefficient 
of the starting point (2), we reach 3 as the day coefficient of the 
terminal date. 

The second rule given on page 140 tells how to find the day sign of 
the terminal date. Dividing the given number by 20, we have: 
5,799-^20 = 289^. Counting forward the numerator of the frac- 
tional part of the resulting quotient (19) from the day sign of the 
starting point, Kan, in the sequence of the twenty-day signs given 
in Table I, the day sign Akbal will be reached, which will be the 
day sign of the terminal date. Therefore the day of the terminal 
date will be 3 Akbal. 

The third rule, given on page 141, tells how to find the position 
which the day of the terminal date occupied in the 365-day year. 
Dividing the given number by 365, we have: 5,799 4-365 = 15|-|f. 
Counting forward the numerator of the fractional part of the resulting 
quotient, 324, from the year position of the starting date, 7 Tzec, in 
the sequence of the 365 year positions given in Table XV, the position 
6 Zip will be reached as the position in the year of the day of the 
terminal date. The count by means of which the position 6 Zip is 
determined is given in detail. After the year position of the starting 
point, 7 Tzec, it requires 12 more positions (Nos. 8-19, inclusive) 
before the close of that month (see Table XV) will be reached. And 
after the close of Tzec, 13 uinals and the xma kaba kin must pass 
before the end of the year; 13x20 + 5 = 265, and 265 + 12=277. 
This latter number subtracted from 324, the total number of posi- 
tions to be counted forward, will give the number of positions which 
remain to be counted in the next year following: 324 — 277 = 47. 
Counting forward 47 in the new year, we find that it will \ise up the 
months Pop and Uo (20 + 20=40) and extend 7 positions into the 
month Zip, or to 6 Zip. Therefore, gathering together the values 
determined for the several parts of the terminal date, we may say 
that in counting forward 5,799 from the starting point 2 Kan 7 Tzec, 
the terminal date reached will be 3 Akbal 6 Zip. 

For the next example let us select a much higher niunber, say 

322,920, which we will asstune is to be counted forward from the 

starting point 13 Ik Zip. Since this number is above 18,980, we 

may apply our preliminary rule (p. 143) and deduct all the Calendar 

43508°— Bull. 57—15 10 



146 BUREAU OF AMERICAN ETHNOLOGY [Bni-L. 57 

Rounds possible. By turning to Table XVI we see thart 17 Calendar 
Rounds, or 322,660, may be deducted from our number: 322,920- 
322,660 = 260. In other words, we can use 260 exactly as though it 
were 322,920. Dividing by 13, we have 2604-13 = 20. Since there 
is no fraction in the quotient, the numerator of the fraction will be 
0, and counting forward from the day coefficient of the starting 
point, 13, we have 13 as the day coefficient of the terminal date 
(rule 1, p. 139). Dividing by 20 we have 260-h20 = 13. Since there 
is no fraction in the quotient, the numerator of the fraction will be 
0, and counting forward from the day sign of the starting point, Ik 
in Table I, the day sign Ik will remain the day sign of the terminal 
date (rule 2, p. 140). Combining the two values just determined, 
we see that the day of the terminal date wUl.be 13 Ik, or a day of the 
same name as the day of the starting point. This follows also from 
the fact that there are only 260 differently named days (see pp. 41-44) 
and any given day will have to recur, therefore, after the lapse 
of 260 days.i Dividing by 365 we have: 260-^365=||f. Counting 
forward the nmnerator of the fraction, 260, from the year position of 
the starting point, Zip, in Table XV, the position in the year of the 
day of the terminal date will be found to be Pax. Since 260 days 
equal just 13 uinals, we have only to count forward from Zip 13 
uinals in order to reach the year position; that is, Zotz is 1 uinal; 
to Tzec 2 uinals, to Xul 3 uinals, and so on in Table XV to Pax, 
which will complete the last of the 13 uinals (rule 3, p. 141). 

Combining the above values, we ffiid that in counting forward 
322,920 (or 260) from the starting point 13 Ik Zip, the terminal 
date reached is 13 Ik Pax. 

In order to illustrate the method of procedure when the count is 
hackward, let us assume an example of this kind. Suppose we count 
backward the number 9,663 from the starting point 3 Imix 4 Uayeb. 
Since this number is below 18,980, no Calendar Round can be deducted 
from it. Dividing the given nmnber by 13, we have: 9,663-^13 = 
743^. Counting the numerator of the fractional part of this quo- 
tient, 4, hackward from the day coefficient of the starting point, 3, 
we reach 12 as the day coefficient of the terminal date, that is, 2, 1, 
13, 12 (rule 1, p. 139). Dividing the given number by 20, we have: 
9,663 + 20=483-^. Coimting the numerator of the fractional part 
of this quotient, 3, hackward from the day sign of the starting point, 
Imix, in Table I, we reach Eznab as the day sign of the terminal 
date (Ahau, Cauac, Eznab); consequently the day reached in the 
coimt will be 12 Eznab. Dividing the given number by 365, we have 

1 The student can prove tMs point for himself by turning to the tonalamatl wheel in pi. 5; after selecting 
amy particular day, as 1 Ik for example, proceed to count 260 days from this day as a starting point, in 
either direction around the wheel. No matter in which direction he' has counted, whether beginning 
with 13 Imix or 2 Akbal, the 260th day will be 1 Ik again. 



MORLEY] INTRODUCTIOSr TO STUDY OP MAYA HIEROGLYPHS 147 

9,663 4- 365 = 26^^. Counting backward the numerator of the frac- 
tional part of this quotient, 173, from the year position of the starting 
point, 4 Uayeb, the year position of the terminal date will be found to 
be 11 Yax. Before position 4 Uayeb (see Table XV) there are 4 
positions in that division of the year (3, 2, 1, 0) . Counting these hack- 
ward to the end of the month Cumliu (see Table XV), we have left 
169 positions (173—4 = 169); this equals 8 uinals and 9 days extra. 
Therefore, beginning with the end of Cumliu, we may count backward 
8 whole uinals, namely: Cumliu, Kayab, Pax, Muan, Kankin, Mac, 
Ceh, and Zac, which will bring us to the end of Yax (since we are 
counting backward) . As we have left still 9 days out of our original 
173, these must be counted backward from position Zac, that is, 
beginning with position 19 Yax: 19, 18, 17, 16, 15, 14, 13, 12, 11; so 
11 Yax is the position ia the year of the day of the terminal date. 
Assembling the above values, we find that in counting the number 
9,663 backward from the starting point, 2 Imix 4 Uayeb, the terminal 
date is 12 Eznab 11 Yax. Whether the count be forward or back- 
ward, the method is the same, the only difference being in the direc- 
tion of the coiinting. 

This concludes the discussion of the actual arithmetical processes 
involved in coimting forward or backward any given munber from 
any given date; however, before explaining the fifth and final step 
in deciphering the Maya numbers, it is first necessary to show how 
this method of counting was apphed to the Long Count. 

The nmnbers used above in connection with dates merely express 
the difference in time between starting points and terminal dates, 
without assigning either set of dates to their proper positions in Maya 
chronology; that is, in the Long Count. Consequently, since any Maya 
date recurred at successive intervals of 52 years, by the time their 
historic period had been reached, more than 3,000 years after the 
starting point of their chronology, the Maya had upward of 70 dis- 
tinct dates of exactly the same name to distinguish from one another. 

It was stated on page 61 that the 0, or starting point of Maya 
chronology, was the date 4 Ahau 8 Cumhu, from which all subsequent 
dates were reckoned; and further, on page 63, that by recording the 
number of cycles, katuns, trnis, uinals, and kins which had elapsed 
in each case between this date and any subsequent dates in the Long 
Count, subsequent dates of the same name could be readily distin- 
guished from one another and assigned at the same time to their 
proper positions in Maya chronology. This method of fixing a date 
in the Long Count has been designated Initial-series dating. 

The generally accepted method of writing Initial Series is as follows: 
9.0.0.0.0. 8 Ahau 13 Ceh 
The particular Initial-Series written here is to be interpreted thus: 
"Counting forward 9 cycles, katuns, tims, uinals, and kins 



148 BUREAU OP AMERICAN ETHNOLOGY [bull. 57 

from 4 Ahau 8 Cumhu, the starting point of Maya chronology (always 
Tinexpressed in Initial Series), the terminal date reached will be 8 
Ahau 13 Ceh." » Or again: 

9.14.13.4.17. 12 Caban 5 Kayab 
This Inital Series reads thus: "Coimting forward 9 cycles, 14 katuns, 
13 tims, 4 uinals, and 17 kins from 4 Ahau 8 Cumhu, the starting 
point of Maya chronology (unexpressed), the terminal date reached 
will be 12 Caban 5 Kayab." 

The time which separates any date from 4 Ahau 8 Cumhu may 
be called that date's Initial-series value. For example, in the first 
of the above cases the number 9.0.0.0.0 is the Initial-series value of 
the date 8 Ahau 13 Ceh, and in the second the number 9.14.13.4.17 
is the Initial-series value of the date 12 Caban 5 Kayab. It is clear 
from the foregoing that although the date 8 Ahau 13 Ceh, for example, 
had recmred upward of 70 times since the beginning of their chro- 
nology, the Maya were able to distinguish any particiilar 8 Ahau 13 Ceh 
from all the others merely by recording its distance from the starting 
point; in other words, giving thereto its particular Initial-series 
value, as 9.0.0.0.0. in the present case. Simiilarly, any particiilar 12 
Caban 5 Kayab, by the addition of its corresponding Initial-series 
value, as 9.14.13.4.17 in the case above cited, was absolutely fixed 
in the Long Count — that is, iu a period of 374,400 years. 

Returning now to the question of how the counting of numbers was 
applied to the Long Count, it is evident that every date in Maya 
chronology, starting points as well as terminal dates, had its own par- 
ticular Initial-series value, though in many cases these values are not 
recorded. However, in most of the cases in which the Initial-series 
values of dates are not recorded, they may be calculated by means 
of their distances from other dates, whose Initial-series values are 
known. This adding and subtracting of numbers to and from Initial 
Series ^ constitutes the application of the above-described arithmetical 
processes to the Long Count. Several examples of this use are given 
below. 

Let us assume for the first case that the number 2.5.6.1 is to be 
counted forward from the Initial Series 9.0.0.0.0 8 Ahau 13 Ceh. By 
multiplying the values of the katims, tuns, uinals, and kins given in 
Table XIII by their corresponding coefficients, in this case 2, 5, 6, 
and 1, respectively, and adding the resulting products together, we 
find that 2.5.6.1 reduces to 16,321 units of the first order. 

Counting this forward from 8 Ahau 13 Ceh as indicated by the rules 
on pages 138-143, the terminal date 1 Imix 9 Yaxkin will be reached. 

1 The student may prove this for himseU by reducing 9.0.0.0.0 to days (1,296,000), and counting forward 
this number from the date 4 Ahau 8 Cumhu, as described in the rules on pages 138-143. The terminal 
date reached will be 8 Ahau 13 Ceh, as given above. 

2 Numbers may also be added to or subtracted from Period-ending dates, since the positions of such dates 
are also fixed in the Long Count, and consequently may b« used a.? bases of reference for dates whose posi- 
tions in the Long Count are not recotded. 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 149 

Moreover, since the Initial-series value of the starting point 8 Ahau 
13 Ceh was 9.0.0.0.0, the Initial-series value of 1 Imix 9 Yaxkin, the 
terminal date, may be calculated by adding its distance from 8 Ahau 
13 Cell to the Initial-series value of that date : 

9.0.0.0.0 (Initial-series value of starting point) 8 Ahau 13 Ceh 

2.5.6.1 (distance from 8 Ahau 13 Ceh to 1 Imix 9 Yaxkin) 
9.2.5.6.1 (Initial -series value of terminal date) 1 Imix 9 Yaxkin 

That is, by calculation we have determined the Initial-series value 
of the particular 1 Imix 9 Yaxkin, which was distant 2.5.6.1 from 
9.0.0.0.0 8 Ahau 13 Ceh, to be 9;2.5.6.1, notwithstanding that this 
■fact was not recorded- 

The student may prove the accuracy of this calculadon by treating 
9.2.5.6.1 1 Imix 9 Yaxkin as a new Initial Series and counting forward 
9.2.5.6.1 from 4 Ahau 8 Cumhu, the starting point of all Initial Series 
known except two. If our calculations are correct, the former date 
will be reached just as if we had coimted forward only 2.5.6.1 from 
9.0.0.0.0 8 Ahau 13 Ceh. 

In the above example the distance number 2.5.6.1 and the date 
1 Imix 9 Yaxkin to which it reaches, together are called a Secondary 
Series. This method of dating already described (see pp. 74-76 et seq. ) 
seems to have been used to avoid the repetition of the Initial-series 
values for all the dates in an inscription. For example, in the accom- 
panying text — 

9.12. 2. 0.16 5 Cib 14 Yaxkin 

12. 9.15 
[9.12.14.10.11] ^ - 9 Chuen 9 Kankin 

- 5 
[9.12.14.10.16] 1 Cib 14 Kankin 

1. 0. 2. 5 
[9.13.14.13. 1] 5 Imix 19 Zac 

1 In adding two Maya numbers, for example 9.12.2.0.16 and 12.9.5, care should be taken first to arrange 

lite miits under like, as: ( 

9.12. 2. 0.16 

12. 9. 5 



9.12.14.10. 1 
Next, beginning at the right, the kins or units of the 1st place are added together, and after all the 20s 
(here 1) have been deducted from this sum, place the remainder (here 1) in the kin place. Next add the 
uinals, or units of the 2d place, adding to them 1 for each 20 which was carried forward from the 1st place. 
After all the ISs possible have been deducted from this sum (here 0) place the remaindor (here 10) in the 
uinal place. Next add the tuns, or units of the 3d place, adding to them 1 for each 18 which was carried 
forward from the 2d place, and after deducting all the 20s possible (here 0) place the remainder (here 14) 
in the tun place. Proceed in this manner until the highest units present have been added and written 
below. 
Subtraction is just the reverse of the preceding. Using the same numbers: 

9.12. 2.0.16 
12.9. 6 



9.11. 9.9.11 
5 kins from 16=11; 9 uinals from 18 uinals (1 tun has to be borrowed)=9; 12 tuns from 21 tuns (1 katun has 
to be borrowed, which, added to the 1 tun left in the minuend, makes 21 tuns)='9 tuns; katuns from 
11 katuns (1 katun having been borrowed)= 11 katuns; and cycles from 9 cycles= 9 cycles. 



150 BUREAU OF AMEBIOAN ETHNOLOGY [bull. 57 

the only parts actually recorded are the. Initial Series 9.12.2.0.16 
6 Cib 14 Yaxkin, and the Secondary Series 12.9.15 leading to 9 Chuen 

9 Kankin ; the Secondary Series 5 leading to 1 Cib 14 Kankin ; and 
the Secondary Series 1.0.2.5 leading to 5 Imix 19 Zac, The Initial- 
series values: 9.12.14.10.11; 9.12.14.10.16; and 9.13.14.13.1, belong- 
ing to the three dates of the Secondary Series, respectively, do not 
appear in the text at all (a fact indicated by the brackets), but 
are found only by calculation. Moreover, the student should note 
that in a succession of interdependent series hke the ones just given 
the terminal date reached by one number, as 9 Chuen 9 Kankin, 
becomes the starting point for the next number, 5. Again, the ter- 
minal date reached by counting 5 from 9 Chuen 9 Kankin, that is, 
1 Cib 14 Kankin, becomes the starting point from which the next 
number, 1.0.2.5, is counted. In other words, these terms are only 
relative, since the terminal date of one number will be the starting 
point of the next. 

Let us assume for the next example that the number 3.2 is to be 
counted forward from the Initial Series 9.12.3.14.0 5 Ahan 8 TJo. 
Reducing 3 uinals and 2 kins to kins, we have 62 units of the first 
order. Counting forward 62 from 5 Ahan 8 Uo, as indicated by the 
rules on pages 138-143, it is foimd that the terminal date will be 2 Ik 

10 Tzec. Since the Initial-series value of the starting point 5 Ahan 
8 Uo is known, namely, 9.12.3.14.0, the Initial Series corresponding 
to the terminal date may be calculated from it as before: 

9.12.3.14.0 (Initial-series value of the starting point) 6 Ahau 8 TJo 
3.2 (distance from 6 Ahau 8 TJo forward to 2 Ik 10 Tzec) 
[9.12.3.17.2] (Initial-series value of the terminal date) 2 Ik 10 Tzec 

The bracketed 9.12.3.17.2 in the Initial-series value corresponding 
to the date 2 Ik 10 Tzec does not appear in the record but was reached 
by calculation. The student may prove the accuracy of- this result 
by treating 9.12.3.17.2 2 Ik 10 Tzec as a new Initial Series, and 
counting forward 9.12.3.17.2 from 4 Ahau 8 Cumhu (the starting 
point of Maya chronology, imexpressed in Initial Series). If our 
calculations are correct, the same date, 2 Ik 10 Tzec, will be reached, 
as though we had counted only 3.2 forward from the Initial Series 
9.12.3.14.0 5 Ahau 8 XTo. 

One more example presenting a "backward coimt" will suffice to 
illustrate this method. Let us count the number 14.13.4.17 backward 
from the Initial Series 9.14.13.4.17 12 Caban 6 Kayab. Eeducing 
14.13.4.17 to units of the 1st order, we have 105,577. Counting this 
number backward from 12 Caban 5 Kayab, as indicated in the rules 
on pages 138-143, we find that the terminal date will be 8 Ahau 13 Ceh. 
Moreover, since the Initial-series value of the starting point 12 Caban 
6 Kayab is known, namely, 9.14.13.4.17, the Initial-series value of 



MOELDT] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 151 

the terminal date may be calctilated by subtracting the distance num- 
ber 14.13.4.17 from the Initial Series of the starting point: 

9.14.13.4.17 (Initial-series value of the starting point) 12 Caban 5 
Kayab 
14.13.4.17 (distance from 12 Caban 5 Kayab backward to 8 Ahau 
13 Ceh) 
[9. 0. 0.0. 0] (Initial-series value of the terminal date) 8 Ahau 13 
Ceh 
The bracketed parts are not expressed. We have seen elsewhere 
that the Initial Series 9.0.0.0.0 has for its terminal date 8 Ahau 13 Ceh ; 
therefore our calculation proves itself. 

The foregoing examples make it sufficiently clear that the distance 
numbers of Secondary Series may be used to determine the Initial- 
series values of Secondary-series dates, either by their addition to 
or subtraction from known Initial-series dates. 

We have come now to the final step in the consideration of Maya 
numbers, namely, the identification of the terminal dates determined 
by the calctdations given under the fourth step, pages 138-143. This 
step may be summed up as follows: 

Fifth Step in Solving Maya Numbers 

Find the terminal date to which the number leads. 

As explained imder the fourth step (pp. 138-143), the terminal date 
may be found by calctdation. The above direction, however, refers 
to the actual finding of the terminal dates in the texts; that is, where 
to look for them. It may be said at the outset in this connection 
that terminal dates in the great majority of cases follow immediately 
the numbers which lead to them. Indeed, the connection between 
distance numbers and their corresponding terminal dates is far closer 
than between distance numbers and their corresponding starting 
points. This probably results from the fact that the closing dates 
of Maya periods were of far more importance than their opening 
dates. Time was measured by elapsed periods and recorded in terms 
of the ending days of such periods. The great emphasis on the clos- 
ing date of a period in comparison with its opening date probably 
caused the suppression and omission of the date 4 Ahau 8 Cumhu, 
the starting point of Maya chronology, in all Initial Series. To the 
same cause also may probably be attributed the great uniformity in 
the positions of almost all terminal dates, i. e., immediately after the 
numbers leading to them. 

We may formulate, therefore, the following general rule, which the 
student will do well to apply in every case, since exceptions to it are 
very rare: 

Rule. The terminal date reached by a number or series almost 
invariably follows immediately the last term of the number or series 
leading to it. 



152 BtTBEAU Off AMERICAN ETIlNOLOciV |iiiitt.8T 

This applies equally to all terminal dates, whether in Initial Bcries, 
Secondary Series, Calendar-round diitirifi; or I'criod-dnding (luting, 
though in the case of Initial Seriew a peculiar diviHion or partition of 
the terminal date is to be noted. 

Throughout the iuHcriptions, excepting in the case of Initial Scri(w, 
the month parts of the dates almost invariably follow imniediatcily 
the days whose positions in the yvnv they dcwignate, without any 
other glyphs standing between; as, for oxampli', 8 Ahau 13 Ceh, 
12 Caban 5 Kayab, etc. In Initial Si^ries, on tlie other hand, the 
day parts of tlie dates, as 8 Ahau and 12 Caban, in the above exam- 
ples, are almost invariably separated from their corresponding 
month parts, 13 Ceh or 6 Kayab, by s<iveral intervetiirig glyphs. 
The positions of the day parts in Initial-seiies terrruDul dates ar<! 
quite regular according to the terms of the above rule; that is, they 
follow immediately the lowest period of the niiirdxT wliieli iti (^ach 
case shows their distance from the unexpressed starting point, 4 Ahau 
8 Cumhu. The positions of the corresponding month parts are, on 
the other hand, irregular. These, instead of standing immediately 
after the days whose positions in the year they designate, follow at 
the close of some six or seven intervening glyphs. These intefvciiing 
glyphs have been called the Supplementary Scries, though the count 
which they record has not as yd been deciphered.' The month glyph 
in the great majority of cases follows immediately the closing^ glyph 
of the Supplementary Series. The form of this latter sign is always 
immistakable (see fig. 65), and it is further chii-racterized by its 
numerical coefficient, which can never bo anything but 9 or 10." S(!e 
fexamplea of this sign in the figure just mentioned, where both nor- 
mal forms a, c, e, g, and h and head variants h, d, and /are included. 

The student will find this glyph exceedingly helpful in loen-f,ing the 
month parts of Initial-series terminal dntes in the inscriptions. For 
example, let us suppose in deciphering the Initial Series 0.1 6.5.0.0 
8 Ahau 8 Zotz that the number 9.16.5.0.0 has been counted forwiud 



1 The Supplementary Series present perhaps the most promising Hold for future stmly iiml InvestlKfttlon 
In the Maya texts. They clearly have to do with a numerical count of some kind, wtiiih of Itself should 
greatly facilitate progress In their Interpretation, Mr. Goodman (1S97! p. 1 IX) had suggestud that In mmM 
way the Supplementary Series record the dates of the Initial Hcirlns Uiiiy aci'(jrri(»iny accordluK to some 
other and unknown method, though he offers no proof in support of this liypoHicsl;!, Mr. Jlowdil.ili 
(1910: p. 24<) believes they probably relate to time, hucaiisc the Klyfihs of which Hic.y are cDiupojied have 
numbers attached to them. Iln has suggratud the name Supplementary Hf.rliw liy which they are known, 
Implying in the designation that these Hcrics In some way m\\}]<\m\m\, or I'oinplelc Ihu meaning of the 
Initial Series with which they are so closely connected. ThcwrlUsr believes that th(!y trcul, of some 
lunar count. It seems almost certain that the moon glyph occurs reiiral.cdly In the Supplementary 
Series (see fig. 66). 

2 The word "closing" as used here means only that In reading from left to right and from Utp to bottom — 
that Is, in the normal order— the sign shown in IIk. or, is always the last one in the Hii[iplerrientary Herli«, 
usually standing Immediately before the month glyph of the Inll.lal-serlos terminal dale, li, docs not 
signify, however, that the Supplementary Siries wi^i! to bo read In tills direi^Uon, and, Imlecd, there are 
strong indlcatiorj.s that they followed the reverse, order, from right to left and hoMoin to top, 

'' In afew cases the sign shown In fig, (if, occurs elsewhere In the Hnpplementttry Scries than as Its "closing" 
glyph. In such cases its coefficient is not restricted to the number 9 or 10, 



Moelet] INTEODUCTlOlf TO STUDY OF MAYA filEEOGLYPHS 



153 



from 4 Ahau 8 Cumhu (the unexpressed starting point) , and has been 
found by calculation to reach the terminal date 8 Ahau 8 Zotz ; and 
further, let us suppose that on inspecting the text the day part of 
this date (8 Ahau) has been found to be recorded immediately after 
the kins of the number 9.16.5.0.0. Now, if the student wiU foUow 
the next six or seven glyphs until he finds one like any of the forms 
in figure 65, the glyph immediately following the latter sign wiU be 
in all probabihty the month part, 8 Zotz in the above example, of 
an Initial-series' terminal date. In other words, although the 
meaning of the glyph shown in the last-mentioned figure is unknown, 
it is important for the student to recognize its form, since it is almost 
invariably the "indicator" of the month sign in Initial Series. 
In all other cases in the inscriptions, including also the exceptions 











« f g Ti 

Fig. G5. Sign for the "month indicator": a, c, f, ^, A, Normal forms; &, d,/, head variants. 

to the above rule, that is, where the month parts of Initial-series ter- 
minal dates do not immediately follow the closing glyph of the 
Supplementary Series, the month signs follow immediately the day 
signs whose positions in the year they severally designate. 

In the codices the month signs when recorded' usually follow 
immediately the days signs to which they belong. The most notable 
exception ^ to this general rule occurs in connection with the Venus- 
solar periods represented on pages 46-50 of the Dresden Codex, 
where one set of day signs is used with three different sets of month 
signs to form three different sets of dates. For example, in one 
place the day 2 Ahau stands above three different month signs — 3 
Cumhu, 3 Zotz, and 13 Yax — with each of which it is used to form a 

1 In the codices frequently the month parts of dates are omitted and starting points and terminal dates 
alike are expressed as days only; thus, 2 Ahau, 5 Imiz, 7 Kan, etc. This is nearly always the case in 
tonalamatls and in certain series of numbers in the Dresden Codex. 

2 Only a very few month signs seem to be recorded in the Codex Tro-Cortesiano and the Codex Pere- 
sianus. The Tro-Cortesiano has only one (p. 73b), in which the date 13 Ahau 13 Cumhu is recorded 
SIIV^JIIl^ thus(*). Comparothemonthforminthisdatewithflg. 20, z-b'. Mr. Gates (1910: p. 21) 
.|H°il2' •!! aii3 ands throe month signs in the Codex Peresianus, on pp. 4, 7, and 18 at 4c7, 7c2, and 
„,,, * 18b4, respectively. Theflrst of theseislB Zao(**). Compare this form with 
E2ai 'll^^ flg. 20, 0. The second is 1 Yaxkln (t). Compare this form with fig. 20, i-j. 

(^3) »\\K3SP Thn third i« 18 riTimhu /++V son fiir ' 
t tt 



•111^ 



The third is 18 Cumhu (tt); see fig. 20, z-V. 



154 BUIIKAU OP AMBnrOAN ETirNOI.OflV liKiM,. 07 

<lifrerent date — 2 Ahau 3 Cumhu, 2 Ahau 3 Zotz, and 2 Ahau 13 Yax. 

In l,li('H(i |)ii,<rc,H tho monUi ftignH, wilh ii few c.xc.dptions, do nol- follow 
iinmcdiaidJy l.ho diiyH l,o whicli ilicy Ixvlorifj, l)ui on the. c.orit/mry tlmy 
are separated from Uicm by scvcni] inlcrvcninf^ f,'ly|)liH. 'I'liin nhbrc- 
viation in tho nic.ord of tlicHo diitcH was doubUciHH f)rofnp(,(',d hy tlui 
(kiwiro or ncccHsity for cconotnizirif^ H|)n,(;e. In tlic, nbovc exiiin|)l(!, 
instciid of repoatiiif^ tho 2 Ahau with eaeii of ttui two lower month 
sif^riH, 3 Zotz and 13 Yax, hy wriiirif^ it oticc. )i,l)ovo ihc ii|)p(5r rnontli 
si^i), 3 Cumhu, the. HcrWx'. intended tlmt it nhould l)i'. iiHcd in turn 
with each oru? of thethnic, month nif^nHHtandinf^ bolowit, (,o form l.lirc.e 
differ'ciit diiteM, Hiivirif^ by thin ab)»n',viii,tion tlie Hf)ac!(i of two ii\yi>\iH, 
that is, double tiie H()a(',<! ocf.iipiod liy 2 Ahau. 

With tho (!X(;c,[)tioi) of tfin InitiiJ-HcridK duti^H in tlio inHc-ri()f,iotm 
and till! VcnuH-Sohir dat(^H on f)af^f!H ^ono of tfio I)reHd(iri (!odex, wo 
may Hay that the regular ()osiiioti of llic, month glyphH iti Maya writing 
was immediately following the day glyphs whoso positions in thoyoar 
they severally (hisi^riatcd. 

In closing tho prc-si^riintion of this hist step in tho f)ro(',c,ss of dofi- 
pfuiring numbers in th(i texts, the groat value of tho terminal date 
as a final check for all tho calculations involvcid under Hl,i!f)s I 4 
(pp. ].'M-1.5I) should be f)ointcd out. If after having worked out 
the terminal dat,(! of a given nuinljcr a,ccording to thes(! ruii^s the ter- 
minal date thus found shouhl differ from that ac.(,UM,lly recorded under 
step .5, we must accc[)t orxf of th(! following altr'.rnatives; 

1. There is an error in our own calculations; or 

2. There is an error in the original t(!Xt; or 

.3. The case in point lies without the operation of our rules. 
It is always safe for th(! beginner to proc,e(;d on the assumption that 
the first of the above alternatives is the cause of the error; in other 
words, that his own c,alf;ijlations are nl, fault. If the i^cnniiiu,] date as 
calculated does not agree with the terminal date as recorded, tho 
student should repf^at fiis (^alfiuhiJJons several times, chcclcing up each 
operation in order to eiiminatf! tin; jiossihility of a purcily arithmriticul 
error, as a mistake in multiplication. After all attetriftfs to reach 
the recorded terminal date by c,oufiting (tie given nuniffcr from the 
starting point haves failed, the (iroc,ess should be reversed and th(» 
attempt made to reach tho starting (loint by count.ing bm'-kward the 
given numhfir from its recorded terminal date. Sometimes thiw 
reverse f)rocess will work out corntfttly, showing that, there must \w 
some aritlrm(!tical error in our original calculations which we have 
failed t<; df^tfict. However, wlien tjoth f)ro(;esH('H h«,vc faihtd several 
tim(!S to conriec,t the starting point with thi! reriorded terminal date 
by use of the given number, thert; remains tfie pf>ssi[)ility that (•it,lier 
tho starting point or the terminal date, or fierhjips both, do not 
belong to thf; given number. Tlie rules for determining thi« fiw.t 



MORi-UY] INTEODUCTION TO STUDY OF MAYA HIEBOGLYPHS 155 

have been given under step 2, page 135, and step 4, page 138. If 
after applying these to the case in point it seems certain that the 
starting point and terminal date used in the calculations both be- 
long to the given number, we have to fall back on the second of 
•the above alternatives, that is, that there is an error in the original 
text. 

Although very unusual, particularly in the inscriptions, errors in 
the original texts are by no means entirely unknown. These seem 
to be restricted chiefly to errors in numerals, as the record of 7 for 
8, or 7 for 12 or 17, that is, the omission or insertion of one or more 
bars or dots. In a very few instances there seem to be errors in the 
month glyph. Such errors usually are obvious, as will be pointed out 
in connection with the texts in which they are found (see Chapters 
Vand VI). 

If both of the above alternatives are found not to apply, that is, 
if both our calculations and the original texts are free from error, 
we are obhged to accept the third alternative as the source of 
trouble, namely, that the case in point lies without the operation of 
our rules. In such cases it is obviously impossible to go further in 
the present state of our knowledge. Special conditions presented by 
glyphs whose meanings arc unknown may govern such cases. At 
all events, the failm-e of the rules under 1-4 to reach the terminal 
dates recorded as under 5 introduces a new phase of glyph study — 
the meaning of unknown forms with which the beginner has no con- 
cern. Consequently, when a text falls without the operation of the 
rules given in this chapter — a very rare contingency — the beginner 
should turn his attention elsewhere. 



Chapter V 



THE INSCRIPTIONS 

The present chapter will be devoted to the interpretation of texts 
drawn from monuments, a process which consists briefly in the appU- 
cation to the inscriptions ^ of the material presented in Chapters III 
and IV. 

Before proceeding with this discussion it wiU first be necessary to 
explain the method followed in designatii^ particular glyphs in a 





A 


B 


C 


D 


E 


F 


G 


H 


1 


J 


K 


L 


M 


N 


1 






























2 






























3 








a. 






















4 








■ 1 














y 








5 






























6 












P 


















7 






























8 




























9 






























10 




























8 



Fig. 



Diagram showing the method of designating particular glyphs in a text. 



text. We have seen (p. 23) that the Maya glyphs were presented in 
parallel columns, which are to be read two columns at a time, the 
order of the individual glyph-blocks ^ in each pair of columns being 
from left to right and from top to bottom. For convenience in refer- 
ring to particular glyphs in the texts, the vertical columns of glyph- 
blocks are lettered from left to right, thus. A, B, C, D, etc., and the 
horizontal rows numbered from top to bottom, thus, 1, 2, 3, 4, etc. 
For example, in figure 66 the gljrph-blocks in columns A and B are 
read together from left to right and top to bottom, thus, Al Bl, A2 
B2, A3 B3, etc. When glyph-block BlO is reached the next in order 

1 As used throughout this work, the word "inscriptions" is applied only to texts from the monuments. 

2 The term glyph-block has been used instead of glyph In this connection because in many inscriptions 
several different glyphs are included in one glyph-block. In such cases, however, the glyphs within the 
glyph-block follow precisely the same order as the glyph-blocks themselves follow in the pairs of oohimns, 
that is, from left to right and top to bottom. 

156 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 6 




A. ZObMORPH P, QUIRIGUA 





S. STELA 22, NARANJO 



D. STELA 24, NARANJO 



GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR 
AND DOT NUMERALS AND NORMAL-FORM PERIOD GLYPHS 



MORLBY] INTKODUCTION TO STUDY OP MAYA HIEROGLYPHS 157 

is Cl, which is followed by Dl, C2 D2, C3 D3, etc. Again, when DlO 
is reached the next in order is El, which is followed by Fl, E2 F2, 
E3 F3, etc. In this way the order of readii^ proceeds from left to 
right and from top to bottom, in pairs of columns, that is, G H, IJ, 
K L, and M N throughout the inscription, and usually closes with 
the glyph-block in the lower right-hand corner, as NlO in figure 66. 
By this simple system of coordinates any particular glyph in a text 
may be readily referred to when the need arises. Thus, for example, 
in figure 66 glyph a is referred to as D3; glyph /? as F6; glyph y as 
^4; glyph d as NlO. In a few texts the glyph-blocks are so irregu- 
larly placed that it is impracticable to designate them by the above 
coordinates. In such cases the order of the gljrph-blocks will be 
"indicated by numerals, 1, 2, 3, etc. In two Copan texts. Altar S (fig. 
81) and Stela J (pi. 15), made from the drawings of Mr. Maudslay, 
his mmieration of the glyphs has been followed. This nimieration 
appears in these two figures. 

Texts Eecording Initial Series 

Because of the fundamental importance of Initial Series in the 
Maya system of chronology, the first class of texfe represented wiU 
illustrate this method of dating. Moreover, since the normal forms 
for the numerals and the period glyphs wiU be more easily recognized 
by the beginner than the corresponding head variants, the first Initial 
Series given will be found to have all the numerals and period glyphs 
expressed by normal forms .^ 

In plate 6 is figured the drawing of the Initial Series ^ from Zo6- 
morph P at Quirigua, a monmnent which is said to be the finest piece of 
aboriginal sculpture in the western hemisphere. Our text opens with 
one large glyph, which occupies the space of four glyph-blocks, Al- 
•B2.^ Analysis of this form shows that it possesses all the elements 
mentioned on page 65 as belonging to the so-caUed Initial-series 
introducing glyph, without which Initial Series never seem to have 
been recorded in the inscriptions. These elements are: (1) the trinal 

1 Initial Series which have all their period glyphs expressed by normal forms are comparatively rare; 
consequently the four examples presented in pi. 6, although they are the best of their kind, leave some- 
thing to be desired in other ways. In pi. 6, A, for example, the month sign was partially effaced though 
it is restored in the accompanying reproduction; in B of the same plate the closing glyph of the Supple- 
mentary Series (the month-sign indicator) is wanting, although the month sign itself is very clear. 
Again, in D the details of the day glyph and month glyph are partially effaced (restored in the repro- 
duction), and in C, although the entire text is very clear, the month sign of the terminal date irregularly 
follows immediately the day sign. However, in spite of these slight irregularities, it has seemed best to 
present these particular texts as the first examples of Initial Series, because their period glyphs are 
expressed by normal forms exclusively, which, as pointed out above, are more easily recognized on account 
of their greater difEerentiation than the corresponding head variants. 

2 In most of the examples presented in this chapter the full inscription is not shown, only that part of 
the text illustrating the particular point in question being given. For this reason reference will be 
made in each case to the publication in which the entire inscription has been reproduced. The full 
text on Zoomorph P at Quirigua will be found in Maudslay, 1889-1902: n, pis. 63, 54, 55, 56, 57, 59, 63, 64. 

» All glyphs expressed in this way axe to be understood as Inclusive. Thus A1-B2 signlfles 4 glyphs, 
namely, Ai, Bl, A2, B2, 



158 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

superfix, (2) the paii of comblike lateral appendages, (3) the normal 
form of the tun sign, (4) the trinal subfix, and (5) the variable central 
element. As stated above, all these appear in the large glyph Al- 
B2. Moreover, a comparison of,Al-B2 with the introducing glyphs 
given in figure 24 shows that these forms are variants of one and 
the same sign. Consequently, in A1-B2 we have recorded an Initial- 
series introducing glyph. The use of this sign is so highly specialized 
that, on the basis of its occurrence alone in a text, the student is 
perfectly justified in assuming that an Initial Series will immediately 
foUow.^ Exceptions to this rule are so very rare (see p. 67) that the 
beginner wiU do well to disregard them altogether. 

The next glyph after the introducing glj^h in an Initial Series is the 
cycle sign, the highest period ever found in this kind of count^. The 
cycle sign in the present example appears in A3 with the coefficient 
9 (1 bar and 4 dots). Although the period glyph is partially effaced 
in the original enough remains to trace its resemblance to the normal 
form of the cycle sign shown in figiu-e 25, a-c. The outline of the repeated 
Cauac sign appears in both places. We have then, in this glyph, the 
record of 9 cycles^. The glyph following the cycle sign in an Initial 
Series is always the kattm sign, and this should appear in B3, the glyph 
next in order. This glyph is quite clearly the normal form of the katun 
sign, as a comparison of it with figure 27, a, b, the normal form for 
the katun, will show. It has the normal-form muneral 18 (3 bars 
and 3 dots) prefixed to it, and this whole glyph therefore signifies 
18 katuns. The next glyph should record the tuns, and a comparison 
of the glyph in A4 with the normal form of the tun sign in figure 29, 
a, i, shows this to be the case. The nxuneral 5 (1 bar prefixed to the 
tun sign) shows that this period is to be used 5 times; that is, multi- 
plied by 5. The next glyph (B4) should be the uinal sign, and a 
comparison of B4 with figure 31, a-c, the normal form of the uinal sign, . 
shows the identity of these two glyphs. The coefficient of the uinal 
sign contains as its most conspicuous element the clasped hand, 
which suggests that we may have uinals recorded in B4. A com- 
parison of this coefficient with the sign for zero in figure 54 proves 
this to be the case. The next glyph (A5) should be the kin sign, the 
lowest period involved in recording Initial Series. A comparison of 
A5 with the normal form of the kin sign in figure 34, a, shows that these 
two forms are identical. The coefficient of A5 is, moreover, exactly 
hke the coefficient of B4, which, we have seen, meant zero, hence 
glyph A5 stands for Idns. Smnmarizing the above, we may say 
that glyphs A3-A5 record an Initial-series number consisting of 6 
cycles, 18 katuns, 5 tuns, uinals, and kins, which we may write 
thus: 9.18.5.0.0 (see p. 138, footnote 1). 

' The iutroduomg glyph, so far as the writer knows, always stands at the beginning of an inscription, 
or in the second glyph-block, that is, at the top. Hence an Initial Series can never precede it. 
2 The Initial Series on Stela 10 at Tikal is the only exception known. See pp. 123-127. 
' As will appear in the following examples, nearly all Initial Series have 9 as their cycle coefficient. 



MOKLEY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 159 

Now let US turn to Chapter IV and apply the sereral steps there 
given, by means of which Maya numbers may be solved. The firgt 
step on page 134 was to reduce the given number, in this case 
9.18.5.0.0, to units of the first order; this may be done by multiplying 
the recorded coefficients by the numerical values of the periods to 
which they are respectively attached. These values are given in 
Table XIII, and the sum of the products arising from their multi- 
plication by the coefficients recorded in the Initial Series in plate 6, A 
are given below: 

A3= 9X144,000 = 1,296,000 
B3 = 18X 7,200= 129,600 
A4= 5X 360= 1,800 
B4= OX 20= 

A5= Ox 1= 



1, 427, 400 



Therefore 1,427,400 will be the number used in the following calcu- 
lations. 

The second step (see step 2, p. 135) is to determine the starting 
point from which this number is counted. According to rule 2, page 
136, if the number is an Initial Series the starting point, although 
never recorded, is practically always the date 4 Ahau 8 Cumliu. 
Exceptions to thjs nile are so very rare that they may be disregarded 
by the beginner, and it may be taken for granted, therefore, in the 
present case, that our number 1,427,400 is to be counted from the 
date 4 Ahau 8 Cumha. 

The third step (see step 3, p. 136) is to determine the direction of 
the coimt, whether forward or backward. In this connection it was 
stated that the general practice is to count forward, and that the 
studeat should always proceed upon this assumption. However, 
in the present case there is no room for xmcertainty, since the direc- 
tion of the count in an Initial Series is governed by an invariable 
rule. In Initial Series, according to the rule on page 137, the count 
is always forward, consequently 1,427,400 is to be counted forward 
from 4 Ahau 8 Cumhu. 

The foiu^h step (see step 4, p. 138) is to comit the given number 
from its starting point; and the rules governing this process will be 
found on pages 139-143. Since our given niimber (1,427,400) is 
greater than 18,980, or 1 Calendar Roimd, the preliminary rule on 
page 143 applies in the present case, and we may therefore sub- 
tract from 1,427,400 all the Calendar Eounds possible before proceed- 
ing to coimt it from the starting point. By referring to Table 
XVI, it appears that 1,427,400 contains 75 complete Calendar 
Rounds, or 1,423,500; hence, the latter number may be subtracted 



160 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

from 1,427,400 without affecting the value of the resulting terminal 
date: 1,427,400-1,423,500 = 3,900. In other words, in counting 
forward 3,900 from 4 Ahau 8 Cumhu, the same terminal date will 
be reached as though we had counted forward 1,427,400.^ 

In order to find the coefficient of the day of the terminal date, it 
is necessary, by rule 1, page 139, to divide the given number or its 
equivalent by 13; 3,900-^13 = 300. Now since there is no fractional 
part in the resulting quotient, the numerator of an assumed fractional 
part will be 0; coimting forward from the coefficient of the day 
of the starting point, 4 (that is, 4 Ahau 8 Cumhu), we reach 4 as the 
coefficient of the day of the terminal date. 

In order to find the day sign of the terminal date, it is necessary, 
under rule 2, page 140, to divide the given number or its equivalent by 
20 ; 3,900 ^ 20 = 195. Since there is no fractional part in the resultuig 
quotient, the numerator of an assumed fractional part wiU be 0; 
co\mtiQg forward ia. Table I, from Ahau, the day sign of the start- 
Lag point (4 Ahau 8 Cumhu), we reach Ahau as the day sign of the 
terminal date. In other words, in counting forward either 3,900 or 
1,427,400 from 4 Ahau 8 Cumhu, the day reached will be 4 Ahau. 
It remains to show what position in the year this day 4 Ahau distant 
1,427,400 from the date 4 Ahau 8 Cumhu, occupisd. 

In order to find the position in the year which the day of the ter- 
minal date occupied, it is necessary, under rule 3, page 141, to divide 
the given number or its equivalent by 365; 3,900 -h 365 = 10|-|f- 
Since the mmierator of the fractional part of the resiilting quotient is 
250, to reach the year position of the day of the terminal date desired 
it is necessary to count 250 forward from 8 Cumhu, the year position 
of the day of the starting point 4 Ahau 8 Cumhu. It appears from 
Table XV, in which the 365 positions of the year are given, that after 
position 8 Cumhu there are only 16 positions in the year — 11 more 
in Cumhu and 5 in Uayeb. These must be subtracted, therefore, from 
250 in order to bring the coxmt to the end of the year; 250 — 16 =234, 
so 234 is the number of positions we must count forward in the new 
year. It is clear that the first 1 1 uinals in the year will use up exactly 
220 of our 234 positions (11x20 = 220), and that 14 positions will 
be left, which must be counted in the next uinal, the 12th. But the 
12th uinal of the year is Ceh (see Table XV) ; comitiag forward 14 
positions in Ceh, we reach 13 Ceh, which is, therefore, the month 
glyph of our terminal date. In other words, comiting 250 forward 
from 8 Cumhu, position 13 Ceh is reached. Assembling the above 
values, we find that by calculation we have determined the terminal 
date of the Initial Series in plate 6, A, to be 4 Ahau 13 Ceh. 

1 In the present case therefore so far as these oaloulationa are concerned, 3,900 is the equivalent of 
)., 427,400. 



MORLBY] INTRODXTCTION TO STUDY OF MAYA HIEROGLYPHS 161 

At this point there are several checks which the student may apply- 
to his result in order to test the accuracy of his calculations; for 
instance, in the present example if 115, the difference between 365 
and 250 (115 + 250 = 365) is counted forward from position 13 Ceh, po- 
sition 8 Cumhu will be reached if our calculations were correct. This 
is true because there are only 365 positions in the year, and having 
reached 13 Get in counting forward 250 from 8 Cumhu, coimting the 
remaining 115 days forward from day reached by 250, that is, 13 Ceh, 
we should reach our starting point (8 Cumhu) again. Another good 
check in the present case would be to count 'backward 260 from 
13 Ceh; if our calculations have been correct, the starting point 
8 Cumhu wUl be reached. Still another check, which may be applied 
is the following: From Table VII it is clear that the day sign Ahau 
can occupy only positions 3, 8, 13, or 18 in the divisions of the year;' 
hence, if in the above case the coefficient of Ceh had been any other 
number but one of these four, our calculations would have been 
incorrect. 

We come now to the final step (see step 5, p. 151), the actual finding 
of the glyphs in our text which represent the two parts of the ter- 
minal date — the day and its corresponding position in the year. If 
we have made no arithmetical errors in calculations and if the text 
itself presents no irregular and unusual features, the terminal date 
recorded should agree with the terminal date obtained by calcidation. 

It was explained on page 152 that the two parts of an Initial- 
series terminal date are usually separated from each other by several 
intervening glyphs, and further that, although the day part follows 
immediately the last period glyph of the number (the kin glyph), 
the month part is not recorded until after the close of the Supplemen- 
tary Series, usually a matter of six or seven glyphs. Retmning to 
our text (pi. 6, A), we find that the kins are recorded in A5, therefore 
the day part of the terminal date should appear in B5. The gl3rph 
in B5 qmte clearly records the day 4 Ahau by means of 4 dots prefixed 
to the sign shown in figure 16, e'-g' , which is the form for the day 
name Ahau, thereby agreeing, with the value of the day part of the 
terminal date as determined by calculation. So far then we have read 
our text correctly. Following along the next six or seven glyphs, 
A6-Cla, which record the Supplementary Series,^ we reach in Cla 
a sign similar to the forms shown in figure 65. This glyph, which 
always has a coefficient of 9 or 10, was designated on page 152 the 
month-sign "indicator," since it usually immediately precedes the 
month sign in Initial-series terminal dates. In Cla it has the coeffi- 
cient 9 (4 dots and 1 bar) and is followed in Clb by the month part 

1 It should be remembered in this connection, as explained on pp. 47, 55, that the positions in the divi- 
sions of the year which the Maya called 3, 8, 13, and 18 correspond in our method of naming the positions 
of the days in the months to the 4th, 9th, 14th, and 19th positions, respectively. 

2As stated in footnote 1, p. 152, the meaning of the Supplementary Series has not yet been worked out. 

43508°— Bull. 57—15 11 



162 BX7RBAXJ OP AMBEICAN ETHNOLOGY [bcll. 57 

of the terminal date, 13 Ceh. The bar and dot numeral 13 appears 
very clearly above the month sign, which, though partially effaced, 
yet bears sufficient resemblance to the sign for Cell in figure 19, 
u, V, to enable us to identify it as such. 

Our complete Initial Series, therefore, reads: 9.18.5.0.0 4 Ahau 13 
Ceh, and since the terminal date recorded, in B5, Clb agrees with the 
terminal date determined by calculation, we may conchide that this 
text is without error and, furthermore, that it records a date, 4 Ahau 
13 Ceh, which was distant 9.18.5.0.0 from the starting point of Maya 
chronology. The writer interprets this text as signifying that 
9.18.5.0.0 4 Ahau 13 Ceh was the date on which Zoomorph P at Qui- 
rigua was formally consecrated or dedicated as a time-marker, or in 
other words, that Zoomorph P was the monument set up to mark the 
hotun, or 5-tim period, which came to a close on the date 9.18.5.0.0 4 
Ahau 13 Ceh of Maya chronology. ' 

In plate 6, B, is figured a drawing of the Initial Series on Stela 22 at 
Naranjo.^ The text opens in Al with the Initial-series introducing 
gljrph, which is followed in B1-B3 by the Initial-series number 
9.12.15.13.7. The five period glyphs are all expressed by their cor- 
responding normal forms, and the student will have no difficulty in 
identifying them and reading the nxmiber, as above recorded. 

By means of Table XIII this nmnber may be reduced to units of 
the 1st order, in which form it may be more conveniently iised. This 
reduction, which forms the first step in the process of solving Maya 
munbers (see step 1, p. 134), foUows: 

Bl = 9 X 144, 000 = 1, 296, 000 

A2 = 12 X 7, 200 = 86, 400 

B2 = 15X 360= 5,400 

A3 = 13X 20= 260 

B3= 7X 1= 7 



1, 388, 067 
And 1,388,067 will be the munber used in the following calculations. 

The next step is to find the starting point from which 1,388,067 is 
cotmted (see step 2, p. 135). Since this number is an Initial Series, in 
aU probability its starting point will be the date 4 Ahau 8 Cumhu ; at 
least it is perfectly safe to proceed on that assumption. 

The next step is to find the direction of the coimt (see step 3, p. 136) ; 
since our number is an Initial Series, the count can only be forward 
(see rule 2, p. 137).' 

1 The reasons which have led the writer to this conclusion are given at some length on pp. 33-36. 

2 For the full text of this inscription see Maler, 190S b: pi. 36. 

3 Since nothing hut Initial-series texts will be presented in the plates and figures immediately following, 
a tact which the student will readily detect by the presence of the introducing glyph at the head of each 
text, it is unnecessary to repeat tor each new text step 2 (p. 135) and step 3 (p. 136), which explain how to 
determine the starting point of the count and the direction of the count, respectively; and the student 
may assume that the starting point of the several Initial Serie.s hereinafter figured will always be the date 
4 Ahau 8 Cumhu and that the direction of the count will always be forward. 



MOELBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 163 

Having aetermined the number to be counted, the starting point 
from which the count commences, and the direction of the count, we 
may now proceed with the actual process of counting (see step 4, 
p. 138). 

Since 1,388,067 is greater than 18,980 (1 Calendar Eound), we may- 
deduct from the former number all the Calendar Rounds possible (see 
preliminary rule, page 143). According to Table XVI it appears 
that 1,388,067 contains 73 Calendar Rounds, or 1,385,540; after de- 
ducting this from the given number we have left 2,527 (1,388,067 — 
1,385,540), a far more convenient number to handle than 1,388,067. 

Applying rule 1 (p. 139) to 2,527, we have: 2,527 -^ 13 = 194,^, 
and counting forward 5, the munerator of the fractional part of the 
quotient, from 4, the day coefficient of the starting point, 4 Ahau 8 
Cumhu, we reach 9 as the day coefficient of the terminal date. 

Applying rule 2 (p. 140) to 2,527, we have: 2,527^20 = 126^; 
and counting forward 7, the numerator of the fractional part of the 
quotient, from Ahau, the day sign of our starting point, 4 Ahau 8 
Cumhu, in Table I, we reach Manik as the day sign of the terminal 
date. Therefore, the day of the terminal date will be 9 Manik. 

Applying rule 3 (p. 141) to 2,527, we have: 2,527^ 365 = 6ff|; 
and counting forward 337, the numerator of the fractional part of 
the quotient, from 8 Cumhu, the year position of the starting point, 
4 Ahau 8 Cumhu, in Table XV, we reach Kayab as the year position 
of the terminal date. The calculations by means of which Kayab is 
reached are as follows: After 8 Cumhu there are 16 positions in the 
year, which we must subtract from 337; 337 — 16 = 321, which is to 
be counted forward in the new year. This number contains just 1 
more than 16 uinals, that is, 321 = (16x20) + 1; hence it will reach 
through the first 16 uinals in Table XV and to the first position in 
the 17th uinal, Kayab. Combining this with the day obtained 
above, we have for our terminal date determined by calculation, 9 
Manik Kayab. 

The next and last step (see step 5, p. 151) is to find the above date 
in the text. In Initial Series (see p. 152) the two parts of the ter- 
minal date are generally separated, the day part usually following 
immediately the last period glyph and the month part the closing 
glyph of the Supplementary Series. In plate 6, B, the last period glyph, 
as we have seen, is recorded in B3; therefore the day should appear 
in A4. Comparing the glyph in A4 with the sign for Manik in figm-e 
16, j, the two forms are seen to be identical. Moreover, A4 has the 
bar and dot coefficient 9 attached to it, that is, 4 dots and 1 bar; con- 
sequently it is clear that in A4 we have recorded the day 9 Manik, 
the same day as reached by calculation. For some unknown reason, 
at Naranjo the month glyphs of the Initial-series terminal dates do 
not regularly follow the closing glyphs of the Supplementary Series ; 



164 BUEBAXJ OF AMERICAN ETHNOLOGY [bull. 57 

indeed, in the text here under discussion, so far as we can judge from 
the badly effaced glyphs, no Supplementary Series seems to have 
been recorded. However, reversing our operation, we know by- 
calculation that the month part should be Kayab, and by referrinig 
to figure 49 we find the only form which can be used to express the 
position with the month signs — the so-called "spectacles" glyph — 
which must be recorded somewhere in this text to express the idea 
with the month sign Kayab, Further, by referring to figure 19, 
d'-f, we may fix in our minds the sign for the month Kayab, which 
should also appear in the text with one of the forms shown in figure 49. 

Returning to our text once more and following along the glyphs 
after the day in A4, we pass over B4, A5, and B5 without finding a 
glyph resembling one of the forms in figure 49 joined to figiu-e 19, 
d'-f; that is, Kayab. However, in A6 such a glyph is reached, 
and the student will have no difficulty in identifying the month sign 
with d'-f in the above figure. Consequently, we have recorded iu 
A4, A6 the same terminal date, 9 Manik Kayab, as determined by 
calculation, and may conclude, therefore, that our text records without 
error the date 9.12.15.13.7 9 Manik Kayab"^ of Maya chronology. 

The next text presented (pi. 6, C) shows the Initial Series from 
Stela I at Quirigua.^ Again, as in plate 6, A, the introducing glyph 
occupies the space of four glyph-blocks, namely, A1-B2. Immedi- 
ately after this. La A3-A4, is recorded the Initial-series number 
9.18.10.0.0, all the period glyphs and coefficients of which are 
expressed by normal forms. The student's attention is called to the 
form for used mth the uiaal and kin signs in A4a and A4b, respec- 
tively, which differs from the form for recorded with the uinal and 
kin signs in plate 6, A, B4, and A5, respectively. In the latter text 
the uinals and kins were expressed by the hand- and curl form for 
zero shown in figure 54; in the present text, however, the uinals 
and kins are expressed by the form for shown in figure 47, a new 
feature. 

Reducing the above number to units of the 1st order by means of 
Table XIII, we have: 

A3= 9X144,000 = 1,296,000 
B3a = 18x 7,200= 129,600 
B3b = 10x 360= 3,600 
A4a= OX 20= 

A4b= OX 1= 



1,429,200 



1 As will appear later, in connection with the discussion of the Secondary Series, the Initial-series dat» 
of a monument does not always correspond with the ending date of the period whose close the monument 
marks. In other words, the Initial-series date is not always the date contemporaneous with the formal 
dedication of the monument as a time-marker. This point will appear much more clearly when the function 
of Secondary Series has been explained. 

2 For the full text of this inscription see Hewett, 1911: pi. xxxv C. 



MORLBY] INTEODUCTION TO STUDY OP MAYA HIEEOGLYPHS 165 

Deducting from this number all the Calendar Rounds possible, 75 
(see Table XVI), it may be reduced to 5,700 without affectiag its 
value in the present connection. 

Applying rules 1 and 2 (pp. 139 and 140, respectively) to this num- 
ber, the day reached will be found to be 10 Ahau; and by applying 
rule 3 (p. 141), the position of this day in the year will be foimd to be 
8 Zac. Therefore, by calculation we have determined that the ter- 
minal date reached by this Initial Series is 10 Ahau 8 Zac. It remains 
to find this date in the text. The regular position for the day in 
Initial-series terminal dates is immediately following the last period 
glyph, which, as we have seen above, was in A4b. Therefore the day 
glyph should be B4a. An inspection of this latter glyph will show 
that it records the day 10 Ahau, both the day sign and the coefiicient 
being unusually clear, and practically unmistakable. Compare B4a 
with figure 16, e'-g' , the sign for the dg^ name Ahan. Consequently 
the day recorded agrees with the day determined by calctilation. The 
month glyph in this text, as mentioned on page 157, footnote 1, occurs 
out of its regular position, following immediately the day of the 
terminal date. 

As mentioned on page 153, when the month glyph in Initial-series 
terminal dates is not to be found in its usual position, it wUl be foiuid 
in the regular position for the month glyphs in all other kinds of 
dates in theinscriptions, namely, immediately following the day glyph 
to which it belongs. In the present text we foimd that the day, 10 
Ahau, was recorded in B4a; hence, since the month glyph was not 
recorded in its regular position, it must be in B4b, immediately fol- 
lowing the day glyph. By comparing the glyph in B4b with the 
month signs in figure 19, it will be found exactly like the month sign 
for Zac {s-t), and we may therefore conclude that this is our month 
glyph and that it is Zac. The coefficient of B4b is quite clearly 8 and 
the month part therefore reads, 8 Zac. Combining this with the day 
recorded in B4a, we have the date 10 Ahau 8 Zac, which corresponds 
with the terminal date determined by calculation. The whole text 
therefore reads 9.18.10.0.0 10 Ahau 8 Zac. 

It will be noted that this date 9.18.10.0.0 10 Ahau 8 Zac is just 
5.0.0 (5 tuns) later than the date recorded by the Initial Series on 
Zoomorph P at Quirigua (see pi. &, A). As explained in Chapter II 
(pp. 33-34), the interval between succeeding monuments at Qui- 
rigua is in every case 1,800 days, or 5 tims. Therefore, it would seem 
probable that at Quirigua at least this period was the unit used for 
marking the lapse of time. As each 6-tim period was completed, its 
close was marked by the erection of a monument, on which was 
recorded its ending date. Thus the writer believes Zoomorph P 
marked the close of the 5-tun period ending 9.18.5.0.0 4 Ahau 13 Geh, 
and Stela I, the 5-tun period next following, that ending 9.18.10.0.0 



166 



BUEEATJ OF AMERICAN ETHNOLOGY 



[BULL. 57 





10 Ahau 8 Zac. In other words, Zoomorph P and Stela I were two 
successive time-markers, or "period stones," in the chronological 
record at Quirigua. For this 5-tun period so conspicuously recorded 
in the inscriptions from the older Maya cities the writer would 
suggest the name Tiotun, ho meaning 5 in Maya and tun being the 
name of the 360-day period. This word has an etymological parallel 
in the Maya word for the 20-tim period, Icatun, which we have 
seen may have been named directly from its niunerical value, leal 
being the word for 20 ia Maya and Tcaltun contracted to katun, 
thus meaning 20 tuns. Although no glyph for the Tiotun has as yet 
been identified,^ the writer is inclined to believe that the sign in 
figure 67, a, b, which is frequently encountered in the texts, will be 
foimd to represent this time period. The bar at the top in both 
a and h, figure 67, sm-ely signifies 5; therefore the glyph itself must 
mean " 1 tun." This form recalls the very unusual variant of the tim 
from Palenque (see fig. 29, Ji) . Both have the wing and the (*) g^S 
element. * 

The next Initial Series presented (see 
pi. 6, D) is from Stela 24 at Naranjo.^ 
The text opens with the introducing 
glyph, which is in the same relative posi- 
tion as the introducing glyph in the other 
Naranjo text (pi. 6, B) at Al. Then 
follows regularly in B1-B3 the number 
9.12.10.5.12, the ntunbers and period 
glyphs of which are all expressed by normal forms. By this time the 
student should have no difficulty in recognizing these and in deter- 
mining the number as given above. Reducing this according to 
rule 1, page 134, the following result should be obtained: 

Bl= 9X144,000 = 1,296,000 
A2 = 12X 7,200= 86,400 
B2 = 10X 360= 3,600 
A3= 5X 20= 100 

B3 = 12X 1= 12 

1,386, 112 

Deducting' from this number all the Calendar Rounds possible, 73 
(see preliminary rule, p. 143, and Table XVI), we may reduce it to 
572 without affecting its value in so far as the present calculations 
are concerned (1,386,112 — 1,385,540). First applying rule 1, page 

1 So far as the writer loiows, the existence of a period containing 6 tuns has not been suggestBd heretofore. 
The very general practice of closing inscriptions with the end of some particular 6-tun period in the Long 
Count, as 9.18.5.0.0, or 9.18.10.0.0, or 9.18.16.0.0, or 9.19.0.0.0, for example, seems to indicate that this period 
was the unit used for measuring time in Maya chronological records, at least in the southern cities. Conse- 
quently, it seems likely that there was a special glyph to express this unit. 

' For the full text of this inscription see Maler, 1908 b: pi. 39. 

s The student should note that from this point steps 2 (p. 139) and 3 (p. 140) have been omitted in dis- 
cussing each text (see p. 162, footnote 3). 



Fig. 67. Signs representing the hotun, 
or 5-tun, period. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 7 



i 













poo. 







(~~> 






A. STELA B, COPAN 



B. STELA A, COPAN 



GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR 
AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS 



MORLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 167 

139, and next rule 2, page 140^ to this number (572), the student will 
find the day reached to be 4 Eb. And applying rule 3, page 141, he 
will find that the year position reached will be 10 Tax ; ^ hence, the 
terminal date as determined by calculation will be 4 Eb 10 Yax. 

Turning again to the text (pi. 6, B), the next step (see step 5, p. 151) 
is to find the glyphs representing the above terminal date. In this 
connection it should be remembered that the day part of an Initial- 
series terminal date iisually follows immediately the last period 
glyph of the number. The glyph in A4, therefore, should record the 
day reached. Comparing this form with the several day signs in 
figure 16, it appears that A4 more closely resembles the sign for Eb 
(fig. 16, s-m) than any of the others, hence the student may accept 
Eb as the day sign recorded in A4. The 4 dots prefixed to this sign 
show that the day 4 Eb is here indicated. The month sign, as stated 
on page 152, usually follows the last glyph of the Supplementary 
Series; passing over B4, A5, B5, and A6, we reach the latter gljrph 
in B6. Compare the left half of B6 with the forms given in figure 
65. The coefl&cient 9 or 10 is expressed by a considerably ejBfaced 
head numeral. Immediately following the month-sign "indicator" 
is the month sign itself in A7. The student will have little difiiculty 
in tracing its resemblance to the month Yax in figure 19, q, r, although 
in A7 the Yax element itself appears as the prefix instead of as the 
superfix, as ia 2 and r, just cited. This difference, however, is imma- 
terial. The month coefficient is quite clearly 10,^ and the whole 
terminal date recorded will read 4 Eb 10 Yax, which corresponds 
exactly with the terminal date determined by calculation. We may 
accept this text, therefore, as recording the Initial-series date 
9.12.10.5.12 4 Eb 10 Yax of Maya chronology. 

In the foregoing examples nothing but normal-form period glyphs 
have been presented, in order that the first exercises ia deciphering the 
inscriptions may be as easy as possible. By this time, however, the 
student should be sufficiently familiar with the normal forms of the 
period glyphs to be able to recognize them when they are present in 
the text, and the next Initial Series figured wiU have its period glyphs 
expressed by head variants. 

In A, plate 7, is figured the Initial Series from Stela B at Copan.^ 
The introduciag glyph appears at the head of the inscription in Al 

1 In eacli ot the above cases— and, indeed, In all the examples following— the student should perfoim 
the various calculations by which the results are reached, in order to familiarize himself with the work- 
ings of the Maya chronological system. 

2 The student may apply a check at this point to his identification of the day sign in A4 as being that for 
the day Eb. Since the month coefficient in A7 is surely 10 (2 bars), it is clear from Table VII that the 
only days which can occupy this position in any division of the year are Ik, Manik, Eb, and Caban. Now, 
by comparing the sign in A4 with the signs for Ik, Manik, and Caban, c;, j, and a', b', respectively, of fig. 
16, it is very evident that A4 bears no resemblance to any of them; hence, since Eb is the only one left 
which can occupy a position 10, the day sign in A4 must be Eb, a fact supported by the comparison of 
A4 with fig. 16, 5-u, above. 

3 The fuU text of this inscription will be found in Maudslay, 1889-1901: 1, pis. 35-37. 



168 BUEEAXT OF AMERICAN ETHNOLOGY [bull. 57 

and is followed by a head-variant glyph in A2, to which is prefixed a 
bar and dot coefficient of 9. By its position, immediately following 
the introducing glyph, we are justified in assiuning that A2 records 
9 cycles, and after comparing it with d-f, figure 25, where the head 
variant of the cycle sign is shown, this assumption becomes a cer- 
tainty. Both heads have the same clasped hand in the same position, 
across the lower part of the face, which, as e'xplained on page 68, is 
the essential element of the cycle head; therefore, A2 records 9 
cycles. The next glyph, A3, should be the katun sign, and a com- 
parison of this form with the head variant for katim in e-h, figure 27, 
shows this to be the case. The determining characteristic (see p. 
69) is probably the oval in the top of the head, which appears in 
both of these forms for the katun. The katun coefficient is 15 (3 
bars) . The next glyph, A4, should record the tuns, and by comparing 
this form with the head variant for the tun sign in e-g, figure 29, this 
also is found to be the case. Both heads show the same essential 
characteristic — the fieshless lower jaw (see p. 70). The coefficient is 
(compare fig. 47). The uinal head in A5 is equally unmistakable. 
Note the large curl protruding from the back part of the mouth, 
which was said (p. 71) to be the essential element of this sign. 
Compare figure 31, d-f, where the head variant for the uinal is given. 
The coefficient of A5 is like the coefficient of A4 (0), and we have 
recorded, therefore, uinals. The closing period glyph of the Initial 
Series in A6 is the head variant for the kin sign. Compare this form 
with figure 34, e-g, where the Idn head is figured. The determining 
characteristic of this head is the subfixial element, which appears 
also in the normal form for the kin sign (see fig. 34, a). Again, the 
coefficient of A6 is like the coefficient of A4 and A5, hence we have 
recorded here kias. 

The nmnber recorded by the head-variant period glyphs and 
normal-form numerals in A2-A6 is therefore 9.15.0.0.0; reducing this 
by means of Table XIII, we have : 

A2= 9X144,000 = 1,296,000 

A3 = 15X 7,200= 108,000 

A4= OX 360= 

A5= OX 20= 

A6= OX 1= 



1, 404, 000 
Deducting from this munber all the Calendar Rounds possible, 73 
(see Table XVI), it may be reduced to 18,460. Applying to this 
number rules 1 and 2 (pp. 139 and 140, respectively), the day reached 
will be foimd to be 4 Ahau. Applying rule 3 (p. 141), the position of 
4 Ahau in the year will be foimd to be 13 Yax. Therefore the terminal 
date determined by calculation will be 4 Ahau 13 Yax. 



MOBLBY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 169 

According to step 5 (p. 151), the day reached should follow imme- 
diately the last period glyph, which in this case was in A6; hence the 
day should be recorded in A7. This glj^h has a coefficient 4, but 
the glj^h does not resemble either of the forms for Ahau shown in 
B5, plate 6, A, or in B4a, C of the same plate. However, by com- 
paring this glyph with the second variant for the day sign Ahau in 
figure 16, h'-i', the two forms will be found to be identical, and we 
may accept A7 as recording the day 4 Ahau. Immediately follow- 
ing in As is the month sign, again out of its usual place as in plate 
6, C. Comparing it with the month signs in figure 19, it will be found 
to exactly correspond with the sign for Yax in q-r. The coefficient 
is 13. Therefore the terminal date recorded, 4 Ahau 13 Yax, agrees 
with the terminal date reached by calculation, and the whole Initial 
Series reads 9.15.0.0.0 4 Ahau 13 Yax. This date marks the close 
not only of a hotim. in the Long Coimt, but of a katun as well. 

In B, plate 7, is figured the Initial Series from Stela A at Copan.^ 
The introducing glyph appears in Al Bl, and is followed by the 
Initial-series number in A2-A4. The student wiU have no difficulty 
in picking out the clasped hand in A2, the oval in the top of the head 
in B2, the fleshless lower jaw in A3, the large mouth curl in B3, and 
the flaring subfix ki A4, which are the essential elements of the head 
variants for the cycle, katun, tun, uinal, and kin, respectively. Com- 
pare these glyphs with figures 25, d-f, 27, e-Ji, 29, e-g, 31, d-f, and 
34, e-g, respectively. The coefficients of these period glyphs are all 
normal forms and the student will have no difficulty in reading this 
nmnber as 9.14.19.8.0.^ 

Reducing this by means of Table XIII to imits of the 1st order, 
we have: 

A2 = 9 X 144, 000 = 1, 296, 000 

B2 = 14 X 7, 200 = 100, 800 

A3 = 19 X 360 = 6, 840 

B3= 8X 20= 160 

A4= OX 1= 



1, 403, 800 

Deducting from this all the Calendar Rounds possible, 73 (see Table 
XVI), and appljnng rules 1 and 2 (pp. 139 and 140, respectively), to 
the remainder, the day reached will be 12 Ahau. And applying rule 3 
(p. 141), the month reached will be 18 Cumhu, giving for the terminal 
date as reached by calculation 12 Ahau 18 Cumhu. The day should 
be recorded in B4, and an examination of this glyph shows that its 
coefficient is 12, the day coefficient reached by calculation. The 
glyph itself, however, is unlike the forms for Ahau previously encoun- 
tered in plate 6, A, B5 and 0, B4b, and in plate 7, A, A7. Turning 

1 The fuU text of this inscription is given in Maudslay, 1889-1902: i, pis. 27-30. 

2 Note the decoration on the numerical bar. 



170 BUREAU OF AMERICAN ETHNOLOGY [BnLL. 57 

now to ths forms for the day sign Ahau in figure 16, it is seen that the 
form in A4 resembles the third variant / or Tc', the grotesque head, and 
it is clear that the day 12 Ahau is here recorded. At first sight the student 
might think that the month glyph follows in A5, but a closer inspection 
of this form shows that this is not the case. In the first place, since 
the day sign is Ahau the month coefficient must be either 3, 8, 13, or 
18, not 7, as recorded (see Table VII), and, in the second place, the 
glyph itself in A5 bears no resemblance whatsoever to any of the 
month signs in figure 19. Consequently the month part of the Initial- 
series terminal date of this text should follow the closing glyph of 
the Supplementary vSeries. Following along the glyphs next in order, 
we reach in A9 a glyph with a coefiicient 9, although the sign itself 
bears no resemblance to the month-glyph "indicators" heretofore 
encountered (see fig. 65). 

The glyph following, however, in A9b is quite clearly 18 Cumliu (see 
fig. 19, g'-h'), which is the month part of the terminal date as reached 
by calculation. Therefore, since A9a has the coefficient 9 it is prob- 
able that it is a variant of the month-glyph "indicator"; '■ and con- 
sequently that the month gl3'T)h itself follows, as we have seen, in B9. 
In other words, the terminal date recorded, 12 Ahau 18 Gumhu, agrees 
with the terminal date reached by calculation, and the whole text, 
so far as it can be deciphered, reads 9.14.19.8.0 12 Ahau 18 Cumhu. 
The student will note that this Initial Series precedes the Initial Series 
in plate 7, A by exactly 10 uinals, or 200 days. Compare A and B, 
plate 7. 

In plate 8, A, is figured the Initial Series from Stela 6 at Copan.^ 
The introducing glyph occupies the space of four gl3rph-blocks, 
A1-B2, and there follows in A3-B4a the Initial-series number 
9.12.10.0.0. The cycle glyph in A3 is partially effaced; the clasped 
hand, however, the determining characteristic of the cycle head, 
may stiU be distinguished. The katun head in B3 is also unmis- 
takable, as it has the same superfix as in the normal form for the 
katun. At first sight the student might read the bar and dot coeffi- 
cient as 14, but the two middle crescents are purely decorative and 
have no numerical value, and the numeral recorded here is 12 (see 
pp. 88-91). Although the tun and uinal period glyphs in A4a 
and A4b,^ respectively, are effaced, their coefficients may be distin- 
guished as 10 and 0, respectively. In such a case the student is per- 

• So fer as known to the writer, this very unusual variant for tlie closing glyph of the Supplementary 
Series occurs in but two other inscriptions in the Maya territory, namely, on Stela N at Copan. See pi . 26, 
Glyph A14, and Inscription 6 of the Hieroglyphic Stairway at Naranjo, Glyph Al (?). (Maler, 1908 b: 
pi. 27.) 

2 For the full text of this inscription see Maudslay, 1889-1902: i, pis. 105-107. 

s In this glyph-block, A4, the order of reading is irregular; instead of passing over to B4a after reading 
A4a (the 10 tuns), the next glyph to be read is the sign below A4a, A4b, which records uinals, and only 
after this has been read does B4a follow. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 67 PLATE 8 







, M~^^^^, If^'^'Si -i''"!?^>X :-' 

zzi r 1 C_ 




rf-fT^ II '^if^--.ina a 




^. STELA 6, COPAN 



B. STELA 9, COPAN 



GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR 
AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS 



MORLjiY] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 171 

rectly justified in assuming that the tun and uinal signs originally 
stood here. In B4a the Idn period glyph is expressed by its normal 
torm and the Idn coefficient by a head-variant numeral, the clasped 
hand of which indicates that it stands for (see fig. 53, s-w)."- The 
number here recorded is 9.12.10.0.0. 

Reducing this to units of the 1st order by means of Table XIII, 
we have: 

A3= 9X144,000 = 1,296,000 

B3 = 12x 7,200= 86,400 
A4a = 10 X 360 = 3, 600 
A4b= Ox 20= 

B4a= ix 0= 



A- 



1, 386, 000 

Deducting from this number all the Calendar Rounds possible, 73 
(see Table XVI), and applying to the remainder rules 1, 2, and 3 
(pp. 139-141), respectively, the date reached by the resulting calcu- 
lations will be 9 Ahau 18 Zotz. Turning to our text again, the student 
will have little difficulty in identifying B4b as 9 Ahau, the day of the 
above terminal date. The form Ahau here recorded is the grotesque 
head, the third variant j' or fc' in figure 16. Following the next 
glyphs in order, A5-A6, the closing glyph of the Supplementary 
Series is reached in B6a. Compare this glyph with the forms in 
figure 65. The coefficient of B6a is again a head-variant nmneral, as 
in the case of the kin period glyph in B4a, above. The fleshless lower 
jaw and other skull-like characteristics indicate that the numeral 10 
is here recorded. Compare B6a with figure 52, m-r. Since B6a is 
the last glyph of the Supplementary Series, the next glyph B6b 
should represent the month sign. By comparing the latter form 
with the month signs in figure 19 the student will readily recognize 
that the sign for Zotz in e or /is the month sign here recorded. The 
coefficient 18 stands above. Consequently, B4b and B6b represent 
the same terminal date, 9 Ahau 18 Zotz, as reached by calculation. 
This whole Initial Series reads 9.12.10.0.0 9 Ahau 18 Zotz, and 
according to the writer's view, the monument upon which it occurs 
(Stela 6 at Copan) was the period stone for the hotun which began 
with the day 9.12.5.0.1 4 Imix 4 Xul ^ and ended with the day 
9.12.10.0.0 9 Ahau 18 Zotz, here recorded. 

In plate 8, B, is figured the Initial Series from Stela 9 at Copan.^ 
The introducing glyph stands in A1-B2 and is followed by the five 
period glypbs in A3-A5. The cycle is very clearly recorded in A3, 
the clasped hand being of a particularly realistic form. Although 

1 Texts illustrating the head-variant numerals in full will be presented later. 

2 .jjie preceding hotun ended with the day 9.12.5.0.0 3 Ahau 3 Xnl and therefore the opening day of the 
next hotun, 1 day later, will be 9.12,5.0.1 4 Imix 4 Xul. 

3 For the full text of this inscription, see Maudslay, 1889-1902: i, pis. 109, 110. 



1*72 BtJEEAtr OF AMERICAN ETHNOLOGY [bdll. 57 

the coefficient is partially effaced, enough remains to show that it 
was above 5, having had originally more than the one bar which 
remains, and less than 11, there being space for only one more bar or 
row of dots. In all the previous Initial Series the cycle coefficient 
was 9, consequently it is reasonable to assume that 4 dots originally 
occupied the effaced part of this glyph. If the use of 9 cycles in this 
number gives a terminal date which agrees with the terminal date 
recorded, the above assumption becomes a certainty. In B3 six 
katuns are recorded. Note the ornamental dotted ovals on each 
side of the dot in the numeral 6. Although the head for the tun in 
A4 is partially effaced, we are warranted ia assuming that this was 
the period originally recorded here. The coefficient 10 appears 
clearly. The uinal head ia B4 is totally unfamiliar and seems to 
have the fleshless lower jaw properly belonging to the tiui head; 
from its position, however, the 4th in the nimiber, we are justified 
ia calling this glyph the uiaal sign. Its coefficient denotes that uinals 
are recorded here. Although the period glyph in A5 is also entirely 
effaced, the coefficient appears clearly as 0, and from position again, 
5th in the nvunber, we are justified once more ia assimiing that kins 
were originally recorded here. It seems at first glance that the 
above reading of the ntunber A3-A5 rests on several assumptions : 

1. That the cycle coefficient was originally 9. 

2. That the effaced glyph in A4 was a tun head. 

3. That the irregular head ia B4 is a uinal head. 

4. That the effaced glyph in A5 was a kin sign. 

The last three are really certaiaties, since the Maya practice in record- 
ing Initial Series demanded that the five period glyphs requisite — 
the cycle, katun, tun, uinal, and kin — shotdd follow each other ia 
this order, and in no other. Hence, although the 3d, 4th, and 
5th glyphs are either irregular or effaced, they miist have been the 
ttm, uinal, and kin signs, respectively. Indeed, the only important 
assumption consisted ia arbitrarily desigaating the cycle coefficient 
9, when, so far as the appearance of A3 is concerned, it might have 
been either 6, 7, 8, 9, or 10. The reason for choosiag 9 rests on the 
overwhelming evidence of antecedent probability. Moreover, as 
stated above, if the terminal date recorded agrees with the terminal 
date determined by calculation, using the cycle coefficient as 9, our 
assumption becomes a certainty. Designating the above number as 
9.6.10.0.0 then and reducing this by means of Table XIII, we obtaia: 

A3= 9X144,000 = 1,296,000 

B3= 6X 7,200= 43,200 

A4 = 10X 360= 3,600 

B4= OX 30= 

A5= OX 1= 



1, 342, 800 



MOBLET] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 173 

Deducting from this number all the Calendar Rounds possible, 70 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remaiader, the date determined by the resulting 
calculations will be 8 AhaulS Pax. Turning to our text again, the 
student will have, little difficulty in recognizing the first part of this 
date, the day 8 Ahau, in B5. The numeral 8 appears clearly, and the 
day sign is the profile-head li' or i', the second variant for Ahau in 
figure 16. The significance of the element standing between the 
numeral and the day sign is unknown. Followiag along through 
A6, B6, A7, B7, the closing glyph of the Supplementary Series is 
reached ia A8. The glyph itself is on the left and the coefficient, here 
expressed by a head variant, is on the right. The student wUl have 
no difficulty in recognizing the glyph and its coefficient by comparing 
the former with figure 65, and the latter with the head variant for 
10 in figure 52, m-r. Note the fleshless lower j aw in the head numeral 
in both places. The following glyph, B8, is one of the clearest in 
the entire text. The mmieral is 13, and the month sign on comparison 
with figure 19 unmistakably proves itself to be the sign for Pax in c' . 
Therefore the terminal date recorded in B5, B8, namely, 8 Ahau 13 
Pax, agrees with the terminal date determined by calculation; it fol- 
lows, further, that the effaced cycle coefficient in A3 must have been 9, 
the value tentatively ascribed to it in the above calculations. The 
whole Initial Series reads 9.6.10.0.0 8 Ahau 13 Pax. 

Some of the peculiarities of the numerals and signs in this text are 
doubtless due to its very great antiquity, for the monmnent presenting 
this inscription, Stela 9, records the next to earliest Initial Series ^ 
yet deciphered at Copan.^ Evidences of antiquity appear in the 
glyphs in several different ways. The bars denoting 5 have square 
ends and all show considerable ornamentation. This type of bar 
was an early manifestation and gave way in later times to more 
rounded forms. The dots also show this greater ornamentation, 
which is reflected, too, by the signs themselves. The head forms show 
greater attention to detail, giving the whole glj^h a more ornate 
appearance. All this embellishment gave way in later times to more 
simplified forms, and we have represented in this text a stage in glyph 
morphology before conventionalization had worn down the different 
signs to little more than their essential elements. 

In figure 68, A, is figured the Initial Series on the west side of Stela 
C at Quirigua.^ The introducing glyph in A1-B2 is followed by the 
number in A3-A5, which the student will have no difficulty in reading 

' The oldest Initial Series at Copan is recorded on Stela 15, which is 40 years older than Stela 9. For a 
discussion of this text see pp. 187, 188. 

2 An exception to this statement should be noted in an Initial Series on the Hieroglyphic Stairway, 
which records the date 9.5.19.3.0 8 Ahau 3 Zotz. The above remark applies only to the large moiiuments, 
which, the writer believes, were period-marters. Stela 9 is therefore the next to the oldest "period stone" 
yet discovered at Copan. It is more than likely, however, that there are several older ones as yet unde- 
ciphered. 

8 For the full text of this inscription, see Maudslay, 1889-1902: ii, pis. 17-19. 



174 



BXJKEAXJ OF AMERICAN ETHNOLOGY 



[bull. 57 



except for the head-variant numeral attached to the kin sign in A5. 
The clasped hand in this glyph, however, suggests that kins are 
recorded here, and a comparison of this form with figure 53, s-w, con- 
firms the suggestion. The number therefore reads 9.1.0.0.0. K.e- 





FlG. 08. Initial Series showing bar and dot numerals and liead-variant period glyplis: A, Stela C (west 
side), Quirigua; B, Stela M, Copan. 

ducing this ninnber by means of Table XIII to units of the 1st order, 
we obtaia: 

A3 = 9 X 144, 000 = 1, 296, 000 

B3 = 1 X 7, 200 = 7, 200 

A4 = 0X 360= 

B4=0X 20= 

A5=0X 1= 



1, 303, 200 



Deducting from this number all the Calendar Sounds possible, 68 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, we reach for the terminal date 6 Ahau 
13 Yaxkin. Looking for the day part of this date in B5, we find that 
the form there recorded bears no resemblance to 6 Ahau, the day 
determined by calculation. Moreover, comparison of it with the day 
signs in figure 16 shows that it is unlike all of them; further, there is 



MOELBT] INTEODUCTION TO STUDY OF MAYA HIEEOGLYPHS 175 

no bar and dot coefficient. These several points radicate that the 
day sign is not the glyph in B5, also that the day sign is, therefore, 
out of its regular position. The next gljrph in the text, A6, instead 
of being one of the Supplementary Series is the day glyph 6 Ahau, 
which should have been recorded in B5. The student will readily 
make the same identification after comparing A6 with figure 16, e'-g' . 
A glance at the remainder of the text will show that no Supplementary 
Series is recorded, and consequently that the month glyph will be 
found immediately following the day glyph in B6. The form in B6 
has a coefficient 13, one of the four (.3, 8, 13, 18) which the month 
must have, since the day sign is Ahau (see Table VII) . A comparison 
of the form in B6 with the month signs in figure 19 shows that the 
month Yaxkin in Z; or Z is the form here recorded; therefore the ter- 
minal date recorded agrees with the terminal date reached by calcu- 
lation, and the text reads 9.1.0.0.0 6 Ahan 13 Yaxkin.^ 

In figure 68, B, is shown the Initial Series on Stela M at Ctopan.^ 
The introducing glyph appears in Al and the Initial-series niunber 
in Bla-B2a. The student will note the use of both normal-form and 
head-variant period glyphs in this text, the cycle, tun, and uinal in 
Bla, A2a, and A2b, respectively, being expressed by the latter, and 
the katun and kin in Bib and B2a, respectively, by the former. The 
number recorded is 9.16.5.0.0, and this reduces to units of the first 
order, as follows (see Table XIII) : 

Bla= 9X144,000 = 1,296,000 
Blb = 16x 7,200= 115,200 
A2a= 5X 360= 1,800 

A2b= OX 20= 

B2a= Ox 1= 



1, 413, 000 

Deducting from this number aU the Calendar Rounds possible, 74 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached by the 
resulting calculations will be 8 Ahau 8 Zotz. Turning to om: text, the 
student wiU have no difficulty in recognizing in B2b the day 8 Akau. 
The month glyph in this inscription irregularly follows inunediately 

1 Although this date is considerably older than that on Stela 9 at Copan, its several glyphs present none 
of the marlcs of antiquity noted In connection with the preceding example (pi. 8, £ ) . For example , the ends 
of the bars denoting 5 are not square but round, and the head-variant period glyphs do not show the 
same elaborate and ornate treatment as in the Copan text. This apparent contradiction permits of an 
easy explanation. Although the Initial Series on the west side of Stela C at Quirigua undoubtedly refers 
to an earlier date than the Initial Series on the Copan monument, it does not follow that the Quirigua 
monument is the older of the two. This is true because on the other side of this same stela at Quirigua 
is recorded another date, 9.17.5.0.0 6 Ahau 13 Eayab, more than three hundred years later than the Initial 
Series 9.1.0.0.0 6 Ahau 13 Tazkln on the west side, and this later date is doubtless the one which referred 
to present time when this monument was erected. Therefore the Initial Series 9.1,0.0.0 6 Ahau 13 Yaxkin 
does not represent the period which Stela was erected to mark, but some far earlier date in Maya 
history. 

2 For the full text of this inscription see Maudslay, 1889-1902: i, pi. 74. 



176 BUREAU OF AMERICAN ETHNOLOGY [buli.. 57 

the day glyph. Compare the form in A3a with the month signs m 
figure 19 and it ■will be found to be the sign for Zotz (see fig. 19, e-f). 
The coefficient is 8 and the whole glyph represents the month part 
8 Zotz, the same as determined by calculation. This whole Initial 
Series reads 9.16.5.0.0 8 Ahau 8 Zotz. 

The Maya texts presented up to this point have all been drawings 
of originals, which are somewhat easier to make out than either 
photographs of the originals or the originals themselves. However, 
in order to familiarize the student with photographic reproductions 
of Maya texts a few will be inserted here illustratuig the use of bar 
and dot nmnerals with both normal-form and head-variant period 
glyphs, with which the student should be perfectly familiar by this 
time. 

In plate 9, .4, is figured a photograph of the Initial Series on the front 
of Stela 11 at Yaxchilan.* The introducing glyph appears in Al Bl ; 9 
cycles in A2 ; 16 katuns in B2, 1 tun in A3, uinals in.B3, and kins in 
B4. The student wUl note the clasped hand in. the cycle head, the oval 
in the top of the katim head, the large mouth curl in the uinal head, 
and the flaring postfix in the kin head. The tun is expressed by its 
normal form. The number here recorded is 9.16.1.0.0, and reducing 
this to imits of the first order by means of Table XIII, we have: 

A2 = 9 X 144, 000 = 1, 296, 000 
B2 = 16X 7,200= 115,200 
A3= IX 360= 360 

B3= OX 20= 

A4= Ox 1= 



1,411,560 

Deducting from this number all the Calendar Rounds possible, 74 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively), to the remainder, the termiaal date reached by the 
resulting calculations will be 11 Ahau 8 Tzec, The day part of this 
date is very clearly recorded in B4 immediately after the last period 
glyph, and the student will readily recognize the day 11 Ahau in this 
form. Following along the glyphs of the Supplementary Series in 
Cl Dl, C2 D2, the closing glyph is reached in C3b. It is very clear 
and has a coefficient of 9. The glyph following (D3) should record 
the month sign. A comparison of this form with the several month 
signs in figure 19 shows that Tzec is the month here recorded. Com- 
pare D3 with figure 19, g-Ti. The month coefficient is 8. The ter- 
minal date, therefore, recorded in B4 and D3 (11 Ahau 8 Tzec) agrees 
with the terminal date determined by calculation, and this whole text 
reads 9.16.1.0.0 11 Ahau 8 Tzec. The meaning of the element 

1 For the full text of this inscription see Maler, 1903; n, No. 2, pis. 74, 75. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 9 




A. STELA 11, YAXCHILAN 




B. ALTAR IN FRONT OF STRUCTURE 44, YAXCHILAN 

GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE 
OF BAR AND DOT NUMERALS AND HEAD-VARIANT 
PERIOD GLYPHS 



MORLEY] INTEODUCTIOlir TO STUDY OF MAYA HIEROGLYPHS 177 

between the tun coefficient and the tun sign in A3, which is repeated 
again in D3 between the month coefficient and the month sign, is 
unlcnown. 

In plate 9, B, is figured the Initial Series on an altar in front of 
Structure 44 at Yaxchilan.' The introducing glyph appears in Al Bl 
and is followed by the number in A2-A4. The period glyphs are all 
expressed as head variants and the coefficients as bar and dot nimierals. 
Excepting the kin coefficient in A4, the number is quite easily read 
aS 9.12.8.14. ? An inspection of our text shows that the coefficient 
must be 0, 1, 2, or 3. Let us work out the terminal dates for all four 
of these values, commencing with 0, and then see which of the result- 
ing terminal days is the one actually recorded in A4. Reducing the 
number 9.12.8.14.0 to imits of the first order by means of Table 
XIII, we have: 

A2= 9X144,000 = 1,296,000 

B2 = 12X 7,200= 86,400 

A3= 8X 360= 2,880 

B3 = 14x 20= 280 

A4= OX 1= 



1, 385, 560 
Deducting from this number all the Calendar Rounds possible, 73 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively), to the remainder, the terminal day reached will be 
11 Ahau 3 Pop. Therefore the Initial-series numbers 9.12.8.14.1, 
9.12.8.14.2, and 9.12.8.14.3 will lead to the three days immediately fol- 
lowing 9. 12.8. 14.0 11 Ahau 3 Pop. Therefore our four possible termi- 
nal dates will be: 

9.12.8.14.0 11 Ahau 3 Pop 

9.12.8.14.1 12 Imix 4 Pop 

9.12.8.14.2 13 Ik 5 Pop 

9.12.8.14.3 1 Akbal 6 Pop 

Now let us look for one of these four terminal dates in the text. The 
day reached by an Initial Series is almost invariably recorded imme- 
diately after the last period glyph; therefore, if this inscription is 
regular, the day glyph should be B4. This glyph probably has the 
coefficient 12 (2 bars and 2 numerical dots), the oblong element 
between probably being ornamental only. This number must be 
either 11 or 12, since if it were 13 the 3 dots would all be of the same 
size, which is not the case. An inspection of the coefficient in B4 
eliminates from consideration, therefore, the last two of the above 
four possible terminal dates, and reduces the possible values for the 
kin coefficient in A4 to or 1. Comparing the glyph in B4 with the 
day signs in figure 16, the form here recorded will be found to be iden- 
tical with the sign for Imix in figure 16, a. This eliminates the first 
terminal date above and leaves the second, the day part of which 

1 For the full text ol tUs inscription see Maler, 1903: ii, No. 2, pi. 79, 2. 
43508°— Bull. 57—15 12 



178 BUREAU OF AMBEICAN ETHNOLOGY [bull. 57 

we have just seen appears in B4. This further proves that the kin 
coefficient in A4 is 1. The final confirmation of this identification 
wUl come from the month gijph., which must be 4 Pop if we have 
correctly identified the day as 12 Imix. If, on the other hand, the 
day were 11 Ahau, the month glyph would be 3 Pop. Passing over 
A5 B5, A6 B6, Cl Dl, and C2, we reach in D2a the closing glyph 
of the Supplementary Series, here showing the coefficient 9. Com- 
pare this form with figure 65. The month glyph, therefore, should 
appear in D2b. The coefficient of this glyph, is very clearly 4, thus 
confirming our identification of B4 as 12 Imix. (See Table VII.) 
And finally, the month glyph itself is Pop. Compare D2b with 
figure 19, a. The whole Initial Series in plate 9, B, therefore reads 
9.12.8.14.1 12 Imix 4 Pop. 

In plate 10, is figured the Initial Series from Stela 3 at Tikal.* 
The introducing glyph, though somewhat effaced, may still be rec- 
ognized in Al. The Initial-series number follows in B1-B3. The 
head-variant period glyphs are too badly weathered to show the 
determining characteristic in each case, except the uinal head in A3, 
the mouth curl of which appears clearly, and their identification rests 
on their relative positions with reference to the introducing glyph. 
The reliability of this basis of identification for the period glyphs of 
Initial Series has been thoroughly tested in the texts already pre- 
sented and is further confirmed in this very inscription by the uinal 
head. Even if the large mouth curl of the head in A3 had not proved 
that the uinal was recorded here, we should have assimied this to be 
the case because this glyph, A3, is the fourth from the introducing 
glyph. The presence of the mouth curl therefore confirms the iden- 
tification based on position. The student will have no diffic\ilty in 
reading the number recorded in B1-B3 as 9.2.13.0.0. 

Reducing this number by means of Table XIII to units of the first 
order, we obtain: 

Bl= 9X144,000 = 1,296,000 

A2= 2X 7,200= 14,400 

B2 = 13X 360= 4,680 

A3= OX 20= 

B3= Ox 1= 



1, 315, 080 
Deducting all the Calendar Rounds possible from this number, 69 
(see Table XVI)', and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively) to the remainder, the terminal date reached will 
be 4 Ahau 13 Kayab. It remains to find this date in the text. The 
glyph in A4, the proper position for the day glyph, is somewhat 
effaced, though the profile of the human head may yet be traced 
thus enabling us to identify this form as the day sign Ahau. Com- 

' 1 For the full text of this inscription see Maler, 1911: v, No. 1, pi. 15. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN E7 PLATE 10 




GLYPHS REPRESENTING INITIAL SERIES, SHOW- 
ING USE OF BAR AND DOT NUMERALS AND 
HEAD-VARIANT PERIOD GLYPHS-STELA 3, 
TIKAL 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 11 




GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR 
AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS-STELA 
A (EAST SIDE), QUIRIGUA 



MOKLET] nirTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 179 

pare figure 16, V , i'. The coefficient of A4 is very clearly 4 dots, 
that is, 4, and consequently this glj^jh agrees with the day as de- 
termined by calculation, 4 Ahau. Passing over B4, A5, B5, and A6, 
we reach ia B6 the closing gljrph of the Supplementary Series, here 
recorded with a coefficient of 9. Compare B6 with figure 65. The 
month glyph follows in A7 with the coefficient 13. Comparing this 
latter glyph with the month signs in figiu-e 19, it is evident that the 
month Kayab (fig. 19, d'-f) is recorded in A7, which reads, therefore, 
13 Kayab. .Hence the whole text records the Initial Series 9.2.13.0.0 
4 Ahau 13 Kayab. 

This Initial Series is extremely important, because it records the 
earliest contemporaneous ^ date yet found on a monument '' ia the 
Maya territory. 

In plate 1 1 is figm-ed the Initial Series from the east side of Stela A 
at Quirigua. ^ The introducing glyph appears in A1-B2 and the 
Initial-series nimiber ia A3-A5. The student will have little diffi- 
culty in picking out the clasped hand in A3, the oval in the top of 
the head in B3, the fleshless lower jaw in A4, the mouth ciirl in B4, 
as the essential characteristic of the cycle, katun, tun, and uinal 
heads, respectively. The kin head in A5 is the banded-headdress 
variant (compare fig. 34, i, j), and this completes the number, which 
is 9.17.5.0.0. Reducing this by means of Table XIII to units of the 
first order, we have: 

A3= 9X144,000 = 1,296,000 

B3 = 17X 7,200= 122,400 

A4= 5X 360= 1,800 

B4= OX 20= 

A5= OX 0= 



1, 420, 200 

Deducting from this number all the Calendar Rounds possible, 73 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 

1 As used thiougliout this book, the expression "the contemporaneous date" designates the time when 
the monument on which such a date is found was put into formal use, that is, the time of its erection. As 
will appear later in the discussion of the Secondary Series, many monuments present several dates between 
the extremes of which elapse long periods. Obviously, only one of the dates thus recorded can represent 
the time at which the monument was erected. In such inscriptions the final date is almost invariably 
the one designating contemporaneous time, and the earlier dates refer probably to historical, traditional, 
or even mythological events in the Maya past. Thus the Initial Series 9.0.19.2.4 3 Kan 2 Yax on Lintel 21 
at Yaxchilan, 9.1.0.0.0 6 Ahau 13 Yaxkln on the west side of Stela at Quirigua, and 9.4.0.0.0 13 Ahau 18 
Tax from the Temple of the Inscriptions at Palenque, all refer probably to earlier historical or traditional 
events in the past of these three cities, but they do not indicate the dates at which they were severally 
recorded. As Initial Series which refer to purely mythological events may be classed the Initial Series 
from the Temples of the Sun, Cross, and Foliated Cross at Palenque, and from the east side of Stela C at 
Quirigua, all of which are concerned with dates centering around or at the beginning of Maya chronology. 
Stela 3 at Tikal (the text here under discussion), on the other hand, has but one date, which probably 
refers to the time of its erection, and is therefore contemporaneous. 

2 There are one or two earlier Initial Series which probably record contemporaneous dates; these are not 
inscribed on large stone monuments but on smaller antiquities, namely, the Tuxtla Statuette and the 
Leyden Plate. For the discussion of these early contemporaneous Initial Series, see pp. 194-198. 

8 For the full text of this inscription see Maudslay , 1889-1902: n, pis. 4r-7. 



180 BUEEAU OF AMBEICAN ETHNOLOGY [bull. 57 

respectively) to the remainder, the terminal day reached will be 
found to be 6 Ahau 13 Kayab. 

In B5 the profile variant of the day sign, Ahau, is clearly recorded 
(fig. 16, h' , i'), and to it is attached a head-variant numeral. Com- 
paring this with the head-variant numerals in figures 51-53, the stu- 
dent will have little difficnlty in identifying it as the head for 6 (see 
fig. 51, <-v). Note the so-called "hatchet eye" in A5, which is the 
determining characteristic of the head for 6 (see p. 99). Passing 
over A6 B6, A7 B7, A8 B8, we reach in A9 the closipg gl3T)h of 
the Supplementary Series, here showing the head- variant coefiicient 
10 (see fig. 52, m-r-). . In B9, the next glj^ph, is recorded the month 
13 Kayab (see fig. 19, d'-f). The whole Initial Series therefore 
reads 9.17.5.0.0 6 Ahau 13 Kayab. 

All the Initial Series heretofore presented have had normal-form 
nunlerals with the exception of an incidental head-variant number 
here and there. By this time the student should have become thor- 
oughly familiar with the use of bar and dot numerals in the inscrip- 
tions and should be ready for the presentation of texts showing head- 
variant nmnerals, a more difiicult group of glyphs to identify. 

In plate 12, A, is figured the Initial Series on the tablet from the 
Temple of the Foliated Cross at Palenque.^ The introducing glyph 
appears in Al B2, and is followed by the Initial-series number in 
A3-B7. The student will have little difficulty in identifying the heads 
in B3, B4, B5, B6, and B7 as the head variants for the cycle, katim, 
tun, uinal, and kin, respectively. The head in A3 prefixed to the 
cycle glyph in B3 has for its determining characteristic the forehead 
ornament composed of more than one fart (here, of two parts). As 
explained on page 97, this is the essential element of the head for 1. 
Compare A3 with figure 51, a-e, and the two glyphs will be found to 
be identical. We may conclude, therefore, that in place of the usual 
9 cycles heretofore encountered in Initial Series, we have recorded 
in A3-B3 1 cycle.^ The katim coefficient in A4 resembles closely the 
cycle coefficient except that its forehead ornament is composed of 
but a single part, a large cm-l. As explained on page 97, the heads 
for 1 and 8 are very similar, and are to be distinguished from each 
other only by their forehead ornaments, the former having a forehead 
ornament composed of more than one part, as in A3, and the latter 
a forehead ornament composed of but one part, as here in A4. This 
head, moreover, is very similar to the head for 8 in figure 52, a-f; 
indeed, the only difference is that the former has a fleshless lower 
jaw. This is the essential element of the head for 10 (see p. 100); 
when applied to the head for any other numeral it increases the 
value of the resulting head by 10. Therefore we have recorded in 

1 For the full text of this inscription see Maudslay, 1889-1902: rv, pis. 80-82. 

2 As explained on p. 179, footnote 1, this Initial Series refers probably to some mythological event rather 
than to any historical occurrence. The date here recorded precedes the historic period of the Maya civili- 
zation by upward of 3,000 years. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 12 










A. TEMPLE OF THE FOLIATED 
CROSS, PALENQUE 







B. TEMPLE OF THE SUN, 
PALENQUE 



GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF 
HEAD-VARIANT NUMERALS AND PERIOD GLYPHS 



MORMv] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 181 

A4 B4, 18 (8 + 10) katuns. The tun coefficient in A5 has for its 
aetermmmg characteristic the tun headdress, which, as explained on 
page 99, is the essential element of the head for 5 (see fig. 51, v^s) 
iheretore A5 represents 5, and A5 B5, 5 tuns. The uinal coefEcient 
in Ab Has tor its essential elements the large bulging eye, square irid, 
and sna^like front tooth. As stated on page 98, these characterize 
the head tor 4, examples of which are given in figure 51, j-m. Con- 
sequently, A6 B6 records 4 uinals. The kin coefficient m A7 is quite 
clearly 0. The student will readily recognize the clasped h and, which 
IS the determming characteristic of the head (see p. 101 and fig. 53, 
s-w). The number recorded in A.3-B7 is, therefore, 1.18.5.4.0. 
Reducing this number to" units of the 1st order by means of Table 
XIII, we obtain: 

A3B3 = 1 X 144, 000 = 144, 000 
A4B4 = 18X 7,200 = 129,600 
A5B5= 5X 360= 1,800 

A6B6= 4x 20= 80 

A7B7= OX 1= 



275, 480 
Deducting from this number all the Calendar Rounds possible, 14 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively), the terminal date reached will be 1 Ahau 13 Mac. 
Of this date, the day part, 1 Ahau, is recorded very clearly in A8 BS. 
Compare the head ia AS with the head in A3, which, we have seen, 
stood for 1 and also with figure 51, a-e, and the head in B8 with 
figure 16, Th', i', the profile head for the day sign Ahau. This text is 
irregular in that the month glyph follows immediately the day glyph, 
i. e., in A9. The glyph in A9 has a coefficient 13, which agrees with the 
month coefficient determined by calculation, and a comparison of B9 
with the forms for the months in figure 19 shows that the month 
Mac (fig. 19, w, x) is here recorded. The whole Initial Series there- 
fore reads 1.18.5.4.0 1 Ahau 13 Mao. 

In plate 12, B, is figured the Initial Series on the tablet from the 
Temple of the Sun at Palenque.' The introducing glyph appears in 
AI-B2 and is followed by the Initial-serie^ number in A3-B7. The 
student will have no difficulty in identifying the period glyphs in 
B3, B4, B5, B6, and B7; and the cycle, katun, and tun coefficients 
in A3 A4, and A5, respectively, will be found to be exactly like the 
corresponding coefficients in the preceding Initial Series (pi. 12, A, 
A3 A4 A5), which, as we have seen, record the numbers 1, 18, and 
5 respectively. The uinal coefficient in A6, however, presents a 
new form. Here the determining characteristic is the banded head- 
dress or fillet, which distinguishes the head for 3, as explained on 
pao-6 98 (see fig. 51 h, i). We have then in A6 B6 record of 3 

1 For the full text of this inscription see Maudslay, 1889-1902; iv, pis. 87-89. 



182 BUREAU OP AMEBICAN ETHNOLOGY [bull. 57 

uinals . The kiii coeflB.cieiit in A7 is very clearly 6 . Note the ' ' hatchet 
eye," which, as explained on page 99, is the essential element of 
this head numeral, and also compare it with figure 51, t-^. The 
number recorded ia A3-B7 therefore is 1.18.5.3.6. Reducing this to 
units of the first order by means of Table XIII, we obtain: 

A3B3 = 1 X 144, 000 = 144, 000 
A4B4 = 18X 7,200 = 129,600 
A5B5= 5X 360= 1,800 
A6B6= 3X 20= 60 

A7B7= 6X 1= 6 



275, 466 

Deducting from this number all the Calendar Roimds possible, 14 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141), respectively, to the remainder, the terminal date reached will 
lie 13 Cimi 19 Cell. If this inscription is regular, the day part of the 
^bMe date should follow in A8 B8, the former expressing the coeffi- 
cient and the latter the day sign. Comparing A8 with the head 
numerals in figures 51-53, it will be found to be like the second 
variant for 13 in figure 52, x-b', the essential element of which seems 
to be the pendulous nose surmounted by a curl, the protruding 
mouth fang, and the large bulging eye. Comparing the glyph in B8 
with the day signs in figure 16, it will be seen that the form here 
recorded is the day sign Cimi (fig. 16, h, i). Therefore A8 B8 
expresses the day 13 Cimi, The month glyph is recorded very 
irregularly in this text, since it occm's neither immediately after the 
Supplementary Series or the day sign, but the second glyph after the 
day sign, in B9. A comparison of this form with figure 19, u-v, 
shows that the month Ceh is recorded here. The coefficient is 19. 
Why the gl3T)h in A9 shoidd stand between the day and its month 
glyph is unknown; this case constitutes one of the many unsolved 
problems in the study of the Maya glyphs. This whole Initial Series 
reads 1.18.5.3.6 13 Cimi 19 Ceh. 

The student will note that this Initial Series records a date 14 days 
earlier than the preceding Initial Series (pi. 12, A). That two dates 
should be recorded which were within 14 days of each other, and yet 
were more than 3,000 years earlier than practically all other Maya 
dates, is a puzzling problem. These two Initial Series from the 
Temple of the Sun and that of the Foliated Cross at Palenque, together 
with a Secondary-series date from the Temple of the Cross in the 
same city, have been thoroughly reviewed by Mr. Bowditch (1906). 
The conclusions he reaches and the explanation he offers to account 
for the occurrence of three dates so remote as these are very reason- 
able, and, the writer believes, will be generally accepted by Maya 
students. 



morlet] 



INTEODTTCTION TO STUDY OF MAYA HIEEOGLYPHS 



183 



In figure 69, A, is shown the Initial Series iascribed on the rises 
and treads of the stairway leading to House C in the Palace at 
Palenque.' The introducing glyph is recorded in Al, and the Initial- 
series number follows in B1-B3. The student will readily recognize 
the period glyphs in Bib, A2b, B2b, A3b, and B3b. The head 
expresstQg the cycle coeflB,cient in Bla has for its essential element 
the dots centering around the comer of the mouth. As explained on 
page 100, this characterizes the head for 9 (see fig. 52, g-l, where vari- 
ants for the 9 head are figured) . In Bl, therefore, we have recorded 9 





A 

Fig. 69. Initial Series showing head-variant numerals and period glyphs; A, House C of the Palace 
Group at Palenque; B, Stela P at Copan. 

cycles, the nmnber almost always foimd in Initial Series as the cycle 
coefficient. The essential element of the katun coefficient in A2a is 
the forehead ornament composed of a single part. This denotes the 
head for 8 (see p. 100, and fig. 52, a-f; also compare A2a with the heads 
denoting IS in the two preceding examples, pi. 12, A. Al, and pi. 12, 
B,A4, each of which shows the same forehead ornament). The tun 
coefficient in B2a is exactly like the cycle coefficient just above 
it in Bla; that is, 9, having the same dotting of the face near the 
corner of the mouth. The uinal coefficient in A3a is 13. Com- 
pare this head numeral with AS, plate 12, B, which also denotes 13, 
and also with figiu"e 52, x-h'. The essential elements (see p. 101) 



1 For the full text of this inscription, see Maadslay, 1S89-1902: iv, pi. 23. 



184 BtTEBAXJ or AMEBlCAif ETHIJOLOGY [bull. 57 

are the large pendulous nose surmounted by a curl, the bulging eye, 
and the mouth fang, the last mentioned not appearing in this case. 
Since the kin coefficient in B3a is somewhat eflEaced, let us call it 
for the present' and proceed to reduce our number 9.8.9.13.0 to units 
of the first order by means of Table XIII : 

Bl= 9X144,000 = 1,296,000 
A2= 8X 7,200= 57,600 
B2= 9X 360= 3,240 
A3 = 13X 20= 260 

B3= OX 1= 



1, 357, 100 



Deducting from this number all the Calendar Rounds possible, 71 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, we reach as the terminal date 8 Ahau 
13 Pop. Now let us examine the text and see what is the terminal 
date actually recorded. In A4b the student will have little difficulty 
in recognizing the profile variant of the day sign Ahau (see fig. 16, 
h'. i'). This at once gives us the missing value for the kin coefficient 
in B3, for the day Ahau can never be reached in an Initial Series if 
the kin coefficient is other than 0. Similarly, the day Imix can never 
be reached in Initial Series if the kin coefficient is other than 1, etc. 
Every one of the 20 possible kiu coefficients, to 19, has a corre- 
sponding day to which it will always lead, that is, Ahan to Cauac, 
respectively (see Table I) . Thus, if the kin coefficient in an Initial- 
series number were 5, for example, the day sign of the resulting 
terminal date must be Chicchan, since Clicchan is the fifth name after 
Ahau in. Table I. Thus the day sign in Initial-series terminal dates 
may be determined by inspection of the kin coefficient as well as by 
rule 2 (p. 140), though, as the student will see, both are applications 
of the same principle, that is, deducting all of the 20s possible and 
counting forward only the remainder. Returning to our text, we 
can now say without hesitation that our number is 9.8.9.13.0 and 
that the day sign in A4b is Ahau. The day coefficient in A4a is just 
like the katun coefficient in A2a, having the same determining char- 
actcrictic, namely, the forehead ornament composed of one part. A 
compaiison of this ornament with the ornament on the head for 8 
* '^■x will show that the two forms are identical. The bifurcate 
(IS ...icnt surmounting the head in A4a is a part of the headdress, 
ami as such should not be confused with the forehead ornament. 
Ili f.ulurc to recognize this poiut might cause the student to identify 

"I It is clear Ihat it all the period coefficients above the kin have been correctly identified, even though 
the kin coefficient is unknown, by designating it the date reached will be within 19 days of the date 
originally recorded. Even though its maximum value (19) had originally been recorded here, it could 
have carried the count only 19 days further. By using as the kin coefflcient, therefore,- we can not be 
more than 19 days from the original date. 



morlbt] INTROD-UCTION TO STUDY OF MAYA HIEROGLYPHS 185 

A4a as the head for 1, that is, having a forehead ornanieHfc composed 
of more than one part, instead of the head for 8. The month glyph, 
which follows in B4b, is mifortimately effaced, though its coefficient 
in B4a is clearly the head for 13. Compare B4a with the uinal coeffi- 
cient in A3a and with the heads for 13 in figure 52, x-b'. As recorded, 
therefore, the terminal date reads 8 Ahau 13 ?, thus agreeing in every 
particular so far as it goes with the terminal date reached by calcu- 
lation, 8 Ahau 13 Pop. In all probability the effaced sign in B4b origi- 
nally was the month Pop. The whole Initial Series therefore reads 
9.8.9.13.0 8 Ahau 13 Pop. 

In figure 69, B, is shown the Initial Series from Stela P at Copan.' 
The introducing glyph appears in A1-B2 and is followed by the Initial- 
series number in A3-B4. The student wiU readily identify A3, B3, 
and A4 as 9 cycles, 9 katuns, and 10 tuns, respectively. Note the 
beard on the head representing the number 9 in. both A3a and B3a. 
As explained on page 100, this characteristic of the head for 9 is not 
always present (see fig. 52, g-i). The uinal and kin glyphs have been 
crowded together into one glyph-block, B4, the uinal appearing in 
B4a and the kin in B4b. Both their coefficients are 0, which is 
expressed in each case by the form shown in figure 47. The whole 
number recorded is 9.9.10.0.0; reducing this to tmits of the first order 
by means of Table XIII, we obtain: 

A3 = 9X144,000 = 1,296,000 
B3 = 9X 7,200= 64,800 
A4 =10X 360= 3,600 
B4a= OX 20= 

B4b= OX 1= 



1, 364, 400 



Deducting from this number all of the Calendar Rounds possible, 71 
(see Table XVI),. and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached will be 
2 Ahau 13 Pop. In A5a the day 2 Ahau is very clearly recorded, the 
day sign being expressed by the profile variant and the 2 by two 
dots (incorrectly shown as one dot in the accompanying drawing).^ 
Passing over A5b, B5, and A6 we reach in B6a the closing glyph of 
the Supplementary Series, and in the folloAving glyph, B6b, the 
month part of this terminal date. The coefficient is 13, and compar- 
ing the sign itself with the month signs in figure 19, it will be seen that 
the form in a (Pop) is the month recorded here. The whole Initial 
Series therefore reads 9.9.10.0.0 2 Ahau 13 Pop. 

1 For the full text of this inscription see Maudslay, 1889-1902: t, pis. 88, 89. 

2 While at Copan the writer made a personal examination of this monmnent and found that Mr. Mauds- 
lay's drawing is incorrect as regards the ooefBoient of the day sign. The original has two numerical dots 
between two crescents, whereas the Mauds.lay drawing shows one numerical dot between two distinct 
pairs of crescents, each pair, however, of difterent shape. 



186 



BITEEAU OF AMERICAN ETHNOLOGY 



[bull. 57 





In figure 70 is illustrated the Initial Series "from Zoomorph G at 
Quirigua.^ The introducing glyph appears in A1-B2 and is followed 
ia Cl-Hl by the Initial-series niunber. Glyphs Cl Dl record 9 
cycles. The dots on the head for 9 in Cl are 
partially effaced. In 02 is the katun coefficient 
and ia D2 the katun sign. The determining char- 
acteristic of the head for 7 appears ia C2, namely, 
the scroll passing under the eye and projecting 
upward and in front of the forehead. See page 
100 and figiu-e 51, w. It would seem, then, at 
first sight that 7 katims were recorded in C2 D2. 
That this was not the case, however, a closer ex- 
amination of C2 will show. Although the lower 
part of this glyph is somewhat weathered, enough 
still remains to show that this head originally had a 
fleshless lower jaw, a character increasing its value 
by 10. Consequently, instead of having 7 katuns 
in C2 D2 we have 17 (7 + 10) katuns. Compare 
C2 with figure 53, j-m. In El Fl, 15 tuns are 
recorded. The tim headdress in El gives the value 
5 to the head there depicted (see fig. 51, ti-s) and 
the fleshless lower jaw adds 10, making the value 
of El 15. Compare figure 53, 6-e, where examples 
of the head for 15 are given. Glyphs E2 and F2 
represent uinals and Gl Hi kins; note the 
clasped hand in E2 and Gl, which denotes the 
in each case. This whole number therefore reads 
9.17.15.0.0. Reducing this to units of the first 
order by means of Table XIII, we have: 

Cl Dl= 9X144,000 = 1,296,000 





■3 






a 



p. 




.g 
I 





a 



C2 D2 = 17X 


7,200 = 


122, 400 


El Fl = 15x 


360 = 


5,400 


E2 F2= Ox 


20 = 





G1H1= OX 


1 = 






1, 423, 800 
Deducting from this number all the Calendar 
Rounds possible, 75 (see Table XVI), and apply- 
ing rules 1, 2, and 3 (pp. 139, 140, and 141, respec- 
tively), to the remainder, the terminal day reached 
will be 5 Ahau 3 Muan. The day is recorded in G2 H2. The day sign 
in H2 is quite clearly the grotesque head variant for Ahau in figure 
16, j' — Ic'. The presence of the tun headdress in G2 indicates that the 
coefiicient here recorded must have been either 5 or 15, depending 

1 For the full text of this inscription see Maudslay, 1889-1902: n, pis. 41-44. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 13 




OLDEST INITIAL SERIES AT COPAN-STELA 15 



MOBLET] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 187 

on whether or not the lower part of the head origmally had a flesh- 
less lower jaw or not. In this particular case there is no room for 
doubt, since the numeral in G2 is a day coefficient, and day coeffi- 
cients as stated in Chapter III, can never rise above 13. Conse- 
quently the number 15 can not be recorded in G2, and this form 
must stand for the number 5. 

Passing over II Jl, I2 J2, Kl Ll, K2 L2, we reach in Ml the clos- 
ing glyph of the Supplementary Series, here shown with a coeffi- 
cient of 10, the head having a fleshless lower jaw. The month sign 
follows in Nl. The coefficient is 3 and by compariag the sign itself 
with the month glyphs ia figure 19, it will be apparent that the sign 
for Muan in a' or V is recorded here. The Initial Series of this monu- 
ment therefore is 9.17.15.0.0 5 Ahau 3 Muan. 

In closing the presentation of Initial-series texts which show both 
head-variant numerals and period glyphs, the writer has thought best 
to figure the Initial Series on Stela 15 at Copan, because it is not only 
the oldest Initial Series at Copan, but also the oldest one known in 
which head-variant numerals are used * (see pi. 13). The introducing 
glyph appears at A1-B2. There follows in A3 a number too much 
effaced to read, but which, on the basis of aU our previous experience, 
we are justified in calling 9. Similarly B3 must be the head variant 
of the cycle sign. The numeral 4 is clearly recorded in A4. Note 
the square irid, protruding fang, and mouth curl. Compare A4 with 
figure 51, j-m. Although the glyph in B4 is too much effaced to 
read, we are justified in assuming that it is the head variant of the 
katun sign. The glyph in A5 is the numeral 10. Note the fleshless 
lower jaw and other characteristics of the death's-head. Again we 
are justified in assuming that B5 must be the head variant of the tim 
sign. The glyphs A6, B6 clearly record uinals. Note the clasped 
hand denoting zero in A6, and the curling mouth fang of the uinal 
period glyph in B6. This latter glyph is the full-figure form of the 
uinal sign ^ (a frog). Compare B6 with figure 33, which shows the 
uinal sign on Stela D at Copan. The stela is broken off just below 
the uinal sign and its coefficient; and therefore the kin coefficient 
and sign, the day coefficient and sign, and the month coefficient and 
sign, are missing. Assembling the four periods present, we have 
9.4.10.0.?. CaUing the missing kin coefficient 0, and reducing this 
number to units of the first order by means of Table XIII, we have : 

A3 B3 = 9 X 144, 000 = 1, 296, 000 

■ A4B4= 4x 7,200= 28,800 

A5 B5 = 10 X 360 = 3, 600 

A6B6= OX 20= 

Ox 1= 



1, 328, 400 



1 For the text of this monument see Spinden, 1913: VI, pi. 23, 2. 

2 For the discussion of full-flgure glyphs, see pp. 65-73. 



188 BUBEAU OF AMERICAN- ETHNOLOGY [BnLU 57 

Deducting from this number all the Calendar Rounds possible, 69 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached will be 
12 Ahau 8 Mol. This date is reached on the assumption that the miss- 
ing kin coefficient was zero. This is a fairly safe assimaption, since 
when the tun coefficient is either 0, 5, 10, or 15 (as here) and the uinal 
coefficient is (as here), the kin coefficient is almost inyariably zero. 
That is, the close of an even hotun in the Long Count is recorded. 

While at Copan in May, 1912, the writer was shown a fragment of 
a stela which he was told was a part of this monument (Stela 15). 
This showed the top parts of two consecutive glyphs, the first of 
which very clearly had a coefficient of 12 and the one following of 8. 
The glyphs to which these coefficients belonged were missing, but the 
coincidence of the two numbers 12 (?) 8 (?) was so striking when taken 
into consideration with the fact that these were the day and month 
coefficients reached by calculation, that the writer was inchned to 
accept this fragment as the missing part of Stela 15 which showed 
the terminal date. This whole Initial Series therefore reads: 9.4.10.0.0 
12 Ahau 8 Mol. It is chiefly interesting because it shows the earUest 
use of head-variant numerals known. 

In the foregoing texts plate 12, A, B, figure 69, A, B, and figure 70, 
the head-variant numerals 0, 1, 3, 4, 5, 6, 8, 9, 10, 13, 14, 15, 17, and 18 
have been given, and, excepting the forms for 2, 11, and 12, these 
include examples of all the head numerals.' No more texts specially 
illustrating this type of numeral will be presented, but when any of 
the head numerals not figured above (2, 7, 11, 12, 16, and 19) 
occur in future texts their presence wiU be noted. 

Before taking up the consideration of unusual or irregular Initial 
Series the writer has thought best to figure one Initial Series the 
period glyphs and numerals of which are expressed by full-figure 
forms. As mentioned on page 68, such inscriptions are exceedingly 
rare, and such glyphs, moreover, are essentially the same as head- 
variant forms, since their determining characteristics are restricted 
to their head parts, which are exactly like the corresponding head- 
variant forms. This fact will greatly aid the student in identifying 
the full-figure glyphs in the following text. 

In plate 14 is figured the Initial Series from Stela D at Copan.^ 
The introducing glyph is recorded in Al. The variable central 
element in keeping with the other glyphs of the inscription appears 
here as a full figure, the lower part of which is concealed by the tun- 
sign.^ 

1 The characteristics of the heads lor 7, 14, 16, and 19 will he found in the heads for 17, 4, 6, and 9, respec- 
tively. 

" For the full text of this inscription see Maudslay, 1889-1902; i, pis. 47, 48. 

' The student will note also in connection with this glyph that the pair of comhlike appendages usually 
found are here replaced by a pair of fishes. As explained on pp. 65-66, the flsh represents probably the 
original form from which the comblike element was derived in the process of glyph conventionalization. 
The ful 1 original form of this element is therefore in keeping with the other full-figure forms in this text. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 67 PLATE 14 






'■''^;b 







INITIAL SERIES ON STELA D, COPAN, SHOWING FULL- 
FIGURE NUMERAL GLYPHS AND PERIOD GLYPHS 



MOBLET] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 189 

The Initial-series number itself appears in B1-B3. The cycle sign 
is a grotesque bird, designated by Mr. Bowditch a parrot, an identifi- 
cation which the hooked beak and claws strongly suggest. The 
essential element of the cycle sign, however, the clasped hand, appears 
only in the head of this bird, where the student will readily find it. 
Indeed, the head of this fuU-figure form is nothing more nor less than 
a head-variant cycle glyph, and as such determines the meaning of 
the whole figure. Compare this head with figure 25, d-f, or with any 
of the other head-variant cycle forms figured in the preceding texts. 
This grotesque "cycle bird," perhaps the parrot, is botind to the back 
of an anthropomorphic figure, which we have every reason to suppose 
records the cycle coefiicient. An examination of this figure will show 
that it has not only the dots on the lower part of the cheek, but also 
the beard, both of which are distinctive features of the head for 9. 
Compare this head with figure 52, g-l, or with any other head variants 
for the numeral 9 already figured. Bearing in mind that the heads 
only present the determining characteristics of full-figure glyphs, the 
student will easily identify Bl as recording 9 cycles. 

The katun and its coefiicient are represented in A2, the former by 
a grotesque bird, an eagle according to Mr. Bowditch, and the latter 
by another anthropomorphic figure. The period glyph shows no 
essential element recognizable as such, and its identification as the 
katun sign therefore rests on its position, immediately following the 
cycle sign. The head of the full figure, which represents the katun 
coefiicient, shows the essential element of the head for 5, the tun 
headdress. It has also the fieshless lower jaw of the head for 10. 
The combination of these two elements in one head, as we have seen, 
indicates the muneral 15, and A2 therefore records 15 katuns. Com- 
pare the head of this anthropomorphic figure with figure 53, 6-e. 

The tun and its coefficient are represented in B2. The former 
again appears as a grotesque bird, though in this case of undeter- 
mined nature. Its head, however, very clearly shows the essential 
element of the head-variant tun sign, the fieshless lower jaw. Com- 
pare this form with figure 29, e-g, and the other head-variant tim 
signs already illustrated. The head of the anthropomorphic figure, 
which denotes the tun coefiicient, is just like the head of the anthro- 
pomorphic figure in the preceding glyph (A2), except that in B2 the 
head has no fieshless lower jaw. 

Since the head in A2 with the fieshless lower jaw and the tun 
headdress represents the numeral 15, the head in B2 without the 
former but with the latter represents the numeral 5. Compare the 
head of the anthropomorphic figure in B2 with figure 51, n-s. It is 
clear, therefore, that 5 tuns are recorded in B2. 

The uinal and its coefficient in A3 are equally clear. The period 
glyph here appears as a frog (Maya, uo), which, as we have seen else- 



190 BUREAU OF AMEBIOAN ETHNOLOGY - [boll. 57 

where, may have been chosen to represent the 20-day period because 
of the similarity of its name, uo, to the name of this period, u, or 
uinal. The head of the anthropomorphic figure which clasps the 
frog's foreleg is the head variant for 0. Note the clasped hand across 
the lower part of the face, and compare this form with figure 53, 
s-w. The whole glyph, therefore, stands for uinals. 

In B3 are recorded the kin and its coefficient. The period glyph 
here is represented by an anthropomorphic figure with a grotesque 
head. Its identity, as representing the kins of this nimiber, is better 
established from its position in the nvunber than from its appearance, 
which is somewhat irregular. The kin coefficient is just like the uinal 
coefficient — an anthropomorphic figure the head of which has the" 
clasped hand as its determining characteristic. Therefore B3 records 
kins. 

The whole number expressed by B1-B3 is 9.15.5.0.0; reducing this 
by means of Table XIII to units of the first order^ we have: 

Bl= 9X144,000 = 1,296,000 

A2 = 15X 7,200= 108,000 

B2= 5X 360= 1,800 

A3= OX 20= 

B3= OX 1= 



1, 405, 800 
Deducting from this niunber all the Calendar Rounds possible, 74 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141 respectively), to the remainder, the terminal date reached will 
be 10 Ahau 8 Chen. 

The day part of this terminal date is recorded in A4. The day sign 
Ahau is represented as an anthropomorphic figure, crouchiug within 
the customary day-sign cartouche. The head of this figure is the 
familiar profile variant for the day sign Ahau, seen in figure 16, h', 
i'. This cartouche is clasped by the left arm of another anthropo- 
morphic figure, the day coefficient, the head of which is the skull, 
denoting the niuneral 10. Note the fleshless lower jaw of this head 
and compare it with the same element ui figure 52, m-r. This glyph 
A4 records, therefore, the day reached by the Initial Series, 10 Ahau. 

The position of the month glyph in this text is most unusual. 
Passing over B4, the first glyph of the Supplementary Series, the 
month glyph follows it immediately iu A5. The month coefficient 
appears again as an anthropomorphic figure, the head of which has 
for its determining characteristic the forehead ornament composed 
of one part, denoting the numeral 8. Compare this head with the 
heads for 8, in figure 52, a-f. The month sign itself appears as a large 
grotesque head, the details of which present the essential elements 
of the month here recorded — Chen. Compare with figure 19, o, v. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 15 





^ / IT 






^XJ) 



- - ^f\ 7\/ 



■-"--- »'/■•'-■ 




£ADiJfiitU, 



•f# 



^. THE INSCRIPTION ARRANGED ACCORDING £. KEY TO SEQUENCE OF GLYPHS IN ^ 
TO A MAT PATTERN 



INITIAL SERIES ON STELA J, COPAN 



MORLET] IN-TBODUCTIOlir TO STUDY OF MAYA HIEROGLYPHS 191 

The superfix of figure 16, o, p, has been retained unchanged as the 
superfix in A5b. The element (*) appears just above the eye ^^ 
of the grotesque head, and the element (**) on the left-hand 9g? ^^ 
side about where the ear lobe should be. The whole glyph * ** 
unmistakably records a head variant of the month glyph Chen, and 
this Initial Series therefore reads 9.15.5.0.0 10 Ahau 8 Chen. 

The student will note that this Initial Series records a date just 
5 tuns later than the Initial Series on Stela B at Copan (pi. 7, A). 
According to the writer's opinion, therefore. Stelae B and D marked 
two successive hotims at this city. 

We come now to the consideration of Initial Series which are either 
\mtisual or irregular in some respect, examples of which it is necessary 
to give in order to familiarize the student with all kinds of texts. 

The Initial Series in plate 15, A,^ is figured because of the very 
unusual order followed by its glyphs. The sequence in which these 
succeed each other is given in 5 of that plate. The scheme followed 
seems to have been that of a mat pattern. The introducing 
glyph appears in position (pi. 15, B), and the student will readily 
recognize it in the same position in J. of the same plate. The 
Initial Series number follows in 1, 2, 3, 4, and 5 (pi. 15, B). Eefer- 
ring to these corresponding positions in A, we find that 9 cycles are 
recorded in 1, and 13 katuns in 2. At this point the diagonal glyph- 
band passes under another band, emerging at 3, where the tun sign 
with a coefficient of 10 is recorded. Here the band turns again and, 
crossing backward diagonally, shows uinals in 4. At this point the 
band passes under three diagonals running in the opposite direction, 
emerging at position 5, the glyph in which are recorded kins. 

This number 9.13.10.0.0 reduces by means of Table XIII to units 
of the first order, as follows : 

1 = ■ 9 X 144, 000 = 1, 296, 000 

2 = 13X 7,200= 93,600 

3 = 10X 360= 3,600 
4= OX 20= 
5= OX 1= 



1, 393, 200 



Deducting from this number all the Calendar Rounds possible, 73 
(see Table XVI), and applying niles 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached will be 
7 Ahau 3 Cumhu. Eeferring again to plate 15, B, for the sequence of 
the glyphs in this text, it is clear that the day of this terminal date 
should be recorded in 6, immediately after the kins of the Initial- 
series number in 6. It will be seen, however, in plate 15, A, that 

' For the full text of this inscription, see Maudslay, 1889-1902: i, pis. 66-71, 



192 BXJEEAU OP AMERICAN ETHNOLOGY [bull. 57 

jlyph 6 is effaced, and consequently the day is missing. Passing over 
7, 8, 9, 10, and 11, in J. and B of the plate named, we reach in the 
lower half of 12 the closing glyph of the Supplementary Series here 
shown with a coefficient of 10. Compare this form with figure 65. 
The month glyph, therefore, should follow in the upper half of 13.^ 
This glyph is very clearly the form for the month Cumliu (see fig. 19, g', 
h'), and it seems to have attached to it the bar and dot coefficient 8. 
A comparison of this with the month coefficient 3, determined above 
by calculation, shows that the two do not agree, and that the month 
coefficient as recorded exceeds the month coefficient determined by 
calculation, by 5, or in Maya notation, 1 bar. Since the Initial-series 
number is very clearly 9.13.10.0.0, and since this number leads to the 
terminal date 7 Ahau 3 Cumliu, it would seem that the ancient scribes 
had made an error in this text, recording 1 bar and 3 dots instead of 
3 dots alone. The writer is inclined to believe, however, that the bar 
here is only ornamental and has no numerical value whatsoever, hav- 
ing been inserted solely to balance this glyph. If it had been omitted, 
the month sign would have had to be greatly elongated and its pro- 
portions distorted in order to fill completely the space available. 
According to the -writer's interpretation, this Initial Series reads 
9.13.10.0.0 7 Ahau 3 Cumliu. 

The opposite face of the above-mentioned monument presents the 
same interlacing scheme, though in this case the glyph bands cross at 
right angles to each other instead of diagonally. 

The only other inscription in the whole Maya territory, so far as 
the writer knows, which at all parallels the curious interlacing pattern 
of the glyphs on the back of Stela J at Copan, just described, is Stela H 
at Quirigua, illustrated in figure 71.^ The drawing of this inscription 
appears in a of this figure and the key to the sequence of the glj^pbs in I. 
The introducing glyph occupies position 1 and is followed by the 
Initial Series in 2-6. The student will have little difficulty in iden- 
tifying 2, 3, and 4 as 9 cycles, 16 katuns, and tuns, respectively. 
The uinal and kin glyphs in 5 and 6, respectively, are so far effaced 
that in order to determine the values of their coefficients we shall 
have to rely to a large exient on other inscriptions here at Quirigua. 
For example, every monument at Quirigua which presents an Initial 
Series marks the close of some particular ho tun in the Long Count; 
consequently, all the Initial Series at Quirigua which record these 
hotun endings have for their uinal and kin coefficients.^ This abso- 



1 The student should remember that in this diagonal the direction of reading is from bottom to top 
See pi. 15, B, glyphs 7, 8, 9, 10, 11, 12, etc. Consequently the upper halt of 13 follows the lower half in 
this particular glyph. 

2 Tor the full text of this inscription see Hewett, 1911: pi. xxn B. 

3 A few monuments at Quirigua, namely, Stelae F, D, Jl, and A, have two Initial Series each. In A both 
of the Initial Series have for the coellicients of their uinal and kin glyphs, and in F D E the T 'f 
Series which shows the position of the monument in the Long Count, that is, the Initial Series sh '''^ 
the hotun ending which it^marks, has for its uinal and kin coefficients. ^^ 



MOKLBT] INTBODUCTION TO STUDY OP MAYA HIEROGLYPHS 



193 





lute uniformity in regard to the uinal and kin coefficients in all the 
other Initial Series at Quirigua justifies the assumption that in the 
text here under discussion uinals and kins were originally recorded 
in glyphs 5 and 6, respec- 
tively. Furthermore, an 
inspection of the coeffi- 
cients of these two glyphs 
in figure 71, a, shows that 
both of them are of the 
same general size and 
shape as the tun coeffi- 
cient in 4, which, as we 
have seen, is very clearly 0. 
It is more than probable 
that the lainal and kia co- 
efficients ui this text were 
originally 0, hke the tun co- 
efficient, and that through 
weathering they have been 
eroded down to their pres- 
ent shape. In figure 72, a, is shown the tun coefficient and beside it 
in i, the uinal or kin coefficient. The dotted parts ia i are the lines 
which have disappeared through erosion, if this coefficient was origi- 
nally 0. It seems more than likely from the foregoing that the uinal 
and kin coefficients in this number were originally 0, and proceeding 
on this assumption, we have recorded in glyphs 2-6, figure 71, a, the 
number 9.16.0.0.0. 

Reducing this to units of the first order by means of Table XIII, 
we have: 

5= 9X144,000 = 1,296,000 

6 = 16X 7,200= 115,200 

7= OX 360= 

8= OX 20= 

9= OX 1= 



riG. 71, 



Initial Series on Stela H, Quirigua: a, Mat pattern 
of glyph sequence; h, key to sequence of glyphs in a. 



1,411,200 



Deducting from this number all the Calendar Roimds possible, 74 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively) to the remainder, the terminal date 2 Ahau 13 
Tzec wiU be reached. 

In spite of some weathering, the day part of the terminal date 
appears in giyph. 7 inunediately after the kin glyph in 6. The coeffi- 
cient, though somewhat eroded, appears quite clearly as 2 (2 dots 
separated by an ornamental crescent). The day sign itself is the 
profile variant for Ahau shown in figm-e 16, h', i'. The agreement of 
43508°— Bull. 57—15 ^13 




194 BUKEAIT OF AMERICAN ETHNOLOGY [bull. 57 

the day recorded with the day determined by calculations based on 
the assumption that the kia and uiual coefficients are both 0, of itself 
tends to estabUsh the accuracy of these asstunptions. Passing over 
8, 9, 10, 11, 12, 13, and 14, we reach in 15 the closing glyph of the 
Supplementary Series, and in 16 probably the month glyph. This 
form, although badly eroded, presents no features either in the outline 
of its coefficient or in the sign itself which would prevent it repre- 
senting the month part 13 Tzec. The coefficient is just wide enough 
for three vertical divisions (2 bars and 3 dots), and the month glyph 
itself is divided into two parts, a superfix comprising about one-third 
of the glyph and the maia element the remaining two-thirds. Com- 
pare this form with the sign for Tzec in figure 19, g, Ji. Although 
this text is too much weathered to permit ab- 
solute certainty with reference to the reading of 
this Initial Series, the writer nevertheless be- 
hoves that in all probability it records the date 
given above, namely, 9.16.0.0.0 2 Ahau 13 Tzec. 
If this is so, Stela H is the earhest hotun-marker 
a b at Quirigua.^ 

FIG. 72. The tun, mnai, and The studcut wiU havc, uoticcd from the fore- 
kin coefficients on Stela H, going tcxts, and it has also been stated several 
5^tr:terXSl:r:i times, that the cyde coefficient is ahnost invari- 
the uinai and Mn coefficients ably 9. Indeed, the Only two exceptions to this 
uke the tun coefficient. ^^^ ^ ^^^ mscriptions abeady figured are the 

Initial Series from the Temples of the Foliated Cross and the Sim at 
Palenque (pi. 12, A and B, respectively), in which the cycle coeffi- 
cient in each case was 1. As explained on page 179, footnote 1, these 
two Initial Series refer probably to mythological events, and the dates 
which they record were not contemporaneous with the erection of the 
temples on whose walls they are inscribed; and, finally, Cycle 9 
was the first historic period of the Maya civilization, the epoch 
which witnessed the rise and faU of all the southern cities. 

As explained on page 179, footnote 2, however, there are one or two 
Initial Series which can hardly be considered as referring to mytho- 
logical events, even though the dates which they record fall in a cycle 
earher than Cycle 9. It was stated, finther, in the same place that 
these two Initial Series were not found inscribed on large montiments 
but on smaller antiquities, one of them being a smaU nephrite figxu-e 
which has been designated the Tuxtla Statuette, and the other a 
nephrite plate, designated the Leyden Plate; and, finally, that the 
dates recorded on these two antiquities probably designated contem- 
poraneous events in the historic period of the Maya civilization. 

' In 1913 Mr. M. D. Landry, superintendent of the Quirigua district, Guatemala division of the United 
Fruit Co. , found a still earlier monument about half a mile west of the main group. This has been named 
Stela S. It records the hotim ending prior to the one on Stela H, i. e., 9.15.15.0.0 9 Ahau 18 Xnl. 



MOELET] INTEODUCTION TO STUDY OF MAYA HIEEOGLYPHS 



195 



These two minor antiquities have several points in common. Both 
are made of the same material (nephrite) and both have their glyphs 
incised instead of carved. More important, however, than these 
similarities is the fact that the Initial Series recorded on each of them 
has for its cycle coefficient the numeral 8; ia other words, both record 
dates which fell in the cycle immediately preceding that ,of the his- 
toric period, or Cycle 9. Finally, at least one of these two Initial 



J. 
/ ■■■. 




■;■"■•• : 'r- 

• • \ : 



Fig. 73. The Initial Series on the Tuxtla Statuette, the oldest Initial Series kno-wn (in the early part of 

Cycle 8). 

Series (that on the Leyden Plate), if indeed not both, records a date 
so near the opening of the historic period, which we may assume 
occurred about 9.0.0.0.0 8 Ahau 13 Ceh in roimd numbers, that it may 
be considered as belonging to the historic period, and hence con- 
stitutes the earliest historical inscription from the Maya territory. 



196 BUREAU OF AMERICAN ETHNOLOGY [bdll. 57 

The Initial Series on the first of these minor antiquities, the Tuxtla 
Statuette, is shown in figure 73.i The student will note at the outset 
one veiy important difference between this Initial Series— if mdeed 
it is one, which some have doubted— and those already presented- 
No period glyphs appear in the present example, and consequently 
the Initial-series number is expressed by the second method (p. 129), 
that is, numeration by position, as in the codices. See the discussion 
of Initial Series in the codices in Chapter VI (pp. 266-273) , 
O^ and plates 31 and 32. This at once distinguishes the 
' ■ ' (\ 1 Initial Series on the Ttixtla Statuette from every other 
\<^ I Initial Series in the inscriptions now known. The 
number is preceded by a character which bears some 
general resemblance to the usual Initial-series intro- 
^uo*du™f™g ducing glyph. See figure 74. The most striking point 
glyph (?) of the ^f similarity is the triaal superfix, which is present in 
on the Tux- both signs. The student will have little difficulty in 
tia statuette, reading the number here recorded as 8 cycles, 6 katuns, 
2 tuns, 4 uinals, and 17 kins, that is, 8.6.2.4.17; reducing this to units 
of the first order by means of Table XIII, we have: 
8 X 144, 000 = 1, 152, 000 
6X 7,200= 43,200 
2 X 360 = 720 

4X 20= 80 

17 X 1 = 17 



1, 196, 017 
Solving this Initial-series number for its terminal date, it will be found 
to be 8 Caban Kankin. Returning once more to our text (see fig. 73) , 
we find the day coefficient above reached, 8, is recorded just below 
the 17 kins and appears to be attached to some character the details 
of which are, unfortimately, effaced. The month coefficient and 
the month sign Kankin do not appear in the accompanying text, at 
least in recognizable form. This Initial Series would seem to be, 
therefore, 8.6.2.4.17 8 Caban Kankin, of which the day sign, month 
coefficient, and month sign are effaced or unrecognizable. In spite 
of its unusual form and the absence of the day sign, and the month 
coefficient and sign the writer is inclined to accept the above date as a 
contemporaneous Initial Series.^ 

The other Initial Series showing a cycle coefficient 8 is on the 
Leyden Plate, a drawing of which is reproduced iu figure 75, A. This 
Initial Series is far more satisfactory than the one just described, and 

1 For the full text of this mscription see Holmes, 1907: pp. 691 et seq., and pis. 34-41. 

2 For a full discussion of the Tuxtla Statuette, including the opinions of several writers as to its inscrip- 
tion, see Holmes, 1907: pp. 691 et seq. The present writer gives therein at some length the reasons which 
have led him to accept this inscription as genuine and contemporaneous. 



MOiiLBT] INTEODUCTION TO STUDY OP MAYA HIEROGLYPHS 



197 



its authenticity, generally speaking, is unquestioned. The student 
will easily identify AI-B2 as an Initial-series introducing glyph, even 
though the pair of comblike 
appendages flanking the 
central element and the 
tun tripod are both want- 
ing. , Compare this form 
with figure 24 . The Initial- 
series number, expressed by 
normal-form numerals and 
head-variant period glyphs, 
foUowsinAS-A?. The for- 
mer are all very clear, and 
the mimber may be read 
from them in spite of cer- 
tain irregularities in the cor- 
responding period glyphs. 
For example, the katun 
head in A4 has the clasped 
hand, which is the distin- 
guishing characteristic of 
the cycle head, and as such 
shoiild have appeared in 
the head in A3. Neither 
the tim head ia A5 nor the 
kin head in A7 shows an 
essential element hereto- 
fore found distinguishing 
these particular period 
glyphs. Indeed, the only 
period glyph of the five 
showing the usual essen- 
tial element is the uinal 
head ia A6, where the large 
mouth cm-l appears very 
clearly. However, the 
number recorded here may 
be read as 8.14.3.1.12 from 
the sequence of the coeffi- 
cients — that is, their posi- 
tion with reference to the 
introducing glyph— a reading, moreover, which is confirmed by the 
only known period glyph, the uinal sign, standing in the fourth posi- 
tion after the introducing glyph. 




Fig. 76. Drawings ol the Initial Series: A, On the Leydeu 
Plate. This records a Cyole-s date and next to the Tuxtla 
Statuette Initial Scries, is the earliest known. B, On a lintel 
from the Temple of the Initial Series, Chichen Itza. This 
records a Cycle-10 date, and is one ol the latest Initial Series 
known. 



198 BUREAU OP AMEEICAK ETHNOLOGY [bull. 57 

Reducing this number to units of the first order by means of Table 
XIII, we have: 

A3= 8X144,000 = 1,152,000 
A4 = 14X 7,200= 100,800 
A5= 3X 360= 1,080 
A6= IX 20= 20 

A7 = 12X 1= 12 



1, 253, 912 

Deducting from this number all the Calendar Eounds possible, 66 
(see Table XVI), and appljdng rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached 'will be 
1 Eb Yaxkin. The day part of this date is very clearly recorded 
iu A8, the coefiicient 1 being expressed by one dot, and the day sign 
itself having the hook surrounded by dots, and the prominent teeth, 
both of which are characteristic of the grotesque head which denotes 
the day Eb. See figure 16, s^u,. 

The month glyph appears in A9a, the lower half of which unmis- 
takably records the month Yaxkin. (See fig. 19, ^, Z.) Note the j/ax 
and Tcin elements in each. The only difficulty here seems to be the 
fact that a bar (5) is attached to this glyph. The writer believes, 
however, that the unexplained element (*) is the month co- n^ 
efiicient in this text, and that it is an archaic form for 0. He * 
would explain the bar as being merely ornamental. The whole Initial 
Series reads: 8.14.3.1.12 1 Eb Yaxkin. 

The fact that there are some few irregularities in this text confirms 
rather than invalidates the antiquity which has been ascribed to it 
by the writer. Dating from the period when the Maya were just 
emerging from savagery to the arts and practices of a semicivilized 
state, it is not at all surprising that this inscription should refiect 
the crudities and uncertainties of its time. Indeed, it is quite possi- 
ble that at the very early period from which it probably dates 
(8.14.3.1.12 1 Eb Yaxkin) the period glyphs had not yet become 
sufficiently conventionalized to show individual peculiarities, and 
their identity may have been determined solely by their position 
with reference to the introducing glyph, as seemingly is the case in 
some of the period glyphs of this text. 

The Initial Series on the Leyden Plate precedes the Initial Series 
on Stela 3 at Tikal, the earhest contemporaneous date from the 
monmnents, by more than 160 years, and with the possible exception 
of the Tuxtla Statuette above described, probably records the earliest 
date of Maya history. It should be noted here that Cycle-8 Initial 
Series are occasionally found in the Dresden Codex, though none are 
quite so early as the Initial Series from the Tuxtla Statuette. 



MOELBTj INTBODTJCTION TO STUDY OF MAYA HIEROGLYPHS 199 

Passing over the Initial Series whose cycle coefficient is 9, many of 
which have already been described, we come next to the consideration 
of Initial Series whose cycle coefficient is 10, a very limited number 
indeed. As explained in Chapter I, the southern cities did not long 
survive the opening of Cycle 10, and since Initial-series dating did 
not "prevail extensively in the later cities of the north. Initial Series 
showing 10 cycles are very imusual. 

In figure 75, B, is shown the Initial Series from the Temple of the 
Initial Series at Chichen Itza, the great metropolis of northern Yucatan. 
This inscription is not found on a stela but on the under side of a lintel 
over a doorway leading into a small and comparatively insignificant 
temple. The introducing glyph appears in A1-B2 and is followed by 
the Initial-series number in A3-A5. The student wUl have httle 
difficulty in deciphering all of the coefficients except that belonging 
to the kin in A5, which is a head-variant numeral, and the whole 
nmnber will be found to read 10.2.9.1. ?. The coefficient of the day 
of the terminal date is very clearly 9 (see B5) and the month part, 
7 Zac (see A6). We may now read this Initial Series as 10.2.9.1. ? 9? 
7 Zac ; in other words, the kin coefficient and the day sign are stUl 
indeterminate. First substituting as the missing value of the kin 
coefficient, the terminal date reached will be 10.2.9.1.0 13 Ahau 18 
Yax. But according to Table XV, position 18 Yax is just 9 days 
earlier than position 7 Zac, the month part recorded in A6. Conse- 
quently, in order to reach 7 Zac from 10.2.9.1.0 13 Ahau 18 Yax, 9 
more days are necessary. Counting these forward from 10.2.9.1.0 
13 Ahau 18 Yax, the date reached wiU be 10.2.9.1.9 9 Muluc 7 Zac, 
which is the date recorded on this lintel. Compare the day sign with 
figure 16, m, n, and the month sign with figure 19, s, t. 

Two other Initial Series whose cycle coefficient is 10 yet remain to 
be considered, namely. Stelae 1 and 2 at Quen Santo.' The first of 
these is shown in figure 76, A, but unfortimately only a fragment of 
this monument has been recovered. In A1-B2 appears a perfectly 
regular form of the introducing glyph (see fig. 24), and this is followed 
in A3-B4 by the Initial-series mmaber itself, with the exception of 
the kin, the glyph representing which has been broken off. The 
student will readily identify A3 as 10 cycles, noting the clasped hand 
on the head-variant period glyph, and B3 as 2 katuns. The glyph 
in A4 has very clearly the coefficient 5, and even though it does not 
seem to have the fleshless lower jaw of the tun head, from its position 
alone — after the iinmistakable katun sign in B3 — we are perfectly 
justified in assuming that 5 tuns are recorded here. Both the coeffi- 
cient and the glyph in B4 are unfamiliar. However, as the former 

1 For the full text of these inscriptions, see Seler, 1902-1908: n, 253, and 1901 c: i, 23, fig. 7. During his 
last visit to the Maya territory the writer discovered that Stela 11 at Tikal has a Cycle-lO Initial Series, 
namely, 10.2.0.0.0. 3 Ahau 3 Ceh. 



200. 



BtTEEAU OF AMERICAN ETHNOLOGY 



tBCLL. 57 



must be one of the numerals to 19, inclusive, since it as not one of 
the numerals 1 to 19, inclusive, it is clear that it must be a new form 
for 0. The sign to which it is attached bears no resemblance to either 
the normal form for the umal or the head variant; but since it occu- 
pies the 4th position after the introducing glyph, B4, we are justified 
in assuming that uinals are recorded here. Beyond this we- can 
not proceed with certainty, though the values for the missing parts 




Fig. 76. The Cycle-10 Initial Series from Quen Santo (from drawinp): A, Stela 1; £, Stela 2. There is 
less than a year's difference in time between the Chichen Itza Initial Series and the Initial Series in B. 

suggested below are probably those recorded on the lost fragments 
of the monument. As recorded in A3-B4 this number reads 
10.2.5.0. ?. Now, if we assume that the missing term is filled with 0, 
we shall have recorded the end of an even ho tun in the Long Count, 
and this monument becomes a regular hotun-marker. That this 
monument was a hotun-marker is corroborated by the fact that Stela 
2 from Quen Santo very clearly records the close of the hotun next 
after 10.2.5.0.0, which the writer beheves this monument marks. For 



MOBLET] INT1101>UCTI0N TO STtJDY OF MAYA HIEEOGLYPHS 201 

this reason it seems probable that the glyph which stood in A5 
recorded kins. 

Reducing this number to imits of the first order by means of Table 
XIII, we obtain: 

A3 = 10 X 144, 000 = 1, 440, 000 
B3= 2X 7,200= 14,400 
A4= 5X 360= 1,800 
B4= OX 20= 

A5i= OX 1= 



1, 456, 200 

Deducting from this niunber all the Calendar Eoimds possible, 76 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectirely) to the remainder, the terminal date reached will be 
9 Ahau 18 Yax, and the whole Initial Series originally recorded on 
this monument was probably 10.2.5.0.0 9 Ahau 18 Yax. 

In figure 76, B, is shown Stela 2 from Quen Santo. The workman- 
ship on this monument is somewhat better than on Stela 1 and, more- 
over, its Initial Series is complete. The introducing glyph appears 
in A1-B2 and is followed by the Initial-series number in A3-A5. 
Again, 10 cycles are very clearly recorded in A3, the clasped hand 
of the cycle head still appearing in spite of the weathering of this 
glyph. The katun sign in B3 is almost entirely effaced, though 
sufficient traces of its coefficient remain to enable us to identify it 
as 2. Note the position of the imeffaced dot with reference to the 
horizontal axis of the glyph. Another dot the same distance above 
the axis would come as near the upper left-hand comer of the glyph- 
block as the mieffaced dot does to the lower left-hand comer. More- 
over, if 3 had been recorded here the imeffaced dot would have been 
nearer the bottom. It is clear that 1 and 4 are quite out of the 
question and that 2 remains the only possible value of the numeral 
here. We are justified in asstiming that the effaced period glyph 
was the katun sign. In A4 10 tuns are very clearly recorded; note 
the fleshless lower jaw of the tun head. The uinal head with its 
characteristic mouth curl appears in B4. The coefficient of this latter 
glyph is identical with the uinal coefficient in the preceding text 
(see fig. 76, A) in B4, which we there identified as a form for 0. 
Therefore we must make the same identification here, and B4 then 
becomes uinals. From its position, if not from its appearance, we 
are justified in designating the glyph in A5 the head for the kin 
period; since the coefficient attached to this head is the same as the 
one in the preceding glyph (B4), we may therefore conclude that 
kins are recorded here. The whole number expressed in A3-A5 is 

1 Missing. 



202 BTJEEAXJ OF AMBEICAN ETHNOLOGY [bdli,. 57 

therefore 10.2.10.0.0. Reducing this to miits of the first order by- 
means of Table XIII, we have: 

A3 = 10 X 144, 000 = 1, 440, 000 

B3= 2X 7,200= 14,400 

A4 = 10X 360= 3,600 

B4= OX 20= 

A5= OX 1= 



1, 458, 000 



Deducting from this number all the Calendar Eounds possible, 76 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, 
respectively) to the remainder, the terminal date reached will be 
2 Ahau 13 Chen. Although the day sign in B5 is effaced, the coeffi- 
cient 2 appears quite clearly. The month glyph is recorded in A6. 
The student will have little difficulty in restoring the coefficient as 
13, and the month glyph is certainly either Chen, Yax, Zac, or Ceh 
(compare fig. 19, o and f, q and r, s and t, and u and v, respectively). 
Moreover, since the month coefficient is 13, the day sign in B5 can 
have been only Chicchan, Oc, Men, or Ahan (see Table VII) ; since the 
kin coefficient in A5 is 0", the effaced day sign must have been Ahan. 
Therefore the Initial Series on Stela 2 at Quen Santo reads 10.2.10.0.0 
2 Ahau 13 Chen and marked the hotun immediately following the 
hotim commemorated by Stela 1 at the same site. 

The student will note also that the date on Stela 2 at Quen Santo 
is less than a year later than the date recorded by the Initial Series 
on the Temple lintel from Chichen Itza (see fig. 75, B) . And a glance 
at the map in plate 1 will show, further, that Chichen Itza and Quen 
Santo are separated from each other by almost the entire length 
(north and south) of the Maya territory, the former being in the 
extreme northern part of Yucatan and the latter considerably to the 
south of the central Maya cities. The presence of two monuments 
so close together chronologically and yet so far apart geographically 
is difficult to explain. Moreover, the problem is further complicated 
by the fact that not one of the many cities lying between has yielded 
thus far a date as late as either of these.' The most logical 
explanation of this interesting phenomenon seems to be that while 
the main body of the Maya moved northward into Yucatan after 
the collapse of the southern cities others retreated southward into 
the highlands of Guatemala; that while the northern emigrants 

1 At Seibal a Period-ending date 10.1.0.0.0 5 Ahau 3 Eayab is clearly recorded, but this is some 30 years 
earlier tlian either of the Initial Series here under discussion, a significant period just at this particular 
epoch of Maya history, which we have every reason to believe was filled with stirring events and quickly 
shiftihg scenes. Tikal, with the Initial Series 10.2.0.0.0 3 Ahau 3 Ceh, and Seibal with the same date 
(not as an Initial Series, however) are the nearest, though even these fall 10 years short of the Quen 
Santo and Chichen Itza Initial Series. 



MOELEY] INTRODtrCTIOK TO STUDY OF MAYA HIEROGLYPHS 203 

were colonizing Yucatan the southern branch was laying the founda- 
tion of the civilization which was to flourish later under the name of 
the Quiche and other allied peoples; and finally, that as Chichen Itza 
was a later northern city, so Quen Santo was a later southern 
site, the two being at one period of their existence at least approxi- 
mately contemporaneous, as these two Initial Series show. 

It should be noted in this connection that Cycle-10 Initial Series 
are occasionally recorded in the Dresden Codex, though the dates in 
these cases are aU later than those recorded on the Chichen Itza liatel 
and the Quen Santo stelse. Before closing the presentation of Initial- 
series texts it is first necessary to discuss two very unusual and highly 
irregular examples of this method of dating, namely, the Initial Series 
from the east side of Stela C at Quirigua and the Initial Series from 
the tablet in the Temple of the Cross at Palenque. The dates 
recorded in these two texts, so far as known,' are the only ones which 
are not counted from the starting point of Maya chronology, the date 
4 Ahau 8 Cumhu. 

In figure 77, A, is shown the Initial Series on the east side of Stela C 
at Quirigua.^ The introducing glyp^ appears in A1-B2, and is fol- 
lowed by the Initial-series number in A3-A5. The student will easily 
read this as 13.0.0.0.0. Keduciag this number to imits of the first 
order by means of Table XIII, we have: 

A3 = 13 X 144, 000 = 1, 872, 000 
B3= OX 7,200= 

A4= OX 360= 

B4= OX 20= 

A5= OX 1= 



1, 872, 000 

Deducting from this number all the Calendar Rounds possible, 98 ' 
(see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 
141), respectively, to the remainder, the terminal date reached should 
be, tmder ordinary circumstances, 4 Ahau 3 Kankin. An inspection 
of our text, however, will show that the terminal date recorded in 
B5-A6 is unmistakably 4 AEau 8 Cumhu, and not 4 Ahau 3 Kankin. 
The month part in A6 is unusually clear, and there can be no doubt 

1 Up to the present time no successful interpretation of the inscription on Stela C at Copan has been 
advanced. The inscription on each side of this monument is headed by an introducing glyph, but in 
neither case is this followed by an Initial Series. A number consisting of 11.14.5.1.0 is recorded in connec- 
tion with the date 6 Ahau 18 Eayab, but as this date does not appear to be fixed in the Long Count, there 
is no way of ascertaining whether it is earlier or later than the starting point of Maya chronology. Mr. Bow- 
ditch (1910: pp. 195-196) offers an interesting' explanation of this monument, to which the student is 
referred for the possible explanation of this text. A personal inspection of this inscription failed to 
confirm, however, the assumption on which Mr. Bowditch's conclusions rest. For the full text of this 
inscription, see Maudslay, 1889-1902: i, pis. 39-41. 

2 For the full text of this inscription, see ibid. : n, pis. 16, 17, 19. 

s Table XVI contains only 80 Calendar Hounds (1,518,400), but by adding 18 Calendar Rounds (341,640) 
the number to be subtracted, 98 Calendar Rounds (1,860,040), will be reached. 



204 



BTJEEAU OF AMBEICAN ETHNOLOGY 



[BOI.L. 57 



/^ 


^r^' 


V\S 


fefe 


m 


'■ ^^:^^— ^ 




^Irffii 


^1- 


h: 


C°J 


ss) 



that it is 8 Cumhu. Compare A6 with figure 19, g', h' . If we have 
made no mistake iq calculations, then it is evident that 13.0.0.0.0 
counted forward from the starting point of Maya chronology, 4 Ahau 
8 Cumhu, will not reach the terminal date recorded. Fm-ther, since 
the coimt in Initial Series has never been known to be backward,* 
we are forced to accept one of two conclusions: Either the starting 
point is not 4 Ahan 8 Cumhu, or there is some error in the origjnal text. 

However, there is one way by 
means of which we can ascer- 
tain the date from which the 
number 13.0.0.0.0 is counted. 
The terminal date reached by 
the count is recorded very 
clearly as 4 Ahau 8 Cumhu. 
Now, if we reverse our op- 
eration and count the given 
nmnber, 13.0.0.0.0, backward 
from the known terminal date, 
4 Ahau 8 Cumhu, we reach the 
starting point from which the 
count proceeds. 

Deducting from this niun- 
ber, as before, all the Calen- 
dar Roimds possible, 98 (see 
p. 203, footnote 3), and ap- 
plying rules 1, 2, and 3 (pp. 
139, 140, 141, respectively) 
to the remainder, remember- 
iag that in each operation the 
direction of the count is iack- 
ward, not forward, the starting 
point will be found to be 4 
Ahau 8 Zotz, This is the first 
Initial Series yet encountered 
which has not proceeded from 
the date 4 Ahau 8 Cumhu, and 
until the new starting point here indicated can be substantiated it 
will be well to accept the correctness of this text only with a reser- 
vation. The most we can say at present is that if the number re- 
corded in A3-A5, 13.0.0.0.0, be counted forward from 4 Ahau 8 Zotz 
as a starting point, the terminal date reached by calculation will 
agree with the terminal date as recorded in B5-A6, 4 Ahau 8 Cumhu. 

' Counting 13.0.0.0.0 baclward from the starting point of Maya chronology, i Ahau 8 Cumhu, gives the 
date 4 Ahau 8 Zotz, which is no nearer the terminal date recorded in B5-A6 than the date i Ahau 3 Kan- 
bin reached by counting forward. 





Fig. 77. Initial Series which proceed from a date prior 
to 4 Ahau 8 Cumhu, the starting point of Maya chro- 
nology: A, Stela C (east side) at Quirigua; B, Tem- 
ple of the Cross at Palenque. 



MOBLET] INTBODtrCTION TO STUDY OF MAYA HIEROGLYPHS 205 

Let US next examine the Initial Series on the tablet from the 
Temple of the Cross at Palenque, which is shown ia figure 77, B} 
The introducing glyph appears in A1-B2, and is followed by the 
Initial-series number ia A3-B7. The period glyphs in B3, B4, B5, 
B6, and B7 are all expressed by their corresponding normal forms, 
which will be readily recognized. Passing over the cycle coefficient 
in A3 for the present, it is clear that the katun coefficient in A4 is 19. 
Note the dots around the mouth, characteristic of the head for 9 (fig. 
52, g-l), and the fieshless lower jaw, the essential element of the head 
for 10 (fig. 52, m-r). The combination of the two gives the head in 
A4 the valye of 19. The tun coefficient in A5 is equally clear as 13. 
Note the banded headdress, characteristic of the head for 3 (fig. 51, 
h, i), and the fieshless lower jaw of the 10 head, the combination of 
the two giving the head for 13 (fig. 52, w)} The head for 4 and the 
hand zero sign appear as the coefficient of the tiinal and kin signs in A6 
and A7, respectively. The nmnber will read, therefore, ?.19. 13.4.0. 
Let us examine the cycle coefficient in A3 again. The natural assump- 
tion, of com^e, is that it is 9. But the dots characteristic of the head 
for 9 are not to be found here. As this head has no fieshless lower 
jaw, it can not be 10 or any number above 13, and as there is no 
clasped hand associated with it, it can not signify 0, so we are limited 
to the numbers, 1, 2, 3, 4, 5,^ 6, 7, 8, 11, 12, and 13, as the numeral 
here recorded. Comparing this form with these numerals in figures 
51 and 52, it is evident that it can not be 1, 3, 4, 5, 6, 7, 8, or 13, and 
that it must therefore be 2, 11, or 12. Substituting these three values 
in turn, we have 2.19.13.4.0, 11.19.13.4.0, and 12.19.13.4.0 as the 
possible numbers recorded in A3-B7, and reducing these numbers to 
imits of the first order and deducting the highest number of Calendar 
Rounds possible from each, and applying rules 1, 2, and 3 (pp. 139, 
140, and 141, respectively) to their remainders, the terminal dates 
reached will be: 

2.19.13.4.0 5 Ahau 3 Pax 

11.19.13.4.0 9 Ahau 8 Yax 

12.19.13.4.0 8 Ahau 13 Pop 

If this text is perfectly regular and our calculations are correct, one 
of these three terminal dates wiU. be found recorded, and the value 
of the cycle coefficient in A3 can be determined. 

The terminal date of this Initial Series is recorded in A8-B9 and 
the student will easily read it as 8 Ahau 18 Tzec. The only difference 

1 For the lull text of this inscription, see Maudslay, 1889-1902: iv, pis. 73-77. 

2 As noted in Chapter IV, this is one of the only two heads for 13 found in the inscriptions which is 
composed of the essential element of the 10 head applied to the 3 head, the combination of the two giv- 
ing 13. Usually the head for 13 is represented by a form peculiar to this number aloneand is not built up: 
by the combination of lower numbers as in this case. 

3 Although at first sight the headdress resembles the tun sign, a closer examination shows that it is 
not this element. 



206 BUREAU OP AMEEICAN ETHNOLOGY [boll. 57 

between the day coefficient and the month coefficient is that the latter 
has a fleshless lower jaw, iacreasing its value by 10. Moreover, com- 
parison of the month sign in B9 with g and Ji, figure 19, shows immis- 
takably that the month here recorded is Tzec. But the termiaal 
date as recorded does not agree with any one of the three above 
terminal dates as reached by calculation and we are forced to accept 
one of the two conclusions which confronted us in the preceding text 
(fig. 77, A) : Either the starting point of this Initial Series is not the 
date 4 Ahau 8 Cumliu, or there is some error in the original text.' 

Assuming that the ancient scribes made no mistakes in this inscrip- 
tion, let us coimt backward from the recorded terminal date, 8 Ahau 
18 Tzec, each of the three munbers 2.19.13.4.0, 11.19.13.4.0, and 
12.19.13.4.0, one of which, we have seen, is recorded ia A3-B7. 

Reducing these numbers to units of the first order by means of 
Table XIII, and deducting all the Calendar Rounds possible from 
each (see Table XVI), and, finally, applying rules 1,2, and 3 (pp. 139, 
140, and 141, respectively), to the remainders, the starting points will 
be found to be : 

7 Ahau 3 Mol for 2.19.13.4.0 

3 Ahau 18 Mac for 11.19.13.4.0 

4 Ahau 8 Zotz for 12.19.13.4.0 

Which of these starting points are we to accept as the one from which 
this number is counted? The correct answer to this question will 
give at the same time the value of the cycle coefficient, which, as 
we have seen, must be 2, 11, or 12. Most Maya students have 
accepted as the starting point of this Initial-series mmaber the last 
of the three dates above given, 4 Ahau 8 Zotz, which involves also the 
identification of the cycle coefficient in A3 as 12. The writer has 
reached the same conclusion from the following points : 

1. The cycle coefficient in A3, except for its very unusual headdress, 
is alnaost identical with the other two head-variant numerals, whose 
values are known to be 12. These three head nmnerals are shown 
side by side in figure 52, t-^, t being the form in A3 above, inserted 
in this figure for the sake of comparison. Although these three heads 
show no single element or characteristic that is present in all (see p. 
100), each is very similar to the other two and at the same time is 
dissimilar from all other head-variant numerals. This fact warrants 
the conclusion that the head in A3 represents the n\imeral 12, and if 
this is so the starting point of the Initial Series under discussion is 
4 Ahau 8 Zotz. 

2. Aside from the fact that 12 seems to be the best reading of the 
head in A3, and consequently that the starting point of this number 
is 4 Ahau 8 Zotz, the writer believes that 4 Ahau 8 Zotz should be 



> Similarly, it could be shown tliat the use of every other possible value of the cycle coefflcient will 
not give the terminal date actually recorded. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 16 




INITIAL SERIES AND SECONDARY SERIES ON LINTEL 21, YAXCHILAN 



MOHLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 207 

selected, if for no other reason than that another Initial Series has 
been found which proceeds from this same date, while no other Initial 
Series known is counted from either 7 Ahau 3 Mol or 3 Ahau 18 Mac. 
• As we have seen in discussing the preceding text, from the east side 
of Stela C at Quirigua (fig. 77, A), the Initial Series there recorded 
was counted from the same starting point, 4 Ahau 8 Zotz, as the Initial 
Series from the Temple of the Cross at Palenque, if we read the latter 
as 12.19.13.4.0. This coincidence, the writer believes, is sufficient to 
warrant the identification of the head in A3 (fig. 77, B) as the head 
numeral 12 and the acceptance of this Initial Series as proceeding 
from the same starting point as the Quirigua text just described, 
namely, the date 4 Ahau 8 Zotz. With these two examples the dis- 
cussion of Initial-series texts will be closed. 

Texts Recording Initial Series and Secondary Series 

It has been explained (see pp. 74-76) that in addition to Initial- 
series dating the Maya had another method of expressing their 
dates, known as Secondary Series, which was used when more than 
one date had to be recorded on the same monument. It was stated, 
further, that the accuracy of Secondary-series dating depended solely 
on the question whether or not the Secondary Series was referred to 
some date whose position in the Long Count was fixed either by the 
record of its Initial Series or in some other way. The next class of texts 
to be presented will be those showing the use of Secondary Series in 
connection with an Initial Series, by means of which the Initial-series 
values of the Secondary-series dates, that is, their proper positions 
in the Long Coimt, may be worked out even though they are not 
recorded in the text. 

The first example presented wiU be the inscription on Lintel 21 at 
Yaxchilan, which is figured in plate 16.^ As usual, when an Initial 
Series is recorded, the introducing glyph opens the text and this sign 
appears in Al, being followed by the Initial-series number itself in 
B1-B3. This the student wiU readily decipher as 9.0.19.2.4, record- 
ing apparently a very early date in Maya history, within 20 years of 
9.0.0.0.0 8 Ahau 13 Ceh, the date arbitrarily fixed by the writer as 
the opening of the first great period. 

Reducing this number by means of Table XIII to units of the first 
order ^ and deducting all the Calendar Rounds possible, 68 (see Table 
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respec- 
tively) to the remainder, the terminal date reached wiU be 2 Kan 2 
Yax. This date the student wiU. find recorded in A4 and A7a, glyph 
B6b being the month-sign "indicator," or the closing glyph of the 

1 For the full text of this inscription see Maler, 1903: n, No. 2, pi. 55. 

2 From this point on this step will be omitted, but the student is urged to perform the calculations 
necessary in each case to reach the terminal dates recorded. 



208 BUREAU OP AMEBICAN ETHNOLOGY [bull. 57 

Supplementary Series, here shown with the coefficient 9. Compare 
the day sign in A4a with the sign for Kan in figure 16,/, and the month 
sign in A7a with the sign for Yax m figure 19, q_, r. We have then 
recorded in A1-A4S and A7a the Initial-series date 9,0.19.2.4 2 Kan 
2 Yax. At first sight it would appear that this early date indicates 
the time at or near which this hntel was inscribed, but a closer exami- 
nation reveals a different condition. Followiag along through the 
glyphs of this text, there is reached in C3-C4 still another nxunber ia 
which the normal forms of the katim, tun, and uinal signs clearly 
appear in connection with bar and dot coefficients. The question at 
once arises. Has the munber recorded here anything to do with the 
Initial Series, which precedes it at the begioning of this text? 

Let us first examine this niamber before attempting to answer the 
above question. It is apparent at the outset that it differs from the 
Initial-series numbers previously encountered in several respects: 

1. There is no introducing glyph, a fact which at once eliminates 
the possibUity that it might be an Initial Series. 

2. There is no kin period glyph, the uinal sigh in C3 having two 
coefficients instead of one. 

3. The order of the period glyphs is reversed, the highest period, 
here the katun, closing the series instead of commencing it as here- 
tofore. 

It has been explained (see p. 129) that ia Secondary Series the 
order of the period glyphs is almost invariably the reverse of that 
shown by the period glyphs in Initial Series; and further, that the 
former are usually presented as ascending series, that is, with the 
lowest units first, and the latter invariably as descending series, with 
the highest units first. It has been explained also (see p. 128) that 
in Secondary Series' the kin period glyph is usually omitted, the kin 
coefficient being attached to the left of the uinal sign. Since both 
of these points (see 2 and 3, above) are characteristic of the number 
in C3-C4, it is probable that a Secondary Series is recorded here, and 
that it expresses 5 kins, 16 tiinals, 1 tim, and 15 katuns. Reversing 
this, and writing it according to the notation followed by most Maya 
students (see p. 138, footnote 1), we have as the number recorded bv 
C3-C4, 15.1.16.5. 

Eeduciag this number to units of the first order by means of Table 
XIII, we have: 

C4 =15X7,200 = 108,000 

D3= IX 360= 360 

C3=16X 20= 320 

C3 = 5 X 1 = 5 



108, 685 



1 Since the introducing glyph always accompanies an Initial Series, it has here been included as a part 
of it, though, as has been explained elsewhere, its function is unknown. 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 209 

Since all the Calendar Rounds ■which this number contains, 5 (see 
Table XVI) may be deducted from it ■wi+hout affecting its value, we 
can further reduce it to 13,785 (108,685-94,900), and this •will be the 
number used in the following calculations. 

It was stated (on p. 135) in describing the direction of the count 
that numbers are usually counted forward from the dates next pre- 
ceding them in a text, although this is not invariably true. Applying 
this rule to the present case, it is probable that the Secondary-series 
number 15.1.16.5, which we have reduced to 13,785 imits of the first 
order, is counted forward from the date 2 Kan 2 Yax, the one next 
preceding it in our text, a date, moreover, the Initial-series value of 
which is known. 

Remembering that this date 2 Kan 2 Yax is our new starting point, 
and that the coimt is forward, by applying rules 1, 2, and 3 (pp. 139, 
140, and 141, respectively), to 13,785, the new terminal date reached 
wiU be 7 Muluc 17 Tzec; and this date is recorded in C5-D5. Compare 
C5 with the sign for the day Muluc in figure 16, m, n, and D5 with 
the sign for the month Tzec in figure 19, g, h. Furthermore, by add- 
ing the Secondary-series number 15.1.16.5 to 9.0.19.2.4 (the Initial- 
series number which fixes the position of the date 2 Kan 2 Yax in the 
Long Count) , the Initial-series value of the terminal date of the Sec- 
ondary Series (calculated and identified above as 7 Muluc 17 Tzec) 
can also be determined as follows: 

9. 0.19. 2.4 2 Kan 2 Yax Initial Series 

15. 1.16.5 Secondary-series number 

9.16.1.0.9 7Mulucl7Tzeo Initial Series of the Secondary- 
series terminal date 7 Muluc 
17 Tzec 

The student may verify the above calculations by treating 9.16.1,0.9 
as a new Initial-series number, and counting it forward from 4 Ahau 
8 Cumhu, the starting point of Maya chronology. The terminal date 
reached wiU be found to be the same date as the one recorded in 
C5-D5, namely, 7 Muluc 17 Tzec. 

What is the meaning then of this text, which records two dates 
nearly 300 years apart V It must be admitted at the outset that the 
nature of the events which occurred on these two dates, a matter 
probably set forth in the glyphs of miknown meaning in the text, is 
totally unknown. It is possible to gather from other sources, how- 
ever, some httle data concerning their significance. In the first place, 
9.16.1.0.9 7 Muluc 17 Tzec is ahnost surely the "contemporaneous 
date " of this lintel, the date indicating the time at or near which it 
was formally dedicated or put mto use. This point is estabhshed 
almost to a certainty by the fact that all the other dates known at 
YaxchUan are very much nearer to 9.16.1.0.9 7 Muluc 17 Tzec in point 

1 The number 15.1.16.6 is equal to 108,686 days, or 297J years. 
43508°— Bull. 57—15 14 



210 BUREAU OF AMERICAN ETHNOLOGY [bull. 57 

of time than to 9.0.19.2.4 2 Kan 2 Yax, the Initial-series date recorded 
on this hntel. Indeed, while they range from 9 days * to 75 years 
from the former, the one nearest the latter is more than 200 
years later. This practically proves that 9.16.1.0.9 7 Mulnc 
17 Tzec indicates the "contemporaneous time" of this lintel and that 
9.0.19.2.4 2 Kan 2 Yax referred to some earUer event which took 
place perhaps even before the foimding of the city. And finally, since 
this inscription is on a luitel, we may perhaps go a step further and 
hazard the conclusion that 9.16.1.0.9 7 Mulnc 17 Tzec records the 
date of the erection of the structure of which this luitel is a part. 

We may draw from this inscription a conclusion which will be 
found to hold good in almost ah. cases, namely, that the last date in 
a text almost always indicates the "contemporaneous time" of the 
monument upon which it appears. In the present text, for example, 
the Secondary-series date 7 Mulnc 17 Tzec, the Initial-series value 
of which was found to be 9.16.1.0.9, is in all probability its contem- 
poraneous date, or very near thereto. It will be well to remember 
this important point, since it enables us to assign monuments upon 
which several different dates are recorded to their proper periods in 
the Long Count. 

The next example illustrating the use of Secondary Series with an 
Initial Series is the inscription from Stela 1 at Piedras Negras, figured 
in plate 17.^ The order of the glyphs in this text is somewhat irreg- 
ular. It will be noted that there is an imeven number of glyph 
columns, so that one column will have to be read by itself. The 
natural assumption would be that A and B, C and D, and E and F 
are read together, leaving G, the last column, to be read by itself. 
This is not the case, however, for A, presenting the Initial Series, is 
read first, and then B C, D E, and F G, in pairs. The introducing 
glyph of the Initial Series appears in Al and is followed by the Initial- 
series number 9.12.2.0.16 in A2-A6. The student should be per- 
fectly familiar by this time with the processes involved in counting 
this number from its starting point, and should have no difficidty in 
determing by calculation the terminal date recorded in A7, C2, namely, 
6 Cib 14 Yaxkin.^ Compare A7 with the sign for Cib in figure 16, z, 
and C2 with the sign for Yaxkin in figure 19, Ic, I. The Initial Series 
recorded in A1-A7, C2 is 9.12.2.0.16 5 Cib 14 Yaxkin. 

Passing over the glyphs in B3-E1, the meanings of which are 
unknown, we reach in D2 E2 a number showing very clearly the tun 
and uinal signs, the latter having two coefficients instead of one. 
Moreover, the order of _ these period glyphs is reversed, the lower 
standing first in the series. As explained in connection with the pre- 

ilt is interesting to note in this connection tliat tlie date 9,16.1.0.0 U Ahau 8 Tzec, which is within 9 
days of 9.1C.1.0.9 7 Muluc 17 Tzec, is recorded in four different inscriptions at Yaxchilan,one of which (see 
pi. 9, A ) has already been figured. 

2 For the full text of this inscription see Maler, 1901: n, No. 1, pi. 12. 

3 The month-sign indicator appears in B2 with a coefficient 10. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 17 




INITIAL SERIES AND SECONDARY SERIES ON 
STELA 1, PIEDRAS NEGRAS 



MOBLiT] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 211 

ceding text, these points are both characteristic of Secondary-series 
numbers, and we may conclude therefore that D2 E2 records a num- 
ber of this kind. Finally, since the kin coefEcient in Secondary 
Series usually appears on the left of the uinal sign, we may express 
this number in the commonly accepted notation as follows: 12.9.15. 
Reducing this to units of the first order, we have : 

E2 = 12X360 =4, 320 
D2= 9X 20= 180 
D2 = 15X 1= 15 



4,515 



Eemembering that Secondary-series numbers are usually counted 
from the dates next preceding them in the texts, in this case 5 Cib 
14 Yaxkin, and proceeding according to rules 1, 2, and 3 (pp. 139, 140, 
and 141, respectively), the terminal date of the Secondary Series 
reached will be 9 Cliuen 9 Kankin, which is recorded in Fl Gl, though 
unfortimately these glyphs are somewhat effaced. Moreover, since 
the position of 5 Cib 14 Yaxkin in the. Long Count is known, that is, 
its Initial-series value, it is possible to determine the Initial-series 
value of this new date, 9 Chuen 9 Kankin : 

9.12. 2. 0.16 5 Cib 14 Yaxkin 

12. 9.15 
9.12.14.10.11 9 Chuen 9 Kankin 

But the end of this text has not been reached with the date 9 Chuen 
9 Kankin in Fl Gl. Passing over F2 G2, the meanings of which are 
unknown, we reach in F3 an inverted Ahau with the coefficient 6 
above it. As explained on page 72, this probably signifies 5 kins, 
the inversion of the glyph changing its meaning from that of a par- 
ticular day sign, Ahau, to a general sign for the kin day period (see 
fig. 34, d) . The writer recalls but one other instance in which the 
inverted Ahau stands for the kin sign — on the north side of Stela C 
at Quirigua. 

We have then another Secondary-series niunber consisting of 5 
kins, which is to be coimted from some date, and since Secondary- 
series numbers are usually counted from the date next preceding 
them in the text, we are justified in assuming that 9 Chuen 9 Kankin 
is our new starting point. 

Counting 5 forward from this date, according to rules 1, 2, and 3 
(pp. 139, 140, and 141, respectively), the terminal date reached will be 1 
Cib 14 Kankin, and this latter date is recorded in G3-G4. Compare 
G3 with the sign for Cib in A7 and in figure 16, z, and G4 with the 
sign for Kankin in figure 19, y, z. Moreover, since the Initial-series 
value of 9 Chuen 9 Kankin was calculated above as 9.12.14.10.11, 



212 BUEEAU OF AMEEICAN ETHNOLOGY [bull. 57 

the Initial-series value of this new date, 1 Cib 14 Kankin, also can 
be calculated from it : 

9.12.14.10.11 9 Chuen 9 Kankin 
5 

9.12.14.10.16 1 Cib 14 Kankin 

Passing over G5 as unknown, we reach in G6-G7 another Secondary- 
series number. The student will have little dijBiculty in identifying 
G6 as 2 uinals, 5 kins, and G7 as 1 katun. It will be noted that no 
tun sign appears in this number, which is a very unusual condition. 
By far the commoner practice in such cases in which units of some 
period are involved is to record the period with a coefficient 0. How- 
ever, this was not done in the present case, and since no tuns are 
recorded, we may conclude that none were involved, and G6-G7 
may be written 1.(0). 2. 5. Reducing this number to units of the first 
order, we have: 

G7 = 1X7, 200 = 7, 200 

C) OX 360= 

G6 = 2X 20= 40 

G6 = 5X 1= 5 



7,245 
Remembering that the starting point from which this number is 
counted is the date next preceding it, 1 Cib 14 Kankin, and applying 
rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), the termiaal date 
reached will be 5 Imix 19 Zac ; this latter date is recorded in G8-G9. 
Compare G8 with the sign for Imix in figure 16, a, h, and G9 with the 
sign for Zac in figure 19, s, t. Moreover, since the Initial Series of 
1 Cib 14 Kankin was obtained by calculation from the date next pre- 
ceding it, the Initial Series of 5 Imix 19 Zac may be determined ia the 
same way. 

9.12. 14.10.16 1 Cib 14 Kankin 
1. 0.^2. 5 

9.13. 14.13. 1 5 Imix 19 Zac 

With the above date closes the known part of this text, the remaining 
glyphs, G10-G12, being of unknown meaning. 

Assembling all the glyphs deciphered above, the known part of 
this text reads as follows: 



9.12. 


2. 0.16 
12. 9.15 


A1-A7, 
D2 E2 


C2 


5 Cib 14 Yaxkin 


9.12. 


14.10.11 
5 


FlGl 
F3 




9 Chuen 9 Kankin 


9.12. 


14.10.16 


G3G4 




1 Cib 14 Kankin 


1. 


0.^2. 5 


G6G7 






9.13. 


14.13. 1 


G8G9. 




5 Imix 19 Zac 






1 Not expressec 


1. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 18 









INITIAL SERIES (A) AND SECONDARY SERIES (-B) ON STELA K, QUIRIGUA 



MOKLBT] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 213 

We have recorded here four different dates, of which the last, 
9.13.14.13.1 5 Imix 19 Zac, probably represents the actual date, or 
very near thereto, of this monument.^ The period covered between 
the first and last of these dates is about 32 years, within the range 
of a single lifetime or, indeed, of the tenure of some important office 
by a single individual. The unknown glyphs again probably set forth 
the nature of the events which occurred on the dates recorded. 

In the two preceding texts the Secondary Series given are regular 
in every way. Not only was the count forward each time, but it also 
started in every case from the date immediately preceding the num- 
ber coimted. This regularity, however, is far from universal in Sec- 
ondary-series texts, and the following examples comprise some of 
the more common departures from the xisual practice. 

In plate 18 is figured the Initial Series from Stela K at Quirigua.^ 
The text opens on the north side of this monument (see pi. 18, A) 
with the introducing glyph in A1-B2. This is followed by the Initial- 
series number 9.18.15.0.0 in A3-B4, which, leads to the terminal date 
3 Ahau 3 Yax. The day part of this date the student will find 
recorded in its regular position, A5a. Passing over A5b and B5, the 
meanings of which are unknown, we reach in A6 a Secondary-series 
number composed, very clearly of 10 uinals and 10 kins (10.10), which 
reduces to the following number of units of the first order: 

A6 = 10X20 =200 
A6 = 10X 1= 10 

210 

The first assmnption is that this number is counted forward from the 
terminal date of the Initial Series, 3 Ahau 3 Yax, and performing the 
operations indicated in rules 1, 2, and 3 (pp. 139, 140, and 141, respec- 
tively) the terminal date reached wiU be 5 Oc 8 Uo. Now, although 
the day sign in B6b is clearly Oc (see fig. 16, o-q), its coefficient is 
very clearly 1, not 5, and, moreover, the month in A7a is unmiistak- 
ably 18 Kayab (see fig. 19, d'-f). Here then instead of finding the 
date determined by calculation, 6 Oc 8 Uo, the date recorded is 1 Oc 
18 Kayab, and consequently there is some departure from the prac- 
tices heretofore encountered. 

Since the association of the number 10.10 is so close with (1) the 
terminal date of the Initial Series, 3 Ahau 3 Yax, and (2) the date 
1 Oc 18 Kayab almost immediately following it, it would almost seem 
as though these two dates must be the starting point and terminal 
date, respectively, of this nmnber. If the count is forward, we have 
just proved that this can not be the case; so let us next count the 

1 The writer has recently established the date of this monument as 9. 13. 15. 0. 13 Ahau 18 Pax, or 99 
days later than the above date. 

2 For the full text ot this inscription, see Maudslay, 1889-1902: n, pis. 47-i9. 



214 BUREAU OF AMERICAN ETHNOLOGY . [bull. r,7 

number backward and see whether we can reach the date recorded 
in B6b-A7a (1 Oc 18 Kayab) in this way. 

Covmting 210 backward from 3 Ahau 3 Yax, according to rules 1, 2, 
and 3 (pp. 139, 140, and 141, respectirely), the terminal date reached 
will be 1 Oc 18 Kayab, as recorded in B6b-A7. In other words, the 
Secondary Series in this text is counted backward from the Initial Se- 
ries, and therefore precedes it in point of time. This will appear from 
the Initial-series value of 1 Oc 18 Kayab, which may be determined 
by calculation: 

9.18.15. 0. 3 Ahau 3 Yax 
10.10 

9.18.14. 7.10 1 Oc 18 Kayab 

This text closes on the south side of the monmnent in a very unusual 
manner (see pi. 18, B). In B3a appears the month-sign mdicator, 
here recorded as a head variant with a coefficient 10, and following 
iromediately in B3b a Secondary-series ntimber composed of uinals 
and kins, or, in other words, nothing. It is obvious that in count- 
ing this number 0.0, or nothing, either backward or forward from 
the date next precedmg it in the text, 1 Oc 18 Kayab in B6b-A7a on 
the north side of the stela, the same date 1 Oc 18 Kayab will remain. 
But this date is not repeated in A4, where the terminal date of this 
Secondary Series, 0.0, seems to be recorded. However, if we coimt 
0.0 from the terminal date of the Initial Series, 3 Ahau 3 Yax, we reach 
the date recorded in A4, 3 Ahau 3 Yax,^ and this whole text so far as 
deciphered will read: 

9.18.15. 0. 3 Ahau 3 Yax 
10.10 backward 

9.18.14. 7.10 1 Oc 18 Kayab 

0. forward from Initial Series 

9.18.15. 0. 3 Ahau 3 Yax 

The reason for recording a Secondary-series number equal to zero, 
the writer beheves, was because the first Secondary-series date 1 Oc 
18 Kayab precedes the Initial-series date, which in this case marks 
the time at which this monument was erected. Hence, in order to 
have the closing date on the mommient record the contemporaneous 
time of the monument, it was necessary to repeat the Initial-series 
date; this was accomplished by adding to it a Secondary-series date 
denoting zero. Stela K is the next to the latest hotmi-marker at 
Quirigua following immediately Stela I, the Initial series of which 
marks the hotun ending 9.18.10.0.0 10 Ahau 8 Zac (see pi. 6, C). 

Mr. Bowditch (1910 : p. 208) has advanced a very plausible explana- 
tion to account for the presence of the date 9.18.14.7.10 1 Oc 18 Kayab 

' Although the details of the day and month signs are somewhat effaced, the coefficient in each case is 
3, agreeing with the coefficients in the Initial-series terminal date, and the outline of the month glyph 
suggests that it is probahly Yax. See fig. 19, q, t. 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



215 











on this monument. He shows that at the time when Stela K was 
erected, namely, 9.18.15.0.0 3 Atau 3 Yax, the official calendar had 
outrun the seasons by just 210 days, or exactly 
the number of days recorded in A6, plate 18, A 
(north side) ; and further, that instead of being 
the day 3 Yax, which occurred at Quirigua about 
the beginning of the dry season,^ ia reality the 
season was 210 days behind, or at 18 Kayab, 
about the beginning of the rainy season. This 
very great discrepancy between calendar and 
season could not have escaped the notice of the 
priests, and the 210 days recorded in A6 may 
well represent the days actually needed on the 
date 9.18.15.0.0 3 Ahau 3 Yax to bring the calen- 
dar into harmony with the current season. If 
this be true, then the date 9.18.14.7.0 1 Oc 18 
Kayab represented the day indicated by the sun 
when the calendar showed that the 3d hotun in 
Katim 18 of Cycle 9 had been completed. Mr. 
Bowditch suggests the following free interpreta- 
tion of this passage: "The sun has just set at 
its northern point ^ and we are counting the day 
3 Yax — 210 days from 18 Kayab — which is the 
true date in the calendar according to our tra- 
ditions and records for the sun to set at this 
point on his course." As stated above, the 
writer believes this to be the true explanation 
of the record of 210 days on this monument. 

In figures 78 and 79 are illustrated the Initial 
Series and Secondary Series from Stela J at 
Quirigua.^ For lack of space the introducing 
glyph in this text has been omitted; it occupies 
the position of six glyph-blocks, however, 
A1-B3, after which the Initial-series niunber 
9.16.5.0.0 follows ui A4-B8. This leads to 
the terminal date 8 Ahau 8 Zotz, which is re- 
corded in A9, B9, Bl3, the glyph in Al3 being 
the month-sign indicator here shown with the 
coefficient 9. Compare B9 with the second va- 
riant for Ahau in figure 16 A', i', and Bl3 with 
the sign for Zotz in figure 19, e,f. The Initial- 














FiG. 78. The Initial Series on 
Stela J, Quirigua. 



1 Since the Maya New Year's day, Pop, always fell on the 16th of July, the day 3 Yax always fell on 
Jan. 15th, at the oommeneement of the dry season. 

2 Suice Pop fell on July ieth (Old Style), IS Kayab fell on June 19th, which is very near the summer 
solstice, that is, the seeming northern limit of the sun, and roughly coincident with the beginning of the 
rainy season at Quirigua. 

3 For the full text of this inscription, see Maudslay, 1889-1902: ii, pi. 46. 



^16 



BTJEBAU OP AMEEICAK ETHNOLOGY 



[edll. 57 



series part of this text therefore m A1-B9, Bl3, is perfectly regular 
and reads as follows: 9.16.5.0.0 8 Ahau 8 Zotz. The Secondary Series, 
however, are unusual and differ in several respects from the ones 
heretofore presented. 

The &st Secondary Series inscribed on this monument (see fig. 
79, A) is at B1-B2. This series the student should readily decipher 
as 3 kins, 13 uinals, 11 tuns, and katuns, which we may write 
0.11.13.3. This number presents one feature, which, so far as the 
writer knows, is imique in the whole range of Maya texts. The highest 
order of tmits actually iuvolved in this number is the txm, but for 
some unknown reason the ancient scribe saw fit to add the katun 

sign also, B2, which, how- 
ever, he proceeded to nul- 
lify at once by attaching 
to it the coefficient 0. For 
in so far as the numerical 
value is concemed,ll. 13.3 
and 0.11.13.3 are equal. 
The next peculiarity is 
that the date which fol- 
lows this munber in B3-A4 
is not its terminal date, as 
we have every reason to 
expect, but, on the con- 
trary, its starting point. 
In other words, in this 
Secondary Series the starting point follows instead of precedes the 
number coimted from it. This date is very clearly 12 Caban 5 Kayab ; 
compare B3 with the sign for Caban in figure 16, a', h', and A4 with 
the sign for Kayab in figure 19, d'-f. So far as Stela J is concerned 
there is no record of the position which this date occupied in the Long 
Count; that is, there are no data by means of which its Initial Series 
may be calculated. Elsewhere at Quirigua, however, this date is re- 
corded twice as an Initial Series and in each place it has the same 
value, 9.14.13.4.17. We may safely conclude, therefore, that the date 
in A3-B4 is 9.14.13.4.17 12 Caban 5 Kayab, and use it in oiir cal- 
culations as such. Reducing 0.11.13.3 to tmits of the first order, we 
have: 

B2= 0X7,200 = 
A2 = 11X 360 =3,960 
B1 = 13X 20 = 260 
Bl= 3X 1 = 3 




Fig. 79. The Secondary Series on Stela J, Quirigua. 



4,223 



MOBLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 217 

Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to this 
number, the terminal date reached will be 10 Ahau 8 Chen, which is 
nowhere recorded in the text (see fig. 79, A). 

The Initial Series corresponding to this date, however, may be 
calculated from the Initial Series which we have assigned to the date 
12 Caban 5 Kayab : 

9.14.13. 4.17 12 Caban 5 Kayab 

0.11.13. 3 
9.15. 5. 0. 10 Ahau 8 Chen 

Although the date 9.15.5.0.0 10 Ahau 8 Chen is not actually recorded 
at Quirigua, it is reached on another monument by calculation just 
as here. It has a peculiar fitness here on Stela J in that it is just 
one katun earlier than the Initial Series on this monument (see fig. 
78), 9.16.5.0.0 8 Ahau 8 Zotz. 

The other Secondary Series on this monument (see fig. 79, B) 
appears at B1-A2, and records 18 tuns, 3 uinals, and 14 kins, which 
we may write thus: 18.3.14. As in the preceding case, the date 
following this number in B2-A3 is its starting point, not its terminal 
date, a very unusual feature, as has been explained. This date is 
6 Cimi 4 Tzec — compare B2 with the sign for Cimi in figure 16, h, i, 
and A3 with the sign for Tzec in figure 19, g, Ti — and as far as Stela J 
is concerned it is not fixed in the Long Count. However, elsewhere 
at Quirigua this date is recorded in a Secondary Series, which is 
referred back to an Initial Series, and from this passage its corre- 
sponding Initial Series is found to be 9.15.6.14.6 6 Cimi 4 Tzec. 
Reducing the number recorded in B1-A2, 18.3.14, to units of the 
first order, we have: 

A2 = 18X360 = 6, 480 
B2= 3X 20= 60 
B2 = 14 X 1 = 14 



6,654 



Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to the 
number, the terminal date reached will be 8 Ahau 8 Zotz, which does 
not appear in figure 79, B. The Initial Series corresponding to this 
date may be calculated as follows : 

9.15. 6.14. 6 6 Cimi 4 Tzec 
18. 3.14 

9.16. 5. 0. 8 Ahau 8 Zotz 

But this was the Initial Series recorded on the reverse of this monu- 
ment, consequently the Secondary-series dates, both of which have pre- 



218 BUEEAU OF AMEKICAN ETHNOLOGY [bull. 57 

ceded the Initial-series date in point of time, bring this count up to 
the contemporaneous time of this monmnent, which was 9.16.5.0.0 
8 Ahau 8 Zotz. In view of the fact that the Secondary Series on 
Stela J are both earlier than the Initial Series, the chronological 
sequence of the several dates is better preserved by regarding the 
Initial Series as being at the close of the inscription instead of at the 
beginning, thus: 

9.14.13. 4.17 12 Caban 5 Kayab Figure 79, A, B3-A4 

0.11.13. 3 B1-B2 
[9.15. 5. 0. 0] [10 Ahau 8 Chen] » 
[1.14. 6] 2 

9.15. 6.14. 6 6 Cimi 4 Tzec Figure 79, B, B2-A3 
18. 3.14 B1-A2 

9.16. 5. 0. 8 Ahau 8 Zotz Figure 78, A1-B9, Bl3 

By the above arrangement all the dates present in the text lead up 
to 9.16.5.0.0 8 Ahau 8 Zotz as the most important date, because it 
alone records the particular hotun-ending which Stela J marks. The 
importance of this date over the others is further emphasized by the 
fact that it alone appears as an Initial Series. 

The text of Stela J illustrates two points in connection with Sec- 
ondary Series which the student wiU do well to bear in mind: (1) 
The starting points of Secondary-series munbers do not always pre- 
cede the numbers coimted from them, and (2) the terminal dates and 
starting points are not always both recorded. 
The former point will be illustrated in the following example: 
In plate 19, J., is figured the Initial Series from the west side of Stela 
F at Quirigua.^ The introducing glyph appears in A1-B2 and is 
followed by the Initial-series nmnber in A3-A5. This is expressed 
by head variants and reads as follows: 9.14.13.4.17. The terminal 
date reached by this number is 12 Caban 5 Kayab, which is recorded 
in B5-A6. The student will readily identify the numerals as above 
by comparing them with the forms in figures 51-53, and the day and 
month signs by comparing them with figures 16, a', i', and 19, d'-f, 
respectively. The Initial Series therefore reads 9.14.13.4.17 12 Caban 

5 Kayab.* 

1 Bracketed dates are those which are not actually recorded but which are reached by numbers appearing 
in the text. 

2 Although not recorded, the number 1.14.6 is the distance from the date 9.15.5.0.0 reached by the Second- 
ary Series on one side to the starting point of the Secondary Series on the other side, that is, 9.15.6.14.6 

6 Ciml 4 Tzec. 

3 For the lull text of this inscription see Maudslay, 1889-1902: II, pis. 37, 39, 40. For convenience in 
figuring, the lower parts of columns A and B are shown in B instead of below the upper part. The 
numeration of the glyph-blocks, however, follows the arrangement in the original. 

< This is one of the two Initial Series which justified the assumptions made in the previous text that 
the date 18 Caban 5 Eayab, which was recorded there, had the Initial-series value 9.14.13.4.17, as here. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 19 




INITIAL SERIES U) AND SECONDARY SERIES iB) ON STELA F (WEST 

SIDE), QUIRIGUA 



MOKLET] INTKODTJCTION TO STUDY OF MAYA HIEROGLYPHS 219 

Passing over B6-A10, the meanings of which are unknown, we 
reach in BlO the Secondary-series number 13.9.9. Reducing this to 
units of the first order, we have : 

B6b = 13x360=4, 680 
B6a= 9X 20= 180" 
B6a= 9X 1= 9 



4,869 

Assuming that om- starting point is the date next preceding this 
number in the text, that is, the Initial-series terminal date 12 Caban 
5 Kayab in B5-A6, and applying rules 1, 2, and 3 (pp. 139, 140, and 
141, respectively), the terminal day reached will be 6 Cimi 4 Tzec. 
This date the student will find recorded in plate 19, B, Bllb-Al2a. 
Compare Bllb with the sign for Cimi in figure 16, h, i, and Al2a with 
the sign for Tzec in figure 19, g, h. Moreover, since the Initial-series 
value of the starting point 12 Caban 5 Kayab is known, the Initial- 
series value of the terminal date 6 Cimi 4 Tzec may be calculated 
from it: 

9.14.13. 4.17 12 Caban 5 Kayab 
13. 9. 9 

9.15. 6.14. 6 6 Cimi 4 Tzec 1 

In A15 is recorded the date 3 Ahau 3 Mol (compare Al5a with fig. 16, 
A', i', and Al5b with fig. 19, m, n) and in Al7 the date 4 Ahau 13 Yax 
(compare Al7a with fig. 16, e'~g' and Al7b with fig. 19, q, r). This 
latter date, 4 Ahau 13 Yax, is recorded elsewhere at Quirigua in a 
Secondary Series attached to an Initial Series, where it has the Initial- 
series value 9.15.0.0.0. This value we may assume, therefore, belongs 
to it in the present case, giving us the fidl date 9.15.0.0.0 4 Ahau 13 
Yax. For the present let us pass over the first of these two dates, 
namely, 3 Ahau 3 Mol, the Initial Series of which as well as the reason 
for its record here will better appear later. 

In Bl7-Al8a is recorded another Secondary-series number com- 
posed of 3 kins, 13 uinals, 16 tuns, and 1 katxm, which we may write 
thus: 1.16.13.3. The student will note that the katim coefficient in 
Al8a is expressed by an unusual form, the thtunb. As explained on 
page 103, this has a numerical value of 1. Again, our text presents 
another irregular feature. Instead of being cotmted either forward 
or backward from the date next preceding it in the text; that is, 
4 Ahau 13 Yax in A17, this ntunber is counted from the date following 
it in the text, Hke the two Secondary-series numbers in Stela J, just 
discussed. This starting date recorded in Al8b Bl8a is 12 Caban 5 
Kayab, which, as we have seen, is also the date recorded by the 
Initial Series in plate 19, A, A1-A6. We are perfectly justified in 

1 This is the text in which the Initial-series value 9.15.6.14.6 was found attached to the date 6 Clml 4 Tzec. 



220 BUEEAU OF AMERICAN ETHNOLOGY [bull. 57 

assuming, therefore, that the 12 Caban 5 Kayab in Al8b-B18a had 
the same Initial-series value as the 12 Caban 5 Kayab in plate 19, A, 
B5-A6, namely, 9.14.13.4.17. Reducing the number m Bl7-Al8a, 
namely, 1.16.13.3, to units of the first order, we have: 

Al8a= 1X7,200= 7,200 

Bl7b = 16X 360= 5,760 

Bl7a=13X 20= 260 

Bl7a= 3X 1= 3 

13, 223 

Eemembering that this mnnber is to be counted forward from the 
date 12 Caban 5 Kayab, and applying rules 1, 2, and 3 (pp. 139, 140, 
and 141, respectively), the terminal date reached will be 1 Ahau 3 
Zip, which is recorded in A19. Compare the coefiicient of the day 
sign in Al9a with the coefiicient of the katim sign in Al8a, and the 
day sign itself with the profile variant for Ahau in figure 16, h', i'. 
For the month sign, compare Al9b with figure 19, d. But siace the 
Initial-series value of the starting point is known, we may calculate 
from it the Initial-series value of the new terminal date: 

9.14.13. 4.17 12 Caban 5 Kayab 

1.16.13. 3 
9.16.10. 0. 1 Ahau 3 Zip 

Passing over to the east side of this monument, the student will find 
recorded there the continuation of this inscription (see pi. 20).^ This 
side, like the other, opens with an introducing glyph A1-B2, which 
is followed by an Initial Series in A3-A5. Although this number is 
expressed by head variants, the forms are all familiar, and the student 
will have httle difficulty in reading it as 9.16.10.0.0. The terminal 
date which this number reaches is recorded in B5-B8; that is, V Ahau 
3 Zip, the "month indicator" appearing as a head variant in A8 with 
the head-variant coefficient 10. But this date is identical with the 
date determined by calculation and actually recorded at the close of 
the inscription on the other side of this monimient, and since no later 
date is recorded elsewhere in this text, we may conclude that 
9.16.10.0.0 1 Ahau 3 Zip represents the contemporaneous time of 
Stela F, and hence that it was a regular hottm-marker. Here again, 
as in the case of Stela J at Quirigua, the importance of the "contem- 
poraneous date" is emphasized not only by the fact that all the other 
dates lead up to it, but also by the fact that it is expressed as an 
Initial Series. 

1 Tor the full text of this inscription see Maudslay, 1889-1902: n, pis. 38, 40. 

2 The frontlet seems to be composed of but one element, indicating for this head the value 8 Instead 
of 1. However, as the calculations point to 1, it is probable there was originally another element to the 
frontlet 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 20 




INITIAL SERIES ON STELA F (EAST SIDE), QUIRIGUA 





MOHLBY] INTKODtrCTION TO STUDY OF MAYA HIEEOGLYPHS 221 

We have explained all the dates figured except 3 Ahau 3 Mol in 
plate 19, B, A15, the discussion of which was deferred until after the 
rest of the inscription had been considered. It will be remembered 
in connection with Stela J (figs. 78, 79) that one of the dates reached 
in the course of the calculations was just 1 katun earlier than the 
date recorded by the Initial Series on the same monument. Now, 
one of the Initial-series values corresponding to the date 3 Ahau 3 
Mol here under discussion is 9.15.10.0.0, exactly 1 katun earlier than 
the Initial-series date on Stela 
F. In other words, if we give 
to the date 3 Ahau 3 Mol in A15 
the value 9.15.10.0.0, the cases 
are exactly parallel. WMle it 
is impossible to prove that this 
irarticular Initial Series was the ^. , 

'■ -1 • 7 1 • •1 Fig. 80. Glyphs wliich may disclose the nature o£ the 

one which the ancient scribes events that happened at Quirigua on the dates: 

had in mind when they re- <"• ^- "• i^- *■ " ^^ c*"*" ' ^^^^^ • *>' ^- ^^- '^- "• " 

1 1 ; 1 • 1 ; « • , « ,, , 6 Clml 4 Tzec. 

corded this date 3 Anau 3 Mol, 

the writer believes that the coincidence and parallel here presented are 
sufficient to warrant the assumption that this is the case. The whole 
text reads as follows : 

9.14.13. 4.17 12 Caban 6 Kayab Plate 19, A, A1-A6 

13. 9. 9 Plate 19, A, AlO 

9.15. 6.14. 6 6 Cimi 4 Tzec Plate 19, B, Bllb-Al2a 

[9.15.10. 0. 0] 3 Ahau 3 Mol Plate 19, B, Al5 

[9.15. 0. 0. 0] 4 Ahau 13 Yax Plate 19, B, Al7 
9.14.13. 4.17 12 Caban 5 Kayab Plate 19, B, Al8b Bl8a 

1.16.13. 3 Plate 19, B, Bl7 Al8a 

9.16.10. 0. 1 Ahau 3 Zip Plate 19, B, A19 

(repeated as Initial Series on east side of monument) 
9.16.10. 0. 1 Ahau 3 Zip Plate 20, A1-B5-B8 

The student will note the close similarity between this inscription and 
that on Stela J (figured in figs. 78 and 79), a summary of which appears 
on page 239. Both commence with the same date, 9.14.13.4.17 12 
Caban 5 Kayab; both show the date 9.15.6.14.6 6 Cimi 4 Tzec; both 
have dates which are just 1 katun in advance of the hotims which 
they mark; and finally, both are ho tun-markers. Stela J preceding 
Stela F by just 1 hotun. The date from which both proceed, 
9.14.13.4.17 12 Caban 5 Kayab, is an important one at Quirigua, 
being the earliest date there. It appears on four monuments, namely, 
Stelse J, F, and E, and Zoomorph G. Although the writer has not 
been able to prove the point, he is of the opinion that the glyph 
shown in figure 80, a, tells the meaning of the event which happened 
on this date, which is, moreover, the earliest date at Quirigua which 



222 BUREAU OF AMBBICAN ETHNOLOGY [bull. 57 

it is possible to regard as being contemporaneous. Hence, it is not 
improbable that it might refer to the fomiding of the city or some 
similar event, though this is of coiu-se a matter of speculation. The 
fact, however, that 9.14.13.4.17 12 Caban 5 Kayab is the earhest 
date on fotir different hotun-markers shows that it was of supreme 
importance ia the history of Quirigua. This concludes the discus- 
sion of texts showing the use of Secondary Series with Initial Series. 

Texts Eeookding Period Endings 

It was explained in Chapter III (p. 77) that in addition to Initial- 
series dating and Secondary-series dating, the Maya used still 
another method in fixing events, which was designated Period-ending 
dating. It was explained further that, although Period-ending dating 
was less exact than the other two methods, it served equally well for 
all practical piirposes, since dates fixed by it could not recur until 
after a lapse of more than 18,000 years, a considerably longer period 
than that covered by the recorded history of mankind. Finally, the 
student wiU recall that the katun was said to be the period most 
commonly used in this method of dating. 

The reason for this is near at hand. Practically all of the great 
southern cities rose, floiuished, and fell within the period called Cycle 
9 of Maya chronology. There could have been no doubt throughout 
the southern area which particular cycle was meant when the "cur- 
rent cycle" was spoken of. After the date 9.0.0.0,0 8 Ahau 13 Chen 
had ushered in a new cycle there could be no change in the cycle 
coefficient until after a lapse of very nearly 400 (394.250 -f-) years. 
Consequently, after Cycle 9 had commenced many succeeding gen- 
erations of men knew no other, and in time the term "current cycle" 
came to mean as much on a monument as "Cycle 9." Indeed, in 
Period-ending dating the Cycle 9 was taken for granted and 
scarcely ever recorded. The same practice obtains very generally 
to-day in regard to writing the current century, such expressions as 
July 4, '12, December 25, '13, being frequently seen in place of the 
full forms July 4, 1912, A. D., December 25, 1913, A. D. ; or again, 
even more briefly, 7/4/12 and 12/25/13 to express the same dates, 
respectively. The desire for brevity, as has been explained, prob- 
ably gave rise to Period-ending dating in the first place, and in this 
method the cycle was the first period to be eliminated as superfluous 
for all practical purposes. No one could have forgotten the number 
of the current cycle. 

When we come to the next lower period, however, the katun, we 
find a different state of affairs. The numbers belonging to this 
period were changing every 20 (exactly, 19.71 -I- ) years; that is, three 
or four times in the lifetime of many individuals; hence, there was 



BUREAU OF AMERICAN ETHNOLOGY 



OQO © ® (S> 



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A. STELA 2, COPAN 



23. TEMPLE OF THE FOLIATED 
CROSS, PALENQUE 



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F. TEMPLE OF THE INSCRIPTIONS, PALENQUE 





CEIHC 

JI. STELA C (WEST SIDE), QUIRIGUA 

EXAMPLES OF PERIOD-ENDING DATES IN CYCLE 9 



MOELEY] . INTKODUCTION TO STUDY OF MAYA HIEROGLYPHS 223 

plenty of opportunity for confusion about the number of the katun 
in which a particular event occurred. Consequently, in order to 
insure accuracy the katun is almost always the unit used in Period^ 
ending dating. 

In plate 21 are figured a number of Period-ending dates, the glyphs 
of which have been ranged in horizontal lines, and are numbered 
from left to right for convenience in reference. The true positions 
of these glyphs in the texts from which they have been taken are 
given in the footnotes in each case. In plate 21 , J., is figured a Period- 
ending date from Stela 2 at Copan.^ The date 12 Ahau S Ceh ap- 
pears very clearly in glyphs 1 and 2. Compare the month sign with 
figure 19, u, v. There follows in 3 a glyph the upper part of which 
probably represents the "ending sign" of this date. By comparing 
this form with the ending signs in figure 37 its resemblance to figure 
37, 0, will be evident. Indeed, figure 37, o, has precisely the same 
lower element as glyph 3. In glyph 4 foUows the particular katun, 
11, whose end fell on the date recorded in glyphs 1 and 2. The stu- 
dent can readily prove this for himself by reducing the Period-ending 
date here recorded to its corresponding Initial Series and counting 
the resulting number forward from the common starting point, 4 Ahau 
8 Cumhu, as follows: Since the cycle glyph is not expressed, we may 
fill this omission as the Maya themselves filled it, by supplying Cycle 
9. Moreover, since the end of a katim is recorded here, it is clear 
that all the lower periods — the tuns, uinals, and kins — will have to 
appear with the coefficient 0, as they are ah, brought to their respec- 
tive ends with the ending of any katun. Therefore we may write the 
Initial-series number corresponding to the end of Katun 11, as 
9.11.0.0.0. Treating this number as an Initial Series, that is, first 
reducing it to imits of the first order, then deducting from it all the 
Calendar Eounds possible, and finally applying rules 1, 2, and 3 (pp. 
139, 140, and 141, respectively) to the remainder, the student will find 
that the terminal date reached will be the same as the date recorded 
in glyphs 1 and 2, namely, 12 Ahau 8 Ceh. In other words, the Katun 
11, which ended on the date 12 Ahau 8 Ceh, was 9.11.0.0.0 12 Ahau 
8 Ceh, and both indicate exactly the same position in the Long 
Count. The next example (pi. 21, B) is taken from the tablet in the 
Temple of the Foliated Cross at Palenque.^ In glyph 1 appears the 
date 8 Ahau 8 TJo (compare the month form with fig. 19, h, c) and in 
glyph 3 the "ending" of Katun 13. The ending sign here is the 
variant shown in figure 37, a-h, and it occurs just above the coeffi- 
cient 13. These two glyphs therefore record the fact that Katun 13 
ended with the day 8 Ahau 8 Uo. The student may again test the 
acciiracy of the record by changing this Period-ending date to its 

1 See Maudslay, 18S9-1902; i, pi. 102, west side, glyphs A5b-A7a. 

2 See ibid.: iv, pi. 81, glyphs N15 015. 



224 BXJEEAU OF AMERICAN ETHNOLOGY [BULL. 57 

corresponding Initial-series number, 9.13.0.0.0, and performing the 
various operations indicated in such cases. The resulting Initial- 
series terminal date will be the same as the date recorded in glyphs 1 
and 2, 8 Ahan 8 TJo. 

In plate 21, C, is figured a Period-ending date taken from Stela 23 
at Naranjo.^ The date 6 Ahau 13 Muan appears very clearly in glyphs 
1 and 2 (compare the month form with fig. 19, a' , I'). Glyph 3 is 
the ending sign, here showing three common "ending elements," (1) 
the clasped hand; (2) the element with the curl infix; (3) the tassel- 
hke postfix. Compare this form with the ending signs in figure 37 
l-q, and with the zero signs in figure 54. In glyph 4 is recorded the 
particular katun, 14, which came to its end on the date recorded in 
1 and 2._ The element prefixed to the Katun 14 m glyph 4 is also 
an ending sign, though it always occurs as a prefix or superfix attached 
to the sign of the period whose close is recorded. Examples illus- 
trating its use are shown in figure 37, a-h, with which the ending 
element ia glyph 4 should be compared. The glyphs 1 to 4 m plate 
21, C, therefore record that Katim 14 came to an end on the date 
6 Ahau 13 Muan. As we have seen above, this could be shown to 
correspond with the Initial Series 9.14.0.0.0 6 Ahau 13 Muan. 

This same date, 6 Ahau 13 Muan ending Katun 14, is also recorded 
on Stela 16 at Tikal (see pi. 21, D).' The date itself appears m 
glyphs 1 and 2 and is followed ia 3 by a sign which is almost exactly 
like the ending sign in glyph 3 just discussed (see pi. 21, C). The 
subfixes are identical in both cases, and it is possible to distiaguish 
the lines of the hand element in the weathered upper part of the 
glyph in 3. Compare glyph 3 with the ending signs in figure 37, l~q, 
and with the zero signs in figure 54. As in the preceding example, 
glyph 4 shows the particular katun whose end is recorded here — Katun 
14. The period glyph itself appears as a head variant to which is 
prefixed the same ending prefix or superfix shown with the period 
glyph in the preceding example. See also figure 37, a-h. As above 
stated, the Initial Series corresponding to this date is 9.14.0.0.0 6 
Ahau 13 Muan. 

One more example will sufl&ce to illustrate the use of katun Period- 
ending dates. In plate 21, E,is figured a Period-ending date from 
Stela 4 at Copan.^ In glyphs 1 and 2 appears the date 4 Ahau 13 Yax 
(compare the month in glyph 2 with fig. 19, q, r), which is followed 
by the ending sign in 3. This is composed of the hand, a very com- 
mon "ending" element (see fig. 37, j, Tc) with a grotesque head super- 
fix, also another "ending sign" (see i, r, u, v of the plate just 
named). In glyph 4 follows the particular katun (Katun 15) whose 

1 See Maler, 1908 b: iv, No. 2, pi. 38, east side, glyphs A17-B18. 

2 See ibid., 1911: v, pi. 26, glyphs A1-A4. 

8 See Maudslay, 1889-1902; j, pi, 104, glyphs A7, B7, 



MOKLET] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 225 

end is here recorded. This date corresponds to the Initial Series 
9.15.0.0.0 4 Ahau 13 Yax. 

Cases where tun endings are recorded are exceedingly rare. 
The bare statement that a certain tim, as Tun 10, for example, had 
come to its end left much to be desired in the way of accuracy, since 
there was a Tim 10 in every katun, and consequently any given tun 
recurred after an interval of 20 years; in other words, there were 
three or four difJerent Tim lO's to be distinguished from one another 
in the average lifetime. Indeed, to keep them apart at all it was 
necessary either to add the particular katun in which each fell or to 
add the date on which each closed. The former was a step away 
from the brevity which probably prompted the use of Period-ending 
dating in the first place, and the latter imposed too great a task on 
the memory, that is, keeping Ln mind the 60 or 70 various tun end- 
ings wMch the average lifetime included. For these reasons tim- 
ending dates occur but rarely, only when there was little or no doubt 
concerning the particiilar katim in which they fell. 

In plate 21, F, is figured a tun-ending date from the tablet in the 
Temple of the Inscription at Palenque.' In glyph 1 appears an ending 
sign showing the hand element and the grotesque fiattened head (for 
the latter see fig. 37, i, r, u, v), both common ending signs. The 
remaining element, another grotesque head with a flaring postfix, is 
an unusual variant of the tun head found only at Palenque (see fig. 
29, lb). The presence of the tun sign with these two ending signs 
indicates probably that some tun ending follows. Glyphs 2 and 3 
record the date 5 Ahau 18 Tzec, and glyph 4 records Tun 13. We 
have here then the record of a Tun 13, which ended on the date 
5 Ahau 18 Tzec. But which of the many Tun 13s in the Long Count 
was the one that ended on this particular date ? To begin with, we are 
perfectly justified in assuming that this particular tim occiirred some- 
where in Cycle 9, but this assumption does not aid us greatly, since 
there were twenty different Tun 13s in Cycle 9, one for each of the 
twenty katuns. However, in the full text of the inscription from 
which this example is taken, 5 Ahau 3 Chen is the date next preceding, 
and although the fact is not recorded, this latter date closed Katim 8 
of Cycle 9. Moreover, shortly after the tim-ending date here under 
discussion, the date " 3 Ahau 3 Zotz, end of Katun 9," is recorded. It 
seems likely, therefore, that this particular Tun 13, which ended on 
the date 5 Ahau 18 Tzec, was 9.8.13.0.0 of the Long Count, after 
9.8.0.0.0 but before 9.9.0.0.0. Reducing this number to units of the 
first order, and applying the several rules given for solving Initial 
Series, the terminal date of 9.8.13.0.0 will be found to agree with the 
terminal date recorded in glyphs 2 and 3, namely, 5 Ahau 18 Tzec, 

1 See Maudslay, 1R89-1902: iv, pi. 60, glyphs M1-N2. 
43508°— Bull. 57—15 15 



226 BUEEAU OF AMEKICAN ETHNOLOGY [bull. 57 

and this tun ending corresponded, therefore, to the Initial Series 
9.8.13.0.0' 5 Ahau 18 Tzec. 

Another txin-ending date from Stela 5 at Tikal is figured in plate 
21, G} In glyphs 1 and 2 the date 4 Ahau 8 Yaxkin appears, the 
month sign being represented as a head variant, which has the essen- 
tial elements of the sign for Yaxkin (see fig. 19, h, I). FoUowing this 
in glyph 3 is Txm 13, to which is prefixed the same ending-sign 
variant as the prefixial or superfixial elements in figure 37, i, r, u, v. 
We have recorded here then "Tun 13 ending on 4 Ahau 8 Yaxkin," 
though there seems to be no mention elsewhere in this inscription 
of the number of the katun in which this particular tun feU. By 
referring to Great Cycle 54 of Goodman's Tables (Goodman, 1897), 
however, it appears that Tun 13 of Katun 15 of Cycle 9 closed with 
this date 4 Ahau 8 Yaxkin, and we may asstune, therefore, that this 
is the correct position in the Long Count of the tun-ending date here 
recorded. This date corresponds to the Initial Series 9.15.13.0.0 4 
Ahau 8 Yaxkin. 

There is a very unusual Period-ending date on the west side of 
Stela C at Quirigua^ (see pi. 21, ff). In glyphs 1 and 2 appears the 
nimiber kins, uinals, 5 tuns, and 17 katuns, which we may write 
17.5.0.0, and following this in glyphs 3 and 4 is the date 6 Ahau 13 
Kayab. At first sight this would appear to be a Secondary Series, 
the number 17.5.0.0 being counted forward from some preceding 
date to reach the date 6 Ahau 13 Kayab recorded just after it. The 
next date preceding this on the west side of Stela C at Quirigua is the 
Initial-series terminal date 6 Ahau 13 Yaxkin, illustrated together with 
its corresponding Initial-series number in figure 68, A. However, 
aU attempts to reach the date 6 Ahau 13 Kayab by counting either 
forward or backward the number 17.5.0.0 from the date 6 Ahau 13 
Yaxkin will prove imsuccessful, and we must seek another explana- 
tion for the four glyphs here \mder discussion. If this were a Period- 
ending date it would mean that Tun 5 of Katim 17 came to an end 
on the date 6 Ahau 13 Kayab. Let us see whether this is true. 
Ass umin g that our cycle coefiicient is 9, as we have done in all the 
other Period-ending dates presented, we may express glyphs 1 and 2 
as the following Initial-series number, provided they represent a 
period ending, not a Secondary-series niunber: 9.17.5.0.0. Keduc- 
ing this nimaber to units of the 1st order, and applyiag the rules 
previously given for solving Initial Series, the terminal date reached 
will be 6 Ahau 13 Kayab, identical with the date recorded ia glyphs 
3 and 4. We may conclude, therefore, that this example records the 
fact that "Tun 5 of Katun 17 ended on the date 6 Ahau 13 Kayab," 
thLs beiag identical with the Initial Series 9.17.5.0.0 6 Ahau 13 Kayab. 

1 Maler, 1911: v, pi. 17, east side, glyphs A4-A5. 

2 See Maudslay, 1889-1902: n, pi. 19, west side, glyphs B10-A12. 



BUREAU OF AMERICAN ETHNOLOGY 






i 





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A. CYCLE 13; TEMPLE OF THE CROSS, PALENQUE 










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a CYCLE 2: TEMPLE OF THE FOLIATED CROSS, PALENQUE 







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J). CYCLE 10; STELA 11, SEIBAL 



BULLETIN 57 PLATE 22 



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P. CYCLE 10: ZOOMORPH G, QUIRIGUA 




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G. CYCLE 8; TEMPLE OF THE CROSS, PALENQUE 

EXAMPLES OF PERIOD-ENDING DATES IN CYCLES OTHER THAN CYCLE 9 



MOKLBY] INTEODUCTION TO STUDY OF MAYA HIEROGLYPHS 227 

The foregoing Period-ending dates have all been in Cycle 9, even 
though this fact has not been recorded in any of the above examples. 
We come next to the consideration of Period-ending dates which 
occurred in cycles other than Cycle 9. 

In plate 22, A, is figured a Period-ending date from the tablet in 
the Temple of the Cross at Palenque.^ In glyphs 1 and 2 appears 
the date 4 Ahau 8 Cumhu (compare the month form la glyph 2 with 
fig. 19, g', Ti'), and in glyph 3 an ending sign (compare glyph 3 with 
the ending signs in fig. 37, l-g, and with the zero signs in fig. 54). 
There follows in glyph 4, Cycle 13. These four glyphs record the fact, 
therefore, that Cycle 13 closed on the date 4 Ahau 8 Cumhu, the start- 
ing point of Maya chronology. This same date is again recorded on 
a round altar at Piedras Negras (see pi. 22, B)? In glj^jhs 1 and 2 
appears the date 4 Ahau 8 Cumhu, and in glyph 3a the endiag sign, 
which is identical with the ending sign in the preceding example, 
both having the clasped hand, the subfix showing a curl infix, and 
the tassel-like postfix. Compare also figure 37, Z-g, and figine 54. 
Glyph 3b clearly records Cycle 13. The dates in plate 22, A, B, are 
therefore identical. In both cases the cycle is expressed by its 
normal form. 

In plate 22, 0, \s figured a Period-ending date from the tablet in the 
Temple of the Foliated Cross at Palenque.^ In glyph 1 appears an 
ending sign in which the hand element and tassel-like postfix show 
clearly. This is followed in glj^h 2 by Cycle 2, the clasped hand on 
the head variant unmistakably indicating the cycle head. Finally, 
in glyphs 3 and 4 appears the date 2 Ahau 3 Uayeb (compare the 
month form with fig. 19, i') .^ The glyphs in plate 22, C, record, there- 
fore, the fact that Cycle 2 closed on the date 2 Ahau 3 Uayeb, a fact 
which the student may prove for himself by converting this Period- 
ending date into its corresponding Initial Series and solving the same. 
Since the end of a cycle is recorded here, it is evident that the katun, 
tun, uinal, and kin coefficients must all be 0, and our Initial-series 
number will be, therefore, 2.0.0.0.0. Keducing this to tinits of the 
1st order and proceeding as in the case of Initial Series, the terminal 
date reached will be 2 Ahau 3 Uayeb, just as recorded in glyphs 3 
and 4. The Initial Series corresponding to this Period-ending date 
will be 2.0.0.0.0 2 Ahau 3 Uayeb. 

These three Period-ending dates (pi. 22, A-C) are not to be consid- 
ered as referring to times contemporaneous with the erection of the 
monuments upon which they are severally inscribed, since they pre- 

1 See Maudslay, 1889-1902: IV, pi. 7.5, glyphs D3-C5. 

2 See Maler, 1901: II, No. 1, pi. 8,-glyphs A1-A2. 
8 See Maudslay, op. olt., pi. 81, glyphs C7-D8. 

i It will be remembered that TTayeb was the name tor the xma kaba Un, the 5 closing days of the year. 
Dates which fall in this period are exceedmgly rare, and in the inscriptions, so tar as the writer knows, 
have been found only at Palenque and Tikal. 



228 BUREAU OF AMEKIOAN ETHNOLOGY [BULL. 57 

cede the opening of Cycle 9, the first historic epoch of the Maya civ- 
iUzation, by periods ranging from 2,700 to 3,500 years. As explained 
elsewhere, they probably referred to mythological events. There is 
a date, however, on a tablet in the Temple of the Cross at Palenque 
which falls in Cycle 8, being fixed therein by an adjo inin g Period- 
ending date that may have been historical. This case is figured in 
plate 22, G} In glyphs 4 and 5 appears the date 8 Ahau 13 Ceh 
(compare the month form in gljrph 5 with fig. 16, u, v). This is fol- 
lowed in glyph 6 by a sign which shows the same ending element as 
the fomas in figure 37, i, r, u, v, and this in turn is followed by Cycle 

9 in glyph 7. The date recorded in this case is Cycle 9 ending on the 
date 8 Ahau 13 Ceh, which corresponds to the Initial Series 9.0.0.0.0 
8 Ahau 13 Ceh. 

Now, in glyphs 1 and 2 is recorded the date 2 Caban 10 Xul (com- 
pare the day sign with fig. 16, a', b', and the month sign with fig. 
19, i, j), and following this date in glyph 3 is the number 3 kins, 6 
uitials, or 6.3. This looks so much like a Secondary Series that we 
are justified in treating it as such imtil it proves to be otherwise. As 
the record stands, it seems probable that if we count this number 
6.3 in glyph 3 forward from the date 2 Caban 10 Xul in glyphs 1 and 
2, the terminal date reached wiU be the date recorded in glyphs 4 
and 5; that is, the next date following the number. Reducing 6.3 
to units of the first order, we have: 

Glyph 6 = 6X20 = 120 
Glyph 6 = 3 X 1= 3 

123 

Counting this number forward from 2 Caban 10 Xul according to the 
rules which apply in such cases, the terminal day reached will be 
8 Ahau 13 Ceh, exactly the date which is recorded ui glyphs 4 and 5. 
But this latter date, we have just seen, is declared by the text to have 
closed Cycle 9, and therefore corresponded with the Initial Series 
9.0.0.0.0 8 Ahau 13 Ceh. Hence, from this known Initial Series we 
may calculate the Initial Series of the date 2 Caban 10 Xul by sub- 
tracting from 9.0.0.0.0 the number 6.3, by which the date 2 Caban 

10 Xul precedes the date 9.0.0.0.0 8 Ahau 13 Ceh: 

9. 0. 0. 0. 8 Ahau 13 Ceh 

6. 3 
8.19.19.11.17 2 Caban 10 Xul 

This latter date fell in Cycle 8, as its Initial Series indicates. It is 
quite possible, as stated above, that this date may have referred to 
some actual historic event in the annals of Palenque, or at least of 

1 See Maudslay, 1889-1902: iv, pi. 77, glyphs P14-E2. Glyphs Q15-P17 are omitted from pi 22 G, as 
they appear to be uncalendrioal. 



MOKLBT] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 229 

the southern Maya, though the monument upon which it is recorded 
probably dates from an epoch at least 200 years later. 

In a few cases Cycle-10 ending dates have been found. Some of 
these are surely "contemporaneous," that is, the monuments upon 
which they appear really date from Cycle 10, whUe others are as 
surely "prophetic," that is, the monuments upon which they are 
found antedate Cycle 10. Examples of both kinds follow. 

In plate 22, E, is figured a Period-ending date from Stela 8 at Copan.' 
Glyphs 1 and 2 declare the date 7 Ahau 18 ?, the month sign in gljT)h 
2 being effaced. In glyph 3 is recorded Cycle 10, the cycle sign being 
expressed by its corresponding head variant. Note the clasped hand, 
the essential characteristic of the cycle head. Above this appears the 
same endingsignas that shown in figure 37, a-h, and it would seem prob- 
able, therefore, that these three glyphs record the end of Cycle 10. 
Let us test this by changing the Period-ending date in glyph 3 into 
its corresponding Initial-series number and then solving this for the 
resulting terminal date. Since the end of a cycle is here indicated, 
the katun, tim, uinal, and kin coefficients must be and the Initial- 
series nmnber will be, therefore, 10.0.0.0.0. Reducing this to units 
of the first order and applying the rules indicated in such cases, the 
resulting terminal date will be found to be 7 Ahau 18 Zip. But this 
agrees exactly with the date recorded in glyphs 1 and 2 so far as the 
latter go, and since the two agree so far as they go, we may conclude 
that glyphs 1-3 in plate 22, E, express "Cycle 10 ending on the date 
7 Ahau 18 Zip." Although this is a comparatively late date for 
Copan, the writer is inclined to beheve that it was "contemporane- 
ous" rather than "prophetic." 

The same can not be said, however, for the Cycle-10 ending date 
on Zoomorph G at Quirigua (see pi. 22, F). Indeed, this date, as will 
appear below, is almost surely "prophetic" in character. Glyphs 1 
and 2 record the date 7 Ahau 18 Zip (compare the month form in glyph 
2 with fig. 19, d) and glyph 3 shows very clearly " the end of Cycle 
10." Compare the ending prefix in glyph 4 with the same element 
in fig. 37, a-lh. Hence we have recorded here the fact that "Cycle 
10 ended on the date 7 Ahau 18 Zip," a fact proved also by calcula- 
tion in connection with the preceding example. Does this date rep- 
resent, therefore, the contemporaneous time of Zoomorph G, the time 
at which it was erected, or at least dedicated? Before answering 
this question, let us consider the rest of the text from which this 
example is taken. The Initial Series on Zoomorph G at Quirigua has 
already been shown in figure 70, and, according to page 187, it records 
the date 9.17.15.0.0 5 Ahau 3 Muan. On the groimds of antecedent 
probability, we are justified in assuming at the outset that this date 

1 See Maudslay, 1889-1902: I, pi. 109, glyphs Cl Dl, A2. 



230 BUEEAU OF AMERICAN ETHNOLOGY [boll. 57 

therefore indicates the epoch or position of Zoomorph G in the Long 
Count, becatise it alone appears as an Initial Series. In the case of all 
the other monuments at Quirigua/ where there is but one Initial 
Series in the inscription, that Initial Series marks the position 
of the monument in the Long Coimt. It seems likely, therefore, 
judging from the general practice at Quirigua, that 9.17.15.0.0 5 Ahau 
3 Muan was the contemporaneous date of Zoomorph G, not 10.0.0.0.0 
7 Ahau 18 Zip, that is, the Initial Series corresponding to the Period- 
ending date here under discussion (see pi. 22, F).^ 

Other featm-es of this text point to the same conclusion. In addi- 
tion to the Initial Series on this monument there are upward of a 
dozen Secondary-series dates, all of which except one lead to 
9.17.15.0.0 5 Ahau 3 Muan. Moreover, this latter date is recorded 
thrice in the text, a fact which poiats to the conclusion that it was 
the contemporaneous date of this monument. 

There is still another, perhaps the strongest reason of all, for believ- 
ing that Zoomorph G dates from 9.17.15.0.0 5 Ahau 3 Muan rather 
than from 10.0.0.0.0 7 Ahau 18 Zip. If assigned to the former date, 
every hotun from 9.15.15.0.0 9 Ahau 18 Xul to 9.19.0.0.0 9 Ahau 18 
Mol has its corresponding marker or period-stone at Quirigua, there 
being not a single break in the sequence of the fourteen monuments 
necessary to mark the thirteen hotun endings between these two dates. 
If, on the other hand, the date 10.0.0.0.0 7 Ahau 18 Zip is assigned to 
this monument, the hottm ending 9.17.15.0.0 6' Ahau 3 Muan is left 
without its corresponding montiment at this city, as are also all the 
hotuns after 9.19.0.0.0 9 Ahau 18 Mol up to 10.0.0.0.0 7 Ahau 18 Zip, 
a total of four in all. The perfect sequence of the monuments at 
Quirigua developed by regarding Zoomorph G as dating from 
9.17.15.0.0 5 Ahau 3 Muan, and the very fragmentary sequence which 
arises if it is regarded as dating from 10.0.0.0.0 7 Ahau 18 Zip, is of 
itself practically sufficient to prove that the former is the correct date, 
and when taken into consideration with the other points above men- 
tioned leaves no room for doubt. 

If this is true, as the writer beheves, the date "Cycle 10 ending on 
7 Ahau 18 Zip" on Zoomorph G is "prophetic" in character, since it 
did not occur until nearly 45 years after the erection of the monu- 
ment upon which it was recorded, at which time the city of Quirigua 
had probably been abandoned, or at least had lost her prestige. 

Another Cycle-10 ending date, which differs from the preceding in 
that it is almost surely conteniporaneous, is that on Stela 11 at Seibal, 

1 This excludes Stola C, which has two Initial Series (see figs. 68 and 77), though neither ol them, as 
explained on p. 176, footnote 1, records the date of this monument. The true date of this monument Is 
declared by the Period-ending date figured in pi. 21, H, which is 9.17.0.0.0 6 Ahau 13 Eayab. (See p. 
226.) 

2 See Maudslay, 1889-1902: ii, pi. 44, west side, glyphs G4 H4, FS. 



MOKLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 231 

the latest of the great southern sites.* This is figured in plate 22, D. 
Glyphs 1 and 2 show very clearly the date 7 Ahau 18 Zip, and glyph 
3 declares this to be" at the end of Cycle 10." ^ Compare the ending- 
sign superfix in glyph 3 with figure 37, a-li. This glyph is followed 
by 1 katun in 4, which in turn is followed by the date 5 Ahau 3 Kayab 
in 5 and 6. Finally, glyph 7 declares "The end of Katun 1." Count- 
ing forward 1 katun from 10.0.0.0.0 7 Ahau 18 Zip, the date reached 
will be 5 Ahau 3 Kayab, as recorded by 5 and 6, and the Initial Series 
corresponding to this date will be 10.1.0.0.0 5 Ahau 3 Kayab, as 
declared by glyph 7. See below: 

10.0.0.0.0 7 Ahau 18 Zip 

1.0.0.0 
10.1.0.0.0 5 Ahau 3 Kayab 
End of Katun 1. 

This latter date is found also on Stelae 8, 9, and 10, at the same 
city. 

Another Cycle-10 ending date which was probably " prophetic", like 
the one on Zoomorph G at Quirigua, is figured on Altar S at Copan 
(see fig. 81). In the first glyph on the left appears an Initial-series 
introducing glyph; this is followed in glyphs 1-3 by the Initial- 
series number 9.15.0.0.0, which the student will find leads to the 
terminal date 4 Ahau 13 Yax recorded in glyph 4. This whole 
Initial Series reads, therefore, 9.15.0.0.0 4 Ahau 13 Yax. In glyph 
6a is recorded 5 katuns and in glyph 7 the date 7 Ahau 18 Zip, in 
other words, a Secondary Series.^ Reducing the number in glyph 
6a to units of the first order, we have: 

6a = 5x7, 200 = 36, 000 

OX 360= 

Not recorded OX 20= 

OX 1= 



36, 000 

Counting this number forward from the date 4 Ahau 13 Yax, the 
terminal date reached wdl be found to agree with the date recorded 
in glyph 7, 7 Ahau 18 Zip. But turning to our text again, we find 
that this date is declared by glyph 8a to be at the end of Cycle 10. 
Compare the ending sign, which appears as the superfix in glyph 8a, 
with figure 37, a-li. Therefore the Secondary-series date 7 Ahau 18 

1 The dates 10.2.5.0.0 9 Ahau 18 Yax and 10.2.10.0.0 2 Ahau 13 Chen on Stete 1 and 2, respectively, at 
Quen Santo, are purposely excluded from this statement. Quen Santo is in the highlands ot Guatemala 
(see pi. 1) and is well to the south ot the Usamacintla region. It rose to prominence probably after the 
collapse of the great southern cities and is to be considered as inaugurating a new order of things, if not 
indeed a new civiUzation. 

2 See Maler, 1908 a: IV, No. 1, pi. 9, glyphs E2, F2, A3, and A4. 

' The student win note that the lower periods (the tun, uinal, and kin signs) are omitted and consequently 
are to be considered as having the coefficient 0. 



232 



BUBEAU OF AMEKICAN ETHNOLOGY 



[BULL. 57 



Zip, there recorded, closed Cycle 10. The same fact could have been 
determined by adding the Secondary-series number m glyph 6a to 
the Initial-series number of the starting point 4 Ahau 13 Yax in 

glyphs 1-3: 

9.15.0.0.0 4 Ahau 13 Yax 

5.(0.0.0) 

10. 0.0.0.0 7 Ahau 18 Zip 




Fig. 81. The Initial Series, Secondary Series, and Period-ending date on Altar S, Copan. 

The "end of Cycle 10 " in glyph 8a is merely redundancy. The writer 
believes that 9.15.0.0.0 4 Ahau 13 Yax indicates the present time of 
Altar S rather than 10.0.0.0.0 7 Ahau 18 Zip, and that consequently 
the latter date was "prophetic" in character, as was the same date 
on Zoomorph G at Quirigua. One reason whica renders this prob- 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 23 




INITIAL SERIES, SECONDARY SERIES, AND PERIOD- 
ENDING DATES ON STELA 3, PIEDRAS NEGRAS 



MOELBT] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 233 

able is that the sculpture on Altar S very closely resembles, the 
sculpture on Stelse A and B at Copan, both of which date from 
9.15.0.0.0 4 Ahau 13 Yax. A possible explanation of the record of 
Cycle 10 on this monument is the following: On the date of this 
monument, 9.15.0.0.0 4 Ahau 13 Yax, just three-fourths of Cycle 9 
had elapsed. This important fact would hardly have escaped the 
attention of the old astronomer-priests, and they may have used this 
monument to point out that only a quarter cycle, 5 katuns, was left 
in Cycle 9. This concludes the discussion of Cycle-10 Period-ending 
dates. 

The student will note in the preceding example (fig. 81) that 
Initial-series, Secondary-series, and Period-ending dating have all 
been used together in the same text, glyphs 1-4 recording an Initial- 
series date, glyphs 6a and 7, a Secondary-series date, and glj^jhs 7 
and 8a, a Period-ending date. This practice is not at all imusual in 
the inscriptions and several texts Ulustrating it are figured below. 

Texts Eecording Initial Series, Secondary Series, and Period 

Endings 

In plate 23 is shown the inscription on Stela 3 at Piedras Negras. 
The introducing glyph appears in Al and is followed by the Initial- 
series number 9.12.2.0.16 in Bl-BS. This number reduced to units 
of the first order and counted forward from its starting point will 
be found to reach the terminal date 5 Gib 14 Yaxkin, which the student 
will readily recognize in A4-B7; the "month-sign indicator" appear- 
ing very clearly in A7, with the coefficient 9 affixed to it. Compare 
the day sign in A4 with figure 16, z, and the month sign in B7 with 
figure 19, Ti, I. The Initial Series recorded in A1-A4, B7 reads, there- 
fore, 9.12.2.0.16 5 Gib 14 Yaxkin. In Cl Dl is recorded the number 
kins, 10 uinals, and 12 tuns; that is, 12.10.0, the first of several 
Secondary Series in this text. Keducuig this to units of the first 
order and counting it forward from the terminal date of the Initial 
Series, 5 Gib 14 Yaxkin, the terminal date of the Secondary Series 
will be found to be 1 Gib 14 Kankin, which the student will find 
recorded in C2b D2a. The Initial-series value of this latter date 
may be calculated as follows : 

9.12 2. 0.16 5 Gib 14 Yaxkin 

12.10. 
9.12.14.10.16 1 Gib 14 Kankin 

Following along the text, the next Secondary-series number appears 
in D4-C5a and consists of 10 kins,' 11 uinals, 1 tun, and 1 katun; that 

1 The usual positions of the uinal and \m coefficients in D4a are reversed, the kin coefficient 10 standing 
above the uinal sign instead of at the left of it. The calculations show, however, that 10, not 11, is the kin 
coefficient. 



234 BXJEEATJ OF AMEEICAN ETHNOLOGY [BnLL. 57 

is, 1.1.11.10. Reducing this number to units of the first order and 
counting it forward from the date next preceding it in the text, that 
is, 1 Cib 14 Kankiu in C2b D2a, the new terminal date reached will 
be 4 Cimi 14 TJo, which the student will find recorded in D5-C6. 
Compare the day sign in D5 with figure 16, Ti, i, and the month 
sign in C6 with figure 19, 6, c. The Initial-series value of this new 
date may be calculated from the known Initial-series value of the 
preceding date : 

9.12.14.10.16 1 Cib 14 Kankin 
1. 1.11.10 

9.13.16. 4. 6 4 Cimi 14 Uo 

The third Secondary Series appears in El and consists of 15 kins,^ 8 
tiinals, and 3 tuns, or 3.8.15. Reducing this number to units of the 
first order and counting it forward from the date next preceding it 
in the text, 4 Cimi 14 TJo, in D5-C6, the new terminal date reached 
will be 11 Imix 14 Yax, which the student will find recorded in E2 F2. 
The day sign in E2 appears, as is very unusual, as a head variant of 
which only the headdress seems to show the essential element of the 
day sign Imix. Compare E2 with figure 16, a, h, also the month 
sign in F2 with figure 19, q, r. The Initial Series of this new terminal 
date may be calculated as above : 

9.13.16. 4. 6 4 Cimi 14 TJo 

3. 8.15 
9.13.19.13. 1 11 Imix 14 Yax 

The fourth and last Secondary Series in this text follows in F6 and 
consists of 19 kins and 4 uinals, that is, 4.19. Reducing this number 
to imits of the first order and counting it forward from the date next 
preceding it in the text, 11 Imix 14 Yax in E2 F2, the new terminal 
date reached will be 6 Ahau 13 Muan, which the student will find 
recorded in F7-F8. Compare the month sign in F8 with figure 19, 
a' i'. But the gljrph following this date in F9 is very clearly an 
ending sign; note the hand, tassel-Hke postfix, and subfixial element 
showing the ciu-l infix, all of which are characteristic ending elements 
(see figs. 37, l-q, and 54). Moreover, in FlO is recorded "the end 
of Katim 14." Compare the ending prefix in this glyph with figure 
37, a-Ji. This would seem to indicate that the date in F7-F8, 6 Ahau 
13 Muan, closed Katun 14 of Cycle 9 of the Long Count. Whether 
this be true or not may be tested by finding the Initial-series value 
corresponding to 6 Ahau 13 Muan, as above: 

9.13.19.13. 1 11 Imix 14 Yax 

•4.19 
9.14. 0. 0. 6 Ahau 13 Muan 

1 In this number alao the positions of the uinal and kin coefficients are reversed. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 24 




ir-T- 



zi 






fGrmJ 







(( 




du 








ElSfef 









INITIAL SERIES, SECONDARY SERIES, AND PERIOD-ENDING DATES 
ON STELA E (WEST SIDE), QUIRIGUA 



MOHLEY] INTBODUCTION TO STUDY OP MAYA HIEROGLYPHS 235 

This shows that the date 6 Ahau 13 Muan closed Katun 14, as glyphs 
F9-F10 declare. This may'also be verified by changing " the end of 
Katun 14" recorded in F9-F10 into its corresponding Initial-series 
value, 9.14.0.0.0, and solving for the terminal date. The day reached 
by these calculations will be 6 Ahau 13 Muan, as above. This text, in 
so far as it has been deciphered, therefore reads : 



9.12. 2. 0.16 


6 Cib 14 Yaxkin 


A1-A4, B7 


12.10. 




ClDl 


9.12.14.10.16 


1 Cib 14 Kankin 


C2b D2a 


1. 1.11.10 




D4-C5a 


9.13.16. 4. 6 


4 Cimi 14 Uo 


D5-C6 


3. 8.15 




El 


9.13.19.13. 1 


11 Imix 14 Yax 


E2F2 


4.19 




F6 


9.14. 0. 0. 


6 Ahau 13 Muan 


F7-F8 


End of Katun 14 




F9-F10 



The inscription just deciphered is worthy of special note for several 
reasons. In the first place, all its dates and numbers are not only 
exceedingly clear, thus facilitating their identification, but also unusu- 
ally regular, the niunbers being counted forward from the dates next 
preceding them to reach the dates next following them in every case; 
all these features make this text particularly well adapted for study 
by the beginner. In the second place, this inscription shows the 
three principal methods employed by the Maya in recording dates, 
that is, Initial-series dating. Secondary-series dating, and Period-end- 
ing dating, aU combined in the same text, the example of each one 
being, moreover, unusually good. Finally, the Initial Series of this 
inscription records identically the same date as Stela 1 at Piedras 
Negras, namely, 9.12.2.0.16 5 Cib 14 Yaxkin. Compare plate 23 
with plate 17. Indeed, these two monuments, Stelse 1 and 3, stand 
in front of the same building. All things considered, the inscription 
on Stela 3 at Piedras Negras is one of the most satisfactory texts 
that has been fotmd in the whole Maya territory. 

Another example showing the use of these three methods of dating 
in one and the same text is the inscription on Stela E at Quirigua, 
illustrated in plate 24 and figure 82.' This text begins with the Initial 
Series on the west side. The introducing glyph appears in A1-B3 
and is followed by the Initial-series number 9.14.13^4.17 in A4-A6. 
Reducing this number to units of the first order, remembering the 
correction in the ttm coefiicient in A5 noted below, and applying the 
rules previously given for solving Initial Series, the terminal date 

1 For the full text of this inscription, see Maudslay, 1889-1902: n, pis. 28-32. 

2 The student will note that 12, not 13, tuns are recorded in A5. As explained elsewhere Csee pp. 247, 248), 
this is an error on the part of the ancient scribe who engraved this inscription. The correct tun coefficient 
is 13, as used above. 



236 



BUREAU OF AMERICAN ETHNOLOGY 



[BULT>, 57 




:^j 



nsrtw 









c 

Q 










reached will be 12 Caban 5 Kayab. This the 
student 'will readily recognize in B6-B8b, 
the form in B8a being the "month sign 
indicator," l\ereshown with a head-variant 
coefficient 10. Compare B6 with figure 
16, a', &', and B8b with figure 19, d'-f. 
This Initial Series therefore should read 
as follows: 9.14.13.4.17 12 Caban 5 Kayab, 
Following down the text, there is reached 
in BlOb-Alla, a Secondary-series number 
consisting of 3 kins, 13 uinals, and 6 tuns, 
that is, 6.13.3. Counting this number for- 
ward from the date next preceding it in 
the text, 12 Caban 5 Kayab, the date 
reached will be 4 Abau 13 Yax, which the 
student .win find recorded in Bll. Com- 
pare the month form in Bllb with figure 
19, q, r. But since the Initial-series value 
of 12 Caban 5 Kayab is known, the Initial- 
series value of 4 Ahan 13_ Yax may be cal- 
culated from it as follows: 

9.14.13. 4.17 12 Caban 5 Kayab 

6.13. 3 
9.15. 0. 0. 4 Ahau 13 Yax 

The next Secondary-series number ap- 
pears in. Bl2, plate 24, B, and consists of 
6 kins, 14 uinals, and 1 tun, thatis, 1.14.6.' 
The student will find that all efforts to 
reach the next date recorded in the text, 
6 Cimi 4 Tzec in Al3b Bl3a, by counting 
forward 1.14.6 from 4 Ahau 13 Yax in Bll, 
the date next preceding this number, mil 
prove unsuccessful. However, by count- 
ing hackward 1.14.6 from 6 Cimi 4 Tzec, he 
will find the date from which the coimt 
proceeds is 10 Ahau 8 Chen, though this 
latter date is nowhere recorded in this text. 
We have seen elsewhere, on Stela F for ex- 
ample (pi. 19, A, B), that the date 6 Cimi 
4 Tzec corresponded to the Initial-series 
number 9. 15.6. 14.6 ; consequently, we may 
calciilate the position of the unrecorded 



Fia. 82. The Initial Series on Stela E 
(east side), Quirigua. 



1 This Secondary-series number is doubly irregular. In the 
first place, the kin and uinal coefflcients are reversed, the latter 
standing to the left of its sign instead of above, and in the second place, the uinal coefBoient, although It is 
14, has an ornamental dot between the two middle dots. 



MOBLit] INTRODUCTION TO STUDY OF MAYA IIIEEOGLYPHS 237 

date 10 Ahau 8 Chen in the Long Count from this known Initial 
Series, by subtracting ' 1.14.6 from it: 

9.15.6.14.6 6 Cimi 4 Tzec 

1.14.6 
9.1.5.5. 0.0 10 Ahau 8 Chen 

We now Hcc thiit tlicrc ure 5 tuns, that is, 1 hotun, not recorded here, 
namely, the hotun from 9.15.0.0.0 4 Ahau 13 Yax, to 9.15.5.0.0 10 
Ahau 8 Chen, and further, that the Secondary-series number 1.14.6 
in B12 is coimttnl from the unoxprcssc^d date 10 Ahau 8 Chen to reach 
the terminal date 6 Cimi 4 Tzec recorded in Al.3b Bl3a. 

Tlie next Secondary-sorios number appears in Al4b B14 and 
consists of 15 Idns, 16 uinals, 1 tim, and 1 katun, that is, 1.1.16.15. 
As in the preceding case, however, all efforts to reach the date fol- 
lowing this number, 11 Imix 19 Muan in Al5b Bl5a, by counting it 
forward from 6 Cimi 4 Tzec, the date next preceding it in the text, 
will prove unavailing. As before, it is necessary to count it tack- 
ward from 11 Imix 19 Muan to determine the starting point. Per- 
forming this operation, the starting point will be found to be the 
date 7 Cimi 9 Zotz. Since neither of these two dates, 11 Imix 19 
Muan and 7 Cimi 9 Zotz, occurs elsewlu're at Quirigua, we must leave 
their corresponding Initial-seiies values indeterminate for the present. 

Th(^ last vSecondary Series in this text is recorded in Al7b Bl7a 
and consists of 19 kins,^ 4 uinals, and 8 tuns. Reducing this number 
to units of the first order and counting it forward from the date next 
preceding it in the text, 11 Imix 19 Muan in Al5b Bl5a, the terminal 
date rc^aehed will be 13 Ahau 18 Cumhu, which the student will find 
recorded in A18. Compare the month sign with figure 19, g' , Ji'. 
But immediately following this date in Bl8a is Katun 17 and in the 
upper part of Bl'Sb the hand-denoting ending. These glyphs Al8 
and Bis would seem to indicate, therefore, that Katun 17 came to 
an end on the date 13 Ahau 18 Cumhu. That they do, may be proved 
beyond all doubt by changing tliis period ending into its corresponding 
IniLial-series number 9.17.0.0.0 and solving for the terminal date. 
This will be found to be 13 Ahau 18 Cumhu, which is recorded in 
A18. This latter date, therefore, liii,d the following position in the 
Long Count: 9.17.0.0.0 13 Ahau 18 Cumhu. But having determined 
the position of this latter date in the Long Count, that is, its Initial- 
series value, it is now possible to fix the positions of the two dates 
11 Imix 19 Muan and 7 Cimi 9 Zotz, which we were obliged to leave 
indeterminate above. Since the date 13 Ahau 18 Cumhu was derived 

1 Since we counted badtward 1.14.6 from 6 Clml 4 Tzec to reach 10 Ahau 8 Chen, we must subtract 1.14.6 
from the Initial-series value of 6 Clml 4 Tzec to reach the Initlal-serie.s value of 10 Ahau 8 Chen. 

2 It is obvious that tho kin and uinal ooofTicIonts are loversed In A 171) since the coelBcient above the uinal 
sign is very clearly 19, an impossible value for the uinal cocfllcient in the Inscriptions, 19 uinals always 
being written 1 tun, 1 uinal. Therefore the 19 must be the kin coefficient. See also p. 110, footnote 1. 



238 BUREAU OF AMEEICAN ETHNOLOGY [bull. 57 

by counting forward 8.4.19 from 11 Imix 19 Muan, the Initial-series 
value of the latter maybe calculated by subtracting 8.4.19 from the 
Initial-series value of the former: 

9.17. 0. 0. 13 Ahau 18 Cumlm 

8. 4.19 
9.16.11.13. 1 11 Imix 19 Muan 

And since the date 11 Imix 19 Muan was reached by counting for- 
ward 1.1.16.15 from 7 Cimi 9 Zotz, the Initial-series value of the latter 
may be calculated by subtracting 1.1.16.15 from the now known 
Initial-series value of the former : 

9.16.11.13. 1 11 Imix 19 Muan 

1. 1.16.15 
9.15. 9.14. 6 7 Cimi 9 Zotz 

Although this latter date is not recorded in the text, the date next 
preceding the number 1.1.16.15 is 6 Cimi 4 Tzec, which corresponded 
to the Initial Series 9.15.6.14.6 6 Cimi 4 Tzec, as we have seen, a 
date which was exactly 3 tuns earlier than 7 Cimi 9 Zotz, 9.15.9.14.6- 
9-.15.6.14.6 = 3.0.0. 

The inscription on the west side closes then in Al8 B18 with the 
record that Katun 17 ended on the date 13 Ahau 18 Cumhu. The 
inscription on the east side of this same monument opens with this 
same date expressed as an Initial Series, 9.17.0.0.0 13 Ahau 18 Cumhu. 
See figure 82, A1-A6, A7,i and AlO. 

The reiteration of this date as an Initial Series, when its position 
in the Long Count had been fixed unmistakably on the other side of 
the same monument by its record as a Period-ending date, together 
with the fact that it is the latest date recorded in this inscription, 
very clearly indicates that it alone designated the contemporaneous 
time of Stela E, and hence determines the fact that Stela E was a 
hotun-marker. This whole text, in so far as deciphered, reads as 
follows : 

West side: 9.14.13.' 4.17 12 Caban 5 Kayab Plate 24, ^,Al-B6,B8b 

6.13. 3 Plate24,^,B10b-Alla 
9.15. 0. 0. 4 Ahau 13 Yax Plate 24, A, Bll 

[5. 0. 0] Undeclared 

9.15. 5. 0. 10 Ahau 8 Chen 

1.14. 6 Plate 24, B, B12 
9.15. 6.14. 6 6 Cimi 4 Tzec Plate 24, B. Al3b B13a 

[3. 0. 0] Undeclared 

1 The first glyph of the Supplementary Series, BOa, yery irregularly stands between the kin period glyph 
and the day part of the terminal date. 

2 Incorrectly recorded as 12. See pp. 247, 248. 



MOKLEY] INTBODUCTION TO STUDY OP MAYA HIEROGLYPHS 



239 



9.15. 9.14. 6 

1. 1.16.15 

9.16.11.13. 1 

8. 4.19 

9.17. 0. 0. 

End of Katun 17 

East side: 9.17. 0. 0. 



7 Cimi 9 Zotz 



11 Imix 19 Muan 



13 Ahau 18 Cumhu 



13 Aliau 18 Cumhu 



Undeclared 
Plate 24, B, Al4b B14 
Plate24,5,Al5bB15a. 
Plate 24, B, Al7b B17a 
Plate 24, B, Al8 
Plate 24, B, B18 
Figure 82, A1-A6, A7, 
AlO 



Comparing the summary of the inscription on Stela E at Quirigua, 
just given, with the summaries of the inscriptions on Stelae J and F, 
and Zoomorph G, at the same city, all four of which are shown side 
by side in Table XVII,^ the interrelationship of these four monu- 
ments appears very clearly. 

Table XVII. INTERRELATIONSHIP OF DATES ON STEL^ E, P, AND J 
AND ZOOMORPH G, QUIRIGUA 



Date 


Stela J 


stela F 


stela E 


Zoomorpli 
G 


9.14.13. 4.17 


13 Caban 5 Kayab 


X 


X 


X 


X 


9.15. 0. 0. 


4 AUau 13 Yax 


- 


X 


X 


- 


9.15. 5. 0. 


10 Ahau 8 Chen 


X 


- 


X 


- 


9.15. 6.14. 6 


6 Cimi 4 Tzec 


X 


X 


X 


X 


9.15. 9.14. 6 


7 Cimi 9 Zotz 


- 


- 


X 


- 


9.15.10. 0. 


3 Ahau 3 Mol 


- 


X 


- 


- 


9.16. 5. 0. 


8 AHAU 8 ZOTZ 


X 


- 


- 


- 


9.16.10. 0. 


1 AHAtr 3 ZIP 


- 


X 


- 


- 


9.16.11.13. 1 


11 Imix 19 Muan 


- 


- 


X 


- 


9.17. 0. 0. 


13 AHATT 18 CUMHTJ 


- 


- 


X 


- 


9.17.18. 0. 


S AHAU 3 MUAN 


- 


- 


- 


X 



In spite of the fact that each one of these four monuments marks a 
different hotun in the Long Count, and consequently dates from a 
different period, all of them go back to the same date, 9.14.13.4.17 
12 Caban 5 Kayab, as their original starting point (see above). This 
date would almost certainly seem, therefore, to indicate some very 
important event in the annals of Quirigua. Moreover, since it is 
the earliest date found at this city which can reasonably be regarded 
as having occurred during the actual occupancy of the site, it is not 
improbable that it may represent, as explained elsewhere, the time 
at which Quirigua was founded.^ It is necessary, however, to cau- 

1 In this table the numbers showing the distances have been omitted and all dates are shown in terms 
of their corresponding Initial-series numbers, in order to facilitate their comparison. The contempo- 
raneous date of each monument is given in bold-faced figures and capital letters, and the student will 
note also that this date not only ends a hotun in each case but is, further, the latest daLe in each text. 

2 The Initial Series on the west side of Stela D at Quirigua is 9.16.13.4.17 8 Caban 5 Yaxkln, which was 
just 2 katuns later than 9.14.13.4.17 12 Caban B Kayab, or, in other words, the second katun anniversary. 
If the term armiversary may be thus used, of the latter date. 



240 BUKBAU OF AMEEICAN ETHNOLOGY [boll. 57 

tion the student that the above explanation of the date 9.14.13.4.17 
12 Caban 5 Kayab, or indeed any other for that matter, is m the 
present state of our knowledge entirely a matter of conjecture. 

Passing on, it will be seen from Table XVII that two of the monu- 
ments, namelv, Stel« E and F, bear the date 9.15.0.0.0 4 Alan 3 
Yax, and two others, Stelse E and J, the date 9.15.5.0.0 10 Ahan 8 
Chen, one hotun later. All four come together again, however, 
with the date 9.15.6.14.6 6 Cimi 4 Tzec, which is recorded on each. 
This date, like 9.14.13.4.17 12 Caban 5 Kayab, designates probably 
another important event in Quirigua history, the nature of which, 
however, again escapes us. After the date 9.15.6.14.6 6 Cimi 4 Tzec, 
these monuments show no further correspondences, and we may pass 
over the intervening time to their respective closing dates with but 
scant notice, with the exception of Zoomorph G, which records a 
haK dozen dates in the hotun that it marks, 9.17.15.0.0 5 Ahau 3 
Muan. (These latter are omitted from Table XVII.) 

This concludes the presentation of Initial-series, Secondary-aeries, 
and Period-ending, dating, with which the student should be suJBi- 
ciently familiar by this time to continue his researches independently. 

It was explained (see p. 76) that, when a Secondary-series date 
could not be referred ultimately to either an Initial-series date 
or a Period-ending date, its position in the Long Count could 
not be determined with certainty, and furthermore that such a date 
became merely one of the 18,980 dates of the Calendar Round and 
could be fixed only within a period of 52 years. A few examples of 
Calendar-round dating are given in figure 83 and plate 25. In 
figure S3 , .4, is shown a part of the inscription on Altar M at Quirigua.' 
In Al Bl appears a number consisting of kins, 2 viinaJs, and 3 tuns, 
that is, 3.2.0, and following this m A2b B2, the date 4 Ahau 13 Yax, 
and in A3b B3 the date 6 Ahau 18 Zac. Compare the month glyphs 
in B2 and B3 with q and r, and s and t, respectively, of figure 19. 
This has every appearance of being a Secondary Series, one of the 
two dates being the starting point of the number 3.2.0, and the 
other its terminal date. Reducing 3.2.0 to units of the first order, 
we hare : 

Bl =3X360 = 1,080 
Al=2x 20= 40 
Al=OX 1= 

1, 120 

Counting this number forward from 4 Ahau 13 Yax, the nearest date 
to it in the text, the terminal date reached -vnH be fovmd to be 6 Ahau 
18 Zac, the date which, we have seen, was recorded in A3b B3 It 

1 For the tiill text of tliis inscription, see Maudslay, 1889-1902; n, pi. so. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 25 




CALENDAR-ROUND DATES ON ALTAR 5, TIKAL 



MOHLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 



241 



is clear, therefore, that this text records the fact that 3.2.0 has been 
counted forward from the date 4 Ahau 13 Yax and the date 6 Ahau 
18 Zac has been reached, but there is nothing given by means of 
which the position of either of these dates in the Long Count can be 
determined; consequently either of these dates will be foimd recur- 
ring like any other Calendar-round date, at intervals of every 52 
years. In such cases the first assumption to be made is that one of 
the dates recorded the close of a hotun, or at least of a tun, in Cycle 
9 of the Long Count. The reasons for this assumption are quite ob- 




oa^g(^0^ 








A B 

F:q. 83. . Calendar-round dates: A, Altar M, Quirigua; B, Altar Z, Copan. 

vious. The overwhelmiog majority of Maya dates fall in Cycle 9, and 
nearly all inscriptions have at least one date which closed some hotun 
or tvm of that cycle. Referring to Goodman's Tables, La which the 
tun endtags of Cycle 9 are given, the student will find that the date 
4 Ahau 13 Yax occurred as a tim ending in Cycle 9, at 9.15.0.0.0 
4 Ahau 13 Yax, ia which position it closed not only a hotim but also 
a kattm". Hence, it is probable, although the fact is not actually 
recorded, that the Initial-series value of the date 4 Ahau 13 Yax in 
this text is 9.15.0.0.0 4 Ahau 13 Yax, and if this is so the Initial-series 
value of the date 6 Ahau 18 Zac will be : 





9.15.0.0.0 4 Ahau 13 Yax 




3.2.0 




9.15.3.2.0 6 Ahau 18 Zac 


43508°- 


-Bull. 57—15 16 



242 BTJEEAXJ OP AMEEICAN ETHNOLOGY [BULL. 57 

In the case of this particular text the Initial-series value 9.15.0.0.0 
might have been assigned to the date 4 Ahau 13 Yax on the ground 
that this Initial-series value appears on two other monuments at 
Quirigua, namely, Stelae E and F, with this same date. 

In figure 83, B, is shown a part of the inscription from Altar Z at 
Copan.^ In Al Bl appears a number consisting of 1 kin, 8 uinals 
and 1 ttm, that is, 1.8.1, and following this in B2-A3 is the date 13 
Ahau 18 CumhTi, but no record of its position in the Long Count. 
If 13 Ahau 18 Cumhu is the terminal date of the number 1.8.1 the 
starting point can be calculated by coimting this number backward 
givmg the date 12 Cauac 2 Zac. On the other hand, if 13 Ahau 18 
Cumhu is the starting point, the terminal date reached by counting 
1.8.1 forward will bo 1 Imix 9 Mol. However, since an ending prefix 
appears just before the date 13 Ahau 18 Cumhu in A2 (compare fig. 
37, a-h), and smce another, though it must be admitted a very unusual 
ending sign, appears just after this date in A3 (compare the prefix 
of B3 with the prefix of fig. 37, o, and the subfix with the subfixes 
of l-n and g of the same figure), it seems probable that 13 Ahau 18 
Cumhu is the terminal date and also a Period-ending date. Eeferring 
to Goodman's Tables, it will be found that the only tun in Cycle 9 
which ended with the date 13 Ahau 18 Cumhu was 9.17.0.0.0 13 Ahau 
18 Cumhu, which not only ended a hotim but a katun as well.^ If 
this is true, the imrecorded starting point 12 Cauac 2 Zac can be 
shown to have the following Initial-series value : 

9.17. 0.0. 13 Ahau 18 Cumhu 

1.8. 1 Backward 
9.16.18.9.19 12 Cauac 2 Zac 

In each of the above examples, as we have seen, there was a date 
which ended one of the katuns of Cycle 9, although this fact was not 
recorded in connection with either. Because of this fact, however 
we were able to date both of these monuments with a degree of prob- 
ability amoimting almost to certainty. In some texts the student 
will find that the dates recorded did not end any katun, hotun or 
even tun, in Cycle 9, or in any other cycle, and consequently such 
dates can not be assigned to their proper positions in the Long Count 
by the above method. 

The inscription from Altar 5 at Tikal figured in plate 25 is a case 
in point. This text opens with the date 1 Muluc 2 Muan in glyphs 
1 and 2 (the first glyph or starting point is indicated by the star). 

1 For the full text of this inscription, see Maudslay, 1889-1902: i, pi. 112. 
a Every fourth hotun ending in the Long Count was a katun ending at the same time, namely: 
9.16. 0.0.0 2 Ahau 13 Tzec 

9.16. 5.0.0 8 Abau 8 Zotz 
9.16.10.0.0 lAhau 3 Zip 
9.16.15.0.0 7 Ahau 18 Pop 

9.17. 0.0.0 13 Ahau 18 Cumhu 
etc. 



MOELBY] INTEODUCTION TO STUDY OF MAYA JIIEROGLYPHS 243 

Compare glyph 1 with figure 16, m, n, and glyph 2 with figiire 19, 
a', I'. In glyphs 8 and 9 appears a Secondary-series number con- 
sisting of 18 kins, 11 uiaals, and 11 tuns (11.11.18). Reducing this 
number to units of the first order and counting it forward from the 
date next preceding it in the text, 1 Muluc 2 Muan in glyphs 1 and 2, 
the terminal date reached will be 13 Manik Xul, which the student 
will find recorded in glyphs 10 and 11. Compare glyph 10 with 
figure 16, j, and glyph 11 with figure 19, i, j. The next Secondary- 
series number appears in glyphs 22 and 23, and consists of 19 kins, 
9 uinals, and 8 tuns (8.9.19). Reducing this to imits of the first order 
and co\mting forward from the date next preceding it in the text, 13 
Manik Xul in glyphs 10 and 11, the terminal date reached will be 
11 Cimi 19 Mac, which the student will find recorded in glyphs 24 
and 25. Compare glyph 24 with figure 16, Ji, i, and glyph 25 with 
figure 19, w, x. Although no number appears in glyph 26, there 
follows in glyphs 27 and 28 the date 1 Muluc 2 Eankin, which the 
student will find is just three days later than 11 Cimi 19 Mac, that 
is, one day 12 Manik Kankin, two days 13 lamat 1 Kankin, and 
three days 1 Muluc 2 Kankin. 

In spite of the fact that all these numbers are counted regularly 
from the dates next preceding them to reach the dates next following 
them, there is apparently no glyph in this text which will fix the 
position of any one of the above dates in the Long Coxmt. Moreover, 
since none of the day parts show the day sign Ahau, it is evident 
that none of these dates can end any uinal, tun, katun, or cycle in 
the Long Cornit, hence their positions can not be determined by the 
method used in fixing the dates in figure 83, A and B. 

There is, however, another method by means of which Calendar- 
ro\md dates may sometimes be referred to their proper positions in 
the Long Count. A monument which shows only Calendar-roimd 
dates may be associated with another monument or a building, the 
dates of which are fixed in the Long Count. In such cases the fixed 
dates usually will show the positions to which the Calendar-round 
dates are to be referred. 

Taking any one of the dates given on Altar 5 in plate 25, as the last, 
1 Muluc 2 Kankin, for example, the positions at which this date 
occurred in Cycle 9 may be determined from Goodman's Tables to 
be as follows: 

9. 0.16. 5.9 1 Muluc 2 Kankin 

9. 3. 9. 0.9 1 Muluc 2 Kankin 

9. 6. 1.13.9 1 Muluc 2 Kankin 

9. 8.14. 8.9 1 Muluc 2 Kankin 

9.11. 7. 3.9 1 Muluc 2 Kankin 

9.13.19.16.9 1 Muluc 2 Kankin 

9.16.12.11.9 1 Muluc 2 Kankin 

9.19. 5. 6.9 1 Muluc 2 Kankin 



244 BUREAU OF AMERICAN ETHNOLOGY [BULL. 57 

Next let us ascertain whether or not Altar 5 was associated with any- 
other monument or building at Tikal, the date of which is fixed 
unmistakably in the Long Count. Says Mr. Teobert Maler, the dis- 
coverer of this monument:' "A little to the north, fronting the north 
side of this second temple and very near it, is a masonry quadrangle 
once, no doubt, containing small chambers and having an entrance 
to the south. In the middle of this quadrangle stands Stela 16 in 
all its glory, still unharmed, and in front of it, deeply buried in the 
earth, we found Circular Altar 5, which was destined to become so 
widely renowned." It is evident from the foregoing that the altar 
we are considering here, called by Mr. Maler "Circular Altar 5," was 
found in connection with another monument at Tikal, namely, 
Stela 16. But the date on this latter moniunent has abeady been 
deciphered as "6 Ahau 13 Muan ending Katun 14" (see pi. 21, D; 
also p. 224), and this date, as we have seen, corresponded to the 
Initial Series 9.14.0.0.0 6 Ahau 13 Muan. 

Our next step is to ascertain whether or not any of the Initial- 
series values determined above as belonging to the date 1 Muluc 2 
Kankiu on Altar 5 are near the Initial Series 9.14.0.0.0 6 Ahau 13 
Muan, which is the Initial-series date corresponding to the Period- 
ending date on Stela 16. By comparing 9.14.0.0.0 with the Initial- 
series values of 1 Muluc 2 Kankin given above the student will find 
that the fifth value, 9.13.19.16.9, corresponds with a date 1 Muluc 2 
Kankin, which was only 31 days (1 uinal and 11 kins) earher than 
9.14.0.0.0 6 Ahau 13 Muan. Consequently it may be concluded that 
9.13.19.16.9 was the particular day 1 Muluc 2 Kankin which the 
ancient scribes had in mind when they engraved this text. From 
this known Initial-series value the Initial-series values of the other 
dates on Altar 5 may be obtained by calculation. The texts on Altar 
5 and Stela 16 are given below to show their close connection: 

Altar 5 

9.12.19.12. 9 1 Muluc 2 Muan glyphs 1 and 2 

11.11.18 glyphs 8 and 9 

9.13.11. 6. 7 13 Manik Xul glyphs 10 and 11 

8. 9.19 glyphs 22 and 23 

9.13.19.16. 6 11 Cimi 19 Mac glyphs 24 and 25 

(3) undeclared 

9.13.19.16. 9 1 Muluc 2 Kankin glyphs 27 and 28 

(1.11) (Time between the two monuments, 31 days.) 

Stela 16 
9.14.0.0.0 6 Ahau 13 Muan A1-A4 



1 Maler, 1911: No. 1, p. 40. 



MOKLBY] INTI^ODUCTION TO STUDY OF MAYA HIEROGLYPHS 



245 



Sometimes, however, monuments showing Calendar-round dates stand 
alone, and in guch cases it is almost impossible to fix their dates in the 
Long Count. At Yaxchilan in particular Calendar-round dating 
seems to have been extensively employed, and for this reason less 
progress has been made there than elsewhere in deciphering the 
inscriptions. 

Eeroes in the Originals 

Before closing the presentation of the subject of the Maya inscrip- 
tions the writer has thought it best to insert a few texts which show 



ffS^ 




^o(^ on 


fe- 


Gi)Cii)C^ OU 


Uc2:»is 











Fig. 84. 



Texts showing actual errors in the originals: A, Lintel, Yaxchilan; i?, Altar Q, Copan; C, 
Stela 23, Naranjo. 



actual errors in the originals, mistakes due to the carelessness or over- 
sight of the ancient scribes. 

Errors in the original texts may be divided into two general classes : 
(1) Those which are revealed by inspection, and (2) those which do 
not appear until after the indicated calculations have been made 
and the results fail to agree with the glyphs recorded. 

An example of the first class is illustrated in figure 84, A. A very 
cursory inspection of this text — an Initial Series from a lintel at Yax- 
chilan — will show that the uinal coefiicient in Cl represents an impos- 
sible condition- from the Maya point of view. This glyph as it stands 



246 BUREAU OP AMEEICAN ETHNOLOGY [bull. 57 

unmistakably records 19 uinals, a number which had no existence in 
the Maya system of numeration, smce 19 uinals are always recorded 
as 1 tun and 1 uinal.^ Therefore the coefficient in Cl is incorrect oa 
its face, a fact we have been able to determine before proceeding with 
the calculation indicated. If not 19, what then was the coefficient 
the ancient scribe should have engraved in its place ? Fortunately 
the rest of this text is unusually clear, the Initial-series number 
9.15.6. ?.l appearing in Bl-Dl, and the terminal date which it 
reaches, 7 Imix 19 Zip, appearing in C2 D2. Compare C2 with figure 
16, a, b, and D2 with figure 19, d. We know to begin with that the 
uinal coefficient must be one of the eighteen numerals to 17, inclu- 
sive. Trying first, the number will be 9.15.6.0.1, which the student 
will find leads to the date 7 Imix 4 Chen. Our first trial, therefore, 
has proved unsuccessful, since the date recorded is 7 Imix 19 Zip. 
The day parts agree, but the month parts are not the same. This 
month part 4 Chen is useful, however, for one thing, it shows us how 
far distant we are from the month part 19 Zip, which is recorded. 
It appears from Table XV that in counting forward from position 
4 Chen just 260 days are required to reach position 19 Zip. Conse- 
quently, our first trial number 9.15.6.0.1 falls short of the number neces- 
sary by just 260 days. But 260 days are equal to 13 uinals; therefore 
we must increase 9.15.6.0.1 by 13 uinals. This gives us the number 
9.15.6.13.1. Reducing this to units of the first order and solving for 
the terminal date, the date reached will be 7 Imix 19 Zip, which agrees 
with the date recorded in C2 D2. We may conclude, therefore, that 
the uinal coefficient inCl should have been 13, instead of 19 as recorded. 
Another errdr of the same kind — that is, one which may be detected 
by inspection — is shown in figure 84, B. Passing over glyphs 1, 2, 
and 3, we reach in glyph 4 the date 5 Kan 13 Uo. Compare the 
upper half of 4 with figure 16,/, and the lower half with figure 19, 1, c. 
The coefficient of the month sign is very clearly 13, which represents 
an impossible condition when used to indicate the position of a day 
whose name is Kan ; for, according to Table VII, the only positions 
which the day Kan can ever occupy in any division of the year 
are 2, 7, 12, and 17. Hence, it is evident that we have detected an 
error in this text before proceeding with the calculations indicated. 
Let us endeavor to ascertain the coefficient which should have been 
used with the month sign in glyph 4 instead of the 13 actually recorded. 
These glyphs present seemingly a regular Secondary Series, the start- 
ing point being given in 1 and 2, the number in 3, and the terminal 
date in 4. Counting this number 3.4 forward from the starting 
point, 6 Ahau 13 Kayab, the terminal date reached will be 5 Kan 
12 TJo. Comparing this with the terminal date actually recorded, 
we find that the two agree except for the month coefficient. But 
since the date recorded represents an impossible condition, as we 

1 For a seeming exception to tliis statement, in the codices, see p. 110, footnote 1. 



MOBLBY] INTRODUCTION TO STUDY OF MATA HIEROGLYPHS 24Y 

have shown, we are justified in assuming that the month coefficient 
which should have been used in glyph 4 was 12, instead of 13. In 
other words, the craftsman to whom the sculpturing of this inscrip- 
tion was intrusted engraved here 3 dots instead of 2 dots, and 1 orna- 
mental crescent, which, together with the 2 bars present, would have 
given the month coefficient determined by calculation, 12. An error 
of this kind might occur very easily and indeed in many cases may 
be apparent rather than real, being due to weathering rather than to 
a mistake in the original text. 

Some errors in the inscriptions, however, can not be detected by 
inspection, and develop only after the calculations indicated have 
been performed, and the results are foimd to disagree with the glyphs 
recorded. Errors of this kind constitute the second class mentioned 
above. A case in point is the Initial Series on the west side of Stela 
E at Quirigua, figured in plate 24, A. In this text the Initial-series 
number recorded in A4-A6 is very clearly 9.14.12.4.17, and the ter- 
minal date in B6-B8b is equally clearly 12 Caban 5 Kayab. Now, if 
this number 9.14.12.4.17 is reduced to units of the first order and is 
counted forward from the same starting point as practically all other 
Initial Series, the terminal date reached will be 3 Caban 10 Kayab, 
not 12 Caban 5 Kayab, as recorded. Moreover, if the same number 
is counted forward from the date 4 Ahau 8 Zotz, which may have 
been another starting point for Initial Series, as we have seen, the 
terminal date reached will be 3 Caban 10 Zip, not 12 Caban 5 Kayab, 
as recorded. The inference is obvious, therefore, that there is some 
error in this text, since the number recorded can not be made to 
reach the date recorded. An error of this kind is difficult to detect, 
because there is no indication in the text as to which glyph is the one 
at fault. The first assumption the writer makes in such cases is 
that the date is correct and that the error is in one of the period- 
glyph coefficients. Referring to Goodman's Table, it wiU be found 
that the date 12 Caban 5 Kayab occurred at the following positions 
in Cycle 9 of the Long Count: 

9. 1. 9.11.17 12 Caban 5 Kayab 

9. 4. 2. 6.17 12 Caban 5 Kayab 

9. 6.15. 1.17 12 Caban 6 Kayab 

9. 9. 7.14.17 12 Caban 5 Kayab 

9.12. 0. 9.17 12 Caban 5 Kayab 

9.14.13. 4.17 12 Caban 5 Kayab 

9.17. 5.17.17 12 Caban 5 Kayab 

9.19.18.12.17 12 Caban 5 Kayab 

An examination of these values will show that the sixth in the list, 
9.14.13.4.17, is very close to the number recorded in our text, 
9.14.12.4.17. Indeed, the only diflference between the two is that 
the former has 13 tuns while the latter has only 12. The similarity 
between these two numbers is otherwise so close and the error in this 



248 BXJEEAU OF AMEEICAN ETHNOLOGY [BDLL. 57 

event would be so slight — the record of 2 dots and 1 ornamental 
crescent instead of 3 dots — that the conclusion is almost inevitable 
that the error here is in the tun coefficient, 12 having been recorded 
instead of 13. In this particular case the Secondary Series and the 
Period-endiag date, which follow the Initial-series number 
9.14.12.4.17, prove that the above reading of 13 tuns for the 12 
actually recorded is the one correction needed to rectify the error in 
this text. 

Another example indicating an error which can not be detected by 
inspection is shown in figure 84, C. In glyphs 1 and 2 appears the 
date 8 Eznab 16 Uo (compare glyph 1 with fig. 16, c', and glyph 2 
with fig. 19, 6, c). In glyph 3 follows a number consisting of 17 kins 
and 4 uinals (4.17). Finally, in glyphs 4 and 5 is recorded the date 
2 Men 13 Yaxkin (compare glyph 4 with fig. 16, y, and glyph 5 with 
fig. 19, Tc, I). This has every appearance of being a Secondary Series, 
of which 8 Eznab 16 TIo is the starting point, 4.17, the number to be 
counted, and 2 Men 13 Yaxkin the terminal date. Reducing 4.17 to 
imits of the first order and counting it forward from the start- 
ing point indicated, the terminal date reached will be 1 Men 13 
Yaxkin. This differs from the terminal date recorded in glyphs 
4 and 5 in having a day coefficient of 1 instead of 2. Since this 
involves but a very sUght change in the original text, we are probably 
justified in asstuning that the day coefficient in glyph 4 should have 
been 1 instead of 2, as recorded. 

One more example will suffice to show the kind of errors usually 
encountered in the inscriptions. In plate 26 is figured the Initial 
Series from Stela N at Copan. The introducing glyph appears in Al 
and is followed by the Initial-series number 9.16.10.0.0 ia A2-A6, 
all the coefficients of which are unusually clear. Reducing this to 
units of the first order and solving for the terminal date, the date 
reached will be 1 Ahau 3 Zip. This agrees with the terminal date 
recorded in A7-A15 except for the month coefficient, which is 8 in 
the text instead of 3, as determined by calculation. Assunodng that 
the date recorded is correct and that the error is in the coefficient of 
the period glyphs, the next step is to find the positions in Cycle 9 at 
which the date 1 Ahau 8 Zip occurred. Referring to Goodman's 
Tables, these will be found to be: 

9. 0. 8.11.0 1 Ahau 8 Zip 

9. 3. 1. 6.0 1 Ahau 8 Zip 

9. 5.14. 1.0 1 Ahau 8 Zip 

9. 8. 6.14.0 1 Ahau 8 Zip 

9.10.19. 9.0 1 Ahau 8 Zip 

9.13.12. 4.0 1 Ahau 8 Zip 

9.16. 4.17.0 1 Ahau 8 Zip 

9.18.17.12.0 1 Ahau 8 Zip 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 26 













lU ' 



t^,. 



l\ /-^Ml 



\ fiw: 



-T-p 







INITIAL SERIES ON STELA N, COPAN, SHOWING 
ERROR IN MONTH COEFFICIENT 



MOELBT] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 249 

The number in the above hst coming nearest to the number recorded 
in this text (9.16.10.0.0) is the next to the last, 9.16.4.17.0. But in 
order to reach this value of the date 1 Ahau 8 Zip (9.16.4.17.0) with 
the number actually recorded, two considerable changes in it are first 
necessary, (1) replacing the 10 tuns in A4 by 4 tims, that is, changing 

2 bars to 4 dots, and (2) replacing uinals in A5 by 17 uinals, that is, 
changing the sign to 3 bars and 2 dots. But these changes involve 
a very considerable alteration of the original, and it seems highly 
improbable, therefore, that the date here intended was 9.16.4.17.0 
1 Ahau 8 Zip. Moreover, as any other number in the above list 
involves at least three changes of the niunber recorded in order to 
reach 1 Ahau 8 Zip, we are forced to the conclusion that the error 
miist be in the terminal date, not in one of the coefficients of the 
period glyphs. Let us therefore assimie in our next trial that 
the Initial-series number is correct as it stands, and that the error 
lies somewhere in the terminal date. But the terminal date reached 
in counting 9.16.10.0.0 forward in the Long Coimt will be 1 Ahau 

3 Zip, as we have seen on the preceding page, and this date differs 
from the terminal date recorded by 5 — 1 bar in the month coefficient. 
It would seem probable, therefore, that the bar to the left of the month 
sign in Al5 should have been omitted, in which case the text would 
correctly record the date 9.16.10.0.0 1 Ahau 3 Zip. 

The student will note that in all the examples above given the 
errors have been in the numerical coefficients, and not in the signs 
to which they are attached; in other words, that although the 
numerals are sometimes incorrectly recorded, the period, day, and 
month glyphs never are. 

Throughout the inscriptions, the exceptions to this rule are so 
very rare that the beginner is strongly advised to disregard them al- 
together, and to assume when he ffiids an incorrect text that the error 
is in one of the numerical coefficients. It should be remembered 
also in this connection that errors in the inscriptions are exceed- 
ingly rare, and a glyph must not be condemned as incorrect until 
every effort has been made to explain it in some other way. 

This concludes the presentation of texts from the inscriptions. 
The student will have noted in the foregoing examples, as was stated 
in Chapter II, that practically the only advances made looking toward 
the decipherment of the glyphs have been on the chronological side. 
It is now generally admitted that the relative ages ' of most Maya 
monuments can be determined from the dates recorded upon them, 
and that the final date in almost every inscription indicates the time 
at or near which the monument bearing it was erected, or at least 
formally dedicated. The writer has endeavored to show, moreover, 

1 That is the age of one compared with the age of another, without reference to their actual age as 
expressed in terms of our own chronology. 



250 BUEEAU OF AMERICAN ETHNOLOGY [bull. 57 

that many, if indeed not most, of the monuments, were "time mark- 
ers" or "period stones," in every way similar to the "period stones" 
which the northern Maya are known to ^ have erected at regularly 
recurring periods. That the period which was used as this chrono- 
logical unit may have varied in different locahties and at different 
epochs is not at all improbable. The northern Maya at the time of 
the Spanish Conquest erected a "period stone" every katun, while 
the evidence presented in the foregoing texts, particularly those from 
Quirigua and Copan, indicates that the chronological unit in these 
two cities at least was the hotun, or quarter-katun period. What- 
ever may have been the chronological unit used, the writer believes 
that the best explanation for the monuments found so abundantly 
in the Maya area is that they were "period stones," erected to com- 
memorate or mark the close of successive periods. 

That we have succeeded in deciphering, up to the present time, only 
the calendric parts of the inscriptions, the chronological skeleton 
of Maya history as it were, stripped of the events which would vitalize 
it, should not discourage the student nor lead him to minimize the 
importance of that which is already gained. Thirty years ago the 
Maya inscriptions were a sealed book, yet to-day we read in the 
glyphic writing the rise and fall of the several cities in relation to one 
another, and follow the course of Maya development even though we 
can not yet fill in the accompanying backgroimd. Future researches, 
we may hope, will reconstruct this background from the undeciphered 
glyphs, and will reveal the events of Maya history which alone can 
give the corresponding chronology a human interest. 

1 See Chapter II for the discussion of this point and the quotations from contemporary authorities, both 
Spanish and native, on which the above statement is based. 



Chapter VI 

THE CODICES 

The present chapter will treat of the apphcation of the material 
presented in Chapters III and IV to texts drawn from the codices, 
or hieroglyphic manuscripts; and since these deal in great part with 
the tonalamatl, or sacred year of 260 days, as we have seen (p. 31), 
this subject will be taken up first. 

Texts Recording Tonalamatls 

The tonalamatl, or 260-day period, as represented in the codices is 
usually divided into five parts of 52 days each, although tonala- 
matls of four parts, each containing 65 days, and tonalamatls of ten 
parts, each containing 26 days, are not at all uncommon. These 
divisions are further subdivided, usually into unequal parts, all the 
divisions in one tonalamatl, however, having subdivisions of the 
same length. 

So far as its calendric side is concerned,^ the tonalamatl may be 
considered as having three essential parts, as follows: 

1. A column of day signs. 

2. Red numbers, which are the coefficients of the day signs. 

3. Black numbers, which show the distances between the days 
designated by (1) and (2). 

The number of the day signs in (1), usually 4, 5, or 10, shows the 
number of parts into which the tonalamatl is divided. Every red 
number in (2) is used oncer with, every day sign in (1) to designate a 
day which is reached in counting one of the black numbers in (3) 
forward from another of the days recorded by (1) and (2). The 
most important point for the student to grasp in studying the Maya 
tonalamatl is the fundamental difference between the use of the red 
numbers and the black numbers. The former are used only as day 
coefficients, and together with the day signs show the days which 
begia the divisions and subdivisions of the tonalamatl. The black 
numbers, on the other hand, are exclusively time counters, which show 
only the distances between the dates indicated by the day signs and 
their corresponding coefficients among the red numbers. They show 
in effect the lengths of the periods and subperiods into which the 
tonalamatl is divided. 

' As explained on p. 31, tonalamatls were probably used by the priests in making prophecies or divina- 
tions. This, however, is a matter apart from their composition, that is, length, divisions, dates, and 
method of counting, which more particularly concerns us here. 

251 



252 BUEEAU OF AMERICAN ETHNOLOGY [bull. 57 

Most of the numbers, that is (2) and (3), in the tonalamatl are 
presented in a horizontal row across the page or pages ' of the manu- 
script, the red alternating with the black. In some instances, how- 
ever, the numbers appear in a vertical column or pair of columns, 
though in this case also the same alternation in color is to be ob- 
served. More rarely the numbers are scattered over the page indis- 
criminately, seemingly without fixed order or arrangement. 

It will be noticed in each of the tonalamatls given in the following 
examples that the record is greatly abbreviated or skeletonized. In 
the first place, we see no month signs, and consequently the days 
recorded are not shown to have had any fixed positions in the year. 
Furthermore, since the year positions of the days are not fixed, any 
day could recur at intervals of every 260 days, or, in other words, 
any tonalamatl with the divisions peculiar to it could be used m 
endless repetition throughout time, commencing anew every 260 
days, regardless of the positions of these days in succeeding years. 
Nor is this omission the only abbreviation noticed in the presentation 
of the tonalamatl. Although every tonalamatl contained 260 days, 
only the days commencing its divisions and subdivisions appear in 
the record, and even these are represented in an abbreviated form. 
For example, instead of repeating the numerical coefficients with each 
of the day signs in (1), the coefficient was written once above the 
column of day signs, and in this position was regarded as belong- 
ing to each of the different day signs in turn. It follows from this 
fact that all the main divisions of the tonalamatl begin with days the 
coefficients of which are the same. Concerning the beginning days 
of the subdivisions, a still greater abbreviation is to be noted. The 
day signs are not shown at all, and only their numerical coefficients 
appear in the record. The economy of space resulting from the 
above abbreviations in writing the days will appear very clearly in 
the texts to follow. 

In reading tonalamatls the first point to be determined is the name 
of the day with which the tonalamatl began. This will be found thus: 

Rule 1. To find the beginning day of a tonalamatl, prefix the first 
red number, which will usually be found immediately above the col- 
umn of the day signs, to the uppermost ^ day sign in the column. 

From this day as a starting point, the first black number in the text 
is to be counted forward; and the coefficient of the day reached wiU 
be the second red number in the text. As stated above, the day 
signs of the beginning days of the subdivisions are always omitted. 
From the second red number, which, as we have seen, is the coeffi- 

1 The codices are folded like a screen or fan, and when opened form a continuous strip sometimes several 
yards in length. As will appear later, in many cases one tonalamatl runs across several pages of the 
manuscript. 

2 If there should be two or more columns of day signs the topmost sign of the left-hand column is to be 
read first. 



MOELBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 253 

cient of the beginning day of the second, subdivision of the first divi- 
sion, the second black number is to be counted forward in order to 
reach the third red number, which is the coefl&cient of the day begin- 
ning the third subdivision of the first division. This operation is 
continued until the last black number has been counted forward from 
the red number just preceding it and the last red number has been 
reached. 

This last red number will be found to be the same as the first red 
number, and the day which the count will have reached wiU be shown 
by the first red number (or the last, since the two are identical) used 
with the second day sign in the column. And this latter day will be 
the beginning day of the second division of the tonalamatl. From 
this day the count proceeds as before. The black numbers are 
added to the red numbers immediately preceding them in each case, 
until the last red number is reached, which, together with the third 
day sign in the column, forms the beginning day of the third division 
of the tonalamatl. After this operation has been repeated imtU the 
last red nmnber in the last division of the tonalamatl has been 
reached — that is, the 260th day — the count wiU be found to have 
reentered itseK, or in other words, the day reached by counting for- 
ward the last black number of the last division will be the same as 
the beginning day of the tonalamatl. 

It follows from the foregoing that the sum of aU the black numbers 
multiplied by the number of day signs in the column — the number 
of main divisions in the tonalamatl — will equal exactly 260. If any 
tonalamatl fails to give 260 as the result of this test, it may be regarded 
as incorrect or irregular. 

The foregoing material may be reduced to the following: 

Rule 2. To find the coefficients of the beginning days of succeeding 
divisions and subdivisions of the tonalamatl, add the black numbers 
to the red numbers immediatelj' preceding them in each case, and, 
after subtracting aU the multiples of 13 possible, the resulting num- 
ber will be the coefficient of the beginning day desired. 

Rule 3. To find the day signs of the beginning days of the suc- 
ceeding divisions and subdivisions of the tonalamatl, count forward 
in Table I the black number from the day sign of the beginning day 
of the preceding division or subdivision, and the day name reached 
in Table I will be the day sign desired. If it is at the beginning of one 
of the nmin divisions of the tonalamatl, the day sign reached will be 
found to be recorded in the column of day signs, but if at the begin- 
ning of a subdivision it will be unexpressed. 

To these the test rule above given may be added : 

Rule 4. The sum of all the black numbers multiplied by the 
number of day signs in the column of day signs wiU equal exactly 260 
if the tonalamatl is perfectly regular and correct. 



254 BUKEAIT OF AMERICAN ETHNOLOGY [bull. 57 

In plate 27 is figured page 12 of the Dresden Codex. It wiU be 
noted that this page is divided into three parts by red division lines ; 
after the general practice these have been designated a, b, and c, a 
being applied to the upper part, i to the middle part, and c to the 
lower part. Thus "Dresden 12b" designates the middle part of 
page 12 of the Dresden Codex, and "Dresden 15c" the lower part of 
page 15 of the same manuscript. Some of the pages of the codices 
are divided into four parts, or again, into two, and some are not 
divided at all. The same description applies in all cases, the parts 
being lettered from top to bottom in the same manner throughout. 

The first tonalamatl presented will be that shown in Dresden 12b 
(see the middle division in pi. 27). The student will readily recog- 
nize the three essential parts mentioned on page 251 : (1) The column 
of day signs, (2) the red numbers, and (3) the black nimibers. Since 
there are five day signs in the column at the left of the page, it is 
evident that this tonalamatl has five main divisions. The first point 
to establish is the day with which this tonalamatl commenced. 
According to rule 1 (p. 252) this will be found by prefixing the first red 
number to the topmost day sign in the column. The first red number 
in Dresden 12b stands in the regular position (above the column of 
day signs), and is very clearly 1, that is, one red dot. A comparison 
of the topmost day sign in this column with the forms of the day signs 
in figure 17 will show that the day sign here recorded is Ix (see fig. 
17, t), and the opening day of this tonalamatl will be, therefore, 1 Ix. 
The next step is to find the beginning days of the succeeding subdi- 
visions of the first main division of the tonalamatl, which, as we have 
just seen, commenced with the day 1 Ix. According to rule 2 (p. 
253), the first black number — in this case 13, just to the right of and 
slightly below the day sign Ix — is to be added to the red munber 
immediately preceding it — in this case 1 — in order to give the coeffi- 
cient of the day beginning the next subdivision, aU 13s possible 
being first deducted from the resulting number. Fm-thermore, this 
coefficient wiU be the red number next following the black number. 

Applying this rule to the present case, we have : 

1 (first red number) -1-13 (next black number) =14. Deducting all 
the 13s possible, we have left 1 (14 — 13) as the coefficient of the 
day beginning the next subdivision of the tonalamatl. This number 
1 wiU be found as the red number immediately following the first 
black number, 13. To find the corresponding day sign, we must 
turn to rule 3 (p. 253) and count forward in Table I this same black 
number, 13, from the preceding day sign, in this case Ix. The day 
sign reached wiU be Manik. But since this day begins only a sub- 
division in this tonalamatl, not one of the main divisions, its day 
sign will not be recorded, and we have, therefore, the day 1 Manik, 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 27 




PAGE 12 OF THE DRESDEN CODEX, SHOWING 
TONALAMATLS IN ALL THREE DIVISIONS 



MOELI^T] INTRODUCTION TO STUDY OF MAYA HIEEOGLYPHS 255 

of which the 1 is expressed by the second red number and the name 
part Manik only indicated by the calculations. 

The beginning day of the next subdivision of the tonalamatl may 

now be calculated from the day 1 Manik by means of rules 2 and 3 

(p. 253) . Before proceeding with the calculation incident to this step 

it will be necessary Jfirst to examine the next black number in our 

tonalamatl. This will be foimd to be composed of this sign (*), ( ^^ 

to which 6 (1 bar and 1 dot) has been affixed. It was explained * 

on page 92 that in representing tonalamatls the Maya had to have a 

sign which by itself would signify the number 20, since numeration by 

position was impossible. This special character for the number 20 

was given in figure 45, and a comparison of it with the sign here under 

discussion will show that the two are identical. But in the present 

example the number 6 is attached to this sign thus: (**), C^j^ 

and the whole number is to be read 20 + 6=26. This ** 

number, as we have seen in Chapter IV, would ordinarily have been 

: written thus (f) : 1 unit of the second order (20 xmits of the first 

t order) +6 units of the first order = 26. As explained on page 

92, however, numeration by position — that is, columns of imits— 

was impossible in the tonalamatls, in which many of the niunbers 

appear in a horizontal row, consequently some character had to be 

devised which by itself would stand for the number 20. 

Returning to our text, we find that the "next black number" is 
26 (20 + 6), and this is to be added to the red number 1 next pre- 
ceding it, which, as we have seen, is an abbreviation for the day 
1 Manik (see rule 2, p. 253). Adding 26 to 1 gives 27, and deducting 
all the 13s possible, namely, two, we have left 1 (27 — 26); this num- 
ber 1, which is the coefficient of the beginning day of the next subdi- 
vision, will be found recorded just to the right of the black 26. 

The day sign corresponding to this coefficient 1 will be fotmd by 
counting forward 26 in Table I from the day name Manik. This will 
give the day name Ben, and 1 Ben will be, therefore, the beginning 
day of the next subdivision (the third subdivision of the first main 
division) . 

The next black niunber in our text is 13, and proceeding as before, 
this is to be added to the red ntunber next preceding it, 1, the abbre- 
viation for 1 Ben. Adding 13 to 1 we have 14, and deducting all the 
23s possible, we obtain 1 again (14-13), which is recorded just to 
the right of the black 13 (rule 2, p. 253).' Counting forward 13 in 
Table I from the day name Ben, the day name reached will be Cimi, 
and the day 1 Cimi will be the beginning day of the next part of the 
tonalamatl. But since 13 is the last black number, we should have 
reached in 1 Cimi the beginning day of the secorid main division of 

» In the original this last red dot has disappeared. The writer has inserted it here to avoid confusing 
the beginner in his first acquaintance with a tonalamatl. 



256 BUEEAU OF AMEEICAIT ETHNOLOGY [BULL. 57 

the tonalamatl (see p. 253), and this is found to be the case, since 
the day sign Cimi is the second in the colmnn of day signs to the left. 
Compare this form with figm-e 17, i, j. The day recorded is therefore 
1 Cimi. 

The first division of the tonalamatl under discussion is subdivided, 
therefore, into three parts, the first part commencing with the day 
1 Ix, containing 13 days; the second commencing with the day 1 
Manik, containing 26 days ; and the third commencing -vdth the day 
1 Ben, containing 13 days. 

The second division of the tonalamatl commences with the day 
1 Cimi, as we have seen above, and adding to this the first black 
number, 13, as before, according to rules 2 and 3 (p. 253), the begin- 
ning day of the next subdivision will be found to be 1 Cauac. Of 
this, however, only the 1 is declared (see to the right of the black 13). 
Adding the next black number, 26, to this day, according to the above 
rules the beginning day of the next subdivision will be found to be 
1 Chicchan. Of this, however, the 1 again is the only part declared. 
Adding the next and last black number, 13, to this day, 1 Chicchan, 
according to the rules just mentioned the beginning day of the next, 
or third, main division will be found to be 1 Eznab. Compare the 
third day sign in the column of day signs with the form for Eznab in 
figure 17, z, a'. The second division of this tonalamatl contains, 
therefore, three parts: The fiirst, commencing with the day 1 Cimi, 
containing 13 days; the second, commencing with the day 1 Cauac, 
containing 26 days; and the third, commencing with the day 1 
Chicchan, containing 13 days. 

Similarly the third division, commencing with the day 1 Eznab, 
could be shown to have three parts, of 13, 26, and 13 days each, com- 
mencing with the day 1 Eznab, 1 Chuen, and 1 Caban, respectively. 
It could be shown, also, that the fourth division commenced with the 
day 1 Oc (compare the fourth sign in the column of day signs with 
figure 17, o), and, further, that it had three subdivisions containing 
13, 26, and 13 days each, commencing with the days 1 Oc, 1 Akbal, 
and 1 Muluc, respectively. Finally, the fifth and last division of the 
tonalamatl will commence with the day 1 Ik. Compare the last day 
sign in the column of day signs with figure 17, c, d; and its three 
subdivisions of 13, 26, and 13 days each with the days 1 Ik, 1 Men, 
and 1 Imix, respectively. The student will note also that when the 
last black number, 13, has been added to the beginning day of the 
last subdivision of the last division, the day reached will be 1 Ix, the 
day with which the tonalamatl commenced. This period is con- 
tinuous, therefore, reentering itself immediately on its conclusion and 
commencing anew. 



MOKLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 257 

There follows below an outline ' of this particular tonalamatl: 



1st Division 2d Division 3d Division 4th Division 5th Division 



let part, 13 days, beginning 
with day 

2d part, 26 days, beginning 
with day 

3d part, 13 days, beginning 
with day 

Total number o£ days 



llx 

1 Manik 

1 Ben 

52 



1 Cimi 
1 Cauac 

1 Chicchan 

52 



1 Eznab 
1 Chuen 

1 Caban 

52 



lOc 

1 Akbal 

1 Muluc 

52 



Ilk 
1 Men 

1 Imix 

52 



Next tonalamatl: 1st Division, 1st part, 13 days, beginning with the day 1 Ix, etc. 

We may now apply rtile 4 (p. 253) as a test to this tonalamatl. 
Multiplying the smn of all the black niunbers, 13+26 + 13=52, by 
the nxmiber of day signs in the column of day signs, 5, we obtain 260 
(52 X 5), which proves that this tonalamatl is regular and correct. 

The student will note in the middle division of plate 27 that the 
pictures are so arranged that one picture stands under the first sub- 
divisions of all the divisions, the second picture under the second 
subdivisions, and the third under the third subdivisions. It has 
been conjectured that these pictures represent the gods who were the 
patrons or guardians of the subdivisions of the tonalamatls, under 
which each appears. In the present case the first god pictured is 
the Death Deity, God A (see fig. 3) . Note the fleshless lower j aw, the 
truncated nose, and the vertebrae. The second deity is unknown, 
but the third is again the Death God, having the same characteristics 
as the god in the first picture. The cloak worn by this deity in the 
third picture shows the crossbones, which would seem to have been 
an emblem of death among the Maya as among us. The glyphs 
above these pictures probably explain the nature of the periods to 
which they refer, or perhaps the ceremonies peculiar or appropriate 
to them. In many cases the name glyphs of the deities who appear 
below them are given; for example, in the present text, the second 
and sixth glyphs in the upper row ^ record in each case the fact that 
the Death God is figured below. 

The glyphs above the pictures offer one of the most promising 
problems in the Maya field. It seems probable, as just explanied, 
that the four or six glyphs which stand above each of the pictures ui 
a tonalamatl tell the meaning of the picture to which they are 
appended, and any advances made, looking toward their decipher- 
ing, will lead to far-reaching residts in the meaning of the nonnu- 

1 This and similar outlines which follow are to be read down in columns. 

2 The fifth sign in the lower row is also a sign of the Death God (see fig. 3). Note the eyelashes, suggesting 
the closed eyes of the dead. 

43508°— Bull. 57—15 17 



258 BUEEAU OF AMBEICAN- ETHNOLOGY [BULL. 57 

merical and noncalendric signs. In part at least they show the 
name glyphs of the gods above which they occur, and it seenas not 
unlikely that the remaining gl3T)hs may refer to the actions of the 
deities who are portrayed; that is, to the ceremonies in which they 
are engaged. More extended researches along this line, however, 
must be made before this question can be answered. 

The next tonalamatl to be examined is that shown in the lower 
division of plate 27, Dresden 12c. At first sight this would appear 
to be another tonalamatl of five divisions., like the preceding one, 
but a closer examination reveals the fact that the last day sign in 
the column of day signs is like the first, and that consequently there 
are only four different signs denoting four divisions. The last, or 
fifth sign, like the last red number to which it corresponds, merely 
indicates that after the 260th day the tonalamatl reenters itself and 
commences anew. 

Prefixing the first red mmiber, 13, to the first day sign, Chuen (see 
fig. 17, f, q), according to rule 1 (p. 262), the beginning day of the 
tonalamatl wiU be found to be 13 Chuen. Adding to this the first 
black number, 26, according to rules 2 and 3 (p. 253), the beguming 
day of the next subdivision wiU. be found to be 13 Caban. Since this 
day begins only a subdivision of the tonalamatl, however, its name 
part Caban is omitted, and merely the coefficient 13 recorded. Com- 
mencing with the day 13 Caban and adding to it the next black 
number in the text, again 26, according to rules 2 and 3 (p. 253), the 
beginning day of the next subdivision will be found to be 13 Akbal, 
represented by its coefficient 13 only. Adding the last black number 
in the text, 13, to 13 Akbal, according to the rules just mentioned, 
the beginning day of the next part of the tonalamatl will be found to 
be 13 Cib. And since the black 13 which gave this new day is the 
last black number in the text, the new day 13 Cib will be the begin- 
ning day of the next or sec<md division of the tonalamatl, and it will 
be recorded as the second sign in the column of day signs. Compare 
the second day sign in the column of day signs with figure 17, v, w. 

Following the above rules, the student •vidll have no difficulty in 
working out the beginning days of the remaining divisions and sub- 
divisions of this tonalamatl. These are given below, though the 
student is urged to work them out independently, using the follow- 
ing outline simply as a check on his work. Adding the last black 
number, 13, to the begiiming day of the last subdivision of the last 
division, 13 Eznab, will bring the coimt back to the day 13 Chuen 
with which the tonalamatl began: 



MOBLEY] INTRODUCTION TO STUDY OP MAYA HIEROGLYPHS 



259 



1st Division 



2d Division 



3d Division 



Uh Division 



iBt part, 26 days, beginning 
with day 

2d part, 26 days, beginning 
•with day , 

3d part, 13 days, beginning 
with day 

Total number of days 



13 Chuen 

13 Caban 

13 A]£bal 
65 



13 Cib 

13 Ik 

13 Lamat 
65 



13Imix 
13 Manik 

13 Ben 

65 ' 



13 Cimi 

13 Eb 

13 Eznab 
65 



Next tonalamatl: Ist division, 1st part, 26 days, beginning with the day 13 
Chuen, etc. 

Applying the test rule to this tonalamatl (see rule 4, p. 253), we 
have: 26+26 + 13 = 65, the sum of the black numbers, and 4 the 
number of the day signs in the column of day signs,^ 65X4 = 260, 
the exact number of days in a tonalamatl. 

The next tonalamatl (see the upper part of pi. 27, that is, Dresden 
12a) occupies only the latter two-thirds of the upper division, the 
black 12 and red 11 being the last black and red numbers, respec- 
tively, of another tonalamatl. 

The presence of 10 day signs arranged in two parallel columns of 
five each would seem at first to indicate that this is a tonalamatl of 
10 divisions, but it develops from the calculations that instead there 
are recorded here two tonalamatls of five divisions each, the first 
column of day signs designating one tonalamatl and the second 
another quite distinct therefrom. 

The first red numeral is somewhat effaced, indeed all the red has 
disappeared and only the black outline of the glj^ih remains. Its 
position, however, above the column of day signs, seems to indicate 
its color and use, and we aire reasonably safe in stating that the first 
of the two tonalamatls here recorded began with the day 8 Ahau. 
Adding to this the first black number, 27, the beginning day of the 
next subdivision will be found to be 9 Manik, neither the coefficient 
nor day sign of which appears in the text. Assuming that the calcu- 
lation is correct, however, and adding the next black number, 25 
(also out of place), to this day, 9 Manik, the beginning day of the 
next part will be 8 Eb. But since 25 is the last black number, 8 Eb 
will be the beginning day of the next main division and should appear 
as the second sign in the first column of day signs. Comparison of 
this form with figure 17, r, will show that Eb is recorded in this place. 



1 The last sign Chuen, as mentioned above, is only a repetition of the first sign, Indicating that the 
tonalamatl has re-entered itself. 



260 



BUREAU OF AMEBICAN ETHNOLOGY 



[BULL. 57 



In this manner all of the beginning days could be worked out as 
below: 



1st part, 27 days, beginning 
■with day 

2d part, 25 days, beginning 
with day ^ 

Total number of days 



1st Division 



8 Ah.au 

9 Manik 

52 



2d Division 



8£b 

9 Cauac 

52 



3d Division 



8 Kan 

9 Chuen 
52 



4tli Division 



8Cib 

9 Akbal 
52 



5tli Division 



8 Lamat 

9 Men 

52 



The application of rule 4 (p. 253) to this tonalamatl gives: 
5 X 52 = 260, the exact number of days in a tonalamatl. As previously 
explained, the second column of day signs belongs to another tonala^ 
matl, which, however, utilized the same red 8 as the first and the 
same black 27 and 25 as the first. The outline of this tonalamatl, 
which began with the day 8 Oc, follows: 



1st part, 27 days, begin- 
ning with day 

2d part, 25 days, begin- 
ning with day 

Total number of days in. . 



1st Division 



8 0c 

9 Caban 

52 



2d Division 



8Ik 

9 Muluc 

52 



3d Division 



Six 

Olmix 

52 



4th Division 



5tli Division 



8 Cimi 8 Eznab 



9 Ben 

52 



9 Chicchan 
52 



The application of rule 4 (p. 253) to this tonalamatl gives: 
5 X 52 = 260, the exact number of days in a tonalamatl. It is inter- 
esting to note that the above tonalamatl, beginning with the day 
8 Oc, commenced just 130 days later than the first tonalamatl, which 
began with the day 8 Ahau. In other words, the first of the two 
tonalamatls in Dresden 12a wag just half completed when the second 
one commenced, and the second half of the first tonalamatl began 
with the same day as the first half of the second tonalamatl, and 
vice versa. 

The tonalamatl in plate 28, upper division, is from Dresden 15a, 
and is interesting because it illiistrates how certain missing parts 
may be filled in. The first red number is missing and we can only 
say that this tonalamatl began with some day Ahau. However, 
adding the first black numbeff, 34, to this day ? Ahau, the day reached 
will be 13 Ix, of which only 13 is recorded.. Since 13 Ix was reached 
by counting 34 forward from the day with which the count must have 
started, by counting back 34 from 13 Ix the starting point will be 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 28 















PAGE 15 OF THE DRESDEN CODEX, SHOWING 
-j-QMA^I flMATiB |N ALL THREE DIVISIONS 



MOELBT] 



INTEODUCTION TO STUDY OP MAYA HIEROGLYPHS 



261 



found to be 5 Ahau, and we may supply a red bar above the column 
of the day signs. Adding the next black number, 18, to this day 
13 Ix, the beginning day of the next division will bo found to be 5 Eb, 
which appears as the second day sign in the column of day signs. , 

The last red number is 5, thus establishing as correct our restora- 
tion of a red 5 above the column of day signs. From here this tona- 
lamatl presents no unusual features and it may be worked as follows : 





1st Division 


2d Division 


3d Division 


4th Division 


6th Division 


let part, 34 days, beginning 
with dav 


5 Ahau 

13 Ix 

52 


6Eb 

13 Cimi 
52 


6 Kan 

13 Eznab 

52 


6Cib 

13 Oc 

52 


5 Xamat 


2d part, 18 days, beginning 
with, dav 


13 Ik 


Total number of days 


52 



Applying rule 4 (p. 253), we have: 5X52=260, the exact number 
of days in a tonalamatl. The next tonalamatl (see lower part of pi. 
28, that is, Dresden 15c) has 10 day signs arranged in two parallel 
coluimis of 5 each. This, at its face value, would seem to be divided 
into 10 divisions, and the calculations confirm the results of the pre- 
hminary inspection. 

The tonalamatl opens with the day 3 lamat. Adding to this the 
first black nimaber, 12, the day reached will be 2 Ahau, of which only 
the 2 is recorded here. Adding to 2 Ahau the next black number, 
14, the day reached will be 3 Ix. And since 14 is the last black num- 
ber, this new day will be the beginning of the next division in the 
tonalamatl and will appear as the upper day sign in the second col- 
umn.' Commencing with 3 Ix and adding to it the first black num- 
ber 12, the day reached will be 2 Cimi, and adding to this the next 
black number, 14, the day reached will be 3 Ahau, which appears as 
the second glyph in the first column. This same operation if carried 
throughout will give the following outline of this tonalamatl : 





1st Division 


2d Division 


3d Division 


4th Division 


5th Division 


1st part, 12 days, beginning 


3 Lamat 

2 ATiau 

26 


3Ix 

2 Cimi 
26 


3 Aliau 

2Eb 

26 


3 Cimi 

2 Eznab 

26 


3Eb 


2d part, 14 days, beginning 


2 Kan 


Total number of days 


26 



1 As previously stated, the order ol reading the glyphs in columns is from left to right and top to bottom. 



262 BUEEAtl 


OF AMERICAlSr ETHNOLOGY 

(Concluded) i 


[BULL. 57 




eth Division 


7tti Division 


8th Division 


9tli Division 


lOUi Division 


Ist part, 12 dayB, beginning 

with, day 

2d part, 14 days, beginning 


3 Ezuab 

2 0c 

26 


3 Eau 

2Cib 

26 


3 0c 

2Ik 

26 


3Cib 

2 Lamat 
26 


3Ik 
2 Ix 


Total number of days 


26 



Applying rule 4 (p. 253) to this tonalamatl, we have: 10 X 26 =260, 
the exact number of days in a tonalamatl. 

The tonalamatl which appears in the middle part on plate 28 — that 
is, Dresden 15b — extends over on page 16b, where there is a black 13 
and a red 1. The student wiU have little difficulty ia reaching the 
result which follows: The last day sign is the same as the first, and 
consequently this tonalamatl is divided into four, instead of five, 
divisions : 



1st Division 2d Division 3d Division 4th Division 



1st part, 13 days, beginning 

with, day 

2d part,^ 31 days, beginning 

with day 

3d part, 8 days, beginning 

with day 

4th part, 13 days, beginning 

with day 

Total number of days 



Ilk 
1 Men 
6 Cimi 

llx 

65 



1 Manik 
1 Ahau 
6 Chuen 

1 Cauac 

65 



lEb 

1 Chicchau 

6Cib 

lEan 

65 



1 Caban 

lOc 

6 Imix 

1 Muluc 
65 



Applying rule 4 (p. 253) to this tonalamatl, we have: 4X65 = 260, 
the exact number of days ia a tonalamatl. The tonalamatls hereto- 
fore presented have all been taken from the Dresden Codex. The 
following examples, however, have been selected from tonalamatls in 
the Codex Tro-Cortesianus. The student will note that the workman- 
ship in the latter manuscript is far inferior to that in the Dresden 
Codex. This is particularly true with respect to the execution of 
the glyphs. 

The first tonalamatl figured from the Codex Tro-Cortesianus (see 
pi. 29) extends across the middle part of two pages (Tro-Cor. 10b, 
lib). The four day signs at the left indicate that it is divided into 
four divisions, of which the first begins with the day 13 Ik.' Adding 
to this the first black number 9, the day 9 Chuen is reached, and pro- 
ceeding in this manner the tonalamatl may be outlined as follows : 



1 The right-hand dot of the 13 is effaced. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 29 





MIDDLE DIVISIONS OF PAGES 10 AND 11 OF THE CODEX 

TRO-CORTESIANO, SHOWING ONE TONALAMATL 

EXTENDING ACROSS THE TWO PAGES 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 30 




PAGE 113 OF THE CODEX TRO-CORTESIANO, SHOWING 
TONALAMATLS IN THE LOWER THREE SECTIONS 



MoBLitYl INTEODUCTION T6 STUDY OF MAYA HIEKOGLYPHS 263 



1st part, 9 days, beginning 

with day 

2d part, 9 days, beginning 

with day 

3d port, 10 days, beginning 

with day 

4th part, days, beginning 

with day 

5th i)art, 2 days, beginning 

with day 

6th part, 10 days, beginning 

with day 

7th part, 6 days, beginning 

with day 

8th part, 7 days, beginning 

with day 

9th part, 7 ■ days, beginning 

with day 

Total number of days 



lat Division 


2d Division 


3d Division 


4 th Division 


18 He 


13 Manik 


18 Eb 


18 Caban 


9 Chuen 


ecib 


9Imix 


9Ciml 


SAhau 


5 Chlcchan 


fiOc 


5 Men 


2 0o 


2 Men 


2AIiau 


2 Chioohan 


BClb 


Blmlx 


8Cimi 


8 Chuen 


10 Eznab 


10 Akbal 


10 Lamat 


10 Ben 


7 Lamat 


7 Ben 


7 Eznab 


7 Akbal 


12 Ben 


12 Eznab 


12 Akbal 


12 Lamat 


6Ahau' 


6 Chlochan' 


6 0ci 


6 Men' 


65 


65 


65 


65 



1 The manuscript has Inoorroctly 7. 

Applying rule 4 (p. 253) to this tonalamatl, we have: 4x65 = 260, 
the exact number of days in a tonalamatl. 

Another set of interesting tonalamatls is figured in plate 30, Tro- 
Cor., 102.' The first one on this page appears in the second division, 
102b, and is divided into five parts, as the column of five day signs 
shows. The order of reading is from left to right in the pair of 
number columns, as will appear in the following outline of this tona- 
lamatl : 





1st Division 


2d Division 


3d Division 


4th Division 


6th Division 


JhI, part, 2 days, begin- 












niiif? with day 


4 Manlk 


4 Cauao 


4 Chuen 


4 Akbal 


4 Men 


2d part, 7 days, begin- 












nint,' with day 


6 Muluo 


eimlx 


6 Ben 


6 Chicchan 


6 Caban 


H(l iiart, 2 days, begin- 












ning with day 


ISCib 


13 Lamat 


13 Ahau 


13 Eb 


13 Kan 


4th part, 10 days, bogin- 












nin^' with day 


2 Eznab 


2 0o 


2 Ik 


2Ix 


2Cimi 


5th part, 9 days, begin- 












ning with day 


12 Lamat 


12 Ahau 


12 Eb 


12 Kan 


12Clb 


6th part, 22 dayH, begin- 












ning with day 


8 Caban 


8 Muluo 


8Imlx 


8 Ben 


8 Chicchan 


Total number of days — 


52 


52 


62 


52 


52 



' In tho title ot plttto 30 the page number should road 102 Instead ol 113. 



264 



BUHEAU or AMERICAN ETHNOLOGY 



[BULL. 57 



Applying rule 4 (p. 253) to this tonalamatl, we have: 5x52 = 260, 
the exact number of days in a tonalamatl. The next tonalamatl on 
this page (see third division in pi. 29, that is, Tro-Cor., 102c) is inter- 
esting chiefly because of the fact that the pictures which went with 
the third and fourth parts of the five divisions are omitted for want 
of space. The outline of this tonalamatl follows: 



1st Division 



2d Division 



3d Division 



4th Division 



5th Division 



1st part, 17 daya, beginning 
with day 

2d part, 13 daya, beginning- 
with day 

3d part, 10 days, beginning 
with day 

4th part, 12 days, begin- 
ning with day 

Total number of days 



4 Ahau 
8 Caban 
8 0c 

5 Ahau 

52 



4Eb 

SMiiluc 

8Ik 

SEb 

52 



4 Kan 
8 Imiz 
8Ix 

5 Ean 

52 



4Cib 
8 Ben 
8 Cimi 

5Cib 

52 



4 Lamat 

8 Chicchan 
8 Eznab 

5 Lamat 
52 



Applying rule 4 (p. 253) to this tonalamatl, we have: 5 X 52 = 260, 
the exact number of days in a tonalamatl. The last tonalamatl in 
plate 29, Tro-Cor., 102d, commences with the same day, 4 Ahau, as 
the preceding tonalamatl and, like it, has five divisions, each of which 
begins with the same day as the corresponding division in the tona^. 
lamatl just given, 4 Ahau, 4 Eb, 4 Kan, 4 Gib, and 4 lamat. Tro-Cor. 
102d differs from Tro-Cor. 102c in the number and length of the parts 
into which its divisions are divided. 

Adding the first black number, 29, to the beginning day, 4 Ahau, 
the day reached will be 7 Muluc, of which only the 7 appears in the 
text. Adding to this the next black number, 24, the day reached 
will be 5 Ben. An examination of the text shows, however, that the 
day actually recorded is 4 Eb, the last red number with the, second 
day sign. This latter day is just the day before 5 Ben, and since the 
sum of the black numbers in this case does not equal any factor of 
260 (29 4-24 = 53), and since changing the last black number from 
24 to 23 would make the sum of the black numbers equal to a factor 
of 260 (29 -h 23 = 52), and would bring the count to 4 Eb, the day 
actually recorded, we are justified in assuming that there is an error 
in our original text, and that 23 should have been written here instead 
of 24. The outline of this tonalamatl, corrected as suggested, follows: 



MOBLET] INTEODtrCTlON TO STUDY OP MAYA HIEROGLYPHS 



265 



1st part, 29 days, beginning 
■with day 

2d part, 23 ' days, begin- 
ning with day 

Total number of days , 



1st Division 


2d Division 


3d Division 


4Aliau 


4Eb 


4 Kan 


7 Muluo 


7Imiz 


7 Ben 


52 


52 


52 



4lh Division 



4Cib 

7 Cliicchan 

52 



qtli Division 



4 Lamat 

7 Caban 

52 



1 Tile manuscript incorrectly has 24. 

Applying rule 4 (p. 253) to this tonalamatl, we have: 52 X 5 = 260, 
the exact number of days in a tonalamatl. 

The foregoing tonalamatls have been taken from the pages of the 
Dresden Codex or those of the Codex Tro-Cortesiano. Unfortunately, 
in the Codex Peresianus no complete tonalamatls remain, though one 
or two fragmentary ones have been noted. 

No matter how they are divided or with what days they begin, all 
tonalamatls seem to be composed of the same essentials : 

1. The calendric parts, made up, as we have seen on page 251, of 
(a) the column of day signs; (6) the red numbers; (c) the black 
numbers. 

2. The pictures of anthropomorphic figures and animals engaged 
in a variety of pursuits, and 

3. The groups of four or six glyphs above each of the pictures. 

The relation of these parts to the tonalamatl as a whole is practi- 
cally determined. The first is the calendric background, the chron- 
ological framework, as it were, of the period. The second and third 
parts amplify this and give the special meaning and significance to 
the subdivisions. The pictures represent in all probability the deities 
who presided over the several subdivisions of the tonalamatls in 
which they appear, and the glyphs above them probably set forth 
their names, as well as the ceremonies connected with, or the prog- 
nostications for, the corresponding periods. 

It will be seen, therefore, that in its larger sense the meaning of 
the tonalamatl is no longer a sealed book, and while there remains 
a vast amount of detail yet to be worked out the foundation has 
been laid upon which future investigators may build with confidence. 

In closing this discussion of the tonalamatl it may not be out of 
place to mention here those whose names stand as pioneers in this 
particular field of glyphic research. To the investigations of Prof. 
Ernst Forstemann we owe the elucidation of the calendric part of 
the tonalamatl, and to Dr. Paul Schellhas the identification of the 
gods and their corresponding name glyphs in parts (2) and (3), above. 
As pointed out at the beginning of this chapter, the most promising 



266 BtffeEAtT OF AMERICAN ETHNOLOGY tsuLL.S? 

line of research in the codices is the groups of glyphs above the 
pictures, and from their decipherment will probably come the deter- 
mination of the meaning of this interesting and unusual period. 

Texts Recoeding Initial Series 

Initial Series in the codices are unusual and indeed have been 
found, up to the present time, in only one of the three known Maya 
manuscripts, namely, the Dresden Codex. As represented in this 
manuscript, they differ considerably from the Initial Series heretofore 
described, all of which have been drawn from the inscriptions. This 
difference, however, is conj&ned to unessentials, and the system of 
counting and measuring time in the Initial Series from the inscrip- 
tions is identical with that in the Initial Series from the codices. 

The most conspicuous difference between the two is that in the 
codices the Initial Series are expressed by the second method, given 
on page 129, that is, numeration by position, while in the inscriptions, 
as we have seen, the period glyphs are used, that is, the first method, 
on page 105. Although this causes the two kinds of texts to appear 
very dissimilar, the difference is only superficial. 

Another difference the student will note is the absence from the 
codices of the so-called Initial-series "introducing glyph." In a few 
cases there seems to be a sign occupying the position of the intro- 
ducing glyph, but its identification as the Initial-series "introducing 
glyph" is by no means sure, and, moreover, as stated above, it does 
not occur in all cases in which there are Initial Series. ' 

Another difference is the entire absence from the codices of Sup- 
plementary Series; this count seems to be confined exclusively to the 
monuments. Aside from these points the Initial Series from the two 
sources differ but little. All proceed from identically the same start- 
ing point, the date 4 Alian 8 Cnmlm, and all have their terminal dates 
or related Secondary-series dates recorded immediately after them. 

The first example of an Initial Series from the codices wiU be found 
in plate 31 (Dresden 24), in the lower left>-hand corner, in the second 
column to the right. The Initial-series number here recorded is 
9.9.16.0.0, of which the zero in the 2d place (uinab) and the zero 
in the 1st place (Mns) are expressed by red numbers. This use of 
red numbers in the last two places is due to the fact that the zero 
sign in the codices is always red. 

The student will note the absence of all period glyphs from this 
Initial Series and will observe that the multiplicands of the cycle, 
katun, tun, uinal, and kin are fixed by the positions of each of the 
corresponding multipliers. By referring to Table XTV the values of 
the several positions in the second method of writing the numbers 
will be found, and using these with their corresponding coefficients 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 57 PLATE 31 




PAGE 24 OF THE DRESDEN CODEX, SHOWING 
INITIAL SERIES 



MOELET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 267 

in each case the Initial-series number here recorded may be reduced 
to units of the 1st order, as follows: 



9X144,000 = 1,296,000 
9 X 7, 200 = 64, 800 
16 X 360= 5,760 
Ox 20 = 

OX 1= 



1,366,560 



Deducting from this number all the Calendar Rounds possible, 72 
(see Table XVI), it maybe reduced to zero, since 72 Calendar Rounds 
contain exactly 1,366,560 units of the first order. See the preliminary 
rule on page 143. 

Applying rules 1, 2, and 3 (pp. 139, 140, and 141) to the remainder, 
that is, 0, the terminal date of the Initial Series will be found to be 
4 Ahau 8 CnmlLn, exactly the same as the starting point of Maya 
chronology. This must be true, since counting forward from the 
date 4 Ahau 8 Cumliu, the date 4 Ahau 8 Cumliu will be reached. 
Instead of recording this date immediately below the last period of 
its Initial-series number, that is, the kins, it was written below the 
number just to the left. The terminal date of the Initial Series we 
are discussing, therefore, is 4 Ahau 8 Cumhu, and it is recorded just 
to the left of its usual position in the lower left-hand corner of plate 
31. The coefficient of the day sign, 4, is effaced but the remaining 
parts of the date are perfectly clear. Compare the day sign Ahau 
with the corresponding form in figure 17, c', d' , and the month sign 
Cumhu with the corresponding form in figure 20, 2-6'. The Initial 
Series here recorded is therefore 9.9.16.0.0 4 Ahau 8 Cumhu. Just 
to the right of this Initial Series is another, the number part of which 
the student will readily read as follows: 9.9.9.16.0. Treating this 
in the usual way, it may be reduced thus : 

9X144,000 = 1,296,000 
9 X 7, 200 = 64, 800 
9X 360= 3,240 

16 X 20= 320 

OX 1= 



1, 364, 360 



Deducting from this number all the Calendar Rounds possible, 71 
(see Table XVI), it maybe reduced to 16,780. Applying to this 
number rules 1, 2, and 3 <pp. 139, 140, and 141, respectively), its 
terminal date will be found to be 1 Ahau 18 Kayab; this date is 
recorded just to the left below the kin place of the preceding Initial 



268 BITEEAXT OF AMEEICAN ETHITOLOGY tBtiLL. 57 

Series. Compare the day sign and month sign of this date with 
figures 17, c' , d' , and 20, x, y, respectively. This second Initial 
Series in plate 31 therefore reads 9.9.9.16.0 1 Ahau 18 Eayab. In 
connection with the first of these two Initial Series, 9.9.16.0.0 4 Ahau 
8 Cumhu, there is recorded a Secondary Series. This consists of 6 
tuns, 2 uinals, and kins (6.2.0) and is recorded just to the left of 
the first Initial Series from which it is counted, that is, in the left- 
hand column. 

It was explained on pages 136-137 that the almost universal direc- 
tion of counting was forward, but that when the count was backward 
in the codices, this fact was indicated by a special sign or symbol, 
which gave to the number it modified the significance of "backward " 
or "minus." This sign is shown in figure 64, and, as explained on 
page 137, it usually is attached only to the lowest period. Returning 
once more to our text, in plate 31 we see this "backward" sign — a 
red circle surmounted by a knot — surrounding the kins of this 
Secondary-series number 6.2.0, and we are to conclude, therefore, 
that this number is to be counted backward from some date. 

Counting it backward from the date which stands nearest it in our 
text, 4 Ahau 8 Cumhn, the date reached will be 1 Ahau 18 Eayab. 
But since the date 4 Ahau 8 Cnmhu is stated in the text to have corre- 
sponded with the Initial-series value 9.9.16.0.0, by deducting 6.2.0 
from this number we may work out the Initial-series value for this 
date as follows: 

9.9.16. 0.0 4 Ahau 8 Cumhu 

6. 2.0 Backward 
9.9. 9.16.0 1 Ahau 18 Kayab 

The accuracy of this last calculation is established by the fact that 
the Initial-series value 9.9.9.16.0 is recorded as the second Initial 
Series on the page above described, and corresponds to the date 1 
Ahau 18 Kayab as here. 

It is difTicult to say why the terminal dates of these two Initial 
Series and this Secondary Series should have been recorded to the 
left of the numbers leading to them, and not just helow the numbers 
in each case. The only explanation the writer can offer is that the 
ancient scribe wished to have the starting point of his Secondary- 
series number, 4 Ahau 8 Cumhu, recorded as near that number as 
possible, that is, just below it, and consequently the Initial Series 
leading to this date had to stand to the right. This caused a dis- 
placement of the corresponding terminal date of his Secondary 
Series, 1 Ahau 18 Kayab, which was written under the Initial Series 
9.9.16.0.0; and since the Initial-series value of 1 Ahau 18 Kayab also 
appears to the right of 9.9.16.0.0 as 9.9.9.16.0, this causes a displace- 
ment in its terminal date likewise. 



MOBLBY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 269 

Two Other Initial Series will suffice to exemplify this kind of count 
in the codices. In plate 32 is figured page 62 from the Dresden 
Codex. In the two right-hand columns appear two black numbers. 
The first of these reads quite clearly 8.16.15.16.1, which the student 
is perfectly justified in assuming is an Initial-series number consist- 
ing of 8 cycles, 16 katuns, 15 tuns, 16 uinals, and 1 kin. Moreover, 
above the 8 cycles is a glyph which bears considerable resemblance 
to the Initial-series introducing glyph (see fig. 24,/). Note in particular 
the trinal superfix. At all events, whether it is an Initial Series or 
not, the first step in deciphering it will be to reduce this number to 
units of the first order: 

8X144,000 = 1, 152,000 
16 X 7,200= 115,200 

15 X 360= 5,400 

16 X 20 = 320 
IX 0= 1 



1, 272, 921 



Deducting from this number all the Calendar Rounds possible, 67 
(see Table XVI), it may be reduced to 1,261. Applying rules 1, 2, 
and 3 (pp. 139, 140, and 141, respectively) to this remainder, the 
terminal date reached will be 4 Imix 9 Mol. This is not the terminal 
date recorded, however, nor is it the terminal date standing below 
the next Initial-series number to the right, 8.16.14.15.4. It would 
seem then that there must be some mistake or unusual feature about 
this Initial Series. 

Immediately below the date which stands vmder the Initial-series 
niunber we are considering, 8.16.15.16.1, is another number consisting 
of 1 tun, 4 uinals, and 16 kins (1.4.16). It is not improbable that 
this is a Secondary-series mmiber connected in some way with our 
Initial Series. The red circle surmounted by a knot which surroimds 
the 16 kins of this Secondary-series munber (1.4.16) indicates that 
the whole number is to be counted backward from some date. Ordi- 
narily, the first Secondary Series in a text is to be counted from the 
terminal date of the Initial Series, which we have found by calcula- 
tion (if not by record) to be 4 Imix 9 Mol in this case. Assuming 
that this is the case here, we might count 1.4.16 hackward from the 
date 4 Imix 9 Mol. 

Performiag all the operations indicated in such cases, the termuml 
date reached will be found to be 3 Chicchaii 18 Zip ; tliis is very close 
to the date which is actually recorded just above the Secondary- 
series number and just below the Initial-series niunber. The date 
here recorded is 3 Chicchan 13 Zip, and it is not improbable that the 



270 BXTBEATT OF AMEBICA^f ETHSOLOGT [BTix. 57 

ancient scribe intended to write instead 3 CMcchan 18 Zip, the date 
indicated by the calculations. We probably have here: 

8.16.15.16. 1 ^4 Imix 9 Mpl) 

1. 4.16 Backward 
8.16.14.11. 5 3 CMcclian 18* Zip 

Tn these calculations the terminal date of the Initial Series, 4 Imix 
9 ICol, is suppressed, and the only date g^ven is 3 CMccIiaii 18 Zip, 
the terminal date of the Secondary Series. 

Another Initial Series of this same kind, one in which the terminal 
date is not recorded, is shown just to the ri^t of the preceding in 
plate 32. The Initial-series number 8.16.14.15.4 there recorded 
reduces to units of the first order as follows : 

8X144,000 = 1,152,000 
16 X 7,200= 115,200 

14 X 360= 5,040 

15 X 20= 300 
4X 1= i 



1, 272, ryU 



Deducting from this ntnnber all the Calendar Bounds possible, 67 
(see Table XVI), it will be reduced to 884, and applying rules 1, 2, 
and 3 (pp. 139, 140, and 141, respectively) to this remainder, the 
terminal date reached will be 4 Kan 17 Yazkiii. This date is not 
recorded. There follows below, however, a Secondary-series number 
coiLsisting of 6 uinals and 1 kin (6.1). The red circle around the 
lower term of this (the 1 kin) indicates that the whole number, 6.1, 
is to be counted hachrard from some date, probably, as in the pre- 
ceding case, from the terminal date of the Initial Series above it. 
Assuming that this is the case, and counting 6.1 backward from 
S. 16. 14. 15. 4 4 Kan 17 Yaxkiii, the terminal date reached will be 13 
Akbal 16 Pop, again very close to the date recorded immediately 
above, 13 Akbal 15 Pop. Indeed, the date as recorded, 13 Akhal 
15 Pop, represents an impossible condition from the ilaya point of 
view, since the day name Akl^l could occupy only the first, sixth, 
eleventh, and sixteenth positions of a month. See Table \ 11. Con- 
sequently, throuo^ lack of space or carelessness the ancient scribe 
who painted this book failed to add one dot to the three bars of the 
month sign s coefficient, thus Tnaking it 16 instead of the 15 actually 
recorded. We are obliged to make some correction in this coefficient, 
since, as explained above, it is obviously incorrect as it stands. 
Since the addition of a single dot brings the whole date into harmony 
with the date determined by calculation, we are probably justified 

> iaiamaaij Feccrded astiia tlie text. 



MOBLEY] 



INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 271 



in making the correction here suggested, 
therefore: 



We have recorded here 



8.16.14.15.4 

6.1 

8.16.14. 9.3 



(4 Kan 17 Yaxkin) 

Backward 

13 Akbal 16 » Pop 



In these calculations the terminal date of the Initial Series, 4 Kan 
17 Yaxkin, is suppressed and the only date given is 13 Akbal 16 Pop, 
the termiaal date of the Secondary Series. 

The above will suffice to show the use of Initial Series m the 
codices, but before leaving this subject it seems best to discuss 
briefly the dates recorded by these Initial Series in relation to the 
Initial Series on the monuments. According to Professor Forste- 
mann^ there are 27 of these altogether, distributed as follows: 



Page 24 
Page 24 
Page 31 
Page 31 
Page 31 
Page 43 
Page 45 
Page 51 
Page 51 
Page 52 
Page 52 
Page 52 
Page 52 
Page 58 



4 


2* 



9. 9.16. 0. 0» 
9. 9. 9.16. 
8.16.14.15. 
8.16. 3.13. 

10.13.13. 3. 
9.19. 8.15. 
8.17.11. 3. 
8.16. 4. 8. 0^ 

10.19. 6. 1. 8" 
9.16. 4.11.18' 
9.19. 5. 7. 8^ 
9.16. 4.10. 8 
9.16. 4.11. 3 
9.18. 2. 2. 



Page 58: 
Page 62 : 
Page 62: 
Page 63 : 
Page 63: 
Page 63: 
Page 63: 
Page 70: 
Page 70: 
Page 70: 
Page 70: 
Page 70: 
Page 70: 



9.12.11.11. 
8.16.15.16. 1 
8.16.14.15. 4 
8.11. 8. 7. 
8.16. 3.13. 

10.13. 3.16. 

10.13.13. 3. 
9.13.12.10. 
9.19.11.13. 

10.17.13.12.12 

10.11. 3.18.14 
8. 6.16.12. 
8.16.19.10. 



4» 
2 





There is a wide range of time covered by these Initial Series ; indeed, 
from the earliest 8.6.16.12.0 (on p. 70) to the latest, 10.19.6.1.8 (on 
p. 51) there elapsed more than a thousand years. Where the differ- 
ence between the earliest and the latest dates is so great, it is a matter 
of vital importance to determine the contemporaneous date of the 
manuscript. If the closing date 10.19.6.1.8 represents the time at 
which the manuscript was made, then the preceding dates reach back 

1 Incorrectly recorded as 15 in the text. 

2 Bull. S8, Bur. Amer. Ethn., p. 400. 

3 The terminal dates reached have been omitted, since for comparative work the Initial-series num- 
bers alone are sufficient to show the relative positions in tiie Long Count. 

< The manuscript incorrectly reads 10.13.3.13.2; that is, reversing the position of the tun and uinal coeffi- 
cients. 

5 The manuscript incorrectly reads 8.16.4.11.0. The uinal coefficient is changed to an 8, above. 

6 The manuscript incorrectly reads 10.19.6.0.8. The uinal coefficient is changed to 1, above. 

' The manuscript incorrectly reads 9.16.4.10.18. The uinal coefficient is changed to 11, above. 

8 The manuscript incorrectly reads 9.19.8.7.8. The tun coefficient is changed to 6, above. 

' The manuscript incorrectly reads 10.8.3.16.4. The katun coefficient is changed to 13, above. These 
corrections are all suggested by Professor Forstemann and are necessary if the calculations he suggests are 
correct, as seems probable. 



272 BUREAU OF AMERICAN ETHNOLOGY [bull. r,7 

for more than a thousand years. On the other hand, if 8.6.16.12.0 
records the present time of the manuscript, then all the followmg 
dates are prophetic. It is a difhcult question to answer, and the 
best authorities have seemed disposed to take a middle course, 
assigning as the contemporaneous date of the codex a date ubout the 
middle of Cycle 9. Says Professor Forstemann {Bulletin 28, p. 402) 
on the subject: 

In my opinion my demonstration also definitely proves that these large numbers 
[the Initial Series] do not proceed from the future to the past, but from the past, 
through the present, to the future. Unless I am quite mistaken, the highest numbers 
among them seem actually to reach into the future, and thus to have a prophetic 
meaning. Here the question arises, At what point in this series of numbers does the 
present lie? or, Has the wiiter in different portions of his work adopted different 
points of time as the present? If I may venture to express my conjecture, it seems 
to me that the first large number in the whole manuscript, the 1,366,560 in the second 
column of page 24 [9.9.16.0.0 4 Ahau 8 Cumhu, the first Initial Series figured in plate 
31], has the greatest claim to be interpreted as the present point of time. 

In a later article {Bulletin 28, p. 437) Professor Forsteniann says: 
"But I think it is more probable that the date farthest to the right 
(1 Ahau, 18 Zip . . . ) denotes the present, the other two 
[namely, 9.9.16.0.0 4 Ahau 8 Cumhu and 9.9.9.16.0 1 Ahau 18 Kayab] 
alluding to remarkable days in the future." He assigns to this date 
1 Ahau 18 Zip the position of 9.7.16.12.0 in the Long Count. 

The writer believes this theory to be untenable because it involves 
a correction in the original text. The date which Professor Forste- 
mann calls 1 Ahau 18 Zip actually reads 1 Ahau 18 Uo, as he himself 
admits. The month sign he corrects to Zip in spite of the fact that 
it is very clearly Uo. Compare this form with figure 20, 6, c. The 
date 1 Ahau 18 TJo occurs at 9.8.16.16.0, but the writer sees no reason 
for believing that this date or the reading suggested by Professor 
Forstemann indicates the contemporaneous time of this manuscript. 

Mr. Bowditch assigns the manuscript to approximately the same 
period, selecting the second Initial Series in plate 31, that is, 
9.9.9.16.0 1 Ahau 18 Kayab: "My opinion is that the date 9.9.9.16.0 
1 Ahau 18 Kayab is the present time with reference to the time of 
writing the codex and i.s the date from which the whole calculation 
starts.'" The reasons which have led Mr. Bowditch to this conclu- 
sion are very convincing and will make for the general acceptance of 
his hypothesis. 

Although the writer has no better suggestion to offer at the present 
time, he is inclined to believe that both of these dates are far too 
early for this manuscript and that it is to be ascribed to a very much 
later period, perhaps to the centuries following immediately the colo- 
nization of Yticatan. There can be no doubt that very early dates 
appear in the Dresden Codex, but rather than accept one so early as 

1 Bowditch, 1909: p. 279. 



BUREAU OF AMERICAN ETHNOLOGY 



BULLETIN 67 PLATE 32 







-f. I ^ . •••• Ji \ 

\i ' I- 








PAGE 62 OF THE DRESDEN CODEX, SHOWING THE 
SERPENT NUMBERS 



MOBLET] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 273 

9.9.9.16.0 or 9.9.16.0.0 as the contemporaneous date of the manu- 
script the writer would prefer to believe, on historical grounds, that 
the manuscript now known as the Dresden Codex is a copy of an 
earlier manuscript and that the present copy dates from the later 
Maya period in Yucatan, though sometime before either Nahuatl or 
Castilian acculturation had begun. 

Texts Recording Serpent Numbers 

The Dresden Codex contains another class of numbers which, so 
far as known, occur nowhere else. These have been called the Serpent 
numbers because their various orders of units are depicted between 
the coils of serpents. Two of these serpents appear in plate 32. 
The coils of each serpent inclose two different numbers, one in red 
and the other in black. Every one of the Serpent numbers has six 
terms, and they represent by far the highest numbers to be found in 
the codices. The black number in the first, or left-hand serpent in 
plate 32, reads as follows: 4.6.7.12.4.10, which, reduced to units of 
the first order, reads : 

4X2,880,000=11,520,000 
6X 144,000= 864,000 
7X 7,200= 50,400 



12 X 


360 = 


4,320 


4X 


20 = 


80 


10 X 


1 = 


10 



12,438,810 

The next question which arises is. What is the starting point from 
which this number is counted ? Just below it the student will note 
the date 3 Ix 7 Tzec, which from its position would seem almost surely 
to be either the starting point or the terminal date, more probably 
the latter. Assuming that this date is the terminal date, the starting 
point may be calculated by counting 12,438,810 hackward from 3 Ix 
7 Tzec. Performing this operation according to the rules laid down 
in such cases, the starting point reached will be 9 Kan 12 Xul, but 
this date is not found in the text. 

The red number in the first serpent is 4.6.11.10.7.2, which reduces 
to — 

4X2, 880, 000 = 1 1, 520, 000 

6 X 144, 000 = 864, 000 



llX 


7,200= 79,200 


10 X 


360= 3,600 


7X 


20= 140 


2X 


1= 2 




12, 466, 942 



43508°— Bull. 57—15 18 



274 BXTEEAtr OF AMBKICAN ETHNOLOGY '''^'" 

Assuming that the date below this number, 3 Cimi 14 Kayab, was its 
terminal date, the starting point can be reached by counting back- 
ward. This will be foimd to be 9 Kan 12 Kayab, a date actually- 
found on this page (see pi. 32), just above the animal figure emerging 
from the second serpent's mouth. 

The black number in the second serpent reads 4.6.9.1.5.12.19, which 
reduces as follows: 

4X2, 880, 000 = 11, 520, 000 



6X 


144,000= 864,000 


9X 


7,200= 64,800 


15X 


360 = 5, 400 


12 X 


20= 240 


19X 


1= 19 




12, 454, 459 



Assuming that the date below this number, 13 Akbal 1 Kankin, 
was the terminal date, its starting point can be shown by calculation 
to be just the same as the starting point for the previous number, 
that is, the date 9 Kan 12 Kayab, and as mentioned above, this date 
appears above the animal figure emerging from the mouth of this 
serpent. 

Tho last Serpent number in plate 32, the red number in the second 
serpent, reads, 4.6.1.9.15.0 and reduces as follows: 



4X2,880,000 = 


11, 


, 520, 000 


6X 144,000 = 




864, 000 


IX 7,200 = 




7,200 


9X 360 = 




3, 240 


15X 20 = 




300 


OX 1 = 









12, 


, 394, 740 



Assuming that the date below this number, 3 Kan 17 TIo,' was its 
terminal date, its starting point can be shown by calculation to be 
just the same as the starting point of the two preceding numbers, 
namely, the date 9 Kan 12 Kayab, which appears above this last 
serpent. 

It will be seen from tlie foregoing that tliror; of the four Serpent 
dates above described are counted from the date 9 Kan 12 Kayab, a 
date actually recorded in the text just above them. The aU-important 
question of course is, What position did the date 9 Kan 12 Kayab 
oceupj" in the Long Count ? The page (62) of the Dresden Codex we 

1 The manuscript has incorrectly 16 TTo. It is obviofus this can not be correct, since from Table 
\^I Kan can occupy only the 2d, 7th, 12th, or 17th position in the months. The correct reading here as 
we shall see, is probably 17 Uo. This reading requires only the addition of a single dot. 



MORLBT] INTRODUCTION TO STUDY OF MAYA HIEKOGLYPHS 275 

are discussing sheds no light on this question. There are, however, 
two other pages in this Codex (61 and 69) on which Serpent numbers 
appear presenting this date, 9 Kan 12 Kayab, under conditions which 
may shed light on the position it held in the Long Count. On page 
69 there are recorded 15 katuns, 9 tuns, 4 uinals, and 4 Mns (see fig. 
85); these are immediately followed by the date 9 Kan 12 Kayab. 
It is important to note in this connection that, unlike almost every 
other number in this codex, this number is expressed by the first 
method, the one in which the period glyphs are used. As the date 
4 Ahau 8 Cumhu appears just above in the text, the first supposition 
is that 15.9.4.4 is a Secondary-series number which, if counted for- 
ward from 4 Ahau 8 Cumhu, the starting point of Maya chronology, 
will reach 9 Kan 12 Kayab, the date recorded immediately after it. 
Proceeding on this assumption and performing the — »»,, 
operations indicated, the terminal date reached will p^ ((^\ 
be 9 Kan 7 Cumhu, not 9 Kan 12 Kayab, as recorded. ^^ v-»^ 
The most plausible explanation for this number and J^^ •(Tp) 
date the writer can offer is that the whole constitutes *^§ • '.^^...o 
a Period-ending date. On the west side of Stela C at ^^^*||(|^ 
Quirigua, as explained on page 226, is a Period- vLm^y'lIss 
ending date almost exactly hke this (see pi. 21, H). fio. go. Exam- 
On this monument 17.5.0.0 6 Ahau 13 Kayab is record- ^^1°^ ""* 

. " method of nu- 

ed, and it was proved by calculation that 9.17.5.0.0 merationinthe 
would lead to this date if counted forward from the <=<"3i<'es (part of 

page 69 of the 

startmg point ot Maya chronology. In effect, then, Dresden co- 
this 17.5.0.0 6 Ahau 13 Kayab was a Period-ending '^'''^• 
date, declaring that Tun 5 of Katun 17 (of Cycle 9, unexpressed) 
ended on the date 6 Ahau 13 Kayab. 

Interpreting in the same way the glyphs in figure 85, we have the 
record that Kin 4 of Uinal 4 of Tun 9 of Katun 15 (of Cycle 9, unex- 
pressed) fell (or ended) on the date 9 Kan 12 Kayab. Changing this 
Period-ending date into its corresponding Initial Series and solving 
for its terminal date, the latter date will be found to be 13 Kan 12 Ceh, 
instead of 9 Kan 12 Kayab. At first this would appear to be even farther 
from the mark than our preceding attempt, but if the reader will admit 
a slight correction, the above number can be made to reach the date 
recorded. The date 13 Kan 12 Ceh is just 5 uinals earher than 9 Kan 
12 Kayab, and if we add one bar to the four dots of the uinal coeffi- 
cient, this passage can be explained in the above manner, and yet 
agree in all particulars. This is true since 9.15.9.9.4 reaches the date 
9 Kan 12 Kayab. On the above grounds the writer is inclined to 
believe that the last three Serpent numbers on plate 32, which were 
shown to have proceeded from a date 9 Kan 12 Kayab, were counted 
from the date 9.15.9.9.4 9 Kan 12 Kayab. 



276 



BUEEATJ OP AMEEICAN ETHNOLOGY 



[BULL. 57 



Texts Recording Ascending Series 

There remains one other class of numbers which should be described 
before closing this chapter on the codices. The writer refers to the 
series of related numbers which cover so many pages of the Dresden 
Codex. These commence at the bottom of the page and increase 
toward the top, everj' other number in the series being a multiple of 
the first, or beginning number. One example of this class will 
suffice to illustrate all the others. 

In the lower right-hand corner of plate 31 a series of this kind 
commences with the day 9 Ahau.' Of this series the number 8.2.0 
just above the 9 Ahan is the first term, and the day 9 Ahau the first 
terminal date. As usual in Maya texts, the starting point is not 
expressed ; by calculation, however, it can be shown to be 1 Ahau ^ 
in this particular case. 

Counting forward then 8.2.0 from 1 Ahau, the unexpressed starting 
point, the first terminal date, 9 Ahau, wiU be reached. See the lower 
right-hand corner in the following outfine, in which the Maya num- 
bers have all been reduced to miits of the first order : 



151,840 ^ 


113,880 = 


75,920 ^ 


37,960 ' 


1 Ahau 


1 Ahau 


1 Ahau 


1 Ahau 


185,120 


68,900 


33,280 


9,100 


1 Ahau 


1 Ahau 


1 Ahau 


1 Ahau 


35,040 


32,120 


29,200 


26,280 


6 Ahau 


11 Ahau 


3 Ahau 


8 Ahau 


23,360 


20,440 


17,520 


14,600 


13 Ahau 


5 Ahau 


10 Ahau 


2 Ahau 


11,680' 


8,760 


5,840 


2,920 


7 Ahau 


12 Ahau 


4 Ahau 


9 Ahau 



(Unexpressed starting point, 1 Ahau.) 

In the above outfine each number represents the total distance of 
the day just below it from the unexpressed starting point, 1 Ahau, not 
the distance from the date immediately preceding it in the series. 
For example, the second number, 5,840 (16.4.0), is not to be counted 
forward from 9 Ahau in order to reach its terminal date, 4 Ahau, but 
from the unexpressed starting point of the whole series, the day 1 
Ahau. Similarly the third number, 8,760 (1.4.6.0), is not to be 
coimted forward from 4 Ahau in order to reach 12 Ahau, but from 
1 Ahau instead, and so on throughout the series. 

1 In the text the coefficient appears to be 8, but in reality it is 9, the lower dot having been covered by 
the marginal line at the bottom. 

2 Counting backward 8.2.0 (2,920) from 9 Ahau, 1 Ahau is reached. 

3 Professor Forstemann restored the top terms of the four numbers in this row, so as to make them read 
as given above. 

^ The manuscript reads 1.12.5.0, which Professor Forstemann corrects to 1.12.8.0; in other words, chang- 
ing the uinal from 5 to 8. This correction is fully justified in the above calculations. 



MonLEY] INTRODUCTION TO STUDY OF MAYA HIEROGLYPHS 277 

Beginning with the number 2,920 and the starting point 1 Ahau, 
the fii'st twelve terms, that is, tlie numbers in the three lowest rows, 
are the first 12 multiples of 2,920. 

2,920- 1X2,920 20,440= 7x2,920 

5,840= 2X2,920 23,360= 8X2,920 

8,760= 3X2,920 26,280= 9X2,920 

11,680= 4X2,920 29,200 = 10X2,920 

14,600= 5X2,920 32,120 = 11x2,920 

17,520= 6X2,920 35,040 = 12X2,920 

The days recorded under each of these numbers, as mentioned above, 
are the terminal dates of these distances from the starting point, 
1 Ahau. Passmg over the fourth row from the bottom, which, as 
will appear presently, is probably an interpolation of some land, the 
thirteenth mmaber — that is, the right-hand one in the top row — is 
37,960. But 37,960 is 13x2,920, a continuation of our series the 
twelfth term of which appeared in the left-hand number of the third 
row. Under the thirteenth number is set down the day 1 Ahau ; in 
other words, not until the thirteenth multiple of 2,920 is reached is 
the terminal day the same as the starting point. 

With this thirteenth term 2,920 ceases to be the unit of increase, and 
the thu'teeth term itself (37,960) is used as a difference to reach the 
remaining three terms on this top Une, all of which are multiples of 
37,960. 

37,960 = 1 X 37,960 or 13 X 2,920 

75,920 = 2 X 37,960 or 26 X 2,920 
113,880 = 3X37,960 or 39X2,920 
151,840 = 4X37,960 or 52x2,920 

Countmg forwaril each one of these from the starting point of this 
entire sorios, 1 Ahau, each will be found to reach as its terminal day 
1 Ahau, as recorded under each. The fourth line from the bottom is 
more difl&cult to understand, and the explanation offered by Professor 
Foretemanu, that the first and thii'd terms and the second and fom-th 
are to be combined by addition or subtraction, leaves much to be 
desired. Omitting this row, however, the remaining numbers, those 
wliich are multiples of 2,920, admit of an easy explanation. 

In the first place, the opening term 2,920, wliich serves as the unit 
of increase for the entire series up to and including the 13th term, is 
the so-called Venus-Solar period, containing S-Solai" years of 365 
days each and 5 Venus yeai-s of 584 days each. This important 
period is the subject of extended treatment elsewhere in the Dresden 
Codex (pp. 46-60), in which it is repeated 39 times in all, divided 
into three equal divisions of 13 periods each. The 13th term of our 
series 37,960 is, as we have seen, 13x2,920, the exact number of 



278 BUKEAU OF AMERICAX ETHNOLOGY (Binx. 57 

days treated of in the upper divisions of pages 46-50 of the Dresden 
Codex. The 14th term (75,920) is the exact number of days treated 
of in the first two divisions, and finally, the 15th, or next to the last 
term (113,880), is the exact number of days treated of in all tlu-ee 
divisions of these pages. 

This 13th term (37,960) is the first in wMch the tonalamatl of 260 
days comes into harmony with the Venus and Solar years, and as 
such must have been of very great importance to the Maj-a. At the 
same time it represents two Cabndar Rounds, another important 
chronological count. With the next to the last term (113,880) the 
Mars year of 780 days is brought into harmony with all the other 
periods named. This number, as just mentioned, represents the sum 
of all the 39 Venus-Solar periods on pages 46-50 of the Dresden 
Codex. This next to the last number seems to possess more remark- 
able properties than the last number (151,840), in which the Mars 
year is not contained without a remainder, and the reason for its 
record does not appear. 

The next to the last term contains : 

438 Tonalamatls of 260 days each 
312 Solar years of 365 days each 
195 Venus years of 584 days each 
• 146 Mars years of 780 days each 

39 Venus-Solar periods of 2,920 days each 
6 Calendar Rotmds of 18,980 days each 

It wiU be noted in plate 31 that the concealed starting point of this 
series is the day 1 Ahan, and that just to the left on the same plate 
are two dates, 1 Ahau 18 Eayab and 1 Ahau 18 Uo, both of which show 
this same day, and one of which, 1 Ahan 18 Kayab, is accompanied 
by its corresponding Initial Series 9.9.9.16.0. It seems not unlikely, 
therefore, that the day 1 Ahau with which this series commences was 
1 Ahan 18 Kayab, which in turn was 9.9.9.16.0 1 Ahan 18 Eayab of 
the Long Count. This is rendered somewhat probable by the fact 
that the second division of 13 Venus-Solar periods on pages 46-50 
of the Dresden Codex also has the same date, 1 Ahan 18 Kayab, as 
its terminal date. Hence, it is not improbable (more it would be un- 
wise to say) that the series of numbers which we have been dis- 
cussing was counted from the date 9.9.9.16.0. 1 Ahan 18 Eayab. 

The foregoing examples cover, in a general way, the material 
presented in the codices; there is, however, much other matter which 
has not been explained here, as unfitted to the needs of the beginner. 
To the student who wishes to speciahze in this field of the glyphic 
writing the writer reconxmends the treatises of Prof. Ernst Forste- 
mann as the most valuable contribution to this subject. 



INDEX 



Page 

Abbkeviation in dating, use 222, 252 

Addition, method 149 

Adultery, punishment 9-10 

Agxjilar, S. de, oh Maya records 36 

Ahholpop (offlcial), duties 13 

Ahkulel (deputy-chief), powers 13 

Ahpuch (god), nature 17 

Alphabet, nonexistence 27 

Amusements, nature 10 

Arabic system of numbers, Maya parallel . . 87, 96 

Architecture, development 5 

Arithmetic, system 87-155 

Ascending series, texts recording 276-278 

Astronomical computations— 

accuracy 32 

in codices 31-32, 276-278 

Aztec — 

calendar 58-59 

ikomomatic hieroglyphics 29 

rulersbip succession 16 

Backward sign— 

glyph 137 

use 137, 268 

B AKHALAL (city), founding 4 

Bar, numerical value 87-88 

Bar and dot numerals — 

antiquity 102-103 

examples, plates showing 157, 

167,170,176,178,179 
form and nature 87-95 

Batab (chief), powers 13 

Bibliography xv-xvi 

Bowditch, C. p.— 

cited 2, 4.5, 65, 117, 134, 203 

on dating system 82-83, 214-215, 272 

on hieroglyphics 30, 33, 71 

on Supplementary Series 152 

works vii-viii 

Brinton, Dt. D. G.— 

error by 82 

on hieroglyphics 3, 23, 27-28, 30, 33 

on numerical system 91 

Calendar— 

harmonization . . .' 44, 215 

starting point 41-43, 60-62, 113-114 

subdivisions 37-86 

SeeaZsoCALENDAR Hound; Chronology; 
Dating; Long Count. 

Calendar Round— 

explanation 51-59 

glyph 59 



Page 
Calendar-round dating— 

examples 240-245 

limitations 76 

Chakanputan (city), founding and destruc- 
tion 4 

Chichen Itza (city)— 

history 3, 4, 5, 202-203 

Temple of the Initial Series, lintel, inter- 
pretation 199 

Chilan balam— 

• books of 3 

chronology based on 2 

Chronology— 

basis 58 

correlation 2 

duration 222 

starting point... 60-62,113-114,124-125,147-148 
See also Calendar. 
Cities, southern — 

occupancy of, diagi-am showkig 15 

rise and fall of 2-5 

Civilization, rise and tall 1-7 

Closing sign of Supplementary Series, 

glyph 152-153,170 

Closing signs. See Ending signs. 

Clothing, character 7-8 

COCOM FAMILY, tyranny 5-6, 12 

Codex Peresianus, tonalamatls named in. . 265 

Codex Tro-Cortesianus, texts 262-265 

Codices— 

astronomical character 31-32, 276-278 

character in general 31,252 

colored glyphs used in 91, 251 

dates of 203 

day signs in 39 

errors 270-271, 274 

examples from, interpretation 251-278 

glyphs for twenty (20) used in 92, 130 

historical nature 32-33, 35-36 

Initial-series dating in 266 

examples 266-273 

interpretation 31-33, 254-278 

numeration glyphs used in 103-104, 129-134 

order of reading 22, 133, 135, 137, 252-253 

tonalamatls in 251-266 

zero glyph used in 94 

Coefficients, numerical. See Numerical 
coefficients. 

COGOLLUDO, C. L., on dating system 34,84 

Colored glyphs, use of, in codices 91, 251 

Commerce, customs 9 

Computation, possibility of en'ors in 164-155 

Confederation, formation and disruption. . 4-5 

279 



280 



INDEX 



COPAN (city) — 

Altar Q, error on 

Altar S, interpretation 

Altar Z, interpretation 

history 

Stela A, interpretation 

Stela B, interpretation 

Stela D, interpretation 

Stela J, interpretation 

Stela M, interpretation 

Stela N, error on- 

interpretation 114-118, 

Stela P, interpretation 

Stela 2, interpretation 

Stela 4, interpretation 

Stela 6, interpretation 

Stela 8, interpretation 

Stela 9, antiquity 

interpretation 

Stela 15, interpretation 

Ceesson, H. T., cited 

Customs. See MiNSEEs akb customs. 
Cycle — 

glyphs 

length 

number of, in great cycle 

numbering of, in inscriptions 108, 

Cycle 8, dates 194-198, 

Cycle 9 — 

dates 172,183,18.5,187, 

prevalence in Maya dating 

Cycle 10, dates 199-203, 

Cycle, Geeat— 

length 

number of cycles in 

Cycles, Geeat, Great, and Highee — 

discussion 

glyphs - 

omitted in dating 



246,248 
231-233 
. 242 
15 
169-170 
167-169 
188-191 
191-192 
175-176 
24.S-249 
248-249 
185 
223 
224-225 
170-171 



173 
171-173 

187-188 
27 



68 
62,135 
107-114 
227-233 
228-229 

194,222 

194 

229-233 

135,162 
107-114 

114-129 
. 118 
. 126 



Dates— 

abbreviation 222,252 

errors in computing 154-155 

errors in originals 245-250, 270-2U, 274 

interpretation, in Initial Series. 157-222, 233-245 

in Period Endings 222-245 

in Secondary Series 207-222, 233-245 

monuments erected to mark 33-35, 249-250 

of same name, distinction between 147-151 

repetition 147 

sho\*'n by red glyphs in codices 251 

Dates, Initial. See lurnAL-SEEiES dating. 

Dates, Initial and Secondaey, interpreta- 
tion 207-222 

Dates, Imitiax, Secondaey, and Peeiod- 
ENDDfG, interpretation 233-245 

Dates, Peeiod-exdikg. See Peeiod-ending 
dates. 

Dates, Peophetic— 

examples 229-233 

use 271-272 

Dates, Secondaey. S<c Secondaet-sekies 

DATING. 

Dates, Teemdtal— 

absence 218 

finding 138-154 

importance 154-155 

position 151-154 



Dating— Page 

methods 46-47, 63-86 

change 4 

See alio Calendae-eound dating; 
Initial-seeies; Peeiod-ending; 
Secondaey-seeies. 

starting point 60-62, 113-114, 124-125 

determination 135-136 

DAT- 
first of year 52-53 

glyphs 38,39,72,76 

coefficients 41-43,47-48 

position 127-128 

omission 127-128, 208 

identification 41-43, 46-48 

names 37-41,112 

numbers 111-112 

position m solar year 52-58 

round of. 42^4 

Days, Inteecalaey, lack ol 45 

Days, unlucky, dates 45-46 

Death, fear of 11,17 

Death God — 

glyph 17,257 

nature 17 

Decimal system, paralleL 129 

See oteo Vigesimal system. 
Desteuction of the Wohld, description. - . 32 

Divination, codices used for 31 

DrvoKCE, practice 9 

Dot, numerical value 87-88 

Dot and BAB numbees. See Bae aih) dot 

numbees. 
Deesden codex— 

date 271-273 

publication iii 

texts 254-262,266-278 

plates showing 32,254,260,266,273 

Deunkenness, prevlaence 10 

Ek Ahau (god), nature 17-18 

Ending signs— 

in Period-ending dates 102 

in "zero" 101-102 

Enumeeation— 

systems 87-134 

comi)arison 133 

See also Numeeals. 

Ebbobs in texts— 

examples 245-250,270-271,274 

plate showing 248 

Featheeed Seepent (god), nature 16-17 

FiBEE-PAPEB BOOKS. See Codices. 

Fish, used in introducing glyph 65-66, 188 

Fiye-tun peeiod. See Hotdn. 

E6KSTEMANN, Prof. EENST — 

cited 26,137 

investigations iii,265,276 

methods of solving numerals 134 

on hieroglyphics 30 

on prophetic dates 272 

Full-figube glyphs — 

nature 67-68, 188-191 

plate showing iss 

See aim Time peeiods. 

Fdnebal CUSTOMS, description 11-12 

FuTUBE LIFE, belief as to 19 



INDEX 



281 



Glyph block, definition 166 

Glyphs. See Hieeogltphs. 

Gods, nature 16-19 

Goodman, J. T.— 

chronologic tables of 134 

cited 2, 44, 116-117, 123 

investigation iii-iv 

on introducing glyph 66 

on length of great cycle 108 

on Supplementary Series 152 

Government, nature 12-16 

Gkeat Cycle— 

length 135 

number of cycles in 107-114 

Haab (solar year)— 

first day 62-66 

glyph 47 

nature 44-51 

position of days in 48, 62-58 

subdivisions 45 

Habitat oe the Maya 1-2 

map 1 

Hair, method of dressing 7 

Halach Unnc (chief), powers 12-13 

Hand, used as ending sign 101-102 

Head-variant numerals- 

antiquity 73, 102-103 

characteristics 97-103 

derivation 74 

discovery iii 

explanation 24-28, 87, 96-104 

forms 96-104 

value 103 

identification 96-103 

parallel to Arabic numerals 87 

plates showing 167, 170, 176, 178, 179, 180 

use of, in time-period glyphs 67-74, 104 

See also Fuli^figure glyphs. 

Hewett, Dr. E. L., cited 164, 192 

Hieroglyphs— 

antiquity iii, 2 

proofs 173, 175 

character iv, 26-30 

classification 26 

decipherment 23-25, 31, 249-250 

errors in interpretation 164-155 

errors in original text 245-260 

methods 134-166 

inversion of significance 211 

mat pattern 191-194 

materials inscribed upon 22 

modifications 23-26 

order of reading 23, 

129, 133, 135, 136-138, 156, 170, 268 

original errors 245-250 

progress iv, 250 

symmetry 23-24, 88-91, 128 

textbooks vii 

See also Numerals. 

Hieroglyphs, closing, use. . . 101-102, 152-153, 170 

Hieroglyphs, introducing, use in dating. . 64-68 

Hbtory— 

codices containing 32-33 

dates 179, 221-222, 228-229, 249-260 

decipherment iv-v, 26,250 

dates only 249-250 



Page 
History- Continued. 

outline 2-7 

recording, methods 33-36 

Hodge, ¥. W., letter of transmittal iii-v 

Holmes, W. H., cited 196 

Hospitality, customs 10 

Hotun period 166 

Hunting, division of spoils 9 

Ideographic writing, argument for 27-28 

Ikonom ATic writing, nature 28-29 

Initial-series dating — 

bar and dot numbers in, examples 157-167, 

176-180 

plates showing 157, 167, 170, 176, 178, 179 

disuse 84-86, 199 

examples, interpretation 157-222, 233-240 

plates showing 157, 167, 170, 

176, 178, 179, 180, 187, 
188,191,207,210,213, 
218, 220, 233, 235, 248 

explanation 63-74, 147-148 

head-variant numbers, examples 167-176, 

180-188 

plates showing 167, 170, 176, 178, 179, 180 

introducing glyph, identification by 136 

irregular forms of, examples . . . 191-194, 203-207 

order of reading 129, 136-138, 170, 268 

position of month signs in 152-154 

reference to Long Count 147-151 

regular forms of, interpretation 167-191 

replacement by ukahlaykatunob dating. 84-85 

starting point 108, 109, 113-114, 

125-126, 136, 159, 162, 203-207 

used in codices 266 

examples. . . : 266-273 

plate showing 266 

used on monuments 85 

Inscriptions on monuments— 

cycles in, numbering. 108-113 

date of, contemporaneous 179, 

194, 203, 209-210, 213, 220-222 

date of carving, usual 194 

day signs in 38 

errors 245-260 

historical dates 179 

interpretation 33-35 

examples 166-250 

method 134-155 

length of great cycle used in 107-114 

niuneration glyphs. See Numerals. 
Sec o!so Monuments; Stel«. 
Introducing glyph— 

lack 208 

nature 64-68, 125-127, 136, 157-168 

Inverted glyph, meaning 211 

Itzamna (god), nature 16 



Justice, rules of. . 



Katun (time period)— 

glyph 

identification in u kahlay katunob 79-82 

length 62,136 

monument erected to mark end 260 

naming 80-82 

series of. 79.86 

use of, in Period-ending dates 222-225 



282 



INDEX 



Kin. See Day. 
KxiKULCAN (god), nature. 



Page 
16-17 



Laeok, customs 9 

Landa, Bishop Diego de— 

biography - 7 

on Maya alphabet 27 

on Maya calendar 42, 44, 45, 84 

on Maya customs 7, 13-14, 19 

on Maya records 34, 36 

Landey, M. D., investigations 194 

Letben Plate, interpretation 179, 194-198 

LlTEKATUHE, list XV-Xvi 

See also Bibliogkaphy. 
Long Count— 

date fixing in 147-151, 240-245 

nature 60-63 

See also Chronology. 

Maize GoD,nature 18 

Malee, Teobeet— 

cited 162, 

166, 170, 176, 177, 178, 207, 210, 224, 226, 227, 231 

on Altar 5 at TIkal 244 

Manners and customs, description 7-21 

Marriage customs 8-9 

Maes-Solar period, relation to tonalamatl. 278 

Mat pattern of glyphs 191-194 

Maudslay, a. p.— 

cited 157, 167, 169, 170, 171, 173, 175, 179, 

180, 181, 183, 185, 186, 188, 191, 203, 
205, 213, 215, 218, 220, 223, 224, 225, 
226, 227, 228, 229, 230, 235, 240, 242 

on zero glyph 93 

Maya, surviving tribes 1-2 

Maya, Southern— 

cities 2-4 

occupancy of, diagram showing 15 

government 15-16 

rise and fall 2-4 

Mayapan (city)— 

history 4-6 

mortuary customs 12 

time records 33-34 

Military customs, nature 10-11 

Minus sign. See Backward sign. 
Month. See XJinal. 
Monuments— 

age 249-250 

date of erection 179, 

194, 203, 209-210, 213, 220-222 

historical dates on 179 

period-marking function 33-35, 249-250 

texts. See Inscriptions. 

See also Stel.^;. 

Moon, computation of revolutions 32 

MOELEY, S. G., on Books of Chilan Balam. . 3 
Mythology, dates 179, 180, 194, 228 

Nacon (ofBclal), duties 13 

Nahua, influence on Maya 5-6 

Naranjo (city)— 

antiquity 16 

Stela 22, interpretation 162-164 

Stela 23, error in 248 

interpretation 224 

Stela 24, Interpretation 166-167 

Supplementary Series, absence 163-164 



Normal date, fixing of 61 

Normal forms of time-peeiod glyphs. 

See Time PERIODS. 
North Star, deification 18 

NXTMBERS, EXPRESSION— 

high 103-134 

thirteen to nineteen 96, 101, 111-112 

Numerals- 

bar and dot system 87-95 

examples, plates showing 157, 

167,170,176,178,179 

colors 91, 251 

combinations of, tor higher numbers. . . 105-107 

forms 87-104 

head-variant forms 24-25, 87, 96-104 

plates showing 167, 170, 176, 178, 179, 180 

one to nineteen, bar and dot forms 88-90 

head -variant forms 97-101 

order of reading 23, 129, 133, 137-138, 156, 170 

ornamental variants 89-91 

parallels to Roman and Arabic systems.. 87 

solution 134-155 

systems 87-134 

comparison 133 

See also Vigesimal system. 

transcribing, mode 138 

See also Hiekoglyphs; Thirteen; 
Twenty; Zero. 
Numerical coefficients 127-128 

Palenqtie (city)— 

history 15 

palace stairway inscription, interpre- 
tation 183-185 

Temple of the Cross, tablet, interpreta- 
tion 205-207,227 

Temple of the Foliated Cross, tablet, in- 
terpretation 180-181, 223-224, 227 

Temple of the Inscriptions, tablet, inter- 
pretation 84, 225-226 

Temple of the Sun, tablet, interpreta- 
tion 181-1S2 

PEEIOD-ENDING DATES— 

ending glyph 102 

examples, interpretation 222-240 

plates showing 223, 227, 233, 235 

glyphs 77-79, 102 

katun used in 222-225 

nature 222 

tun used in 225-226 

Period-marking Stones. See Monuments. 
Phonetic writing — 

argument for 26-30 

traces discovered.-. iv, 26-30 - 

PlEDRAS Negras (city)— 

altar inscription, interpretation 227 

antiquity 15 

Stela 1, interpretation 210-213 

Stela 3, interpretation 233-235 

Plongeon, F. Le, cited 27 

Ponce, Alonzo, on Maya records 36 

Priesthood, organization ; 20-21 

Prophesying, codices used for 31 

Prophetic dates — 

examples 229-233 

use 271-272 



INDEX 



288 



QuEN Sahto (city)— 

history 231 

Stela 1, interpretation 199-201 

Stela 2, interpretation 201-203 

QuiRiGUA (city)— 

Altar M, interpretation 240-242 

five-tun period used at 165-166 

tounding of, possible date 221-222 

monuments 192 

Stela A, interpretation 179-180 

Stela C, interpretation. 173-175, 179, 203-204, 226 

Supplementary Series, absence 175 

Stela D, interpretation 239 

Stela E, error in 247-248 

Interpretation 236-240 

Stela F, interpretation 218-222, 239-240 

plates showing 218, 220 

Stela H, interpretation 192-194 

Stela I, interpretation 164-166 

Stela J, interpretation 215-218, 239-240 

Stela K, interpretation 213-215 

Zoomorph G, interpretation 186-187, 

229-230,239-240 
Zoomorph P, interpretation 157-162 

Eeading, order of 23, 

129, 133, 135, 138, 156, 170, 268 

Religion, nature 16-21 

Eenaissance, commencement . .' 4 

Rochefoucauld, F. A. de la, alphabet de- 
vised by 27 

Roman system of numbers, parallel 87 

RosNT, Leon de, cited 27 

Rulekship— 

nature 12-13 

succession 13-14 

Scarification, practice 7 

SCHELLHAS, Dr. PAUL, investigations 265 

Sculpture, development 2-3 

Secondary-series dating — 

examples, interpretation 207-222, 233-240 

plates showing . 207, 210, 213, 218, 220, 233, 235 

explanation 74-76, 207 

irregular forms 236 

order of reading 129, 137-138, 208 

reference to Initial Series 209-211, 217-218 

starting point. . 76, 135-136, 208-210, 218, 240-245 

determination 240-245 

Seibal (city)— 

antiquity 15 

Stela 11, interpretation 230-231 

Selee, Dr. Eduaed— 

cited 2, 43, 199 

on Aztec calendar 58 

on hieroglyphics 30 

Serpent numbers — 

interpretation 273-275 

nature 273 

range 32, 273 

Slaves, barter in 9 

Southern Maya. See Maya, southern. 

Spanish conquest, influence 6-7 

Spectacle glyph, function 94 

Spinden, Dr. H. J.— 

cited 187 

works 4 



SiEL.*:— Page 

character 22 

dates 33, 83-84 

inscriptions on 22, 33-35 

See also Monuments, and names of cities. 

Stones, inscriptions on 22 

Supeefix, effect 120-122 

Supplementary Series— 

closing sign 152-133, 170 

explanation 152, 161 

lack of, examples 163-164, 175 

position 152, 238 

Symmetry m glyphs, modifications due to.-. 23-24, 

88-91, 128 

Terminal dates— 

determination 138-151 

importance as check on calculations.. . 154^155 
position 151-154 

Textbooks, need for vii 

Thirteen— 

glyphs 96,205 

numbers above, expression 96, 101, 111-112 

Thomas, Dr. Cyrus- 

cited , 31 

on Maya alphabet 27 

Thompson, E. H., investigations 11 

TiKAL (city)— 

Altar 5, interpretation 242-245 

antiquity 127 

history 15 

Stela 3, importance 179 

interpretation 178-179 

Stela 5, Interpretation 225 

Stela 10, interpretation 114-127 

Stela 16, association with Altar 5 244 

interpretation 224, 244 

Time— 

counting backward 146-147 

counting forward 138-146 

glyphs for, only ones deciphered 26, 31 

lapse of, determination 134-156 

expression 63-64, 105-107 

indicated by black glyphs 251 

marked by monuments 33-35, 249-2S0 

method of describing 46-48 

recording 33-35 

use of numbers 134 

starting point 60-62, 113-114, 124^125 

See also Chronology. 

Time-marking stones. See Monuments. 

Time periods— 

full-figure glyphs 07-68, 188-191 

plate showing igg 

head-variant glyphs 67-74 

plates showing 167, 170, 176, 178, 179, 180 

length 62 

normal glyphs 07-74 

plate showing 157 

omission of 128 

reduction to days 134-135 

See also CrcLn; GreatCycle; Haab: Ka- 
tun; Tonalamatl; Tun; Uinal. 

ToNALAMATL (time period) — 

graphic representation 93 

interpretation 254-266, 



284 



rSTDEX 



IoxAi_<j£Aii. (tEiii£ period) — Coiitinae<L Page 

nature -tl-44,2B5 

relatkn to zen> £izii- 9S-94 

iuinm^ pomt 253-253 

r-:'ii~L>iiHis 44 

texts iceoidiiig 251-2B6 

esentialpaFts oL 265 

nserfglnfclar'Wwiai.. 93,130,2^260,263 

Bsedmeodiccs... 251-366 

plates dnwing. 254, 26a 262, 363 

TKffH ffi dir fnafciiwi _. 251 

wlieelofdajs- 43 

See dtga Xeas, s^ched. 

TEiSsLAnOS OF Q.TPSS — 

errors ._ 154-133 

metlicids .., 134-135 

pragiess 250 

Trx (time peruid) — 

giyi*- -- TO 

ksigth 62,135 

tiseof, in Feriod-Qidiiig dates 225-226 

TirXEia. STAmETCE, mterpretaSioffii—. 17^,1^-196 

TTrE3iTF— 

^iyi*s. 91-92.130 

seed Sor, In codices 92.130 

□eedlesszie^ of , in iuscriptitKis 92 

cse oCin 2S4.28).263 

UiXii.— 

days. 42 

Srstday. 53 

gJjlfa- 94 

gijiiL jo-n 

iQlgth 45. a 135 

list -_ 45 

names and gtyp&s £ek _ 4>-v51 

XT KiHUx ELuirsoB dattsg — 

aecnraey. .S2 

antiqoit}-. .._ __ aa-SB 

etpfctiwtwm. T9-?6 

kzitnn seqnaice io— 52 



U K<m.<Y Katitsob dahsg — Continned. Page 

Older of leadii^ I3f 

repfafympfitof Initial-sgiea dating by.-- «4-^ 

rx](Ai.(eit]r),iDa!idiiig 4 

VEStrS-SOtiB PEBKH) — 

dlYfaODS. 31-32 

rplafeiftii tt\ t Knat:^m-> El 32.277-27^ 

VigganHT. stXTSxaas — 

diseoTery. iii 

..- 63-^11)5^34 

fl 

iBdmeadiees 266-2:3 

YgXAgmsgE, S, J-, flB Haya le ew ds 36 

TCiB Goi>,natare 17 

WEi«Bi3,<4aaaeter..- lO-ll 

WoRU>, destmetios- pfopfaeey 33 

WOSLB EPOCH, ^ypli 125J27 

WoasHiP. laaetieea 19-29 

WKZfise. Set 'BssxoGL'vrBacs; Xiimsraxs; 

XiMiS Ek (god), natnre. _.. 13 

TiXCHiEiX (oty) — 

IfTTtri, error in 245-216 

Untel2l,mt»piEtatkB 207-210 

Steiall.liitapretatitim VK-tT! 

Stroegge 44, fnterpretatfon 177-1X8 

YEiB, SajCKES, use in divinatLOE 251 

Str^mhm Tf>ir.T ai»»ti. 
YUCAIAS — 

eoiimizatum i-i 

Span^iccaiqiiest. S^7 

«3ter3i^i{)ij _. 1 

Tcif Kjlax (god), nature i- 

Zebo — 

SJ^K. K-95,Iffll-MB 

- 98-&t 

- 93 



o 



^^^'