18013	----	Note: Project Gutenberg also has an HTML version of this file which includes the original illustrations. See 18013-h.htm or 18013-h.zip: (http://www.gutenberg.net/dirs/1/8/0/1/18013/18013-h/18013-h.htm) or (http://www.gutenberg.net/dirs/1/8/0/1/18013/18013-h.zip) Transcriber's Note: A number of typographical errors have been maintained in this version of this book. A complete list is found at the end of the text. Papers of the Peabody Museum of American Archaeology and Ethnology, Harvard University Vol. IV.--No. 1 REPRESENTATION OF DEITIES OF THE MAYA MANUSCRIPTS by DR. PAUL SCHELLHAS Second Edition, Revised With 1 Plate of Figures and 65 Text Illustrations Translated by Miss Selma Wesselhoeft and Miss A. M. Parker Translation revised by the Author Cambridge, Mass. Published by the Museum December, 1904. NOTE. In order to make more widely known and more easily accessible to American students the results of important researches on the Maya hieroglyphs, printed in the German language, the Peabody Museum Committee on Central American Research proposes to publish translations of certain papers which are not too lengthy or too extensively illustrated. The present paper by one of the most distinguished scholars in this field is the first of the series. F. W. PUTNAM. Harvard University September, 1904. PREFACE. Since the first edition of this pamphlet appeared in the year 1897, investigation in this department of science has made such marked progress, notwithstanding the slight amount of material, that a revision has now become desirable. It can be readily understood, that a new science, an investigation on virgin soil, such as the Maya study is, makes more rapid progress and develops more quickly than one pertaining to some old, much explored territory. In addition to numerous separate treatises, special mention should be made of Ernst Förstemann's commentaries on the three Maya manuscripts (Kommentar zur Mayahandschrift der Königlichen öffentlichen Bibliothek zu Dresden, Dresden 1901, Kommentar zur Madrider Mayahandschrift, Danzig 1902, and Kommentar zur Pariser Mayahandschrift, Danzig 1903) which constitute a summary of the entire results of investigation in this field up to the present time. The proposal made in the first edition of this pamphlet, that the Maya deities be designated by letters of the alphabet, has been very generally adopted by Americanists, especially by those in the United States of America. This circumstance, in particular, has seemed to make it desirable to prepare for publication a new edition, improved to accord with the present state of the science. Warmest thanks are above all due to Mr. Bowditch, of Boston, who in the most disinterested manner, for the good of science, has made possible the publication of this new edition. January, 1904. P. SCHELLHAS. THE MATERIAL OF THE MANUSCRIPTS. The three manuscripts which we possess of the ancient Maya peoples of Central America, the Dresden (Dr.), the Madrid (Tro.-Cort.) and the Paris (Per.) manuscripts, all contain a series of pictorial representations of human figures, which, beyond question, should be regarded as figures of gods. Together with these are a number of animal figures, some with human bodies, dress and armor, which likewise have a mythologic significance. The contents of the three manuscripts, which undoubtedly pertain to the calendar system and to the computation of time in their relation to the Maya pantheon and to certain religious and domestic functions, admit of the conclusion, that these figures of gods embody the essential part of the religious conceptions of the Maya peoples in a tolerably complete form. For here we have the entire ritual year, the whole chronology with its mythological relations and all accessories. In addition to this, essentially the same figures recur in all three manuscripts. Their number is not especially large. There are about fifteen figures of gods in human form and about half as many in animal form. At first we were inclined to believe that further researches would considerably increase the number of deities, but this assumption was incorrect. After years of study of the subject and repeated examination of the results of research, it may be regarded as positively proved, that the number of deities represented in the Maya manuscripts does not exceed substantially the limits mentioned above. The principal deities are determined beyond question. The way in which this was accomplished is strikingly simple. It amounts essentially to that which in ordinary life we call "memory of persons" and follows almost naturally from a careful study of the manuscripts. For, by frequently looking attentively at the representations, one learns by degrees to recognize promptly similar and familiar figures of gods, by the characteristic impression they make as a whole, or by certain details, even when the pictures are partly obliterated or exhibit variations, and the same is true of the accompanying hieroglyphs. A purely inductive, natural science-method has thus been followed, and hence this pamphlet is devoted simply to descriptions and to the amassing of material. These figures have been taken separately out of the manuscripts alone, identified and described with the studious avoidance of all unreliable, misleading accounts and of all presumptive analogies with supposedly allied mythologies. Whatever cannot be derived from the manuscripts themselves has been wholly ignored. Hypotheses and deductions have been avoided as far as possible. Only where the interpretation, or the resemblance and the relations to kindred mythologic domains were obvious, and where the accounts agreed beyond question, has notice been taken of the fact so that the imposed limitations of this work should not result in one-sidedness. Since, for the most part, the accounts of Spanish authors regarding the mythology of the Mayas correspond only slightly or not at all with these figures of gods, and all other conjectures respecting their significance are very dubious, the alphabetic designation of the deities, which was tentatively introduced in the first edition of this work, has been preserved. This designation has proved to be practical. For the plate at the end of this pamphlet, examples as characteristic as possible of the individual figures of gods have been selected from the manuscripts. It is a well known fact that we possess no definite knowledge either of the time of the composition or of the local origin of the Maya manuscripts. The objection might, therefore, be raised that it is a hazardous proceeding to treat the material derived from these three manuscripts in common, as if it were homogeneous. But these researches themselves have proved beyond a doubt, that the mythologic import of the manuscripts belongs to one and the same sphere of thought. Essentially the same deities and the same mythologic ideas are, without question, to be found in all the manuscripts. The material of the inscriptions has been set entirely at one side, because the style of representation contained in them, both of the mythologic forms and of the hieroglyphs, renders comparison exceedingly difficult. In this field especial credit is due to Förstemann and Seler, for the work they have done in furtherance of interpretation, and mention should not be omitted of the generosity with which the well known promoter of Americanist investigations, the Duke of Loubat, has presented to the Berlin Museum of Ethnology costly originals of reliefs and inscriptions for direct study. The representations on the reliefs from the Maya region, it is true, give evidence of dealing with kindred mythologic conceptions. Figures and hieroglyphs of gods, made familiar by the manuscripts, can also be found here and there. But on the whole so little appears in support of instituting a comparison with the manuscripts, that it seems expedient to leave the inscriptions for independent and special study. I. REPRESENTATIONS OF GODS. A. The Death-God. [Illustration: Figs. 1-6] God A is represented as a figure with an exposed, bony spine, truncated nose and grinning teeth.[10-1] It is plainly to be seen that the head of this god represents a skull and that the spine is that of a skeleton. The pictures of the death-god are so characteristic in the Maya manuscripts that the deity is always easily recognized. He is almost always distinguished by the skeleton face and the bony spine. Several times in the Dresden manuscript the death-god is pictured with large black spots on his body and in Dr. 19b a woman with closed eyes, whose body also displays the black spots, is sitting opposite the god. While the Aztecs had a male and a female death-deity, in the Maya manuscripts we find the death-deity only once represented as feminine, namely on p. 9c of the Dresden manuscript. Moreover the Dresden manuscript contains several different types of the death-god, having invariably the fleshless skull and (with the exception of Dr. 9c) the visible vertebrae of the spine. Several times (Dr. 12b and 13b) he is represented apparently with distended abdomen. A distinguishing article of his costume is the stiff feather collar, which is worn only by this god, his companion, the war-god F, and by his animal symbol, the owl, which will both be discussed farther on. His head ornament varies in the Dresden Codex; in the first portion of the manuscript, relating in part to pregnancy and child-birth (see the pictures of women on p. 16, et seq.), he wears on his head several times a figure occurring very frequently just in this part of the Dresden Codex and apparently representing a snail (compare Dr. 12b and 13b), which among the Aztecs is likewise a symbol of parturition. In view of these variations in the pictures of the Dresden Codex, it is very striking that in the Codex Tro.-Cortesianus, there is only one invariable type of the death-god. [10-1] See Plate for representations of the gods, A-P A distinguishing ornament of the death-god consists of globular bells or rattles, which he wears on his hands and feet, on his collar and as a head ornament. As can be distinctly seen in Dr. 11a, they are fastened with bands wound around the forearm and around the leg; in Dr. 15c these bells are black. Among the symbols of the death-god a cross of two bones should be mentioned, which is also found in the Mexican manuscripts. This cross of bones seems to occur once among the written characters as a hieroglyph and then in combination with a number: Tro. 10.* The figure [Death-god symbol] is also a frequent symbol of the death-god. Its significance is still uncertain, but it also occurs among the hieroglyphs as a death-sign and as a sign for the day Cimi (death). The hieroglyphs of the death-god have been positively determined (see Figs. 1 to 4). Figs. 1 and 2 are the forms of the Dresden manuscript and Figs. 3 and 4 are those of the Madrid manuscript. God A is almost always distinguished by two hieroglyphs, namely Figs. 1 and 2 or 3 and 4. Moreover the hieroglyphs are always the same, have scarcely any variants. Even in Dr. 9c, where the deity is represented as feminine, there are no variations which might denote the change of sex. The hieroglyphs consist chiefly of the head of a corpse with closed eyes, and of a skull. The design in front of the skull in Figs. 2 and 4 and under it in Fig. 3 is a sacrificial knife of flint, which was used in slaying the sacrifices, and is also frequently pictured in the Aztec manuscripts. The dots under Fig. 1 are probably intended to represent blood. The death-god is represented with extraordinary frequency in all the Maya manuscripts. Not only does the figure of the god itself occur, but his attributes are found in many places where his picture is missing. Death evidently had an important significance in the mythologic conceptions of the Mayas. It is connected with sacrifice, especially with human sacrifices performed in connection with the captive enemy. Just as we find a personification of death in the manuscripts of the Mayas, we also find it in the picture-writings of the ancient Mexicans, often surprisingly like the pictures of the Maya codices. The Aztec death-god and his myth are known through the accounts of Spanish writers; regarding the death-god of the Mayas we have less accurate information. Some mention occurs in Landa's Relacion de las cosas de Yucatan, §XXIII, but unfortunately nothing is said of the manner of representing the death-god. He seems to be related to the Aztec Mictlantecutli, of whom Sahagun, Appendix to Book III, "De los que iban al infierno y de sus obsequias," treats as the god of the dead and of the underworld, Mictlan. When the representations of the latter, for example in the Codex Borgia, and in the Codex Vaticanus No. 3773, are compared with those of the Maya manuscripts, there can be hardly a doubt of the correspondence of the two god figures. In the Codex Borgia, p. 37, he is represented once with the same characteristic head ornament, which the death-god usually wears in the Maya manuscripts, and in the Codex Fejervary, p. 8, the death-god wears a kind of breeches on which cross-bones are depicted, exactly as in Dr. 9 (bottom). Bishop Landa informs us that the Mayas "had great and immoderate dread of death." This explains the frequency of the representations of the death-god, from whom, as Landa states, "all evil and especially death" emanated. Among the Aztecs we find a male and a female death-deity, Mictlantecutli and Mictlancihuatl. They were the rulers of the realm of the dead, Mictlan, which, according to the Aztec conception, lay in the north; hence the death-god was at the same time the god of the north. It agrees with the calendric and astronomic character of the Maya deities in the manuscripts, that a number of the figures of the gods are used in connection with specified cardinal points. Since, according to the Aztec conception, the death-god was the god of the north, we might expect that in the Maya manuscripts also, the death-god would be always considered as the deity of the north. Nevertheless this happens only _once_, namely in the picture at the end of Codex Cort., pp. 41 and 42. Elsewhere, on the other hand, this god is connected with other cardinal points, thus Dr. 14a with the west or east (the hieroglyph is illegible, but it can be only west or east), and in Dr. 27c with the west. It is interesting to note that once, however, in a series of cardinal points, the hieroglyph of the death-god connected with the numeral 10 stands just in the place of the sign of the north; this is on Tro. 24* (bottom). In regard to the name of the death-god in the Maya language, Landa tells us that the wicked after death were banished to an underworld, the name of which was "Mitnal", a word which is defined as "Hell" in the Maya lexicon of Pio Perez and which has a striking resemblance to Mictlan, the Aztec name for the lower regions. The death-god Hunhau reigned in this underworld. According to other accounts (Hernandez), however, the death-god is called Ahpuch. These names can in no wise serve as aids to the explanation of the hieroglyphs of the death-god, since they have no etymologic connection with death or the heads of corpses and skulls, which form the main parts of the hieroglyph. Furthermore, the hieroglyphs of the gods certainly have a purely ideographic significance as already mentioned above, so that any relation between the names of the deities and their hieroglyphs cannot exist from the very nature of the case. The day of the death-god is the day Cimi, death. The day-sign Cimi corresponds almost perfectly with the heads of corpses contained in the hieroglyphs of the death-god. A hieroglyphic sign, which relates to death and the death-deity and occurs very frequently, is the sign Fig. 5, which is probably to be regarded as the ideogram of the owl. It represents the head of an owl, while the figure in front of it signifies the owl's ear and the one below, its teeth, as distinguishing marks of a bird of prey furnished with ears and a powerful beak. The head of the owl appears on a human body several times in the Dresden manuscript as a substitute for the death-deity, thus Dr. 18c, 19c, 20a and 20c and in other places, and the hieroglyphic group (Fig. 5) is almost a regular attendant hieroglyph of the death-god. A series of other figures of the Maya mythology is connected with the death-god. This is evident from the fact that his hieroglyphs or his symbols occur with certain other figures, which are thus brought into connection with death and the death-deity. These figures are as follows: 1. His companion, god F, the god of war, of human sacrifice and of violent death in battle, apparently a counterpart of the Aztec Xipe, who will be discussed farther on. 2. The moan bird. See beyond under Mythological Animals, No. 1. 3. The dog. See the same, No. 3. 4. A human figure, possibly representing the priest of the death-god (see Dr. 28, centre, Dr. 5b and 9a). The last figure is a little doubtful. It is blindfolded and thus recalls the Aztec deity of frost and sin, Itztlacoliuhqui. A similar form with eyes bound occurs only once again in the Maya manuscripts, namely Dr. 50 (centre). That this figure is related to the death-god is proved by the fact that on Dr. 9a it wears the Cimi-sign on the middle piece of the chain around its neck. Furthermore it should be emphasized that the Aztec sin-god, Itztlacoliuhqui, likewise appears with symbols of death. 5. An isolated figure, Dr. 50a (the sitting figure at the right). This wears the skull as head ornament, which is represented in exactly the same way as in the Aztec manuscripts (see Fig. 6). 6. Another isolated figure is twice represented combined with the death-god in Dr. 22c. This picture is so effaced that it is impossible to tell what it means. The hieroglyph represents a variant of the death's-head, Cimi. It seems to signify an ape, which also in the pictures of the Mexican codices was sometimes used in relation to the death-god. The symbols of the death-god are also found with the figure without a head on Dr. 2 (45)a, clearly the picture of a beheaded prisoner. Death symbols occur, too, with the curious picture of a hanged woman on Dr. 53b, a picture which is interesting from the fact that it recalls vividly a communication of Bishop Landa. Landa tells us, the Mayas believed that whoever hanged himself did not go to the underworld, but to "paradise," and as a result of this belief, suicide by hanging was very common and was chosen on the slightest pretext. Such suicides were received in paradise by the goddess of the hanged, Ixtab. Ix is the feminine prefix; tab, taab, tabil mean, according to Perez' Lexicon of the Maya Language, "cuerda destinada para algun uso exclusivo". The name of this strange goddess is, therefore, the "Goddess of the Halter" or, as Landa says, "The Goddess of the Gallows". Now compare Dr. 53. On the upper half of the page is the death-god represented with hand raised threateningly, on the lower half is seen the form of a woman suspended by a rope placed around her neck. The closed eye, the open mouth and the convulsively outspread fingers, show that she is dead, in fact, strangled. It is, in all probability, the goddess of the gallows and halter, Ixtab, the patroness of the hanged, who is pictured here in company with the death-god; or else it is a victim of this goddess, and page 53 of the manuscript very probably refers, therefore (even though the two halves do not belong directly together), to the mythologic conceptions of death and the lower regions to which Landa alludes. 7. Lastly the owl is to be mentioned as belonging to the death-god, which, strange to say, is represented nowhere in the pictures realistically and so that it can be recognized, although other mythologic animals, as the dog or the moan bird, occur plainly as animals in the pictures. On the other hand, the owl's head appears on a human body in the Dresden manuscript as a substitute for the death-deity itself, for example on Dr. 18c, 19c, 20a and 20c and elsewhere, and forms a regular attendant hieroglyph of the death-god in the group of three signs already mentioned (Fig. 5). Among the antiquities from the Maya region of Central America, there are many objects and representations, which have reference to the cultus of the death-god, and show resemblances to the pictures of the manuscripts. The death-god also plays a role, even today, in the popular superstitions of the natives of Yucatan, as a kind of spectre that prowls around the houses of the sick. His name is Yum Cimil, the lord of death. B. The God With the Large Nose and Lolling Tongue. [Illustration: Figs. 7-10] The deity, represented most frequently in all the manuscripts, is a figure with a long, proboscis-like, pendent nose and a tongue (or teeth, fangs) hanging out in front and at the sides of the mouth, also with a characteristic head ornament resembling a knotted bow and with a peculiar rim to the eye. Fig. 7 is the hieroglyph of this deity. In Codex Tro.-Cortesianus it usually has the form of Fig. 8. God B is evidently one of the most important of the Maya pantheon. He must be a universal deity, to whom the most varied elements, natural phenomena and activities are subject. He is represented with different attributes and symbols of power, with torches in his hands as symbols of fire, sitting in the water and on the water, standing in the rain, riding in a canoe, enthroned on the clouds of heaven and on the cross-shaped tree of the four points of the compass, which, on account of its likeness to the Christian emblem, has many times been the subject of fantastic hypotheses. We see the god again on the Cab-sign, the symbol of the earth, with weapons, axe and spears, in his hands, planting kernels of maize, on a journey (Dr. 65b) staff in hand and a bundle on his back, and fettered (Dr. 37a) with arms bound behind his back. His entire myth seems to be recorded in the manuscripts. The great abundance of symbolism renders difficult the characterization of the deity, and it is well-nigh impossible to discover that a single mythologic idea underlies the whole. God B is quite often connected with the serpent, without exhibiting affinity with the Chicchan-god H (see p. 28). In Dr. 33b, 34b and 35b, the serpent is in the act of devouring him, or he is rising up out of the serpent's jaws, as is plainly indicated also by the hieroglyphs, for they contain the group given in Fig. 10, which is composed of the rattle of the rattlesnake and the opened hand as a symbol of seizing and absorption. God B himself is pictured with the body of a serpent in Dr. 35b and 36a (compare No. 2 of the Mythological Animals). He likewise occurs sitting on the serpent and in Dr. 66a he is twice (1st and 3d figures) pictured with a snake in his hand. God B sits on the moan head in Dr. 38c, on a head with the Cauac-sign in Dr. 39c, 66c, and on the dog in Dr. 29a. All these pictures are meant to typify his abode in the air, above rain, storm and death-bringing clouds, from which the lightning falls. The object with the cross-bones of the death-god, on which he sits in Dr. 66c, can perhaps be explained in the same manner. As the fish belongs to god B in a symbolic sense, so the god is represented fishing in Dr. 44 (1). His face with the large nose and the tongue (or fangs) hanging out on the side in Dr. 44 (1)a (1st figure) is supposed to be a mask which the priest, representing the god, assumes during the religious ceremony. Furthermore the following four well-known symbols of sacrificial gifts appear in connection with god B in the Dresden manuscript; a sprouting kernel of maize (or, according to Förstemann, parts of a mammal, game), a fish, a lizard and a vulture's head, as symbols of the four elements. They seem to occur, however, in relation also to other deities and evidently are general symbols of sacrificial gifts. Thus they occur on the two companion initial pages of the Codex Tro.-Cortesianus, on which the hieroglyphs of gods C and K are repeated in rows (Tro. 36-Cort. 22. Compare Förstemann, Kommentar zur Madrider Handschrift, pp. 102, 103). God B is also connected with the four colors--yellow, red, white and black--which, according to the conception of the Mayas, correspond to the cardinal points (yellow, air; red, fire; white, water; black, earth) and the god himself is occasionally represented with a black body, for example on Dr. 29c, 31c and 69. This is expressed in the hieroglyphs by the sign, Fig. 9, which signifies black and is one of the four signs of the symbolic colors for the cardinal points. God B is represented with all the _four cardinal points_, a characteristic, which he shares only with god C, god K, and, in one instance, with god F (see Tro. 29*c); he appears as ruler of all the points of the compass; north, south, east and west as well as air, fire, water and earth are subject to him. Opinions concerning the significance of this deity are much divided. It is most probable that he is Kukulcan, a figure occurring repeatedly in the mythology of the Central American peoples and whose name, like that of the kindred deity Quetzalcoatl among the Aztecs and Gucumatz among the Quiches, means the "feathered serpent", "the bird serpent". Kukulcan and Gucumatz are those figures of Central American mythology, to which belong the legends of the creation of the world and of mankind. Furthermore Kukulcan is considered as the founder of civilization, as the builder of cities, as hero-god, and appears in another conception as the rain-deity, and--since the serpent has a mythologic relation to water--as serpent deity. J. Walter Fewkes, who has made this god-figure of the Maya manuscripts the subject of a monograph (A Study of Certain Figures in a Maya Codex, in American Anthropologist, Vol. VII, No. 3, Washington, 1894), also inclines to the belief that B is the god Kukulcan, whom he conceives of as a serpent-and rain-deity. This view has been accepted by Förstemann (Die Tagegötter der Mayas, Globus, Vol. 73, No. 10) and also by Cyrus Thomas (Aids to the Study of the Maya Codices, Washington, 1888). The same opinion is held also by E. P. Dieseldorff, who, a resident of Guatemala, the region of the ancient Maya civilization, has instituted excavations which have been successful in furnishing most satisfactory material for these researches (see Dieseldorff: Kukulcan, Zeitschrift für Ethnologie, 1895, p. 780). Others have considered god B as the first parent and lord of the heavens, Itzamná who has a mythologic importance analogous to that of Kukulcan. Itzamná is also held to be the god of creation and founder of civilization and accordingly seems to be not very remotely allied to the god Kukulcan. Others again, for example Brasseur de Bourbourg and Seler, have interpreted the figure of god B to represent the fourfold god of the cardinal points and rain-god Chac, a counterpart of the Aztec rain-god Tlaloc. The fact that this god-figure is so frequently connected with the serpent and the bird is strongly in favor of the correctness of the supposition, that we should see in god B a figure corresponding to the Kukulcan of tradition. Thus we see the god represented once with the body of a serpent and with a bird near by (Cort. 10b), while B's hieroglyph appears both times in the text. God B is also pictured elsewhere repeatedly with a serpent body, thus for example on Dr. 35b, 36a. On pages 4-6 of the Codex Cortesianus he is pictured six times and each time in connection with a serpent. The accounts we have received concerning the mythology of the Maya peoples are very meagre and owing to the uncertainty respecting the origin of the Maya manuscripts, it cannot even be determined which of these accounts are applicable to the Maya manuscripts, or, indeed, whether they are applicable at all. For it is by no means positively proved that these manuscripts did not originate in regions of Maya culture, regarding which we have received no accounts at all. As our present purpose is purely that of description and determination, it remains quite unimportant which of these recorded figures of gods shall be regarded as god B. God B is nearly allied to, but in no wise identical with, the deity with the large ornamented nose, designated by K, who will be discussed farther on. God K is an independent deity designated by a special hieroglyph, but like C he stands in an unknown relation to God B (for details see K). Finally it should be mentioned, that god B never appears with death symbols. He is clearly a deity of life and creation, in contrast to the powers of death and destruction. His day seems to be Ik (aspiration, breath, life). (Compare Förstemann, Die Tagegötter der Mayas, Globus, Vol. 73, No. 10). C. The God with the Ornamented Face. [Illustration: Figs. 11-16] This is one of the most remarkable and most difficult figures of the Maya manuscripts, and shows, at the same time, how imperfect must be the information we have received in regard to the Maya mythology, since from the frequency of his representations he is obviously one of the most important deities and yet can be identified with none of the representations of gods handed down to us. His hieroglyph is definitely determined (Figs. 11, 12). The circular design in front of the forehead of the hieroglyph head seems, as a variant from the Codex Tro. (Fig. 12) leads us to suppose, to denote the ideographic representation of pouring out or emptying a vessel, the contents of which flow into the mouth of the god. Another variant of this prefix occurs in Tro. 13*b; Fig. 15, the symbol of the sacrificial knife, and instead of the prefix the numeral 13 occurs in one instance! (Tro. 12*c). The head alone, without any accessory symbol whatever, is also found a few times, not in the text, however, but only in the pictures, for example Cort. 10 (bottom) and Tro. 13* (bottom). This deity does not occur very often in the Dresden manuscript, the places where it is depicted are: Dr. 5a, 6c, 13b, 35a, 68a, and as a subordinate figure on 8c, 42a. His hieroglyph occurs alone a few times, as in Dr. 4; it is more frequent in the Madrid manuscript. It appears on pp. 15 to 18 of the Paris manuscript. In regard to the significance of this deity, he doubtless represents the personification of a heavenly body of astronomic importance, probably the polar star. In Codex Cort. 10 (bottom), his head is represented surrounded by a nimbus of rays, which can only mean a star (see Fig. 13). On the lower part of the same page, the third picture from the left, we again see the deity hanging from the sky in a kind of rope. Furthermore it appears in Codex Tro. 20, 22 and 23 (centre) Fig. 14, in the familiar rectangular planet signs. Tro. 17* (at the top) the head surmounts the cross-shaped tree of god B, which denotes the lofty, celestial abode. Indeed, these passages prove positively that a heavenly body underlies the idea of this deity. Furthermore, the head of this god recurs in entire rows in the calendric group of tabular form on the so-called initial page of the Codex Tro. 36, with its continuation in the Cort. p. 22, and in exactly the same manner in the allied passage of Tro. 14 (middle and bottom). In addition, his head is contained in the symbol for the north (Fig. 16); the head contained in this sign is in fact nothing else than the head of god C. Brinton also accepts this interpretation of god C. According to Förstemann (Die Mayahieroglyphen, Globus, Vol. 71, No. 5), the fact that the figure of god C in the Tonalamatl in Dr. 4a-10a occurs on the day Chuen of the Maya calendar, which corresponds to the day Ozomatli, the ape, in the Aztec calendar, seems to indicate that the singular head of C is that of an _ape_, whose lateral nasal cavity (peculiar to the American ape or monkey) is occasionally represented plainly in the hieroglyph picture. Hence it might further be assumed that god C symbolizes not the polar star alone, but rather the entire _constellation of the Little Bear_. And, in fact, the figure of a long-tailed ape is quite appropriate to the constellation, at any rate decidedly more so than the Bear; indeed, it suggests the prehensile tail by means of which the ape could attach himself to the pole and in the form of the constellation swing around the pole as around a fixed point. These astronomical surmises seem to be contradicted by the fact that god C, as already stated, is represented with all the four cardinal points (compare for example Cort. 10 and 11, bottom), which would certainly seem to harmonize ill with his personification of the north star, unless we assume, that in a different conception of the polar star he is ruler of the cardinal points, which are determined from him as a centre. It has already been remarked of B, that the deity C appears to stand in some sort of relation to him. In fact, we find on those pages of the Dresden manuscript, where B is represented with the four cardinal points, that the hieroglyph of C almost always occurs in the text also (for example Dr. 29, et seq., especially Dr. 32c). Indeed, C's hieroglyph is connected even with the signs of the symbolic colors of the cardinal points, already mentioned in connection with B. Finally, it should be borne in mind, that god C also seems to be connected in some way with the serpent (compare Dr. 36b, 1st and 3d pictures). According to Förstemann, the day ruled by C seems to be Chuen. D. The Moon- and Night-God. [Illustration: Figs. 17-20] This is a deity who is pictured in the form of an old man with an aged face and sunken, toothless mouth. He is frequently characterized by a long, pendent head ornament, in which is the sign Akbal, darkness, night, which also appears in his hieroglyph before the forehead of the deity, surrounded by dots as an indication of the starry sky. His name-hieroglyph is Fig. 17, and a second sign almost always follows (Fig. 18) which evidently serves likewise as a designation of the god, just as god A also is always designated by _two_ hieroglyphs. The second sign consists of two sacrificial knives and the sign of the day Ahau, which is equivalent to "king". The head of this deity appears in reduced, cursive form as the sign of the moon (Fig. 20). This character also has the significance of 20 as a number sign in the calendar. The association of these ideas probably rests upon the ancient conceptions, according to which the moon appearing, waxing, waning and again disappearing, was compared to man, and man in primeval ages was the most primitive calculating machine, being equivalent, from the sum of his fingers and toes, to the number 20. Twenty days is also the duration of that period during which the moon (aside from the new moon) is really _alive_. Moreover the sign (Fig. 20) appears in many places as a counterpart of the sign for the sun. God D occurs once as feminine in the same passage mentioned above, in which the death-deity is also pictured as feminine (Dr. 9c). In a few other places the god is, curiously enough, depicted with a short beard, as Dr. 4c, 7a, 27b. He seems to stand in an unknown relation to the water-goddess I (see this deity) with the serpent as a head ornament, compare Dr. 9c, where apparently this goddess is represented, though the text has D's sign; still it is possible that god D is pictured here with the attributes of goddess I. God D is not connected with the grim powers of destruction; he never appears with death symbols. In Dr. 5c and 9a he wears the snail on his head. He seems, therefore, like god A to be connected with birth. In Dr. 8c he is connected with god C, and this is quite appropriate, if we look upon these gods as heavenly bodies. The aged face, the sunken, toothless mouth are his distinguishing marks. In the Madrid manuscript, where god D occurs with special frequency, his chief characteristic, by which he is always easily recognized, is the single tooth in his under-jaw (see Fig. 19), compare too Dr. 8c, where the solitary tooth is also to be seen. In Dr. 9a (1st figure) the god holds in his hand a kind of sprinkler with the rattles of the rattlesnake, as Landa (Cap. 26) describes the god in connection with the rite of infant baptism (see also Cort. 26, Tro. 7*a and 13*c) A very remarkable passage is Tro. 15*; there a figure is pictured carving with a hatchet a head, which it holds in its hand. Above it are four hieroglyphs. The first shows a hatchet and the moon; the second probably represents simply a head, while the third and fourth are those of god D, the moon-god. This passage, the meaning of which is unfortunately still obscure seems to contain a definite explanation of god D. J. Walter Fewkes has made god D the subject of a special, very detailed monograph (The God "D" in the Codex Cortesianus, Washington, 1895) in which he has treated also of gods B and G, whom he considers allied to D. He believes D to be the god Itzamná, as do also Förstemann, Cyrus Thomas and Seler, and sees sun-gods in all three of these deities. Whether god D is to be separated from G and B as an independent deity, Fewkes thinks is doubtful. Brinton again holds that god D is Kukulcan. These different opinions show, at all events, on what uncertain grounds such attempts at interpretation stand, and that it is best to be satisfied with designating the deities by letters and collecting material for their purely descriptive designation. According to Förstemann the calendar day devoted to D is Ahau. E. The Maize-God. [Illustration: Figs. 21-27] This god bears on his head the Kan-sign and above it the ear of maize with leaves (Fig. 23); compare Dr. 9b (left figure), 11b, 12a, etc. The hieroglyph is definitely determined (Fig. 21). The god is identical with the figures recurring with especial frequency in the Madrid manuscript, the heads of which are prolonged upward and curved backward in a peculiar manner; compare Cort. 15a, 20c, 40 (bottom), Tro. 32*b (Figs. 25-27) and especially the representation in Dr. 50a (Fig. 24), which is very distinct. This head was evolved out of the conventional drawing of the ear of maize; compare the pictures of the maize plant in the Codex Tro., p. 29b (Fig. 22) with the head ornament of the god in Dr. 9b (Fig. 23), 9a, 12a; what was originally a head ornament finally passed into the form of the head itself, so that the latter appears now as an ear of maize surrounded by leaves. Compare the pictures, Figs. 25-27. That these gods with elongated heads are, in point of fact, identical with E is plainly seen from the passage in Dr. 2 (45)c (first figure). There the figure represented, which is exactly like the pictures in the Madrid manuscript, is designated explicitly as god E by the third hieroglyph in the accompanying writing. The hieroglyph of this deity is thus explained; it is the head of the god merged into the conventionalized form of the ear of maize surrounded by leaves. When we remember that the Maya nations practised the custom of artificially deforming the skull, as is seen in particular on the reliefs at Palenque, we may also regard the heads of these deities as representations of such artificially flattened skulls. God E occurs frequently as the god of husbandry, especially in the Madrid manuscript, which devotes much attention to agriculture. He seems to be a counterpart of the Mexican maize-god Centeotl. The passages in the Madrid manuscript (Tro. 29a and Cort. 39a, 40a) are very remarkable, where the deity E is represented in the position of a woman in labor with numerals on the abdomen; perhaps the underlying idea is that of fruitfulness. In the Codex Cort., p. 40, this grain-deity is pictured with a tall and slender vessel before him, which he holds in his hands. It is possible that this is meant to suggest a grain receptacle; to be sure, in the same place, other figures of gods likewise have such vessels in their hands. At any rate, it is interesting to note that in the passage already mentioned (Dr. 50a) god E also holds a similar tall and slender vessel in his hands. According to all appearances the scene pictured in Dr. 50a has reference to the conflict of the grain-god with a death-deity. The latter, the figure sitting on the right, is characterized by a skull as a head ornament (see Fig. 6) and seems to address threats or commands to god E, who stands before him in the attitude of a terrified and cowed individual. Furthermore god E has nothing to do with the powers of the underworld; he is a god of life, of prosperity and fruitfulness; symbols of death are never found in connection with him. Brinton calls this god Ghanan, equivalent to Kan; it is possible, too, that he is identical with a deity Yum Kaax who has been handed down to us and whose name means "Lord of the harvest fields". According to Förstemann the day dedicated to this god is Kan. F. The God of War and of Human Sacrifices. [Illustration: Figs. 28-34] This is a deity closely related to the death-god A, resembling the Aztec Xipe, and may, I think, without hesitation be regarded simply as the god of human sacrifice, perhaps, even more generally, as the god of death by violence. His hieroglyph is Figs. 28-30; it contains the number 11. A variant of this occurs on Dr. 7b, where instead of the 11 there is the following sign: [Hieroglyph] The characteristic mark of god F is a single black line usually running perpendicularly down the face in the vicinity of the eye. This line should be distinguished from the parallel lines of C's face and from the line, which, as a continuation of god E's head resembling an ear of maize, frequently appears on his face, especially as in the variants of the Madrid manuscript (compare Figs. 25-27). These pictures of E can always be unfailingly recognized by the peculiar shape of the head and should be distinguished from those representing F. The black face-line is the distinguishing mark of god F, just as it is of the Aztec Xipe. It sometimes runs in a curve over the cheek as a thick, black stripe, as Cort. 42. Sometimes it encircles the eye only (Dr. 6a) and again it is a dotted double line (Dr. 6b). The hieroglyph of god F likewise exhibits this line and with the very same variants as the god himself. See the hieroglyphs of the god belonging to the pictures in Dr. 6a, 1st and 3d figures, in which the line likewise differs from the other forms (Figs. 30-34). In a few places god F is pictured with the same black lines _on his entire body_, which elsewhere he has only on his face, the lines being like those in Fig. 31, namely Tro. 27*c. Indeed, in Tro. 28*c, the death-god A likewise has these black lines on his body and also F's line on his face; a clear proof of the close relationship of the two deities. These lines probably signify gaping death-wounds and the accompanying rows of dots are intended to represent the blood. Since god F is a death-deity the familiar sign (Fig. 5), which occurs so frequently with the hieroglyphs of A, also belongs to his symbols. F is pictured in company with the death-god in connection with human sacrifice (Cort. 42); an exactly similar picture of the two gods of human sacrifice is given in Codex Tro. 30d; here, too, they sit opposite one another. The identity of this attendant of death with the deity, designated by the hieroglyph with the numeral 11, is proved by the following passages: Tro. 19, bottom (on the extreme right hand without picture, only hieroglyph, see Fig. 29), Dr. 5b, 6a, b, and c and many others. In some of the passages cited (Dr. 5a and b) he is distinguished by an unusually large ear-peg. His hieroglyph occurs with the hieroglyph of the death-god in Dr. 6c, where he is himself not pictured. As war-god, god F occurs combined with the death-god in the passages mentioned above (Tro. 27*-29*c), where he sets the houses on fire with his torch and demolishes them with his spear. God F occurs quite frequently in the manuscripts and must therefore be considered as one of the more important deities. According to Förstemann his day is Manik, the seizing, grasping hand, symbolizing the capturing of an enemy in war for sacrificial purposes. F's sign occurs once, as mentioned above, in fourfold repetition with all the four cardinal points, namely in Tro. 29*c. In ancient Central America the captured enemy was sacrificed and thus the conceptions of the war-god and of the god of death by violence and by human sacrifice are united in the figure of god F. In this character god F occurs several times in the Madrid manuscript in combat with M, the god of travelling merchants (see page 35). Spanish writers do not mention a deity of the kind described here as belonging to the Maya pantheon. G. The Sun-God. [Illustration: Figs. 35-36] God G's hieroglyph (Fig. 35) contains as its chief factor the sun-sign Kin. It is one of the signs (of which there are about 12 in the manuscripts), which has the Ben-ik prefix and doubtless denotes a month dedicated to the sun. There is, I think, no difference of opinion regarding the significance of this deity, although Fewkes, as already stated, is inclined to identify G with B, whom, it is true, the former resembles. It is surprising that a deity who from his nature must be considered as very important, is represented with such comparative infrequency. He occurs only a few times in the Dresden manuscript, for example 22b, 11c, and in the Codex Tro.-Cortesianus none can be found among the figures which could be safely regarded as the sun-god; in no manuscript except the Dresden does a deity occur wearing the sun-sign Kin on his body. But once in the Codex Cort. the figure of D appears with the sun-sign on his head, as pointed out by Fewkes in his article entitled "The God 'D' in the Codex Cortesianus". G's hieroglyph, to be sure, is found repeatedly in the Madrid manuscript, for example Codex Tro. 31c. God G seems to be not wholly without relation to the powers of death; the owl-sign (Fig. 5) occurs once in connection with him (Dr. 11c). Besides the sun-sign Kin, which the god bears on his body, his representations are distinguished by a peculiar nose ornament (Fig. 36) which, as may be seen by comparison with other similar pictures in the Dresden manuscript, is nothing but a large and especially elaborate nose-peg. Similar ornaments are rather common just here in the carefully drawn first part of the Dresden manuscript. Compare Dr. 22b (middle figure), 21 (centre), 17b, 14a, b; occasionally they also have the shape of a flower, for example 12b (centre), 11c (left), 19a. Lastly it is worthy of note, that god G is sometimes represented with a snake-like tongue protruding from his mouth, as in Dr. 11b and c. H. The Chicchan-God. [Illustration: Figs. 37-40] The figure of a deity of frequent occurrence in the Dresden manuscript is a god, who is characterized by a skin-spot or a scale of a serpent on his temple of the same shape as the hieroglyph of the day Chicchan (serpent). Moreover the representations of the god himself differ very much, so that there are almost no other positive, unvarying characteristic marks to be specified. His picture is plainly recognizable and has the Chicchan-mark on the temple in Dr. 11a, 12b and 20b. The hieroglyph belonging to this deity likewise displays the Chicchan-sign as its distinguishing mark. Furthermore several variants occur. The Chicchan-sign has sometimes the form of Fig. 37 and again that of Fig. 38. The prefix likewise differs very much, having sometimes the form of Fig. 37, and again that of Fig. 38 or of Figs. 39 and 40. Thus there are, in all, four different forms of the prefix. It is to be assumed that all these hieroglyphs have the same meaning, notwithstanding their variations. Taking into consideration the frequency of the variations of other hieroglyphs of gods and of the hieroglyphs in the Maya manuscripts in general, it is quite improbable from the nature of the case, that a hieroglyph, which displays so great an agreement in its essential and characteristic elements, should denote several different gods. The dissimilarity which Seler thinks he finds between the forms of the Chicchan-sign in Figs. 37 and 38 and which leads him to assume that Fig. 37 is not a Chicchan-sign at all, but that it denotes another face ornament, cannot be satisfactorily proved, and must be regarded as an arbitrary assumption. The Chicchan-mark in the sign of the day Chicchan also differs very much from that on the bodies of the serpents pictured in the manuuscripts, so that variations of this kind by no means make it necessary to assume that the hieroglyphs actually denote different things. Observe, for example, the different Chicchan-spots on the serpent's body in Tro. 27a. The crenelated, black border of the Chicchan-spot in Fig. 38 passes in rapid cursive drawing almost of itself into the scallops of Fig. 37, a transition to which there are distinct tendencies on the serpent's body in Tro. 27a. Nor does the fact, that under H's hieroglyph different personages are very often pictured, whom we cannot positively identify, compel the assumption that we have here not _one_, but two or more mythical figures, for the same is true of other hieroglyphs of gods. There are many places in the manuscripts where the text contains a definite well-known hieroglyph of a god, while the accompanying picture represents some other deity or some other figure not definitely characterized, perhaps merely a human form (priest, warrior, woman and the like). Thus in Dr. 4a we see H's hieroglyph in the text, but the picture is the figure of god P while in other places we miss the characteristic Chicchan-spot on the figure represented, for example Dr. 4c, 6a, 7b, 7c, 14a, 21c. In the Madrid manuscript, it is true, H's hieroglyph also occurs often enough, but _not in a single instance_ is a deity represented displaying the Chicchan-spot. This fact is, I think, to be explained by the coarser style of the drawing, which does not admit of representing such fine details as in the Dresden manuscript. In the Paris manuscript H's hieroglyph occurs but once (p. 8, bottom). Seler thinks he recognizes in some of the figures represented under H's hieroglyph in the manuscripts, a so-called "young god". Such a deity is unknown and the assumption is entirely arbitrary. Apparently this "young god" is an invention of Brinton. The purely inductive and descriptive study of the manuscripts does not prove the existence of such a personage, and we must decline to admit him as the result of deductive reasoning. In this so-called "young god", we miss, first of all, a characteristic mark, a distinct peculiarity such as belongs to all the figures of gods in the manuscripts without exception and by which he could be recognized. Except his so-called youthfulness, however, no such definite marks are to be found. Furthermore there is no figure of a god in the manuscripts which would not be designated by a definite characteristic hieroglyph. No such hieroglyph can be proved as belonging to the "young god". The figures, which are supposed to have a "youthful appearance" in the Madrid manuscript, often convey this impression merely in consequence of their smallness and of the pitiful, squatting attitude in which they are represented. Furthermore real _children_ do occur here and there, thus, for example, in the Dresden manuscript in connection with the pictures of women in the first part and in Tro. 20*c in the representation of the so-called "infant baptism." That god H has some relation to the serpent must be conjectured from what has been said. Thus, for example, on Dr. 15b, we see his hieroglyph belonging to the figure of a woman with the knotted serpent on her head, in Dr. 4a to the god P, who there bears a serpent in his hand, and in Dr. 35b in connection with a serpent with B's head. What this relation is, cannot now be stated. The day dedicated to god H is Chicchan, and the sign for this day is his distinguishing hieroglyph. I. The Water-Goddess. [Illustration: Fig. 41] In the Dresden manuscript the figure of an old woman, with the body stained brown and claws in place of feet, occurs repeatedly. She wears on her head a knotted serpent and with her hands pours water from a vessel. Evidently we have here a personification of water in its quality of destroyer, a goddess of floods and cloud-bursts, which, as we know, play an important part in Central America. Page 27, of the Codex Troano contains a picture, in which this character of goddess I may be distinctly recognized. In accordance with this character, also on Dr. 74, where something resembling a flood is represented, she wears the cross-bones of the death-god. The goddess is pictured in the manner described in the following places: Dr. 39b, 43b, 67a and 74. The figure corresponding to her in the Madrid manuscript, in Tro. 27 and 34*c, displays some variations, in particular the tiger claws on the feet and the red-brown color of the body are lacking. But the agreement cannot be questioned, I think, when we recall that the Maya manuscripts doubtless originated in different ages and different areas of civilization, circumstances which readily explain such variations. The goddess distinguished in the Madrid manuscript by symbols of flood and water is doubtless the same as goddess I of the Dresden manuscript described above; her unmistakable character of water-goddess in both manuscripts is in favor of this. In both manuscripts she is invariably distinguished by the serpent on her head, which, as we know, is a symbol of the water flowing along and forming waves. Strange to say, a fixed hieroglyph of this goddess cannot be proved with certainty. There is some probability in favor of the sign given in Fig. 41. The well-known oblong signs, which Förstemann (Drei Mayahieroglyphen, published in the Zeitschrift für Ethnologie, 1901, pp. 215-221) interprets as the sign for evil days, frequently occur with her. This would be appropriate for the goddess of floods. In the Dresden manuscript a few similar figures of women are found, who, like goddess I, wear a knotted serpent on the head. Representations of this kind occur in Dr. 9c, 15b, 18a, 20a, 22b and 23b. Whether they are identical with goddess I is doubtful, since there is no symbolic reference to water in these passages. Besides, the hieroglyphs of other known deities occur each time in the above-mentioned places, so that definite mythologic relations must be assumed to exist here between the women repsented and the deities in question. Thus in Dr. 9c we find D's sign, in 15b that of H; on 18a, 22b and 23b we see only the general sign for a woman. In Dr. 20a the signs are effaced. In the Codex Troano goddess I occurs on pp. 25b and 27; there is also a woman with the knotted serpent on her head in Tro. 34*c. In the Codex Cortesianus and in the Paris manuscript these forms are wholly lacking. K. The God with the Ornamented Nose. [Illustration: Figs. 42-43] This god, as already mentioned in connection with B, is not identical with the latter, but is probably closely related to him. His hieroglyph is Fig. 42; Fig. 43 is the form in the Madrid manuscript. He is closely related to god B. He is represented in Dr. 25 (centre) where he is perhaps conceived of as a priest wearing a mask with the face of the god, also in Dr. 7a, 12a (with his own hieroglyph and that of E!), 26 (bottom) with a variant of the sign. His figure without the hieroglyph occurs in Dr. 3. Very frequently the well-known group, 3 Oc, is given with him and in connection with his hieroglyph (in Dr. 3, 7a, 10b (right); without picture, 12a). Förstemann (Drei Mayahieroglyphen, Zeitschrift für Ethnologie, 1901. pp 215-221) sees in this the sign for good days, a proof that we have to do here with a benevolent deity well disposed to mankind, his kinship with B being also in favor of this interpretation. His hieroglyph alone without his picture occurs in Dr. 10b, 49 (middle and bottom), 58 (bottom, left), and Tro. 8*b; with a variant of the attribute in Dr. 24 (third vertical row). A slight variation appears also in Dr. 69 (top, right). In Dr. 65a (middle) B is pictured. But in the text we see K's hieroglyph presented by a hand. The next figure on the same page at the right represents god B with the head of K on his own and the same head once more in his hand. Agreeing with this, we find in the accompanying text the signs of B and K, the latter in a hand. K seems to be pictured again in Dr. 46 (bottom); the passage, however, is somewhat obliterated. The hieroglyph is lacking in this place; it is found, however, on the preceding page 45 (middle). In addition to the passage already mentioned, which represents god K together with B, such double deities again occur in the Paris manuscript, p. 13, where B holds K's head in his hand; in Dr. 34b, where he carries this head on his own and in Dr. 67a where he appears to carry it in a rope. Once, how ever, a variation of these plainly synonymous representations occurs, namely in Dr. 49 (at the top), where we see a _feminine_ form above whose head rises the head of god K. In the Paris manuscript, so far as its defaced condition permits us to recognize the representation, K occurs very frequently, as for example, in Per. 3, 4, 5, 6, 7 and 9 (in part only his head is given, presented by god B, as in the Dresden manuscript). Brinton considers this figure simply as a special manifestation of B and identical with that god. Förstemann thinks that god K is a storm-deity, whose ornamental nose, according to the conventional mode of drawing of the Central American peoples, is intended to represent the blast of the storm. Apparently, however, the deity has an _astronomic significance_ and seems to symbolize a _star_. In favor of this is the fact, that on the so-called initial pages of the Madrid manuscript (Cort. 22-Tro. 36) a row, composed of repetitions of his sign, occurs below the signs of the cardinal points and parallel to a row composed of signs of god C, the god of the polar star and the north. The hieroglyphs of C and K are the only hieroglyphs of gods, which are repeated 13 times on these pages with the 13 days enumerated there. The two gods must, therefore, have either a parallel or an opposite astronomic and calendric meaning. The fact that in Dr. 25 and 26 K appears as regent of the year, is an argument in favor of his astronomic significance. According to Förstemann, Muluc is the day dedicated to god K. In the head of god K we recognize the ornament so common in the temple ruins of Central America--the so-called "elephant's trunk." The peculiar, conventionalized face, with the projecting proboscis-shaped nose, which is applied chiefly to the corners of temple walls, displays unquestionably the features of god K. The significance of god K in this architectural relation is unknown. Some connection with his character as the deity of a star and with his astronomic qualities may, however, be assumed, since, as we know, the temple structures of Central America are always placed with reference _to the cardinal points_. L. The Old, Black God. [Illustration: Fig. 44] God L's features are those of an old man with sunken, toothless mouth. His hieroglyph is Fig. 44, which is characterized by the black face. God L, who is also black, must not be confounded with M whose description follows. L is represented and designated by his hieroglyph in the accompanying text, in Dr. 14b and 14c and Dr. 46b; the figure has the characteristic black face. He appears entirely black in Dr. 7a. The hieroglyph alone occurs in Dr. 21b and 24 (third vertical line in the first passage) with a variation, namely without the Ymix-sign before the head. This deity does not occur in the Madrid and Paris manuscripts. The significance of god L does not appear from the few pictures, which are given of him. In Dr. 46b the god is pictured armed and in warlike attitude. Both in Dr. 14b and 14c he wears a bird on his head and has a Kan in his hand. According to Förstemann, his day is Akbal, darkness, night. Cyrus Thomas (Aids to the Study of the Maya Codices, in the 6th Annual Report of the Bureau of Ethnology, Washington, 1888, p. 358) thinks he is the god Ekchuah, who has come down to us as a black deity. God M seems, however, to correspond to Ekchuah (see the description of M). M. The Black God with the Red Lips. [Illustration: Figs. 45-48] God M's hieroglyph is Figs. 45, 46; it seems to represent an eye rimmed with black, though the figure of the god himself displays an entirely different drawing of the eye (see Fig. 47). The god is found in the Dresden manuscript only three times, namely in Dr. 16b (with a bone in his hand) in picture and sign, in Dr. 13c grouped with an animal, without the hieroglyph, and in Dr. 43a (with his sign) while finally his hieroglyph alone appears in Dr. 56 (top, left) in a group and of a somewhat different form. On the other hand, god M appears with special frequency in the Madrid manuscript, which treats of this deity with great fullness of detail. While he is represented in the Dresden manuscript (16b) with his body striped black and white, and on p. 43a entirely white, he is always entirely black in the Codex Troano. His other distinguishing marks are the following: 1. The mouth encircled by a red-brown border. 2. The large, drooping under lip. By this he can be recognized with certainty also in Dr. 43a. 3. The two curved lines at the right of the eye. His significance can be conjectured. He seems to be of a warlike nature, for he is almost always represented armed with the lance and also as engaged in combat and, in some instances, pierced by the lance of his opponent, god F, for example in Tro. 3c, 7a, 29*a. The peculiar object with parallel stripes, which he wears on his head is a rope from which a package frequently hangs. By means of a rope placed around his head the god frequently carries a bale of merchandise, as is the custom today among the aborigines in different parts of America. On 4b and 5a in the Cod. Tro. this can plainly be seen. All these pictures lead us to conclude, that we have here to do with a god of _travelling merchants_. A deity of this character called Ekchuah has been handed down to us, who is designated explicitly as a _black_ god. In favor of this is also the fact, that he is represented fighting with F and pierced by the latter. For the travelling merchant must, of course, be armed to ward off hostile attacks and these are admirably symbolized by god F, for he is the god of death in war and of the killing of the captured enemy. The god is found in the Codex Troano in the following places and on many pages two or three times: pp. 2, 3, 4, 5, always with the hieroglyph, then without it on pp. 6, 7, 19, 4*c, 14*b, 17*a, 18*b and again with the hieroglyph on pp. 22*a, 23*a, 25*a; finally it is found again without the hieroglyph on pp. 29*a, 30*a, 31*, 32*, 33*, 34*. In the Codex Cortesianus god M occurs in the following places: p. 15, where he strikes the sky with the axe and thus causes rain, p. 19 (bottom), 28 (bottom, second figure), 34 (bottom) and 36 (top). M is always to be recognized by the encircled mouth and the drooping under-lip; figures without these marks are not identical with M, thus for example in Tro. 23, 24, 25, 21*. Tro. 34*a shows what is apparently a variant of M with the face of an old man, the scorpion's tail and the vertebrae of the death-god, a figure which in its turn bears on its breast the plainly recognizable head of M. God M is also represented elsewhere many times with the scorpion's tail, thus for example on Tro. 30*a, 31*a. Besides his hieroglyph mentioned above, Figs. 45 and 46, another sign seems to refer to god M, namely Fig. 48 (compare for example Tro. 5a and Cort. 28, bottom). The head in this sign has the same curved lines at the corner of the eye as appear on the deity himself. Förstemann mentions this sign in his Commentary on the Paris Manuscript, p. 15, and in his Commentary on the Dresden Manuscript, p. 56. He thinks the hieroglyph has relation to the revolution of Venus, which is performed in 584 days. A relation of this kind is, I think, very possible, if we bear in mind that all the god-figures of the manuscripts have more or less of a calendric and chronologic significance in their chief or in their secondary function. It should be mentioned that God M is represented as a rule as an old man with toothless jaw or the characteristic solitary tooth. That he is also related to bee-culture is shown by his presence on p. 4*c of the Codex Troano, in the section on bees. Besides gods L and M, a few quite isolated black figures occur in the Codex Troano, who, apparently, are identical with neither of these two deities, but are evidently of slight importance and perhaps are only variants of other deities. Similar figures of black deities are found in the Codex Tro. 23, 24 and 25 (perhaps this is a black variant of B as god of the storm?) and on 21*c we twice see a black form with the aged face and the solitary tooth in the under jaw (perhaps only a variant of M). In the Codex Cortesianus and in the Dresden manuscript no other black deities occur, but in the Paris manuscript a black deity seems to be pictured once (p. 21, bottom). According to Brinton (Nagualism, Philadelphia 1894, pp. 21, 39), there is among the Tzendals in addition to Ekchuah, a second black deity called Xicalahua, "black lord". N. The God of the End of the Year. [Illustration: Figs. 49-51] We have here a deity with the features of an old man and wearing a peculiar head ornament reproduced in Fig. 50, which contains the sign for the year of 360 days. The god's hieroglyph is Fig. 49, which consists of the numeral 5 with the sign of the month Zac. Förstemann has recognized in god N the god of the five Uayeyab days, which were added as intercalary days at the end of the original year of 360 days, and were considered unlucky days. N is, therefore, the god of the end of the year. Förstemann has discussed him in detail under this title in a monograph published in Globus, Vol. 80, No. 12. It is still open to question whether god N actually occurs in all the places of the Dresden manuscript, which are mentioned by Förstemann. He can be recognized positively on Dr. 17a, 21c (grouped with a woman) and 37a; also on 12c, but in this latter place with pronounced deviations from the usual representations. The figures in Dr. 23c (first group) and 43a (third picture) are doubtful, especially since the hieroglyph of the god is lacking in both instances. The third group in Dr. 21c is equally dubious. Here a woman is pictured sitting opposite a god. The latter seems to be god N, yet in the text we find instead of his sign the hieroglyph given in Fig. 51. It is not impossible that this sign likewise denotes god N. God N is found a few times in the Paris manuscript, for example on p. 4, where he holds K's head in his hands, and on p. 22. O. A Goddess with the Features of an Old Woman. [Illustration: Fig. 52] This goddess occurs only in the Madrid manuscript and is distinguished by the solitary tooth in the under jaw, as a sign of age, the invariable characteristic of aged persons in the manuscripts. She is pictured in the following places: Tro. 5*c, 6*b, and 11*b, c and d, Cort. 10b, 11a, 38a. In Tro. 11* she is represented working at a loom. She does not appear at all in the Dresden and Paris manuscripts. The figures of women mentioned under I with the serpent on their heads, are especially not to be regarded as identical with goddess O, for she never wears the serpent, but a tuft of hair bound high up on her head and running out in two locks. Her hieroglyph is Fig. 52; it is distinguished by the wrinkles of age about the eye. Owing to the limited number of her pictures, there is little to be said concerning the significance of this goddess. P. The Frog-God. [Illustration: Fig. 53] We call him the frog-god because in the Codex Tro. 31, he is pictured in the first and second lines with the club-shaped fingers of a frog, which occur only on this figure. The blue background, which is his attribute twice in the same passage, likewise points to a connection with water, and that the god also has something to do with agriculture may be deduced from the fact that he is pictured sowing seed and making furrows with the planting-stick. The two black parallel stripes at the corner of the eye seem to be folds of skin or marks on the skin, which may represent a peculiarity of this particular species of frog. His head ornament is very characteristic and contains the sign for the year of 360 days. He therefore bears some unknown relation also to the computation of time. It should be recalled in this connection that one of the Maya months is called Uo, frog. The god is pictured again in Tro. 30a and b, Tro. 22 (top, scattering seed) and Cort. 5 (at the very bottom, the figure lying down). Finally his neck ornament must be mentioned, which, as a rule, consists of a neck-chain with pointed, oblong or pronged objects, probably shells. In the Dresden manuscript he occurs but once, Dr. 4a (first figure), with some variations it is true. The text at this place contains H's hieroglyph. God P does not occur in the Peresianus. His hieroglyph is Fig. 53. It occurs in Tro. 31 (top) and can be unerringly recognized by the two black parallel stripes at the corner of the eye; which correspond exactly to the same marks on the face of the picture of the god himself. This is all that can be said respecting this deity from the pictures in the manuscripts. Its meaning is obscure. Seler's assumption that god P is Kukulcan (Zeitschrift für Ethnologie, 1898, p. 403) has certainly very slight foundation, and in view of the material from the manuscripts described in the preceding pages, it is in the highest degree improbable. * * * * * The foregoing is an almost complete enumeration of the god-figures proper in the Maya manuscripts. Whatever other figures of gods occur in the manuscripts are details of slight importance. This is especially true of the Dresden manuscript, which is well nigh exhausted by the types enumerated here; there may be, I think, a few figures still undescribed in the Madrid manuscript, the careless drawing of which renders the identification very difficult. An isolated figure of the Dresden manuscript still remains to be mentioned, concerning which it is doubtful whether it is intended to represent a deity or only a human personage. This is the figure characterized by a peculiar head ornament in Dr. 20b. It is designated in the text by two hieroglyphs, which belong together, Figs. 54 and 55, the latter occurring once with K (Dr. 7a). It seems to represent blowing from the mouth, screaming or speaking. [Illustration: Figs. 54-55] II. MYTHOLOGICAL ANIMALS. 1. THE MOAN BIRD. [Illustration: Figs. 56-59] This bird[41-1] belongs to the death-god as his symbol and attendant. Its hieroglyph (Fig. 56) contains the numeral 13; other forms are Figs. 57-59. It is pictured in Dr. 7c, 10a, 11a, 16c, 18b, and its hieroglyph without the picture is seen in Dr. 8b. A realistic representation of the whole figure of the moan as a bird, occurs on the head of the woman in 16c (1st figure) and 18b. God B sits on the head of the moan in Dr. 38c; the third hieroglyph of the accompanying text refers to this representation. Just as in Dr. 16 and 18, the moan bird appears in Tro. 18*c on the head of a woman. Its character as an attribute of the death-god is expressed by the Cimi-sign, which it wears upon its head (_e. g._, Dr. 10a), and also by the regular occurrence of symbols of the death-god in the written characters, which refer to the moan bird. In the same manner the sign of the owl, Fig. 5, also occurs frequently with it. [41-1] See plate for representations of the Mythological Animals, 1-6. The moan confers name and symbol alike on one of the eighteen months of the Maya year, and thus, as Förstemann conjectures (Die Plejaden bei den Mayas, in Globus, 1894), has an astronomic bearing on the constellation of the Pleiades. According to Brinton the moan is a member of the falcon family and its zoological name is _Spizaetus tyrannus_. 2. THE SERPENT. This is one of the most common and most important mythological animals, and is closely related to different deities, as has already been more fully discussed in connection with the individual cases. Apparently it has no _independent_ significance as a deity. Its most important personification is that in god B, Kukulcan, the feathered serpent. Hence a fixed hieroglyph designating the serpent as a deity, as a mythologic form, does not occur, though there are numerous hieroglyphs which refer to serpents or represent individual parts of the serpent, as its coils, its jaws, the rattles of the rattlesnake, etc. The serpent appears in the mythologic conceptions of the Mayas chiefly as the symbol of water and of time. In the great series of numbers of the Dresden manuscript, certain numbers occur which are introduced in the coils of a large serpent (compare in regard to this, Förstemann, Zur Entzifferung der Mayahandschriften, II, Dresden, 1891). The serpent is very frequently represented in all the manuscripts, sometimes realistically and sometimes with the head of a god, etc. In the Dresden manuscript it occurs in the following places: 1a, 26, 27, 28c, 35b, 36a, 36b, 37b 40, 42a, 61, 62, 65c 66a and 69. It is prominent also in the Madrid manuscript, occurring for example in Cort. 4-6, 12-18, Tro. 25, 26, 27 and elsewhere. 3. THE DOG. [Illustration: Fig. 60] Fig. 60 is its hieroglyph. It is the symbol of the death-god and the bearer of the lightning. The latter follows quite clearly from the picture in Dr. 40b where the god is distinguished by its hieroglyph. This animal is again represented in Dr. 7a, 13c on the right, 21b with its hieroglyph, 29a, 30a (forming a part of 31a, where god B holds the bound dog by the tail), and 39a without the hieroglyph, 47 (bottom) with a variant of the hieroglyph. In Dr. 36a the dog bears the Akbal-sign on its forehead. The writing above it contains a variant of the hieroglyph for the dog; this is the third of the rubric. It shows (somewhat difficult of recognition) the Akbal-sign on the forehead of the dog's head occurring in it, and on the back of the head the Kin-sign, as symbols of the alternation of day and night. The same sign occurs again with adjuncts in Dr. 74 (last line, 2nd sign) and once with the _death-god_ in Dr. 8a. The dog as lightning-beast occurs with the Akbal-sign in the eye instead of on the forehead in Codex Tro. 23*a; here again its hieroglyph is an entirely different one (the third of the rubric). That the dog belongs to the death-god is proved beyond a doubt by the regular recurrence in the writing belonging to the dog, of the hieroglyphs, which relate to this deity, especially of Fig. 5. According to Förstemann his day is Oc. 4. THE VULTURE. [Illustration: Fig. 61] This bird is distinctly pictured as a mythological figure in Dr. 8a. It appears again, in feminine form, together with the dog, in Dr. 13c and also in 19a. In the first passage, its hieroglyph is almost effaced; the hieroglyph is very striking and occurs nowhere else in the whole collection of manuscripts. The body of this animal-deity is striped black and white; in Dr. 38b it is almost entirely black. The same passage displays a second hieroglyph for this figure (Fig. 61); this hieroglyph also occurs with the numeral 4 in Dr. 56b. In Dr. 36b this bird of prey is pictured fighting with the serpent; its hieroglyph occurs in the second form; the serpent is designated by the Chuen, the gaping jaws of the serpent (first character of the rubric). Finally it should be mentioned that the head of this bird occurs frequently as a head ornament, thus in Dr. 11a, 11b, 12b and 14b. Mention should also be made of the realistic representations of the vulture, eating the eye of a human sacrifice (Dr. 3, Tro. 26*a and 27*a). According to Förstemann his day is Cib. 5. The Jaguar. [Illustration: Fig. 62] The jaguar is likewise an animal with mythological significance. It is represented in Dr. 8a, where its hieroglyph is the third sign in the writing; it also occurs in Dr. 26 (at the top). It occurs in Tro. 17 (at the end) with a hieroglyph which represents the jaguar's head and contains the numeral 4 (Fig. 62); again it appears without a hieroglyph on p. 20 (bottom) and on 21 and 22 (bottom). Its day is Ix, and hence it also relates occasionally as year regent to the Ix years, for example in Dr. 26a. 6. The Tortoise. [Illustration: Figs. 63-65] This animal, like the dog, appears as a lightning-beast (see Dr. 40b, middle). Its hieroglyph is Figs. 63, 64. This sign also is connected with the numeral 4, which occurs so often with animals (but not alone with quadrupeds) as to be worthy of attention. The sign of the tortoise without the numeral is seen in Cort. 17a, where the tortoise itself is also represented. It must have reference to the 17th month of the Maya year, for the month Kayab (and apparently also Pop) contains the head of the tortoise (compare Fig. 65). It occurs several times in the Cortesianus, thus on pp. 13, 19, 37, 38; on p. 19 with the hieroglyph (on the top of the lower half of the page, 1st line and at the right of the margin). In Dr. 69 (at the top) we see the sign of the tortoise with the Kin-sign as its eye and the numeral 12; under this group B, with a black body, is seated on the serpent; on the same page the sign occurs again; each time, moreover, apparently as a month-hieroglyph. According to Förstemann the tortoise is the symbol of the summer solstice, as the _snail_, which occurs only as a head ornament in the manuscripts and not independently, is the symbol of the winter solstice; both, as the animals of slowest motion, represent the apparent standstill of the sun at the periods specified. This explains why the month Kayab, in which the summer solstice falls, should be represented by the head of a tortoise, which has for its eye the sun-sign Kin (Förstemann, Zur Entzifferung der Mayahandschriften III, Schildkröte und Schnecke in der Mayaliteratur, Dresden 1892). According to Förstemann its day is Cauac. * * * * * Finally the _owl_ and the _ape_ (or monkey) must be mentioned as animals of mythologic significance, of which we have already spoken in connection with gods A and C. The _scorpion_ also seems to have an important mythologic significance, and appears in the manuscripts in connection with figures of gods, as, for example, in Cort. 7a and Tro. 31*a, 33*a, 34*a (god M with a scorpion's tail). In addition to those discussed in this paper, there are a few animals in the manuscripts, which probably also have a partial mythologic significance, but which have been omitted because they are represented in a naturalistic manner, thus, for example, the deer on Tro. 8, et seq., while idealization (with human bodies, with torches, hieroglyphic character on the head, etc.) should be considered as an unmistakable sign of mythologic meaning. A mythologic significance also seems to belong to the _bee_ which plays so prominent a part of the Codex Troano. Probably the section in question of the Madrid manuscript (1* et seq.) treats of bee-keeping, but incidentally it certainly has to do also with the mythologic conceptions connected with the culture of bees. The _bat_ which is found as a mythological figure on pottery vessels and inscriptions from the Maya region (compare Seler, Zeitschrift für Ethnologie, 1894, p. 577) does not occur in the manuscripts. It is true, however, that hieroglyphic signs, which seem to relate to the head of the bat, occur in isolated cases in the manuscripts. SUMMARY. An enumeration of the most important deities in the manuscripts gives the following results, in connection with which it is to be noted that, of course, the numbers cannot be absolutely correct, because one or another of the pictures occasionally remains doubtful. As far as possible, however, only the _positively_ determined representations have been considered. The deity occurring most frequently in the DRESDEN MANUSCRIPT is god B, who is pictured there 141 times. Following him in point of number in the same manuscript are the death-god A pictured 33 times, god D 19 times, and gods C and E 17 and 14 times respectively. In the MADRID MANUSCRIPT, god D, with 84 pictures, is of most frequent occurrence. He is followed by the maize-god E with 76 pictures, god B with 71, god A with 53, C with 38 and M with 37 pictures. In the PARIS MANUSCRIPT, god E's picture can be verified 8 times, those of C and B 6 times each and that of god A twice; N and K are also frequently represented. An enumeration of all the pictures in all the manuscripts shows that the following deities occur most frequently and are therefore to be considered the most important: 1. God B: pictured 218 times. 2. " D: " 103 " 3. " E: " 98 " 4. " A: " 88 " 5. " C: " 61 " 6. " M: " 40 " 7. " F: " 33 " Furthermore, interesting conclusions can be arrived at, by means of a list of those deities, who occur in the representations of the manuscripts, so _united_ or _grouped together_ as to make it evident that they must stand in some relation to one another. _Mythologic combinations_ of this kind occur among the following deities and mythological animals: 1. In the DRESDEN MANUSCRIPT: D and C, B and C, dog and vulture, bird and serpent, B and K. 2. In the MADRID MANUSCRIPT: F and M, B and M, C and M, E and M, A and E, A and D, A and F, B and C, D and C, D and E. 3. In the PARIS MANUSCRIPT: N and K, B and K. The most common of these combinations are those of the deities A and F, M and F, A and E, D and C. These groups are entirely intelligible, consisting of death-god and war-god, god of the travelling merchants and war-god, death-god and maize-god (as adversaries: meaning famine), night-god and deity of the polar star. [Illustration: I. Gods. A B C D E F G H I K L M N O P II. Mythological Animals. 1 2 3 4 5 6] * * * * * * Transcriber's Note: Typographical errors: Page 10 Footnote 1 missing final period 17 serpent-and rain-deity should read serpent-and-rain-deity 23 Sentence ending with "and 13*c)" does not have a period 29 manuuscripts should read manuscripts 32 repsented should read represented 33 pp 215-221 should read pp. 215-221 42 comma missing following 37b comma missing following 65c Inconsistencies: The placement of punctuation at the end of a word or phrase surrounded by quotation marks is inconsistent, usually it is placed outside the final close quotation mark but occasionally is found inside the mark. 
39683	----	MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM BY CHARLES P. BOWDITCH (From the American Anthropologist (N. S.), Vol. 3, January-March, 1901) NEW YORK G. P. PUTNAM'S SONS 1901 MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM BY CHARLES P. BOWDITCH Dr Brinton, in his _Maya Chronicles_, has translated the following passages from the Book of Chilan Balam of Mani: ... in the thirteenth Ahau Ahpula died; for six years the count of the thirteenth Ahau will not be ended; the count of the year was toward the East, the month Pop began with (the day) fourth Kan; the eighteenth day of the month Zip (that is) 9 Ymix, was the day on which Ahpula died; and that the count may be known in numbers and years, it was the year 1536. And again from the Book of Chilan Balam of Tizimin: The thirteenth Ahau; the death of Ahpulha took place; it was the sixth year when ended the count of the thirteenth Ahau,--the count of the year was from the east (the month) Pop passed on the fourth Kan; on the eighteenth of (the month) Zip, 9 Imix was the day Ahpulha died; it was the year 1536. In his remarks on these books Dr Brinton says: According to the reckoning as it now stands, six complete great cycles were counted, and parts of two others, so that the native at the time of the Conquest would have had eight great cycles to distinguish apart. I have not found any clear explanation how this was accomplished. We do not even know what name was given to this great cycle,[1] nor whether the calendar was sufficiently perfected to prevent confusion in dates in the remote past. [1] It should be noted that the grand cycle, which Dr Brinton refers to, is the period of 13 × 7200 days = 93,600 days or 260 periods of 360 days; while the grand cycle according to Goodman's method is 13 × 144,000 days or 5200 periods of 360 days. It would seem, however, as if the reckoning of time as given in these books is very accurate, fixing a date which would not be duplicated within a limit of thirty-five hundred or four thousand years. The Books of Chilan Balam number the katuns on a different principle from that used on the inscriptions or in the Dresden Codex, but the two methods can be readily and usefully brought together, as the katun itself remains the same in both methods. In the inscriptions the katuns are numbered from 0 to 19, using Goodman's method though not his exact nomenclature, and twenty of them equal one cycle. In the Chilan Balam books, the katuns are named as Katun 13 Ahau, Katun 11 Ahau, etc., these being the days with which they begin or with which the previous katun ended; and as after thirteen katuns the same name is again given, this nomenclature fixes a date within a period which equals 13 multiplied by the number of days in a katun. There has been a difference of opinion as to this number of days in a katun, but it is clear from the Books of Chilan Balam that their reckoning was by terms of 20 × 360 days. The followers of Perez, however, insist that the length of the katun was 24 × 365 days. Sr Perez has indeed made this assertion,[2] but he rests his opinion to a great degree on the fact that the naming of the katuns proceeded in the following order, taking their names from the day Ahau with which they began, viz.: Katun 13 Ahau, Katun 11 Ahau, Katun 9 Ahau, Katun 7 Ahau, etc., and that by starting with a katun which begins with 13 Ahau and counting forward a period of 24 × 365 days, we should reach another katun beginning with 11 Ahau. But the same result is brought about by considering the katun as a period of 20 × 360 days, as has been shown by Dr Seler, among others; and since the Books of Chilan Balam state distinctly that they reckon by so many scores of so-called years, and as the initial dates of the inscriptions all reckon in the same way, it is now generally considered that the katun consisted of 20 × 360 or 7200 days. An objection to considering a katun as 20 × 360 days may be raised in that the Books of Chilan Balam use the word "año" or year, but this can be easily explained by the fact that the Spanish "year" was the period which most nearly agreed with their tun or 360-day period, and that the Books did not pretend to speak with scientific accuracy. [2] Stephens, _Incidents of Travel in Yucatan_, p. 441 et seq. Besides the above count, it is well known that the Mayas had a year-and-month count. This consisted in naming each one of the twenty days and in attaching to each of these days one of the numbers 1 to 13. Besides this, each day so numbered was declared to be a given day of a given month and to occur in a year marked by one of the year bearers--as for instance in the Book of Chilan Balam, already quoted, where the day is given as 9 Ymix 18 Zip in the year 4 Kan. Now this day and this year could recur only after the lapse of fifty-two years or 18,980 days. It should be noted here that in the inscriptions and in the Dresden Codex, the day Ymix was always the day 4, 9, 14, or 19 of any month, showing that the day 1 of the month was Eznab, Akbal, Lamat, or Ben; while in Landa and the Books of Chilan Balam the day Ymix was the day 3, 8, 13, or 18, showing that the day 1 of the month was Cauac, Kan, Muluc, or Ix. That is, the months in modern times began with the day which followed the day with which the months began in more ancient times. As the tables are calculated for the inscriptions, it will be well, in order to facilitate our calculations, to call the day on which Ahpula died the nineteenth of the month Zip, instead of the eighteenth of that month. Given that the katun consisted of 7200 days, a Katun 13 Ahau could not recur until after the lapse of 13 × 7200 or 93,600 days, and the recurrence of any day marked by the year-and-month count, and occupying any particular place in a given katun, could not occur until after the lapse of a period which is found by finding the least common multiple of the two numbers 93,600 and 18,980. This is 6,832,800 days, which is a period of 360 calendar rounds of 18,980 days or of 52 years each. This is equal to 18,720 years, and, in the method of reckoning shown in the initial dates of the inscriptions, would equal 3 grand cycles, 8 cycles, and 9 katuns, or, to use the method of Goodman, 3.8.9.0.0.0. I have said that a day marked by the year-and-month count, and occupying any particular place in a given katun, could not recur until the lapse of this long period. This would be true if the day was specified as being a given day in a given tun in a given katun, or even if the day was stated as falling in a given uinal of a given tun in a given katun. But in the case before us the death of Ahpula is said to have taken place in the Katun 13 Ahau when six tuns or years of that katun remained unexpired. Even with this rather loose designation such a day would not recur within a period of 3500 or 4000 years. The day 4 Ahau 8 Cumhu seems to have been regarded as the beginning day of the beginning cycle of some grand cycle. From this day all the initial series of the inscriptions of Copan and Quirigua, of Piedras Negras and Tikal, so far as we know them, count, except one where this day 4 Ahau 8 Cumhu is itself given. In this place (on Stela C of Quirigua) 4 Ahau 8 Cumhu is reckoned thus: "Grand cycle glyph .13.0.0.0.0.", while in the Temple of the Cross it is declared to be a thirteenth cycle. As this was the beginning date, there is reason to believe that the beginning cycle of a great cycle received the number 13. I give here the first and last terms of a list of the beginning days of the Katuns 13 Ahau in a complete round of 18,720 years occurring after the beginning of the grand cycle called by Goodman Grand Cycle 54, which began with 4 Ahau 8 Cumhu. It is of little consequence what particular number is given to the grand cycle, as the whole series forms a continuous count, and I shall therefore follow Goodman, who gives the number 54 to the grand cycle glyphs common to Copan, Quirigua, etc. If 54.13.0.0.0.0. or the beginning of the grand cycle, called Grand Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Katun 13 Ahau will appear two katuns after this or with the count of 54.13.2.0.0.0. 13 Ahau 8 Mol Year 10 Ix, and other Katuns 13 Ahau will follow at intervals of 13 katuns as here given: 54.13.15.0.0.0. 13 Ahau 8 Pax Year 6 Ix. 1. 8. " 3 Xul 3 Cauac. 2. 1. " 3 Kankin 12 " . . . . . . . . . . . 57.5.19.0.0.0. 13 Ahau 18 Ceh 11 Kan. 6.12 13 Uo 8 Muluc. 7. 5. 13 Yax 4 " 18. 13 Cumhu 13 " 57.8.11.0.0.0. 13 Ahau 8 Mol 10 Ix. But we are seeking a Katun 13 Ahau in which 14 tuns have elapsed and of which 6 tuns still remain unexpired. We must, therefore, add 14 tuns or 14 × 360 days = 5040 days to each of the dates given and we shall then have the following complete list of the beginning days of Tun 14 of Katun 13 Ahau for the term of 18,720 years: 54.13. 2.14.0.0. 9 Ahau 18 Zotz 11 Kan. 15. 18 Ceh 7 Kan. 1. 8. 13 Uo 4 Muluc. 2. 1. 13 Yax 13 Muluc. 14. 13 Cumhu 9 Muluc. 3. 7. 8 Mol 6 Ix. 4. 0. 8 Pax 2 Ix. 13. 3 Xul 12 Cauac. 5. 6. 3 Kankin 8 Cauac. 19. 18 Zip 5 Kan. 6.12. 18 Zac 1 Kan. 7. 5. 13 Pop 11 Muluc. 18. 13 Chen 7 Muluc. 54. 8.11.14.0.0. 13 Kayab 3 Muluc. 9. 4. 8 Yaxkin 13 Ix. 17. 8 Muan 9 Ix. 10.10. 3 Tzec 6 Cauac. 11. 3. 3 Mac 2 Cauac. 16. 18 Uo 12 Kan. 12. 9. 18 Yax 8 Kan. 55.13. 2.14.0.0. 18 Cumhu 4 Kan. -------- 15. 13 Mol 1 Muluc. 1. 8. 13 Pax 10 Muluc. 2. 1. 8 Xul 7 Ix. 14. 8 Kankin 3 Ix. 3. 7. 3 Zotz 13 Cauac. 4. 0. 3 Ceh 9 Cauac. 13. 18 Pop 6 Kan. 5. 6. 18 Chen 2 Kan. 5.19. 18 Kayab 11 Kan. 6.12. 13 Yaxkin 8 Muluc. 7. 5. 13 Muan 4 Muluc. 18. 8 Tzec 1 Ix. 8.11. 8 Mac 10 Ix. 9. 4. 3 Zip 7 Cauac. 17. 3 Zac 3 Cauac. -------- 10.10. 3 Uayeb 12 Cauac. 11.03. 18 Mol 9 Kan. 16. 18 Pax 5 Kan. 12. 9. 13 Xul 2 Muluc. 56.13. 2.14.0.0. 13 Kankin 11 Muluc. 15. 8 Zotz 8 Ix. 1. 8. 8 Ceh 4 Ix. 2. 1. 3 Uo 1 Cauac. 14. 3 Yax 10 Cauac. 3. 7. 3 Cumhu 6 Cauac. 4. 0. 18 Yaxkin 3 Kan. 13. 18 Muan 12 Kan. 5. 6. 13 Tzec 9 Muluc. 5.19. 13 Mac 5 Muluc. 6.12. 8 Zip 2 Ix. 7.5. 8 Zac 11 Ix. 18. 3 Pop 8 Cauac. 8.11. 3 Chen 4 Cauac. 9. 4. 3 Kayab 13 Cauac. 17. 18 Xul 10 Kan. 10.10. 18 Kankin 6 Kan. 11.03. 13 Zotz 3 Muluc. 16. 13 Ceh 12 Muluc. 12. 9. 8 Uo 9 Ix. 57.13. 2.14.0.0. 8 Yax 5 Ix. 15. 8 Cumhu 1 Ix. 1. 8. 3 Mol 11 Cauac. 2. 1. 3 Pax 7 Cauac. 14. 18 Tzec 4 Kan. -------- 3. 7. 18 Mac 13 Kan. 4. 0. 13 Zip 10 Muluc. 4.13. 13 Zac 6 Muluc. 5. 6. 8 Pop 3 Ix. 5.19. 8 Chen 12 Ix. 6.12. 8 Kayab 8 Ix. 7. 5. 3 Yaxkin 5 Cauac. 18. 3 Muan 1 Cauac. 8.11. 18 Zotz 11 Kan. The only places where a year 4 Kan appears are at the dates 55.13. 2.14.0.0.[3] 9 Ahau 18 Cumhu Year 4 Kan, and 57. 2.14.14.0.0. 9 Ahau 18 Tzec Year 4 Kan. But as the words used are that 6 years (or tuns) remained before the end of the katun, and as a slightly longer time than just 6 tuns may have remained, and as the month Zip in which the death of Ahpula occurred is the third month of the year and so is near the beginning of the year 4 Kan, it is quite possible that the beginning of the Tun 14 may have been in the latter part of the preceding year, in which case, in addition to the preceding dates, the following date might be the one which we are seeking: 55. 9.17.14.0.0. 9 Ahau 3 Zac Year 3 Cauac. [3] It is necessary to remember that, by Goodman's methods, these figures represent periods of past time. Thus the number 2 of the katun means that 2 katuns have passed, and that the current katun is what we should call the third; and that 0.0 means that a full count of uinals and kins has occurred and that the current uinal and kin are what we should call the first. As 9 Ymix 19 Zip is said to be in the year 4 Kan, we shall find this date before the dates of the beginning of Tun 14 in the first two cases and after the beginning of Tun 14 in the last case. This date of 9 Ymix 19 Zip will then be numbered thus, placing the three dates in consecutive order: 1) 55.13. 2.13. 3. 1. 6 tuns 299 days to end of Katun 13 Ahau. 2) 55. 9.17.14.11. 1. 5 " 139 " " " " 3) 57. 2.14.13.16. 1. 6 " 39 " " " " In no one of the cases is the date 9 Ymix 19 Zip exactly 6 tuns before the end of the Katun 13 Ahau, but it is possible that the annalist took no account of fractions of tuns, either in excess of the 6 tuns or otherwise. Thus in the first and last cases of the three, as first given, he may have said to himself, "There are but 6 whole tuns remaining of the katun and I will call it 6," or in the second case he may have said: "There are 5 tuns remaining and 139 days besides; I will call it 6 tuns." Whichever was the plan he followed, we can have at present no means of ascertaining except from the results which we obtain by calculation. The date found on Stela 9 of Copan, which is the earliest date of these stelæ of that place, in which the numbers preceding the period glyphs are given by the line-and-dot method, is 54.9.6.10.0.0. This precedes the above dates by the following periods: 1) 0.3.16.3. 3.1. = 548,341 days = 1,502 years 111 days. 2) 1.0.11.4.11.1 = 1,952,861 " = 5,350 " 14 " 3) 2.6. 8.3.16.1 = 4,667,001 " = 12,786 " 111 " If, now, we accept the first date of 55.13.2.13.3.1. as the date of Ahpula's death, we shall have the date of Stela 9 of Copan as A.D. 34, since the death occurred in 1536. If we accept the second date, 55.9.17.14.11.1., as the true one, Stela 9 must represent a date of B.C. 3814, and in the case of the third date, 57.2.14.13.16.1. in which the period to elapse to the end of Katun 13 Ahau is the nearest to an exact 6 tuns, we should throw back Copan to B.C. 11,250. It is not probable, however, that either of the last two dates is correct, both because of the immense time which would have elapsed and because the monuments show signs of no such age. We are therefore left to the date A.D. 34 as the probable date of the earliest stela of Copan which we know of at present. The following table gives the earliest and latest dates in Copan and Quirigua as far as we know them, together with the dates of our calendar corresponding thereto, on the supposition that the above date is rightly deciphered: Copan: Stela 9, 9. 6.10.0.0 A.D. 34. " N, 9.16.10.0.0 = 197 years later than A.D. 34 A.D. 231. Quirigua: " C, 9. 1. 0.0.0 = 108 + " earlier " " say B.C. 75. " K, 9.18.15.0.0 = 241 + " later " " A.D. 275. If this is correct, Copan lasted, so far as the erection of stelæ is concerned, for about 200 years, and Quirigua for about 350 years, though of course this may be only a small part of the period of their existence. The above calculations have been made on the supposition that the initial dates record the date of the erection of the stelæ, and on the further supposition, as has been stated, that the same principle of calculating time has been continued from the earliest ages. There is, however, some evidence that a change has been made, at least in detail. It has already been seen that the beginning day of the month has been shifted from the Eznab, Akbal series to the Cauac, Kan series of days. What difference this would have made in the relation of the year-and-month count with the long count it is impossible to say without knowing the means used to effect the change; but it is quite likely that this relation was not affected. In the Book of Chilan Balam of Mani is the entry: "The Thirteenth Ahau; then Pop was counted in order." And in the Book of Chilan Balam of Chumayel we find, "The Thirteenth Ahau; Pop was set in order." This statement occurs in the early part of the chronicle, and the calculation of the Ahaus goes on after it in exactly the same way as before it. This setting in order of Pop would not then seem to have made any difference in the long count. At least it is very probable that it means merely that the seasons and the calendar were made to agree. Dr Brinton (_Maya Chronicles_, p. 85) also gives a translation of a part of the Codice Perez, which refers to the "Doubling of the Katuns." The statement is very obscure, but only tends to show that while the counting of the katuns was carried on as in the Books of Chilan Balam, the first of the series was called Katun 8 Ahau instead of Katun 13 Ahau, while the last of the series was Katun 10 Ahau. This would not necessarily change the consecutive order of the katuns, but might merely give a new starting-point. While, therefore, it is impossible to say what change, if any, was made in the reckoning of time, it may be said that there is no evidence at present to show that the old relation of the long count to the year-and-month count and to the count of the Books of Chilan Balam did not continue to the time of the arrival of the Spaniards. Moreover, the date of A.D. 34 for the monuments of Copan and Quirigua is by no means unlikely to be the true one. At all events the above discussion of the reckoning will not be useless if it succeeds in bringing out new facts, and no one will be more ready to recognize any new evidence than I shall be, even if the above deductions shall be shown to be erroneous. * * * * * Transcriber's note: In general every effort has been made to replicate the original text as faithfully as possible, including some instances of inconsistencies of spelling (Ahpula/Ahpulha; Ymix/Imix) and possible irregularities in the use of commas and periods in Mayan dates. 
31610	----	Transcriber's Note A number of typographical errors have been maintained in this version of this book. They have been marked with a [TN-#], which refers to a description in the complete list found at the end of the text. The following codes are used for characters not available in the character set used for this book: + dagger ++ double dagger THE BOOKS OF CHILAN BALAM, The Prophetic and Historic Records of the Mayas of Yucatan. By DANIEL G. BRINTON, M. D. VICE-PRESIDENT OF THE NUMISMATIC AND ANTIQUARIAN SOCIETY OF PHILADELPHIA; MEMBER OF THE AMERICAN PHILOSOPHICAL SOCIETY; THE AMERICAN ANTIQUARIAN SOCIETY; DÉLÉGUÉ OF THE INSTITUTION ETHNOGRAPHIQUE, ETC., ETC. [Illustration] EDWARD STERN & CO., PHILADELPHIA. PREFATORY NOTE. The substance of the present pamphlet was presented as an address to the Numismatic and Antiquarian Society of Philadelphia, at its meeting in January, 1882, and was printed in the _Penn Monthly_, March, 1882. As the subject is one quite new in the field of American archæology and linguistics, it is believed that a republication in the present form will be welcomed by students of these branches. THE BOOKS OF CHILAN BALAM.[5-*] Civilization in ancient America rose to its highest level among the Mayas of Yucatan. Not to speak of the architectural monuments which still remain to attest this, we have the evidence of the earliest missionaries to the fact that they alone, of all the natives of the New World, possessed a literature written in "letters and characters," preserved in volumes neatly bound, the paper manufactured from the bark of a tree and sized with a durable white varnish.[5-+] A few of these books still remain, preserved to us by accident in the great European libraries; but most of them were destroyed by the monks. Their contents were found to relate chiefly to the pagan ritual, to traditions of the heathen times, to astrological superstitions, and the like. Hence, they were considered deleterious, and were burned wherever discovered. This annihilation of their sacred books affected the natives most keenly, as we are pointedly informed by Bishop Landa, himself one of the most ruthless of Vandals in this respect.[5-++] But already some of the more intelligent had learned the Spanish alphabet, and the missionaries had added a sufficient number of signs to it to express with tolerable accuracy the phonetics of the Maya tongue. Relying on their memories, and, no doubt, aided by some manuscripts secretly preserved, many natives set to work to write out in this new alphabet the contents of their ancient records. Much was added which had been brought in by the Europeans, and much omitted which had become unintelligible or obsolete since the Conquest; while, of course, the different writers, varying in skill and knowledge, produced works of very various merit. Nevertheless, each of these books bore the same name. In whatever village it was written, or by whatever hand, it always was, and to-day still is, called "The Book of Chilan Balam." To distinguish them apart, the name of the village where a copy was found or written, is added. Probably, in the last century, almost every village had one, which was treasured with superstitious veneration. But the opposition of the _padres_ to this kind of literature, the decay of ancient sympathies, and especially the long war of races, which since 1847 has desolated so much of the peninsula, have destroyed most of them. There remain, however, either portions or descriptions of not less than sixteen of these curious records. They are known from the names of the villages respectively as the Book of Chilan Balam of Nabula, of Chumayel, of Káua, of Mani, of Oxkutzcab, of Ixil, of Tihosuco, of Tixcocob, etc., these being the names of various native towns in the peninsula. When I add that not a single one of these has ever been printed, or even entirely translated into any European tongue, it will be evident to every archæologist and linguist what a rich and unexplored mine of information about this interesting people they may present. It is my intention in this article merely to touch upon a few salient points to illustrate this, leaving a thorough discussion of their origin and contents to the future editor who will bring them to the knowledge of the learned world. Turning first to the meaning of the name "_Chilan Balam_," it is not difficult to find its derivation. "_Chilan_," says Bishop Landa, the second bishop of Yucatan, whose description of the native customs is an invaluable source to us, "was the name of their priests, whose duty it was to teach the sciences, to appoint holy days, to treat the sick, to offer sacrifices, and especially to utter the oracles of the gods. They were so highly honored by the people that usually they were carried on litters on the shoulders of the devotees."[7-*] Strictly speaking, in Maya "_chilan_" means "interpreter," "mouth-piece," from "_chij_," "the mouth," and in this ordinary sense frequently occurs in other writings. The word, "_balam_"--literally, "tiger,"--was also applied to a class of priests, and is still in use among the natives of Yucatan as the designation of the protective spirits of fields and towns, as I have shown at length in a recent study of the word as it occurs in the the native myths of Guatemala.[7-+] "_Chilan Balam_," therefore, is not a proper name, but a title, and in ancient times designated the priest who announced the will of the gods and explained the sacred oracles. This accounts for the universality of the name and the sacredness of its associations. The dates of the books which have come down to us are various. One of them, "The Book of Chilan Balam of Mani," was undoubtedly composed not later than 1595, as is proved by internal evidence. Various passages in the works of Landa, Lizana, Sanchez Aguilar and Cogolludo--all early historians of Yucatan,--prove that many of these native manuscripts existed in the sixteenth century. Several rescripts date from the seventeenth century,--most from the latter half of the eighteenth. The names of the writers are generally not given, probably because the books, as we have them, are all copies of older manuscripts, with merely the occasional addition of current items of note by the copyist; as, for instance, a malignant epidemic which prevailed in the peninsula in 1673 is mentioned as a present occurrence by the copyist of "The Book of Chilan Balam of Nabula." I come now to the contents of these curious works. What they contain may conveniently be classified under four headings: Astrological and prophetic matters; Ancient chronology and history; Medical recipes and directions; Later history and Christian teachings. The last-mentioned consist of translations of the "_Doctrina_," Bible stories, narratives of events after the Conquest, etc., which I shall dismiss as of least interest. The astrology appears partly to be reminiscences of that of their ancient heathendom, partly that borrowed from the European almanacs of the century 1550-1650. These, as is well known, were crammed with predictions and divinations. A careful analysis, based on a comparison with the Spanish almanacs of that time would doubtless reveal how much was taken from them, and it would be fair to presume that the remainder was a survival of ancient native theories. But there are not wanting actual prophecies of a much more striking character. These were attributed to the ancient priests and to a date long preceding the advent of Christianity. Some of them have been printed in translations in the "_Historias_" of Lizana and Cogolludo, and of some the originals were published by the late Abbé Brasseur de Bourbourg, in the second volume of the reports of the "_Mission Scientifique au Mexique et dans l'Amérique Centrale_." Their authenticity has been met with considerable skepticism by Waitz and others, particularly as they seem to predict the arrival of the Christians from the East and the introduction of the worship of the cross. It appears to me that this incredulity is uncalled for. It is known that at the close of each of their larger divisions of time (the so-called "_katuns_,") a "_chilan_," or inspired diviner, uttered a prediction of the character of the year or epoch which was about to begin. Like other would-be prophets, he had doubtless learned that it is wiser to predict evil than good, inasmuch as the probabilities of evil in this worried world of ours outweigh those of good; and when the evil comes his words are remembered to his credit, while, if, perchance, his gloomy forecasts are not realized, no one will bear him a grudge that he has been at fault. The temper of this people was, moreover, gloomy, and it suited them to hear of threatened danger and destruction by foreign foes. But, alas! for them. The worst that the boding words of the oracle foretold was as nothing to the dire event which overtook them,--the destruction of their nation, their temples and their freedom, 'neath the iron heel of the Spanish conqueror. As the wise Goethe says: "_Seltsam ist Prophetenlied, Doch mehr seltsam was geschieht._" As to the supposed reference to the cross and its worship, it may be remarked that the native word translated "cross," by the missionaries, simply means "a piece of wood set upright," and may well have had a different and special signification in the old days. By way of a specimen of these prophecies, I quote one from "The Book of Chilan Balam of Chumayel," saying at once that for the translation I have depended upon a comparison of the Spanish version of Lizana, who was blindly prejudiced, and that in French of the Abbé Brasseur de Bourbourg, who knew next to nothing about Maya, with the original. It will be easily understood, therefore, that it is rather a paraphrase than a literal rendering. The original is in short, aphoristic sentences, and was, no doubt, chanted with a rude rhythm: "What time the sun shall brightest shine, Tearful will be the eyes of the king. Four ages yet shall be inscribed, Then shall come the holy priest, the holy god. With grief I speak what now I see. Watch well the road, ye dwellers in Itza. The master of the earth shall come to us. Thus prophesies Nahau Pech, the seer, In the days of the fourth age, At the time of its beginning." Such are the obscure and ominous words of the ancient oracle. If the date is authentic, it would be about 1480--the "fourth age" in the Maya system of computing time being a period of either twenty or twenty-four years at the close of the fifteenth century. It is, however, of little importance whether these are accurate copies of the ancient prophecies; they remain, at least, faithful imitations of them, composed in the same spirit and form which the native priests were wont to employ. A number are given much longer than the above, and containing various curious references to ancient usages. Another value they have in common with all the rest of the text of these books, and it is one which will be properly appreciated by any student of languages. They are, by common consent of all competent authorities, the genuine productions of native minds, cast in the idiomatic forms of the native tongue by those born to its use. No matter how fluent a foreigner becomes in a language not his own, he can never use it as does one who has been familiar with it from childhood. This general maxim is ten-fold true when we apply it to a European learning an American language. The flow of thought, as exhibited in these two linguistic families, is in such different directions that no amount of practice can render one equally accurate in both. Hence the importance of studying a tongue as it is employed by natives; and hence the very high estimate I place on these "Books of Chilan Balam" as linguistic material,--an estimate much increased by the great rarity of independent compositions in their own tongues by members of the native races of this continent. I now approach what I consider the peculiar value of these records, apart from the linguistic mould in which they are cast; and that is the light they throw upon the chronological system and ancient history of the Mayas. To a limited extent, this has already been brought before the public. The late Don Pio Perez gave to Mr. Stephens, when in Yucatan, an essay on the method of computing time among the ancient Mayas, and also a brief synopsis of Maya history, apparently going back to the third or fourth century of the Christian era. Both were published by Mr. Stephens in the appendix to his "Travels in Yucatan," and have appeared repeatedly since in English, Spanish and French.[10-*] They have, up to the present, constituted almost our sole sources of information on these interesting points. Don Pio Perez was rather vague as to whence he derived his knowledge. He refers to "ancient manuscripts," "old authorities," and the like; but, as the Abbé Brasseur de Bourbourg justly complains, he rarely quotes their words, and gives no descriptions as to what they were or how he gained access to them.[11-*] In fact, the whole of Señor Perez's information was derived from these "Books of Chilan Balam;" and, without wishing at all to detract from his reputation as an antiquary and a Maya scholar, I am obliged to say that he has dealt with them as scholars so often do with their authorities; that is, having framed his theories, he quoted what he found in their favor and neglected to refer to what he observed was against them. Thus, it is a cardinal question in Yucatecan archæology as to whether the epoch or age by which the great cycle (the _ahau katun_,) was reckoned, embraced twenty or twenty-four years. Contrary to all the Spanish authorities, Perez declared for twenty-four years, supporting himself by "the manuscripts." It is true there are three of the "Books of Chilan Balam"--those of Mani, Káua and Oxkutzcab,--which are distinctly in favor of twenty-four years; but, on the other hand, there are four or five others which are clearly for the period of twenty years, and of these Don Perez said nothing, although copies of more than one of them were in his library. So of the epochs, or _katuns_, of Maya history; there are three or more copies in these books which he does not seem to have compared with the one he furnished Stephens. His labor will have to be repeated according to the methods of modern criticism, and with the additional material obtained since he wrote. Another valuable feature in these records is the hints they furnish of the hieroglyphic system of the Mayas. Almost our only authority heretofore has been the essay of Landa. It has suffered somewhat in credit because we had no means of verifying his statements and comparing the characters he gives. Dr. Valentini has even gone so far as to attack some of his assertions as "fabrications." This is an amount of skepticism which exceeds both justice and probability. [Illustration: SIGNS OF THE MONTHS, FROM THE BOOK OF CHILAN BALAM OF CHUMAYEL.] The chronological portions of the "Books of Chilan Balam" re[TN-1] partly written with the ancient signs of the days, months and epochs, and they furnish us, also, delineations of the "wheels" which the natives used for computing time. The former are so important to the student of Maya hieroglyphics, that I have added photographic reproductions of them to this paper, giving also representations of those of Landa for comparison. It will be observed that the signs of the days are distinctly similar in the majority of cases, but that those of the months are hardly alike. [Illustration: SIGNS OF THE MONTHS, AS GIVEN BY BISHOP LANDA.] The hieroglyphs of the days taken from the "_Codex Troano_," an ancient Maya book written before the Conquest, probably about 1400, are also added to illustrate the variations which occurred in the hands of different scribes. Those from the "Books of Chilan Balam" are copied from a manuscript known to Maya scholars as the "_Codice Perez_," of undoubted authenticity and antiquity.[14-*] The result of the comparison I thus institute is a triumphant refutation of the doubts and slurs which have been cast on Bishop Landa's work and vindicate for it a very high degree of accuracy. The hieroglyphics for the months are quite complicated, and in the "Books of Chilan Balam" are rudely drawn; but, for all that, two or three of them are evidently identical with those in the calendar preserved by Landa. Some years ago, Professor de Rosny expressed himself in great doubt as to the fidelity in the tracing of these hierogylphs[TN-2] of the months, principally because he could not find them in the two codices at his command.[14-+] As he observes, they are _composite_ signs, and this goes to explain the discrepancy; for it may be regarded as established that the Maya script permitted the use of several signs for the same sound, and the sculptor or scribe was not obliged to represent the same word always by the same figure. In close relation to chronology is the system of numeration and the arithmetical signs. These are discussed with considerable fulness, especially in the "Book of Chilan Balam of Káua." The numerals are represented by exactly the same figures as we find in the Maya manuscripts of the libraries of Dresden, Pesth, Paris and Madrid; that is, by points or dots up to five, and the fives by single straight lines, which may be indiscriminately drawn vertically or horizontally. The same book contains a table of multiplication in Spanish and Maya which settles some disputed points in the use of the vigesimal system by the Mayas. A curious chapter in several of the books, especially those of Káua and Mani, is that on the thirteen _ahau katuns_, or epochs of the greater cycle of the Mayas. This cycle embraced thirteen periods, which, as I have before remarked, are computed by some at twenty years each, by others at twenty-four years each. Each of these _katuns_ was presided over by a chief or king, that being the meaning of the word _ahau_. The books above-mentioned give both the name and the portrait, drawn and colored by the rude hand of the native artist, of each of these kings, and they suggest several interesting analogies. They are, in the first place, identical, with one exception, with those on an ancient native painting, an engraving of which is given by Father Cogolludo in his "History of Yucatan," and explained by him as the representation of an occurrence which took place after the Spaniards arrived in the peninsula. Evidently, the native in whose hands the worthy father found it, fearing that he partook of the fanaticism which had led the missionaries to the destruction of so many records of the nation, deceived him as to its purport, and gave him an explanation which imported to the scroll the character of a harmless history. The one exception is the last or thirteenth chief. Cogolludo appends to this the name of an Indian who probably did fall a victim to his friendship to the Spaniards. This name, as a sort of guarantee for the rest of his story, the native scribe inserted in place of the genuine one. The peculiarity of the figure is that it has an arrow or dagger driven into its eye. Not only is this mentioned by Cogolludo's informant, but it is represented in the paintings in both the "Books of Chilan Balam" above noted, and also, by a fortunate coincidence, in one of the calendar-pages of the "_Codex Troano_," plate xxiii., in a remarkable cartouche, which, from a wholly independent course of reasoning, was some time since identified by my esteemed correspondent, Professor Cyrus Thomas, of Illinois, as a cartouche of one of the _ahau katuns_, and probably of the last of them. It gives me much pleasure to add such conclusive proof of the sagacity of his supposition.[15-*] [Illustration] [Illustration: SIGNS OF THE DAYS. The first column on the right is from Landa. The second is from the "_Codex Troano_." The remaining four are from the Book of Chilan Balam of Káua.] There is other evidence to show that the engraving in Cogolludo is a relic of the purest ancient Maya symbolism,--one of the most interesting which have been preserved to us; but to enter upon its explanation in this connection would be too far from my present topic. A favorite theme with the writers of the "Books of Chilan Balam" was the cure of diseases. Bishop Landa explains the "_chilanes_" as "sorcerers and doctors," and adds that one of their prominent duties was to diagnose diseases and point out their appropriate remedies.[18-*] As we might expect, therefore, considerable prominence is given to the description of symptoms and suggestions for their alleviation. Bleeding and the administration of preparations of native plants are the usual prescriptions; but there are others which have probably been borrowed from some domestic medicine-book of European origin. The late Don Pio Perez gave a great deal of attention to collecting these native recipes, and his manuscripts were carefully examined by Dr. Berendt, who combined all the necessary knowledge, botanical, linguistic and medical, and who has left a large manuscript, entitled "_Recetarios de Indios_," which presents the subject fully. He considers the scientific value of these remedies to be next to nothing, and the language in which they are recorded to be distinctly inferior to that of the remainder of the "Books of Chilan Balam." Hence, he believes that this portion of the ancient records was supplanted some time in the last century by medical notions introduced from European sources. Such, in fact, is the statement of the copyists of the books themselves, as these recipes, etc., are sometimes found in a separate volume, entitled "The Book of the Jew,"--"_El Libro del Judio_." Who this alleged Jewish physician was, who left so wide-spread and durable a renown among the Yucatecan natives, none of the archæologists has been able to find out.[18-+] The language and style of most of these books are aphoristic, elliptical and obscure. The Maya language has naturally undergone considerable alteration since they were written; therefore, even to competent readers of ordinary Maya, they are not readily understood. Fortunately, however, there are in existence excellent dictionaries of the Maya of the sixteenth and seventeenth centuries, which, were they published, would be sufficient for this purpose. A few persons in Yucatan have appreciated the desirability of collecting and preserving these works. Don Pio Perez was the first to do so, and of living Yucatecan scholars particular mention should be made of the Rev. Canon Don Crescencio Carrillo y An cona,[TN-3] who has written a good, and I believe the only, description of them which has yet appeared in print.[19-*] They attracted the earnest attention of that eminent naturalist and ethnologist, the late Dr. C. Hermann Berendt, and at a great expenditure of time and labor he visited various parts of Yucatan, and with remarkable skill made _fac-simile_ copies of the most important and complete specimens which he could anywhere find. This invaluable and unique collection has come into my hands since his death, and it is this which has prompted me to make known their character and contents to those interested in such subjects. FOOTNOTES: [5-*] Read before the Numismatic and Antiquarian Society of Philadelphia, at its twenty-fourth annual meeting, January 5th, 1882. [5-+] Of the numerous authorities which could be quoted on this point, I shall give the words of but one, Father Alonso Ponce, the Pope's Commissary-General, who travelled through Yucatan in 1586, when many natives were still living who had been born before the Conquest (1541). Father Ponce had travelled through Mexico, and, of course, had learned about the Aztec picture-writing, which he distinctly contrasts with the writing of the Mayas. Of the latter, he says: "_Son alabados de tres cosas entre todos los demas de la Nueva España, la una de que en su antiguedad tenian caracteres y letras, con que escribian sus historias y las ceremonias y orden de los sacrificios de sus idolos y su calendario, en libros hechos de corteza de cierto arbol, los cuales eran unas tiras muy largas de quarta ó tercia en ancho, que se doblaban y recogian, y venia á queder á manera de un libro encuardenada en cuartilla, poco mas ó menos. Estas letras y caracteres no las entendian, sino los sacerdotes de los idolos, (que en aquella lengua se llaman 'ahkines,') y algun indio principal. Despues las entendieron y supieron léer algunos frailos nuestros y aun las escribien._"--("_Relacion Breve y Verdadera de Algunas Cosas de las Muchas que Sucedieron al Padre Fray Alonso Ponce, Comisario-General en las Provincias de la Nueva España_," page 392). I know no other author who makes the interesting statement that these characters were actually used by the missionaries to impart instruction to the natives; but I learn through Mr. Gatschet, of the Bureau of Ethnology, Washington, that a manuscript written in this manner by one of the early _padres_ has recently been discovered. [5-++] "_Se les quemamos todos_," he writes, "_lo qual á maravilla sentian y les dava pena._"--"_Relacion de las Cosas de Yucatan_," page 316. [7-*] "_Relacion de las Cosas de Yucatan_," page 160. [7-+] "The Names of the Gods in the Kiche Myths of Central America." Proceedings of the American Philosophical Society, Vol. XIX., 1881. The terminal letter in both these words--"_chilan_," "_balam_,"--may be either "_n_" or "_m_," the change being one of dialect and local pronunciation. I have followed the older authorities in writing "_Chilan Balam_," the modern preferring "_Chilam Balam_." Señor Eligio Ancona, in his recently published "_Historia de Yucatan_," (Vol. I., page 240, note, Merida, 1878,) offers the absurd suggestion that the name "_balam_" was given to the native soothsayers by the early missionaries in ridicule, deriving it from the well-known personage in the Old Testament. It is surprising that Señor Ancona, writing in Merida, had never acquainted himself with the Perez manuscripts, nor with those in the possession of Canon Carrillo. Indeed, the most of his treatment of the ancient history of his country is disappointingly superficial. [10-*] For example, in the "_Registro Yucateco_," _Tome III._; "_Diccionario Universal de Historia y Geografia_," _Tome VIII._ (Mexico, 1855); "_Diccionario Historico de Yucatan_," _Tome I._ (Merida, 1866); in the appendix to Landa's "_Cosas de Yucatan_" (Paris, 1864), etc. The epochs, or _katuns_, of Maya history have been recently again analyzed by Dr. Felipe Valentini, in an essay in the German and English languages, the latter in the "Proceedings of the American Antiquarian Society, 1880." [11-*] The Abbé's criticism occurs in the note to page 406 of his edition of Landa's "_Cosas de Yucatan_." [14-*] It is described at length by Don Crescencio Carrillo y Ancona, in his "_Disertacion sobre la Historia de la Lengua Maya_" (Merida, 1870). [14-+] "_Je dois déclarer que l'examen dans tous leurs détails du 'Codex Troano' et du 'Codex Peresianus' m'invite de la façon la plus sérieuse à n'accepter ces signes, tout au moins au point de vue de l'exactitude de leur tracé, qu'avec une certaine réserve._"--Leon de Rosny's "_Essai sur le Déchiffrement de l'Ecriture Hiératique de l'Amérique Centrale_," page 21 (Paris, 1876). By the "_Codex Peresianus_," he does not mean the "_Codice Perez_," but the Maya manuscript in the Bibliothêque[TN-4] Nationale. The identity of the names is confusing and unfortunate. [15-*] "The Manuscript Troano," published in _The American Naturalist_, August, 1881, page 640. This manuscript or codex was published in chromo-lithograph, Paris, 1879, by the French Government. [18-*] "_Declarar las necesidades y sus remedios._"--"_Relation de las Cosas de Yucatan_," page 160. Like much of Landa's Spanish, this use of the word "_necesidad_" is colloquial, and not classical. [18-+] A "_Medicina Domestica_," under the name of "Don Ricardo Ossado, (alias, _el Judio_,)" was published at Merida in 1834; but this appears to have been merely a bookseller's device to aid the sale of the book by attributing it to the "great unknown." [19-*] In his "_Disertacion sobre la Historia de la Lengua Maya ó Yucateca_" (Merida, 1870). Transcriber's Note The following misspellings and typographical errors were maintained. Page Error TN-1 11 re should read are TN-2 13 hierogylphs should read hieroglyphs TN-3 19 An cona should read Ancona TN-4 fn. 14-+ Bibliothêque should read Bibliothèque 
40728	----	NOTES ON THE BIBLIOGRAPHY OF YUCATAN AND CENTRAL AMERICA; COMPRISING YUCATAN, CHIAPAS, GUATEMALA (THE RUINS OF PALENQUE, OCOSINGO, AND COPAN), AND OAXACA (RUINS OF MITLA.) A LIST OF SOME OF THE WRITERS ON THIS SUBJECT FROM THE SIXTEENTH CENTURY TO THE PRESENT TIME. BY AD. F. BANDELIER. FROM PROCEEDINGS OF THE AMERICAN ANTIQUARIAN SOCIETY, OCTOBER 21, 1880. WORCESTER: PRESS OF CHAS. HAMILTON, 311 MAIN STREET. 1881. NOTES ON THE BIBLIOGRAPHY OF YUCATAN AND CENTRAL AMERICA.[1] BY AD. F. BANDELIER. YUCATAN. _Writers of the Sixteenth Century._ JUAN DIAZ, chaplain to Juan de Grijalva. "Itinerario de l' Armata del Re Catholico in India verso la Isola de Iuchathan del anno M. D. XVIII."--Printed first (in the Italian language) as an appendix to the "Itinerario de Ludovico Varthema," in the edition of 1520, and subsequently in the editions of 1522, 1526 and 1535 of the latter book. It was also translated into the English language by Richard Eden, in the "Historie of Travayles," London, 1577, but I am not sure whether the report of Diaz is contained in it. The most popular translation is that by H. Ternaux-Compans, in his first "Recueil de pièces relatives à la conquéte du Méxique," (Vol. X. of his "Voyages, Relations et Mémoires originaux pour servir á l' histoire de la découverte de l' Amérique,") and the latest and best reprint, together with a splendid Spanish translation, is contained in Vol. I. of "Coleccion de Documentos para la Historia de México," 1858, by S^r J. G. Icazbalceta, of México. * * * * * PETRUS MARTYR AB ANGLERIA. "Enchiridion de insulis nuper repertis simulatque incolarum moribus," Basel, 1521. (Separate print of the 4th Decade, which contains the first items about Yucatan ever published in Europe after Diaz's report). "De orbe novo decades Petri Martyris ab Angleria, Mediolaneusis, protonotarii, Cesarei senatoris.--Compluti apud Michaelem de Eguia," in December, 1530. Alcalá. "Opus Epistolarum Petri Martyris Anglerii, Mediolanensis, &c., &c." Also printed by Miguel de Eguia. Alcalá. Of further reprints, and of translations of Peter Martyr's works (the reports on Yucatan are contained in the 4th and 5th Decades), I merely quote: "Novus orbis regionum ac insularum veteribus incognitarum, &c." by Simon Grynæus, Basel, 1532, embodying Dec's 1, 2, 3, _and_ 4. [Footnote 1: The absence of Mr. Bandelier in Mexico, precludes a submission of the proof to his revision, and will account for any errors that may be discovered in the text. PUBLISHING COMMITTEE.] (Also the edition of 1536.)--A French translation of the 4th Decade, by Simon de Colines, Paris, 1532.--A German version, by Hôniger of Kônigshofen.--Hackluyt's reprint of 1587. "De orbe novo Petri Martyris Anglerii, &c., &c.," and finally the complete English translation by Michael Lok and Richard Eden: "De novo Orbe, or the Historie of the West Indies, &c., &c.," London, 1612. I need not dwell on the great importance of Martyr's book, for Yucatan. HERNAN CORTÉS. (His first letter is lost: in place of it the letter of the "Municipality of Vera Cruz," dated 10th July, 1519, contains a short statement about Yucatan. This letter is printed in Vol. I. of "Coleccion de Documentos inéditos para la historia de España," and in Vol. I. of "Historiadores primitivos de Indias," by Enrique de Vedia, Madrid, 1852.--Folsom's translation of 1843. "Despatches of Hernan Cortés, the conqueror of Mexico, &c." substitutes an Introduction by the translator himself.--The earliest mention of this report is found in Robertson: "History of America," Vol. III., p. 289, Edition of 1800, and an abstract is found in Prescott: "Conquest of Mexico," Appendix II., 3d Vol.) "Fifth letter to the Emperor Charles VII.," noticed by Robertson and Prescott; contained, in full, in "Historiadores primitivos de Indias," Vol. I., by Vedia. A full English translation, by Pascual de Gayangos, was published in 1868, by the "Hackluyt Society," vol. 40. JUAN CRISTÓBAL CALVET DE ESTRELLA. "De Rebus Gestis Ferdinandii Cortèsii," written between 1548 and 1560, and printed with a Spanish translation: "Vida de Cortés," by Sr. Icazbalceta in Vol. I. of "Col. de Documentos para la Hist. de México."--Short and meagre. ANDRÉS DE TAPIA. "Relacion hecha por el Señor Andrés de Tapia, sobre la conquista de México." (Icazbalceta's "Coleccion de Documentos, &c." Vol. II. México, 1866.) BENEDETTO BORDONE. "Libro di Benedetto Bordone.--Nel qual si ragione tutte l'Isole del mondo con li loro nomi antichi e moderni," 1528.--Later editions also. GIROLAMO BENZONI. "Historia del Mondo Nuovo," Venice, 1565.--Translated into German by Nicolaus Hoeniger: "Die Neue Welt und Indianischen Kônigreichs, neue und wahrhaffte geschichte, &c., &c.," Basel, 1579.--Incorporated in Théodore De Bry "Grosse Reisen," Parts 4, 5, and 6.--Of other prints I but mention the latest English translation, published by the Hackluyt Society in 1857 (Vol. 21,) under the title of "History of the New World, by Girolamo Benzoni," edited as well as translated by Rear-Admiral W. H. Smyth. There are Italian versions of 1572, French of 1587, and Latin of 1600. BERNAL DIEZ DEL CASTILLO. "Historia verdadera de la Conquista de Nueva España," Madrid, 1632. (There may be two editions of the same year). Of the Spanish reprints I mention here (also contained in "Historiadores primitivos de Indias," Vedia, 1852, Vol. II.), the one of 1837, Paris, 4 Vols. 12^o, and the other of 1854, México, 4 vols. also.--Two English translations are known to me at present: "The True History of the Conquest of Mexico, by Captain Bernal Diez del Castillo," translated by Maurice Keatings, London, 1800.--"The Memoirs of the Conquistador, Bernal Diez del Castillo," translated by John Ingram Lockhart, London, 1844.--There is also a German translation, by P. J. Rehfuss, Bonn, 1838.--Bernal Diez (not Diaz) is very valuable as eye-witness, having been to Yucatan with Cordoba (1517), Grijalva (1518), Cortés (1519),--and finally with the latter to Honduras, passing through Peten. FRAY LORENZO DE BIENVIDA. Letter to the Infanto Philip (II.), dated Yucatan, 10 February, 1548. Original in MS. French translation by H. Ternaux-Compans in "1^{er} Recueil de Piéces concernant le Méxique," Vol. X. 1838, of his collection of "Mémoires et documents Originaux, &c., &c." GONZALO FERNANDEZ DE OVIEDO Y VALDÉS. "Historia General y natural de las Indias," composed of 50 books.--The first 19 books, and part of the 50th, were published by the author as early as 1535,--and the first 20 books as early as 1557,--but the entire work has only been printed in 1851, at Madrid, 4 Vols. folio.--It is full of details concerning Yucatan. FRANCISCO LOPEZ DE GOMARA. "Historia general de las Indias, y todo lo acaescido en ellas dende que se ganaron hasta agora. Y la conquista de México, y de la nueva España, &c." Zaragoza, 1552.--Of this book I quote--e. g.--the following Spanish editions: Medina del Campo, 1553, Antwerp, 2 prints, 1554--Zaragoza, 1555,--and it is also contained in "Historiadores primitivos de Indias," by Andrés Gonzalez Barcia, Madrid, 1749, Vol. II.--and in "Historiadores primitivos de Indias," by Vedia, Madrid, 1852, Vol. I.--There is an Italian version, by Augustino de Cravaliz, Rome, 1556, ("La Histoirie generale delle Indie Occidentali. &c., &c."), and French translations published respectively in 1578, 1587, 1597, and 1605.--Finally, Juan Bautista de San Anton Muñoz Chimalpain Guauhtlehuanitzin made a translation into the Mexican, or "Nahuatl" language, which C. M. Bustamante published at Mexico, in 1826.--I know of no English translation of the work.--It actually consists of two parts, the "Historia General," and the "Conquista de México."--The former contains a short, but fair, description of Yucatan, and the latter a report on Cortés' doings there and matters relating thereto. BARTOLOMÉ DE LAS CASAS. Of the numerous (over forty) writings of the Bishop of Chiapas, I select only "Historia de las Indias," published "at last," Madrid, 1875 and 1876, by the Marquis de la Fuensanta del Valle and Don José Sancho Rayon, in 5 vols. The 5th Vol. contains the famous "Apologética Historia."--Another publication of the "Historia de las Indias," though not as complete, has appeared in Mexico in 2 vols., as the first series of Sr. J. M. Vigel's "Biblioteca Mexicana," 1877 and 1878.--It does not contain the "Apologética."--Fragments of the latter are found in Lord Kingsborough's "Antiquities of Mexico," Vol. VIII. "Brevissima relacion de la destruycion de las Indias," Sevilla, 1552. Of this polemic and strongly tinged memoir there are innumerable versions.--I know of Spanish publications besides the above, and those of London, 1812,--Philadelphia, 1821,--both due to Dr. De Mier,--Madrid, J. A. Llorente, 1822, and México, 1822.--Latin translations: Francfort, 1598; Oppenheim, 1614; Heidelberg, 1664.--French translations: Antwerp, 1579; Amsterdam, 1620; Rouen, 1630; Lyon, 1642; Paris, 1697; Amsterdam, 1698. (The last two contain each five papers of Las Casas), and Paris, 1822. "Oeuvres de Don Bartolomé de las Casas," by J. A. Llorente.--Of Italian Translations (with Spanish text). I allude to those of 1626. Venice.--1630, Id.:--1643, Id., and also of 1645.--There is a German translation of 1599.--Dutch translations: Amsterdam, 1610 and 1621, and 1663.--I know of but one English translation, which bears the title "A Relation of the first voyages and discoveries made by the Spaniards in America, &c., &c." London, 1699,--although Dr. Robertson mentions one of 1693.--Las Casas must be used with great caution. DIEGO DE LANDA. "Relacion de las cosas de Yucatan." Bishop Landa was born in 1524, and died in 1579; his work must therefore have been written between 1549 and the latter date. It was published by the Abbé Brasseur de Bourbourg, in 1860, with a French translation opposite to the Spanish text, and under the title of "Relation des choses de Yucatan."--Republished again in 1864, with some other matter. The merits of Landa are certainly very great, but the real import of his so-called "A. B. C." ("De sus letras forme aqui un a. b. c." pp. 316-319), has been misunderstood and correspondingly misrepresented. The picture which Landa gives us of the customs and organization of the Mayas is completely at variance with some of his other statements. Much close attention is required. "CARTAS DE INDIAS." Vol. I. Madrid, 1878. These contain several letters and reports on Yucatan, from the 16th century. I only refer to one, a complaint of four Indian "gobernadores," dated 12 April, 1567, against the Bishop Diego de Landa, designating him as "principal author of all these evils and troubles...." JOSEPH DE ACOSTA. "Historia natural y moral de Indias," Sevilla, 1590. I merely mention this author, without entering into further bibliographical details about his work. It has been translated into many languages, and--in part or wholly--incorporated in many general collections of "Americana." He says but little about Yucatan, still his book is indispensable to any one studying Yucatecan antiquities. I also advert here to his former publication, which is but little known: "De promulgatione Evangelii apud Barbaros, sive de procuranda Indorum salute," Libros 6; printed in 1589. GERÓNIMO DE MENDIETA. "Historia ecclesiástica Indiana," written about 1590, but printed for the first time, by Sr. J. G. Icazbalceta, at Mexico, in 1870--Contains much and valuable information.--Mendieta has been extensively copied by Torquemada. FRAY TORIBIO DE PAREDES, SURNAMED "MOTOLINIA." "Historia de los Indios de Nueva-España," written about 1540, but published in full only by Sr. Icazbalceta in Vol. I. of "Coleccion de Documentos, &c."--Mentions Yucatan incidentally.--A large part of the work had been printed before in the "Documentos inéditos, &c." under the title of "Ritos Antiguos, Sacrificios é Idolatrias de las Indias de la Nueva-España,"--also in Vol. IX. of Lord Kingsborough.--A Latin version, under the title of "De Moribus Indorum" may have existed once. * * * * * Yucatan is, furthermore, mentioned in many works of a more general character, embodying information gathered mostly from the sources already referred to. I do not, therefore, enter into any lengthy bibliographical sketches of them. SIMON GRYNAEUS. "Novus Orbis," 1532. Already noticed under Petrus Martyr. PETRUS APIANUS. "Cosmographia," 1539, 1545, 1561 (Dutch version), &c. ABRAHAM ORTELIUS. "Theatrum orbis terrarum," 1571, 1588, &c. THOMASO PORCACCHI. "L'isole pio famose del Mondo," 1572, 1576, 1590, &c., &c. G. MERCATOR. "Atlas, six Cosmographical Meditations." Duisburg, 1594. CONRAD LOEW. "Meer oder See-Ansicht Buch." Cologne, 1598. SEBASTIAN MUNSTER. "Cosmographey," 1575, &c. ANDRÉ THEVET. "Les singularites de la France antarctique, autrement nommé Amérique, et de plusieurs Terres et Isles decouvertes de notre temps."--Paris, 1558; Antwerp, 1558; in Italian, at Venice, 1561. I forbear further mention of the polemic works on the origin of the American Indians,--and now turn to some writers whose works are probably lost, or at least not accessible, although there is positive evidence of their former existence. FRAY GERÓNIMO ROMAN. "Republica Indiana"--certainly existed as late as 1630, or "República de las Indias Occidentales." FRAY ALONZO SOLANA. "Noticias Sagradas y profanas de las Antigüedades y Conversion de los Indios de Yucatan." (Written before 1600). DON FRANCISCO MONTEJO. "Carta al Rey sobre la fundacion de la Villa de San Francisco de Campeche, y de la Ciudad de Mérida," 14 June, 1543. (Still at Sevilla, leg. 7. "Cartas de Indias"). In the above list I have not included any Grammar, Vocabulary, Sermonary, "Doctrina," &c., &c., for the use of the Indians of Yucatan, or written in the Maya language, of which several are known. In conclusion, I beg to add the Maya writing, entitled: "SERIES OF KATUNES," published, with an English translation, by Mr. J. L. Stephens, in "Incidents of travels in Yucatan," and by Brasseur de Bourbourg, in "Rel. d. ch. de Y." _Writers of the Seventeenth Century._ ANTONIO DE HERRERA. "Historia general de los hechos de los Castellanos en las Islas y la Tierra firme del mar Océano," Madrid, 1601, 1615, 4 vols. folio. There are two other editions in the original language: Madrid, 1726 and 1730, and Antwerp, 1728. Of this most important book, several translations have appeared, embodying either the whole or only a part.--Thus a French translation of the "Descripcion de las Indias Occidentales," appeared at Amsterdam in 1622 twice, and a French translation of the 1st, 2d and 3d Decades, at Paris, 1671.--A Latin version of the "Descripcion" was also published in 1622, by Colin, at Amsterdam, and a very unreliable English rendering by John Stephens, in 6 vols. 8^o, appeared at London in 1725. Herrera is one of the most important authorities on every subject of which he treats. GREGORIO GARCIA. "Orígen de los Indios del Nuevo Mundo é Indias Occidentales." 1st Edition, 1606; Second Edition, Madrid, 1729, by Barcia.--A very important and valuable work. JUAN DE TORQUEMADA. "Los veinte y uno Libros Rituales y monarchia Indiana, con el orígen y guerras de los Indios occidentales." 1st Edition, Madrid, 1613; 2d Edition, Madrid, 1723. Barcia. AUGUSTIN DE VETANCOURT. "Teatro Mexicano." México, 1698.--2d Edition, in "Biblioteca de la Iberia," México, 1870.--Treats of Yucatan incidentally, speaking of Cortés, &c. The work consists properly of three books: the "Teatro," the "Crónica de la provincia del Santo Evangelio de México," and the "Menologio franciscano." ANTONIO DE REMESAL. "Historia general de las Indias Occidentales, y particular de la gobernacion de Chiapas y Guatemala."--This book has also another title: "Historia de la Provincia de San Vicente de Chyapa y Guatemala de la Orden de San Domingo."--Madrid, 1619 and 1620.--Treats of Yucatan also, following Las Casas generally. An important work. BERNARDO LIZANA. (Lizama or Lizaba?) "Devocionario de Nuestra Señora de Itzmal, Historia de Yucatan é de conquista Espiritual," 1663, according to the Abbé Brasseur and Leon y Pinelo.--E. G. Squier speaks of two works: one "Historia de la Provincia de Yucatan, y su conquista Espiritual," Valladolid, 1633, and the other "Historia de Nuestra Señora de Izamal."--Whichever way may be right, there remains accessible as yet, but a fragment published in Spanish, with a French translation by the Abbé Brasseur in his "Relation des choses de Yucatan," 1864. The fragment is entitled: "Del principio y Fundacion destos cuyos omules deste Sitio y Pueblo de Ytzmal...."--Lizana is of the highest importance and value, and it is much to be regretted that the _entire_ book is of such difficult access. DIEGO LOPEZ DE COGOLLUDO. "Historia de Yucatan."--1st Edition, Madrid, 1688; 2d Edition, Mérida, 1842; 3d Edition, 1867.--Cogolludo has always been regarded as the historian of Yucatan "par excellence." He is indeed indispensable for any study of Yucatan antiquities, but, like all other authors, he must never be implicitly followed. The closest criticism possible is absolutely required. GIL GONZALEZ DÁVILA. "Teatro ecclesiástico de la primitiva Iglesia de los Indios Occidentales." Madrid, 1649. JUAN DIAZ DE LA CALLE. "Memorial y Resûmen breve de Noticias de las Indias Occidentales." Madrid, 1654. * * * * * These constitute the most important sources on Yucatan written during the 17th century. Nearly all of them are of _special_ value, and we would call particular attention to Cogolludo, Lizana, Torquemada, Herrera, and Remesal. Among such authors, who wrote upon the subject and whose writings are not now accessible, I name here: PEDRO SANCHEZ AGUILAR. "Relacion de las Cosas de Yucatan, y Informe contra los Idólatras del Obispado de Yucatan, &c." 1639. FRANCISCO CÁRDENAS. "Relacion de la Conquista y Succesos de Yucatan," 1639. (If existing, probably in Spain). NICOLÁS LIZARRAGA. "Representacion al Rey pidiéndole la Conquista de Itzá y Lacandon, con unas Noticias y Mapa de dichas Tierras." NICOLÁS DE VALENZUELA. An account of the expedition against the Lacandones, written 1695, and comprising 402 pages. I would further call attention to the land titles, such as Deeds, Grants, donations, &c., &c., in Yucatan, some of which go back to the 17th century. These contain occasional references to the Indian settlements, some of which are certainly of great value and importance. Finally, I refer to some general works, treating of Yucatan: SAMUEL PURCHAS. "His Pilgrimage, &c., &c." London, 1613, 1614 and 1617. (This forms the 5th volume of Purchas' great works).--The great work of Purchas, also known as "Hackluytus Posthumous," appeared in 1625, and treats also of Yucatan. O. DAPPER. "Die unbekannte neue Welt, oder Beschreibung des Welt-theils Amerikas, &c." Amsterdam, 1673. This is in fact but a translation of the following: ARIAS MONTANUS. "De Nieuvre en Onbekende Weereld: of Beschryving van America en t' Zuid Lande." Amsterdam, 1671. MATHIAS QUAD. "Enchiridion Cosmographicum: Dass ist, Ein Handbüchlein, der gantzen Welt gelegenheit, &c." Cologne, 1604 and 1608. JOANNES PETRUS MAFFEI. "... historiarum Indicarum libri XVI., &c." Antwerp, 1605--frequently reprinted and translated. JACOBUS VIVERUS. (Van de Vijvere). "Handbook: of Cort begrijp der Caerten Ende Beschryvinghen van allen Landen des Werelds." Amsterdam, 1609. (This is the 2d edition of an anonymous atlas). CORNELIUS WYTFLICT ET ANTHOINE MAGIN. "Histoire universelle des Indes occidentales et orientales," Douay, 1611. GASPARD ENS. "West und Ost-Indischer Lustgart.:...." Cologne, 1618. AUBERTUS MIRAEUS. "De statu religionés christianae...." Cologne, 1619. ATHANASIUS INGA. "West-Indische Spiegel, &c." Amsterdam, 1624. JOHANN PHILIPP ABELIN. (Gottfriedt). "Neue Welt und Americanische Historien." Francfort, a. m. 1655. A. O. EXQUEMELIN. "De Amerikaensche Zee-Roovers." Amsterdam, 1678. (Innumerable translations, &c. &c). EBERHARD WERNER HAPPEL. "Thesaurus Exoticorum." Hamburg, 1688. (Indifferent compilation). I do not include in this hasty bibliographical list any linguistical works whatever,--or writings on the plants and medicinal herbs of Spanish-America. Purposely I omit also Antonio de Solis, whose history of the conquest of Mexico has a great literary, but hardly any scientific, value. _Writers of the Eighteenth Century._ JUAN DE VILLAGUTIERRE Y SOTOMAYOR. "Historia de la Conquista y Reducciones de los Itzaes y Lacandones en la América Septentrional." Madrid, 1701. The first part only, composed of 10 books,--the second part may not have been completed,--at least it has remained unknown till now. The work is of the highest importance, especially for that part of Yucatan which has since hardly been explored. ABBATE FRANCESCO SAVERIO CLAVIGERO. S. J. "Storia antica del Messico." Cesena, 1780, 1781. Spanish translations: London, 1826; México, 1844, id. 1853. English translation: London, 1787. German version: Leipzig, 1789. (The English copy by Sir Charles Cullen),--all these works mention Yucatan also. ANTONIO DE ALCEDO. "Diccionario geográfico-histórico de las Indias Occidentales ó América...." Madrid, 1786-1789. 5 vols. 4^o.--English translation by G. A. Thompson. London, 1812-15. JOSEPH ANTONIO DE VILLA-SEÑOR Y SANCHEZ. "Teatro Americano." México, 1746.--Of indirect value for Yucatan. (2 vols. folio). J. LAFITAN. S. J. "Moeurs des sauvages américains, comparées aux moeurs des premiers temps." Paris, 1724. (There is a Dutch translation: "De Zeden der Wilden van Amerika," but I have no access to its date at present).--The best ethnological work previous to 1850. ABBÉ GUILLAUME THOMAS RAYNAL. "Histoire philosophique et politique des établissements et du commerce des Européens dans les deux Indes." Paris, 1780, and other editions. English translation. Edinburgh, 1782. WILLIAM ROBERTSON. "History of America." (Numberless editions and translations, all too well known to require special mention here).--Highly important. CHEVALIER DE PAUW. "Recherches philosophiques sur les Américains." London, 1771. A strongly negative, and through its exaggerations in that direction, very injudicious work. Still it should be read attentively, as well as the rejoinder to it by Dom Pernetty. GEMELLI CARRERI. (Properly belongs to the 17th century). "Giro del Mondo...." Naples, 1721.--French: "Voyage du Tour du Monde." Paris, 1719. * * * * * In the Library of the Cathedral of Mexico there still exists: ARTURO O'NEIL. "Descripcion, Poblacion, y censo de la Provincia de Yucatan en la Nueva España." 1795. * * * * * We have also notice of the former existence of the following works, by: FRAY ANDRÉS AVENDAÑO. "Diccionario de nombres de personas, ídolos, danzas, y otras antiqüedades de los Indios de Yucatan." "Explicacion de varios Vaticinios de los antiguos Indios de Yucatan." * * * * * To take notice of all the geographical works, cyclopædias, &c., &c., published in the 18th century, and which contain notices of Yucatan, would be a task exceeding far the time and limits of this list. It can easily be proved, however, that the works on especially Yucatecan topics are not numerous. This may be due, in part, to the rigorous exclusion of foreigners from Spanish America, and the consequent decline of intellectual activity towards the close of Spanish domination. The great collection of Juan Bautista Muñoz contains hardly anything on Yucatan. _Writers of the Nineteenth Century._ Here the number of publications increases so rapidly, that I cannot attempt to notice all. Besides, many of the authors are so well known that a mere mention of their names and the titles of their works will suffice. Periodicals containing papers on Yucatan, will be mentioned generally, but detailed reference to special articles can be given only in a few exceptional instances. The latest works will only be alluded to. ALEXANDER VON HUMBOLDT. "Essai politique sur le royaume de la Nouvelle-Espagne." Paris, 1811, 2 vols. 4^o.--Id. Paris, 1811, 5 vols. 8^o.--Paris, 1825-27, 4 vols. 8^o. Spanish translation: Madrid, 1818. English translation by John Black. London, 1811. Also translated into the German. References to Yucatan and its inhabitants may also be found in "Ansichten der Natur," (Notes), and even in "Kosmos." FRIEDRICH VON WALDECK. "Voyage pittoresque et archéologique dans la Province de Yucatan." Paris, 1838. Splendid, but the drawings are mostly restorations,--therefore suspicious. ANTONIO DEL RIO. (The date of this report is: "Palenque 24 June, 1787," and I shall refer to it more particularly under the heading of "Chiapas,"--still, as it contains the report of the Franciscan, Thomas de Soza, on Yucatecan ruins, I place it here also). "Description of the Ruins of an ancient City, discovered near Palenque, in the Kingdom of Gautemala, in Central America; translated from the original manuscript report of Captain Don Antonio del Rio." London, 1822.--There are two German translations: one "Huehuetlapallan, Amerika's grosse Urstadt, &c." Meiningen, 1824, and v. Minutoli's "Beschreibung einer alten Stadt in Guatemala." 1832.--A French translation, by D. B. Warden, in "Antiquités Méxicaines." Vol. II. and, finally, the Spanish original, in "Diccionario universal de Geografia, &c." Vol. VIII.--See also abstract in "Mosaico Mexicano." Vol. II. LORENZO DE ZAVALA. Report on Uxmal, published in Vol. I. of "Antiquités Méxicaines." JOHN L. STEPHENS. "Travels in Central America, Chiapas, and Yucatan." N. York, 1841. "Incidents of travel in Yucatan." N. York, 1843. F. CATHERWOOD. "Views of Ancient Monuments in Central America, Chiapas and Yucatan." N. York, 1844. B. M. NORMAN. "Rambles in Yucatan." N. York, 1843. CHARLES ST. JOHN FANCOURT. "The History of Yucatan." London, 1854.--Not of great value. EMMANUEL VON FRIEDRICHSTHAL. Letter of 21 April, 1841, in "Registro Yucateco," Vol. II., and "Diccionario Universal," Vol. X.--"Les Monuments de l'Yucatan," in "Nouvelles Annales des Voyages," 1841, Vol. 92.--These papers are not very valuable. JUAN GALINDO. Report on the antiquities of Lake Peten. "Antiquités Méxicaines," Vol. I. MODESTO MENDEZ. Report on Tikal. "Zeitschrift für allgemeine Erdkunde," Vol. I.; 1853; also in Siver's "Mittelamerika" and other places. He is, as yet, the only authority on Tikal. JULIUS FROEBEL. "Aus Amerika, Erfahrungen, Reisen, und Studien." Leipzig.--English translation: "Seven years travel in Central America." London, 1861. CARL BARTHOLOMÂUS HELLER. "Reisen in Mexico." Leipzig, 1853.--Rather fair and moderate. DÉSIRÉ CHARNAY, and VIOLLET LE DUC. "Cités et Ruines américaines." Paris, 1863.--Invaluable for its photographs. ARTHUR MORELET. "Voyage dans l'Amérique centrale, l'Ile de Cuba, et la Yucatan." Paris, 1857. English translation by Mrs. E. G. Squier. "Itza, or the unexplored regions of Central America." London, 1871.--A very attractive and valuable work. CHARLES ETIENNE BRASSEUR DE BOURBOURG. "Histoire des Nations Civilisées du Méxique et de l'Amérique centrale." Paris, 1857-9. "Rapport sur les Ruines de Mayapan et d'Uxmal," in "Archives de la Cômission scientifique du Méxique," Vol. II. "Relation des choses de Yucatan." Paris, 1864. (See Landa and Lizana). "Quatre Lettres sur le Méxique." Paris, 1868. "Manuscrit Troano." Paris, 1869-1870. The late Abbé Brasseur was certainly the greatest of all modern travellers in Mexico and Central America, as far as extent of travel and long duration of stay are concerned. He knew those countries better, and had easier access to the natives, than any other similar traveller of this century. His works are therefore, actual mines of wealth so far as old documents are concerned: he has collected and brought to light more manuscripts than any other student. But his honest zeal and unrestrained enthusiasm have led him into paths on which he has wandered lamentably astray. His works are indispensable, though very little of his own conclusions can be believed. JUAN PIO PEREZ. "Cronología antigua de Yucatan," in "Relation des choses de Yucatan." 1864. Diccionario de la Lengua haya. Mérida, 1877. MANUEL OROZCO Y BERRA. "Geografia de las Lenguas y Carta etnogrática de México." México, 1864. AMERICAN ANTIQUARIAN SOCIETY, Worcester, Mass. _Proceedings No. 44._ Oct. 1865, page 63. Report of S. F. Haven, LL.D. _Proceedings No. 55._ Oct. 1870, page 42. Report of S. F. Haven, LL.D. _Proceedings No. 56._ April, 1871, page 7. Report of S. F. Haven, LL.D. _Proceedings No. 66._ April, 1876, page 16. "The Mayas," by Stephen Salisbury, jr. _Proceedings No. 69._ April. 1877, page 70. "Dr. Le Plongeon in Yucatan," by Stephen Salisbury, jr. _Proceedings No. 70._ Oct. 1877, page 89. Report of S. F. Haven, LL.D. _Proceedings No. 71._ April, 1878, page 71. "Terra Cotta Figure from Isla Mujeres," by Stephen Salisbury, jr. Page 91, "The Mexican Calendar Stone," by Philipp J. J. Valentini, Ph.D. _Proceedings No. 72._ Oct. 1878, page 65. "Archæological Communication on Yucatan," by Augustus Le Plongeon, M.D. Page 77, "Notes on Yucatan," by Mrs. Alice D. Le Plongeon. Proceedings No. 73._ April, 1879, page 81. "Mexican Copper Tools," _by Philipp J. J. Valentini, Ph.D. Page 113, "Letter from Dr. Augustus Le Plongeon." _Proceedings No. 74._ Oct. 1879, page 71. "The Katunes of Maya History," by Philipp J. J. Valentini, Ph.D. _Proceedings No. 75._ April, 1880, page 59. "The Landa Alphabet," by Philipp J. J. Valentini, Ph.D. _Proceedings No. 76._ Oct. 1880, page 58. "Mexican Paper," by Philipp J. J. Valentini, Ph.D. Page 82, "Notes on the Bibliography of Yucatan and Central America," by Ad. F. Bandelier. PHILIPP J. J. VALENTINI. "A new, and an old Map of Yucatan," in "Magazine of American History," 1879. ALBERT GALLATIN. "Notes on the semi-civilized nations of Mexico, Yucatan, and Central America," in Vol. I. of "Transactions of the American Ethnological Society." N. York, 1845. A. AUBIN. "Mémoire sur la peinture didactique et l'écriture figurative des anciens méxicaines." Paris, 1859-1861. (4 papers, published also in the "Revue américaine et Orientale." 1st Series, Vols. III., IV. and V.) LÉON DE ROSNY. "Les écritures figuratives et hiéroglyphiques des peuples anciens et modernes." Paris, 1860. "Mèmoire sur la Numération dans la Langue et dans l'écriture sacrée des anciens Mayas." (Compte-Rendu du "Congrés international des américanistes." 1875, Vol. II.) "Essai sur le déchiffrement de l'écriture hiératique de l'Amérique Centrale." Paris, 1876.--Still continued. FRANCISCO PIMENTEL. "Cuadro descriptivo y comparativo de las Lenguas Indígenas de México." México, 1862. German translation, by Isidor Epstein. N. York, 1877. HYACINTHE DE CHARENCY. "Recherches sur le Codex Troano." Paris, 1876. D. GERONIMO CASTILLO. "Diccionario Historico, Biografico y Monumental de Yucatan." Mérida, 1866. 2 vols. SERAPIO BAQUEIRO. "Ensayo Historico sobre las Revoluciones de Yucatan, 1840--1864." Mérida, 1870. 2 vols. GUSTAV KLEMM. "Allgemeine Culturgeschichte der Menschheit." 10 vols. Leipzig, 1843-1852. HEINRICH WÜTTKE. "Die Enstehung der Schrift." EDWARD KING, LORD KINGSBOROUGH. "Antiquities of Mexico." 1831-1848, London, 9 vols. folio. Special value of plates. DE LARENANDIERE. "Méxique et Guatemala," in "Univers pittoresque." Paris, 1843. WM. H. PRESCOTT. "History of the Conquest of Mexico." (Too well known to need any remarks). LEWIS H. MORGAN. "Systems of Consanguinity and Affinity of the Human Family." 1871. (No. 218 of "Smithsonian Contributions to Knowledge.") "American aboriginal Architecture." Johnson's Encyclopedia, Vol. I. "Ancient Society." New York, 1877. HUBERT HOWE BANCROFT. "The Native Races of the Pacific States." 5 vols. N. York, 1875. JOHN D. BALDWIN. "Ancient America." New York, 1872. JOSÉ M. MELGAR Y SERRANO. "Exámen comparativo entre los Signos simbólicos, &c." Vera Cruz, 1872. GUSTAV BRÜHL. "Die Culturvölker Alt-Amerika's." New York, Cincinnati, and St. Louis, 1876, 1877, and 1878. ADOLPH BASTIAN. "Die Culturlaender des alten America's." Berlin, 1878. 2 vols. JOHN T. SHORT. "The North Americans of Antiquity." New York, 1879. * * * * * I further refer to papers in "NOUVELLES ANNALES DES VOYAGES." 1843. By H. Ternaux-Compans. "REGISTRO YUCATECO." Vols. I. and II. And to the publications of CRESCENCIO CARRILLO, Licenciado. (I have but glanced at one of his works). ELIGIO ANCONA. "Historia de Yucatan." Mérida, 1875. 4 vols. MANUEL LARRAINZAR. "Estudios sobre la Historia de América, sus Ruinas y Antigüedades." México, 1875. 5 vols. * * * * * On most of the works like those of Prescott, Bancroft, Baldwin, and others, I need not comment, having already expressed my opinion in "Art of War and Mode of Warfare of the Ancient Mexicans," and "Tenure and Distribution of Lands, and Customs with respect to Inheritance among the Ancient Mexicans."--(10th and 11th Reports of the Peabody Museum). In regard to Yucatecan paintings and carvings, I have expressed my convictions in "Sources for aboriginal history of Spanish America," Vol. 27 of the "Proceedings of the American Association for advancement of Science." 1878. I repeat it, this attempt at a bibliography on Yucatecan antiquities is far from being complete,--many works of greater or less importance having probably been overlooked. CHIAPAS. This district or State contains the well known ruins of Palenque and Ocosingo. Still, but very few of the works hereafter mentioned relate to these places. It is therefore a bibliography of Chiapas and of its aborigines:--Zendal, Zoques, Zotzil, Chiapanecos, &c., and not a special bibliography of Palenque, &c., which I intend to present,--convinced that our lack of knowledge on the aborigines of Chiapas in general is a chief cause of our ignorance about the past history of these remains. A large number of authors treating of Chiapas have already been noticed in regard to Yucatan, and in such cases I merely give the author's name, without the title or any other reference to his works, except when there are special reasons for it. _Writers of the Sixteenth Century._ DIEGO DE GODOY. "Relacion á Hernando Cortez, en que trata del Descubrimiento de diversas Ciudades i Provincias, i Guerra que tuvo con los Indios, &c., de la Provincia de Chamula."--First incorporated in the "Historia general" of Oviedo y Valdés, again in Barcia's "Historiadores primitivos de Indias," and in "Historiadores primitivos de Indias" of Vedia.--French translation by Ternaux-Compans, in 1^{st}, "Recueil de pièces concernant la Méxique, &c."--Also Italian in "Ramusio," Vol. III. GONZALO FERNANDEZ DE OVIEDO Y VALDÉS. HERNAN CORTÉZ.--"Carta quinta." FRANCISCO LOPEZ DE GOMARA. BERNAL DIEZ DEL CASTILLO. (Eye-witness of the conquest of Chiapa.) BARTOLOMÉ DE LAS CASAS. (Especially the "Apologética historia.") GERÓNIMO DE MENDIETA. (Incidental mention.) In the 2d "_Recueil de piecés concernant le Méxique_," of Ternaux-Compans, there is a complaint or letter of an anonymous author against Las Casas, dated Chiapas.--I also refer to "_Cartas de Indias_," Vol. I., containing several letters of Las Casas himself. * * * * * There is, in fact, but very little published about the antiquities of Chiapas, during the 16th century. I do not even mention any of the general collections which have an occasional reference to the name. But few vocabularies are noticed. Still we are informed of the following works, which may yet be in existence, or which at all events have existed once, and were written during the 16th century. FRAY TOMÁS TORRE. "Historia de los principios de la Provincia de Chiapas y Guatemala, del Orden de Santo Domingo." FRAY DOMINGO VICO. "Historia de los Indios, sus fábulas, supersticiones, costumbres, &c., &c." The library of the "Museo Nacional" of the City of Guatemala, contains a number of fragments of a "_Historia de la Provincia de San Vicente Ferrer de Chiapas y Guatemala_," the third book of which is superscribed: "Isagoge histórico apologético general de todas las Indias."--There is no date nor name of author, but it can be conjectured that it was written in the 16th century.--Gregorio García also quotes: _Fray Estévan de Salazar_. "Discurs. Symb. apost." who in turn is said to refer to a book entitled "_Historia, i Relacion de la Teología de los Indios Mexicanos_," said book being lost in a shipwreck, 1564. _Writers of the Seventeenth Century._ GREGORIO GARCIA. ANTONIO DE HERRERA. JUAN DE TORQUEMADA. ANTONIO DE REMESAL. AUGUSTIN DE VETANCOURT. GIL GONZALEZ DÁVILA. JUAN DIAZ DE LA CALLE. AUGUSTIN DÁVILA-PADILLA. "Historia de la Fundacion y Discurso de la Provincia de Santiago de México." 1st edition, Madrid, 1596; 2d edition, Brussels, 1625.--Mentions Chiapas only in connection with the biography of Las Casas.--The first edition has almost disappeared, so that it is practically a book of the 17th century. AUGUSTIN CANO. "Historia de la Provincia de Predicadores de San-Vicente de Chiapas y Guatemala."--Fragment of a MS. at the "Museo Nacional" of Guatemala. * * * * * The following books are known to have existed once: FRAY JUAN ZAPATA Y SANDOVAL. "Cartas al Conde de Gomera ... sobre los Indios de Chiapas." "Cartas al Rey sobre el Estado Dulce Diócesis de Chiapas." * * * * * I make no mention of the compilations and general collections containing references to Chiapas. They are not numerous.--Gregorio García in his book, "Origen de los Indios," has probably the earliest mention of the ruins of Ocosingo, and even perhaps, some indication about those of Palenque.--Cortez who, accompanied by Bernal Diez, passed very near Palenque in 1525, did not take any notice of the pueblo,--which at that time was certainly not inhabited. _Writers of the Eighteenth Century._ NUÑEZ DE LA VEGA. "Constituciones diocesanas del Obispado de Chiapas." Rome, 1702. Important for its reports on the idolatrous rites and the traditions of the aborigines. LORENZO BOTURINI BERNADUCCI. "Idea de una Nueva Historia General de la America Septentrional." Madrid, 1746. Valuable for his mention of the Calendar of Chiapas. MARIANO FERNANDEZ DE VEYTIA Y ECHEVERRIA. "Historia del Origen de las gentes que poblaron la America Septentrional que llaman la Nueva-España, con noticia de los primeros que establecieron la monarquía que en ella floreció de la nacion Tolteca."--This work has been published as lately as 1836, at Mexico, by C. F. Ortega, under the title of "Historia antigua de México."--It contains notices of the calendar of Chiapas. F. X. CLAVIGERO. S. J. (ABBATE.) ANTONIO DE ALCEDO. JOSEPH ANTONIO DE VILLA-SEÑOR Y SANCHEZ. FRANCISCO XIMENEZ. "Crónica de la Provincia de Chiapas y Guatemala,"--of which part of the 7th book is at the "Museo Nacional" of Guatemala. "Historia de la Provincia de predicadores de San Vicente de Chiapas y Guatemala." Written about 1720,--and possibly the same work as the above.--According to Brasseur de Bourbourg, 3 volumes which did not suit or fit together and were the remnants of two MSS. copies of the original, existed at the University of Guatemala in 1855. TORIBIO COSIO. "Relacion histórica de la Sublevacion y Pacificacion de la Provincia de los Tzendales." (May still exist at Mexico.) FRANCISCO VASQUEZ. "Crónica de la Provincia del Ill'mo Nombre de Jesús, del Orden de San Francisco de Guatemala."--Guatemala, 1714 and 1716, 2 vols.--The library of Guatemala ("Museo Nacional") still contains an anonymous MS. of 13 Leaves, "Notas y Advertencias" to the above work.--Whether the "Crónica" itself is at Guatemala, I am unable to say. The book is very scarce. Mr. Squier owned the first volume only. Anonymous. "Relacion de la Sublevacion de los Zendales, en el año de 1712." MS. Perhaps still at the city of Guatemala. RAMON DE ORDOÑEZ Y AGUIAR. "Historia de la Creacion del Cielo y de la Tierra, conforme al sistema de la gentilidad americana." MS. at the "Museo Nacional" of the city of Mexico.--Very important for the traditions of Chiapas. "Memoria relativa á las ruinas de Nachán, en las inmediaciones del pueblo de Santo Domingo del Palenque." MS. formerly belonged to Brasseur de Bourbourg. It was written about 1784, and is the first authentic report on the celebrated ruins. D. NÁXERA. "Vida portentosa del V. P. Fr. Antonio Margil de Jesús." México, 1753. H. VILAPLANA. "Vida portentosa del americano septentrional apóstol Antonio Margil de Jesús...." México, 1763. (Margil was one of the earliest missionaries in Chiapas.) _Documents relative to the explorations of Palenque._ Besides the "Memoria" of Ordoñez already quoted, which first directed attention to the ruined pueblo, there exist the following documents: JOSÉ DE ESTACHERIA. "Expediente sobre el descubrimiento de una gran Ciudad en la provincia de Chiapas, distrito de Guatemala." 28 Nov. 1784. (Archives of the royal Academy, at Madrid).--It is directed to the lieutenant "Alcalde mayor" of Chiapas, at S^{to} Domingo del Palenque, directing him to survey the ruins. JOSEF ANTONIO CALDERON. "Informe, fecho en 15 de Diciembre de 1784." Description of the ruins. MSS. translated and published by Brasseur in "Ruines de Palenque," 1866. ANTONIO BERNASCONI. Other reports on the ruins, accompanied by plans and drawings. MS. in Spain. Date, 13 June, 1578. JUAN BAUTISTA MUÑOZ. Letter to the Marquis de Sonora, written 1786. Translated by Brasseur: "Ruines de Palenque." 1866. ANTONIO DEL RIO. "Descripcion del terreno y poblacion antigua nuevamente descubierta en las inmediaciones del pueblo del Palenque."--I have already referred to it under "Yucatan." Whether the plates of the English edition are genuine, is yet doubtful. * * * * * I must add here, that until about 1820, the state of Chiapas pertained, not to Mexico, but to the captain-generalcy of Guatemala, and consequently all the authorities treating of the latter country may be supposed to contain information about Chiapas also. _Writers of the Nineteenth Century._ (Explorations of Palenque.) JUAN GARRIDO. _Said_ to have written about Palenque in 1805. GUILLERMO DUPAIX AND LUCIANO CASTAÑEDA. "Relacion hecha al Rey, sobre tres expediciones, &c." in 1805, 1806, and 1807. They visited Palenque late in 1807.--Their reports and drawings were first published in 1831, in Vols. IV. and V. of Lord Kingsborough's "Antiquities of Mexico," and an English translation in Vol. VI.--A French and Spanish version, together with all the plates, is contained in "Antiquités mexicaines." Paris, 1834.--The drawings of Castañeda are by far the most complete which we have, although they disagree with many of those of other travellers. This disagreement will be referred to hereafter. JUAN GALINDO. "Palenque et autres lieux circonvoisins." Letter dated 27 April, 1831, in "Antiquités méxicaines," Vol. I.--English translation in the "Literary Gazette," No. 769, London, 1831.--Col. Galindo visited Palenque himself, but he is so enthusiastic that all his statements and even measurements should be taken with many allowances. FRIEDRICH VON WALDECK. "Description des ruines de Palenque," with 56 large plates, in "Monuments anciens du Méxique." Paris, 1866.--M. de Waldeck had spent two years at Palenque (1832-1834,)--his plates are magnificent, but they restore far too much. JOHN L. STEPHENS. "Travels in Central America, Chiapas, and Yucatan." N. York, 1841. "Incidents of Travel in Yucatan." 1843. F. CATHERWOOD. (See Yucatan.) ARTHUR MORELET. (See Yucatan.) Visited P. in 1846. DÉSIRÉ CHARNAY. (See Yucatan.) In 1858. CHARLES ETIENNE BRASSEUR DE BOURBOURG. "Ruines de Palenque," in "Monuments anciens du Méxique," 1866, Paris.--Valuable for the historical introductions and for the numerous references to authorities. The historical essay is a confused and disorderly jumble, barely readable.--The Abbé visited Palenque subsequently--in 1871. To these reports I finally add: CHARLES RAU. "The Palenque tablet in the United States National Museum," Washington, D. C., 1879. (No. 331 of "Smithsonian Contributions to Knowledge.") * * * * * Aside from the numberless historical, archæological, and ethnological works, several of which I have already noticed under "Yucatan," I beg to refer to some specifically Central-American and Mexican sources treating of Chiapas in general, with some occasional mention of Palenque and of Ocosingo, or even without any particular reference to them. DOMINGO JUARROS. "Compendio de la Historia de Guatemala," 1808--1818.--English translation by J. Bailly, London, 1823. FRANCISCO DE PAULA GARCIA L'ELAEZ. "Memorias para la Historia del antiguo Reyno de Guatemala." 3 vols. Guatemala, 1851.--An excellent work, full of valuable and reliable information. HYACINTHE DE CHARENCY. "Le Mythe de Votan." Alençon, 1871.--Ingenious speculations. FÉLIX CABRERA. "Teatro crítico-americano."--Published with the different editions of Del Rio.--Abstract from Nuñez de la Vega, with more or less hypothetical speculations about the origin, life, and doings of "Votan" in Chiapas. MARIANO ROBLES DOMINGUEZ DE MAZARIEGOS. "Memoria histórica de la provincia de Chiapas...." Cadiz, 1813. EMILIO PINEDA. "Descripcion Geógráfica del Departamento de Chiapas y Soconusco." In the "Boletin de la Sociedad de geografia y Estadística de México." Vol. III. Also, México, 1845. JOSÉ DE GARAY. "Reconocimiento del Istmo de Tehuantepec." México, 1844. FRANCISCO PIMENTEL. "Cuadro descriptivo de las Lenguas indígenas, &c." (See Yucatan.) MANUEL OROZCO Y BERRA. "Geografia de las Lenguas." (See Yucatan.) * * * * * In the imperfect list herewith submitted I have frequently included works of which nothing is known save that they once existed. This is done for the purpose of calling attention to them, should any one of them be found in the hands of book owners and collectors here or abroad. Libraries like those of Mr. Lenox or of Mr. John Carter-Brown should be searched for such writings, and copies at least should be secured. The plan of Palenque, made by Bernasconi, in 1785, should also be copied without delay. A copy can be obtained from Madrid, by application to the Royal Academy of Spain. GUATEMALA. (Copan and Chiapas included.) _Writers of the Sixteenth Century._ HERNAN CORTÉS. (4th and 5th letter. Casual mention.) PEDRO DE ALVARADO. Seventeen letters to Hernan Cortés, the first of which is dated: Utlatlan, 11 April, 1524. Only two of those letters were printed, the remaining fifteen are yet in MSS. Mr. E. G. Squier owned MS. copies of the whole, but whither they went at his sale I do not know. The two which were published (11 April and 28 July), appeared in the following works: "Delle navigationi et viaggi, &c." by Gian Battista Ramusio. Venice, Italian version. The "due lettere de Pietro d' Alvarado," are contained in the 3d volume, editions of 1556, 1565, and 1606. OVIEDÓ. "Historia y natural de las Indias." Vol. III. Written between 1535 and 1557, but printed only 1853. Madrid. ANDRÉS GONZALEZ BARCIA. "Historiadores primitivos de Indias." Madrid, 1749, Vol. I. H. TERNAUX-COMPANS. "Premier recueil de piéces relatives à la conquéte du Méxique." Paris, 1838.--French translation. ENRIQUE DE VEDIA. "Historiadores primitivos de Indias." Madrid, 1852. (Vol. I.) These letters, from the conqueror of Guatemala, are very important, and the 15 unpublished ones should be printed at the earliest possible moment. FRANCISCO LOPEZ DE GOMARA. (Quite full, and mentions the earliest author giving the etymology--or rather, an etymology--of the word "Cuauhtemallan"--This is the earliest _printed_ notice about it.) GONZALO FERNANDEZ DE OVIEDO Y VALDÉS. (Has other information besides Alvarado's letters.) BARTOLOMÉ DE LAS CASAS. (Very important, particularly on the interior provinces pertaining or adjacent to his bishopric of Chiapas.) GIROLAMO BENZONI. (Visited Guatemala himself, and although brief, he still is valuable.) PETRUS MARTYR, AB ANGLERIA. (Brief notice, in connection with the movements of Alvarado, in the last decade, Cap's V. and X.--earliest reports on Guatemala in general, received in Europe.) FRAY TORIBIO DE PAREDES, SURNAMED MOTOLINIA. (Not only the "Historia de las Indias de Nueva-España," contains incidental reference to Guatemala,--but there is a trace of a "Viaje á Guatemala."--Yet the latter is still in doubt.) FRAY GÊRONIMO DE MENDIETA. BERNAL DIEZ DEL CASTILLO. (Although a citizen of Spanish Guatemala, his reports are not very full.) "REQUETO DE PLUSIEURS CHEFS D'ATITLAN." Addressed, under date of 1 Feb'y, 1571, to Philip II. Published in French, by H. Ternaux-Compans, in 1^{st} "Recueil de piecés concernant le Méxique," 1838.--It is valuable. PASCUAL DE ANDAGOYA. "Relacion de los sucesos de Pedrarias Dávila en las provincias de Tierra firme ó Castilla del oro, y de lo ocurrido en el descubrimiento de la mar del Sur y costas del Perú y Nicaragua." About 1545.--Original at Sevilla, printed for the first time by Don Martin Fernandez de Navarrete, in 1829. Vol. III. of "Coleccion de los Viajes y Descubrimientos, &c."--English translation, by C. R. Markham, published under the title of "The Narrative of Pascual de Andagoya," by the Hackluyt Society, Vol. 34, 1865.--Slight mention is made of Guatemala. ALONZO DE ZURITA. (Çorita?) "Breve y Sumaria Relacion de los Señores, y maneras y diferencias que habia de ellos en la Nueva-España...."--This important official document, written about 1560, has been published but once in Spanish,--in Vol. II. of "Coleccion de Documentos Inéditos relativos al Descubrimiento, Conquista y Colonizacion de las Posesiones Españolas en América y Oceanía," 1865.--The text is, however, imperfect.--A better original had been used by Ternaux-Compans for his French translation: "Rapport sur les diffirentes classes de la Nouvelle-Espagne."--Zurita is very important on the organization of the Quiché tribes of Guatemala, and he has been almost verbally copied by Herrera. DIEGO GARCIA DE PALACIO. "Carta dírigida al Rey de España," 1576, March 8th.--The chief importance of this report, in connection with this list, consists in its being the earliest notice of the ruins of Copan. Herrera made extensive use of Palacio's writings, but he omitted that part which referred to Copan because it was not confirmed (at his time) by any other testimony. The first publication of Palacio was by Ternaux-Compans, in 1840, "Recueil de Documents et mémoires originaux sur l'histoire des possessions espagnoles, &c."--French translation: fluent, but not always reliable. A Spanish copy appeared in 1866, in Vol. VII. of "Coleccion de Documentos Inéditos...."--A Spanish copy, with English translation, by E. G. Squier, in 1860, as Vol. I. of his "collection of rare and original documents, relations, &c., &c."--Finally. Dr. Alexander von Frantzius published a German translation in 1873, under the heading of "San Salvador and Honduras im Jahre, 1576,"--which is particularly valuable on account of the notes by the translator, as well as by Dr. C. H. Berendt.--Palacio must have visited Copan about 1576, and the fact is established through him that its buildings were in ruins at the time of the Spanish conquest, that is about 1530, and no distinct traditions of their origin left. * * * * * Passing over all general collections and geographical works, &c., &c., of the sixteenth century, I will mention: "CARTAS DE INDIAS." (See Yucatan.) and the miscellaneous collections like _"Colección de Documentos inéditos para la Historia de España," begun by Navarrete_, Miguel Salvá, and Pedro Saing de Barada, in 1842, and still continued. "_Colección de Documentos relativos al Descubrimiento, Conquista y Colonizacion de las Posesiones Españolas en América y Oceanía._" Commenced in 1864, and still continued. (These collections contain chiefly documents from the "Real Archivo de Indias," and although they are of recent date, the papers are all from the earlier times of Spanish conquest and settlement.) * * * * * The library of the "Museo Nacional" at the City of Guatemala (la Nueva), contains the following: RAFAEL ARÉVALO. "Libro de Actas del Ayuntamiento de la Ciudad de Guatemala." (Town book or record, from 1524 to 1530.) "Colección de Documentos antiguos del Archivo del Ayuntamiento de la Ciudad de Guatemala."--(Both bound in one volume and published in 1856 and 1857.) MANUSCRIPTS. "Libro segundo del Cabildo de la Ciudad de Santiago de la Provincia del Guatemala." (1530 to 1541.) "Libro tercero de Cabildo." (1541 to 1543.) "Historia de la Provincia de San Vicente de Chiapa y Guatemala." (Fragmentary.) FRANCISCO HERNANDEZ, CACIQUE OF SOLOLA. (FRANCISCO ERNANDEZ ARANA XAHILA.) "Memorial," written about 1582.--Original owned by Brasseur de Bourbourg, who quotes it under the heading of "Memorial de Tèc-Pan-Atitlan."--It is one of the most important and valuable documents existing on aboriginal topics,--embodying, as it does, a statement of the conquest of Guatemala, written by a native in his own language. "Documentos antiguos de la casa de Ixcuinte-Nèhàib." In addition to these, I must lay particular stress on the "territorial titles" land grants, cessions, leases, or deeds to lands, still held in Guatemala,--or to whatever (if anything) may be left of their records.--Such papers contain frequently interesting, if not important references to antiquities, traditions and historical facts, also to the customs and manners of the Indians. Among the other authorities still perhaps existing, or known to have existed, though of difficult access, I refer to those below, avoiding, of course, Linguistical works, unless they are of direct bearing on other subjects also. JUAN ESTRADA DE RAVAGO (or Juan Strada Salvago.) "Descripcion de las Provincias de Costa Rica, Guatemala, Honduras, Nicaragua y Tierra-firme y Cartagena, &c., &c." 6 May, 1572. (MS. copy of it belonging to E. G. Squier.) "Memorial de las advertencias i cosas que la C. Cath, R'l M. del Rey i su Re. Consejo de Indias manda hacer, &c., &c." (MS. of E. G. Squier.) 1579. FRANCISCO MONTERO DE MIRANDA. "Relacion dírigida al Ill'mo Señor Palacio, &c., &c., sobre la provincia de la Verapaz ó Tierra de Guerra." 1575. (MS. of E. G. Squier.) FRAYLES: FRANCISCO VIANA, LUCAS GALLEGO, and GUILLERMO CADENA. "Relacion de la provincia y tierra de la Vera Paz," 1574. (MS. of Squier.) FRAY TOMÁS CÁRDENAS. "Representaciones al Rey sobre el Estado de los Pueblos de la Vera-Paz." FRAY TOMÁS CASTELAR. "Tratado de los Idolos de Guatemala." "Triunfos de los Mártires del Orden de Predicadores en las Indias." Printed 1580. FRAY TOMÁS TORRE. "Historia de los principios de la Provincia de Chiapas y Guatemala, del Orden de Santo Domingo."--Written prior to 1567. FRAY DOMINGO VICO. "Historia de los Indios, sus Fábulas, Supersticiones, Costumbres, &c." "Teologia para los Indios, en Lengua de Vera Paz." 4 vols. (Still existing.) GERÓNIMO ROMAN. "República Indiana." (See Yucatan.) This list is certainly far from complete, and it may be that among the vocabularies, grammars, and such works now lost, although we know of their former existence, there were some,--perhaps even many,--which contained historical and ethnological matter of great value.--It is hardly possible to avoid all allusions to such subjects in any work on linguistics. But the number of books of that class is too great for the purpose of the present list. _Writers of the Seventeenth Century._ AUGUSTIN DAVILA-PADILLA. (See Yucatan. First edition appeared in 1595.) GREGORIO GARCIA. (Plain and well informed, though brief.) JUAN DE TORQUEMADA. (Important on organization and government, also myths.) ANTONIO DE HERRERA. (Very full and important.) ANTONIO DE REMESAL. (Not as full on antiquities as might be expected.) AUGUSTIN DE VETANCOURT. (Very slight mention.) ENRICO MARTINEZ. (Casual mention.) GIL GONZALEZ DÁVILA. JUAN DIEZ DE LA CALLE. FERNANDO DE ALBA IXTLILXOCHITL. "Relaciones históricas."--Of these, the thirteenth, "De la Venida de los Españoles," is of particular interest for Guatemala,--since it relates in detail Cortés' trip to Honduras. The "Relaciones" are printed in full in Vol. IX. of Lord Kingsborough's Collection,--the 13th however, was published under the title of "Horribles Crueldades de los Conquistadores de México," as appendix to Sahagun's "Hist-general," Vol. III., in 1829. From this, M. Ternaux made a French translation, published by him in 1838, as "Cruautés horribles des Conquérants du Méxique,"--in the first series of his "Voyages et Mémoires originaux, &c." "Historia de los Chichimecos, o' reyes antiguos de Tezcuco."--Casual mention of Guatemala.--Published in Kingsborough, Vol. IX., and translated by Ternaux and printed in French as "Histoire des Chichiméques ou des anciens rois de Tezcuco," in 1840.--(2d Series.)--Besides these, there are found references to Guatemala in the "Sumaria Relacion, de los Toltecas." (Kingsb. IX.)--Ixtlilxochitl, though full of details, is always a very suspicious source.--He is the representative of _one tribe exclusively_. FRANCISCO ANTONIO FUENTES Y GUZMAN. "Recordacion florida; Discurso histórico, natural, material, militar, y político del reyno de Guatemala." MS. of 1690. Original in the municipal archives of the city of Guatemala. Copy at the "Museo Nacional."--Fuentes is like Ixtlilxochitl--both have the same tendency to extol their native tribes--still both must be carefully studied and critically examined.--A publication of Fuentes, well and judiciously annotated, would be highly useful. FERNANDO ESPINO. "Historia de la reduccion y conversion de la Provincia de Taguzgalpa, con la Vida de los tres Mártires."--Printed at Guatemala, 1674.--Whether and where it still exists I do not know. LIONEL WAFER. "A new Voyage and description of the Isthmus of America."--London, 1699. FRAY THOMAS GAGE. "New survey of the West Indies." (A work which is looked upon with great suspicion, because the author, although he evidently went to Guatemala from Mexico, misrepresents a great many facts. Still he cannot be overlooked.)--This book appeared first prior to 1676.--Robertson quotes an English edition of 1677, and that of 1699 is the fourth edition. There are French editions of 1676, 1694-5, 1699 1720, 1721. Dutch of 1682, 1700. German of 1693. Spanish, 1838.--Yet this list is evidently still incomplete, as further material is out of my reach. ANTONIO DE LEON Y PINELO. "Tratado de Confirmaciones Reales de Encomiendas, Oficios, y casos en que se requieren para las Indias Occidentales." Madrid, 1630.--This work is one of the best on many vital points of Spanish administration,--and since the latter is so intimately connected with the past and present condition of the aborigines as to make its knowledge absolutely necessary,--it must be attentively studied.--I shall, for this reason, add below the books of Solòrzano: "Epítome de la Biblioteca Oriental i Occidental, Náutica y Geográfica." Madrid, 1629. 2d Edition, by Barcia, 1737 and 1738. (Important bibliographically.) "Relácion que en el Consejo Real de las Indias hizo el Licenciado ..., sobre la Pacificacion de las Provincias del Manché y Lacandon," 1639. MS. of E. G. Squier. JUAN DE SOLÓRZANO-PEREYRA. "Disputationem de Indiarum jure, sive de mixta Indiarum Occidentalium inquisitione, acquisitione, et retentione tribus libris compehensam." (This is the title of the first volume only, the second volume bears the heading "De Indiarum gubernatione, &c.") Madrid, 1629-1639.--2d edition, 1672. "Política Indiana." Madrid, 1648.--Subsequent editions, 1703, 1736-39, 1776. The latter work is but a Spanish transcription or version of the first. The importance of both is in their clear "exposé" of the principles of right and law, according to which the Spanish Indies were governed.--We are thereby enabled to judge of the true relations existing between the conquering and conquered races, and to detect, how far the original condition of the latter was understood or misunderstood by the former--(and misrepresented?) * * * * * The "Museo Nacional," at Guatemala, has the following manuscripts besides those already mentioned: "Historia de la Provincia de Predicadores de San Vicente de Chiapa y Guatemala."--A fragment, possibly by _Fray Augustin Cano_. "Solicitud que el Padre Fray Augustin Cano hizo al Ill'mo S^r Obispo de Guatemala ... que se hallaba de visita en el pueblo de Cajabon pidiendo amparo para reducir á los indios Choles." "Informé dado al Rey por el _Padre Fray Augustin Cano_ sobre la entrada que por la parte de la Verapaz se hizo al Peten en 1695." "Suma de los Capítulos generales y principales, ordenaciones, &c., de la Provincia de Predicadores de Chiapa y Guatemala." by _Fray Lope de Montoya_. "Vidas de varios Padres de la Provincia de Chiapa y Guatemala del Orden de Indicadores," by _Fray Antonio de Molina_. Whether the "Noticia ó Relacion de los Padres de la Orden de Predicadores que florecian en la Provincia de los Zoques" (anonymous MS.), belongs to the 17th century, I am unable to say. * * * * * Notice of the following books or writings has been communicated to me from various sources: FRAY ANTONIO AROCHENA. "Catálogo y noticia de los Escritores del Orden de San Francisco de la Provincia de Guatemala." (A very important bibliographical composition, to judge from its plan.) FRAY ESTEVAN AVILES. "Historia de Guatemala desde los tiempos de los Indios, hasta la fundacion de la provincia de los franciscanos; poblacion de aquellas tierras, propagacion de los Indios, sus ritos, ceremonias, polícia, y Gobierno." (Said to have been printed at Guatemala in 1663.) FRAY SALVADOR CIPRIANA. "Libro de los Idolos de la Provincia de Zacatula." "Hechos de los Padres Fray Levis Cancer, Fray Bartolomé de las Casas, y Fray Pedro de Angulo, en la predicacion del Evangelio." "Historia de la Entrada de los Españoles en Zacatula." NICOLAS LIZARRAGA. (See Yucatan.) FRAY MELCHOR DE JESUS LOPEZ. "Relacion de la Conversion á la Fé de los Indios de Salamanca." 1690. "Relacion de la Pacificacion de los Indios de Vera-Paz." FRAY PEDRO SOTOMAYOR. "Informacion de los Varones Ilustres del Orden de San Francisco del Reino de Guatemala." DIEGO DE UNZUETA. "Relacion de Guatemala,"--handed to Juan Diez de la Calle in 1648. NICOLAS DE VALENZUELA. (Wrote about the expedition against Lacandon,--in 1695.) FRAY ESTEVAN VERDELETE. "Noticias de la Provincia de Teguzigalpa." (Written between 1593 and 1612.) JUAN ZAPATA Y SANDOVAL. (See Chiapas.) FRAY PEDRO DAZA. "Memorias históricas de la fundacion y predicacion de los Religiosos de la Merced de la Redencion de cautivos en Guatemala." FRAY JOSÉ MORERA. "Noticias de la Provincia de Guatemala, con un Tratado de la Mísion y Martirio de los P. P. Misioneros, Verdelete y Montragudo." (MS. said to be at Guatemala.) FRAY PABLO REBULLIDA. "Informe á la Audiencia de Guatemala sobre el estado actual de la Cristiandad de la Provincia de Talamanca." 1697. "Cartas sobre el caracter de los Indios Terrabas, Talamancas, y Changenes." FRAY PEDRO DE URTIAGA. "Diario del Viaje de los cinco Misioneros desde Querétaro hasta Guatemala."--Printed in 1694, at Guatemala. ALONZO DUARTE. "Relacion de lo que Yo (A. D.) vecino desta ciudad de Santiago de Guatemala entendí y vide quando D. Francisco Valverde vino a sondar el puerto de Cavallos." 1605. MS. pertaining to E. G. Squier. These are certainly not all,--perhaps only a minority of the documents relating to Guatemala,--which originated during the 17th century. In regard to the ruins of Copán,--Fuentes is perhaps (because a number of the last enumerated authors I have not seen) the only one who mentions its ruins, and even gives an enthusiastic description of them,--but Torquemada as well as Herrera relates the tradition of Comizahual, which also relates to Copán. The latter place is, besides, commonly regarded as belonging properly to _Honduras, and only of late has been added_ to Guatemala. I add the following, although they are of scarcely any value for the purpose in view: JOSÉ MONROY. "Estado del Convento de Guatemala, del Orden de nuestra Señora de la Merced." Printed, 1667. DIEGO RODRIGUEZ DE RIBAS. "Disertacion canónica sobre los justos motivos que representa el Reyno de Guatemala, para que el Consejo se serva de erigir en Metropolí ecclesiástica la S. Iglesia Catedral, &c." Printed, 1660. _Writers of the Eighteenth Century._ ANTONIO DE ALCEDO. F. X. CLAVIGERO. (Very slight mention.) The following MSS. are yet at Guatemala "Museo Nacional." PEDRO CORTÉS Y LARRAZ. "Descripcion geográfico moral de la Diócesis de Guatemala." 1768-69. FRAY FRANCISCO XIMENEZ. "Historia de la Provincia de San Vicente de Chiapa y Guatemala de la Orden de los Predicadores." 5 vols. JOSÉ SANCHEZ. "Apuntaciones para la Historia de Guatemala." FERNANDO VELASQUEZ DE GUZMAN. "Relacion de los Obispos de Guatemala." There is, besides, a MS.: "Efemérides de Guatemala desde su fundacion hasta la ruina de 1773."--Anonymous. Printed works: FRAY ISIDRO FÉLIX DE ESPINOSA. "El Peregrino Septentrional Atlante." (Life of Fray Antonio Margil.) México, 1737. FRAY CÁRLOS CADENA. "Breve descripcion de la Noble Ciudad de Santiago de los Caballaros de Guatemala, &c." Mexico, 1774.--2d Edition, Guatemala, 1858. JUAN DE VILLAGUTIERRE Y SOTOMAYOR. (On Vera Paz.) FRANCISCO NUÑEZ DE LA VEGA. (On Chiapas.) TORIBIO COSIO. (In the University Library of Mexico.) FRAY JOSÉ DIEZ. "Noticia de las Misiones de Guatemala." FRAY ILDEFONSO JOSEPH FLORES. "Teología de los Indios." FRAY FRANCISCO VASQUEZ. (See Chiapas.) FRAY FRANCISCO XIMENEZ. (See Chiapas.) It is said that Ximenez wrote two large historical works, one in five volumes, of which but three were finished.--This is a mistake, the entire edition of five volumes is still at Guatemala. The other work, secured by Dr. Scherzer, bears the title "Las Historias del Orígen de los Indios de esta Provincia de Guatemala....," and published by him at Vienna in 1857. (Anonymous MS. said to exist at Guatemala.) "Informe del Provincial de la Orden de Santo Domingo Guatemala, tocante á los negocios de la Vera-Paz." 1724. "Relacion de la Sublevacion de los Zendales." 1712. ANTONIO RODRIGUEZ CAMPAS. "Diario Histórico de Guatemala." FRAY JUAN CARTAJENA. "La S^{ta} Iglesia de Guatemala, madre fecundísima de hijos ilustrissimos." México, 1747. RAMON ORDOÑEZ Y AGUIAR. (See Chiapas.) At Mexico. (A number of the above works may be lost.) _Writers of the Nineteenth Century._ All general works, archæological, historical, and geographical, are left out. I even omit, as abundantly known, Kingsborough, Bancroft, Baldwin, Short, the "Antiquites Méxicaines," the "Cités et Ruines Méxicaines" of Waldeck,--Brasseur de Bourbourg, &c., &c.--Reference to these sources is self-understood. DOMINGO JUARREZ. "Compendio de la Historia de Guatemala." 1808-1818, Guatemala. (Relies too much on Fuentes.) English translation by Bailey. London, 1823. "A statistical and Commercial History of the Kingdom of Guatemala, in Spanish America."--A second Spanish edition appeared in 1857. FRANCISCO DE PAULA GARCIA PELAEZ. (See Chiapas.). "Memorias para la Historia del Antiguo Reyno de Guatemala." 1852. CHARLES ETIENNE BRASSEUR DE BOURBOURG. "Popol Vuh. Le livre Sacré et les Mythes de l'Antiquité Américaine, avec les livres Héroiques et Historiques des Quichés." Paris, 1861. Hardly any work of this century has created such a "mixed" sensation of a serious nature, as this book.--It could be seen at a glance, that no mystification was possible,--but there was a wide field open for discussion on the point of origin, as far as the document itself, the "Popol Vuh," was concerned.--Still the "sensation" has not resulted in much active critical examination, and I think (If I may be permitted to commit such a breach of modesty,) myself the only person attempting a criticism of the "Popol Vuh" on the basis of documentary evidence. Unfortunately, I was unable to prepare my annotations in time for the publication of the 27th Volume of Proceedings of the American Association for the Advancement of Science, in 1878.--Thus only the text of "Sources for aboriginal history of Spanish America," appeared without any documentary evidence attached. One thing is evident, that the "Popol Vuh" was _written_. Now it is a fact very easily proven, that the aborigines of Guatemala had no phonetic alphabet whatever, consequently _that they did not write_.--Therefore the "Popol Vuh" must have been composed, as an instrument in writing, since the conquest; or after 1524.--This is developed utterly independent of the fact that the document hints at two data (p. 343,) indicating the time of its composition to have been after 1550, and prior to 1600.--Therefore it was written in our letters, or perhaps with the aid of the "five characters" invented by Fray Francisco de la Parra, previous to 1560, to indicate sounds for which our alphabet had no signs.--At all events, it was written in the native Quiché idiom, and was only met with incidentally by Fray Francisco Ximenez at the town of Chichicastenango, towards the close of the 17th century.--This Dominican monk translated it into the Spanish language and incorporated both text and translation in the first volume of his "Historia de la provincia de predicadores, &c."--according to Brasseur de Bourbourg's really silly and irritatingly confused bibliography--(p. XIII., "Notice Bibliographique.") Dr. Scherzer certainly deserves credit for having published a Spanish text rendering approximatively the "Popol Vuh," in 1857, and there is no doubt but that it is as correct a rendering of the original Quiché as the French translation of Brasseur de Bourbourg. The filiation of the text being thus established as far back as 1550 to 1600, it remains to investigate the question: how much of it was originally Indian;--if all of it or not? There is no doubt but that the greater part of it is Indian songs, preserved for centuries, and Indian myths and tales--historical traditions--which were recorded by the compiler in the form now before us. But this compiler, or rather--recorder--has given to these tales a chronological sequence,--at least in the first part,--which may hereafter prove conjectural.--Actions are made to succeed to each other, which may yet prove to be without any connection at all.--I do not insist upon this point--since a new translation of the "Popol Vuh" should precede its investigation--but I particularly insist upon a careful and critical study of its first so-called "Chapters." These first chapters give us cosmological Ideas and Notions, purporting to be originally Indian, which, at their very inception, show a singular admixture of foreign elements. The first sentences appear to be transcriptions from the book of Genesis. They are not aboriginally American.--We are therefore led to investigate whether, prior to 1550, European influences could have been brought to bear upon the recollection and the imagination of the natives.--There is very positive evidence to that effect.--The monks, at the earliest stages of conversion, used paintings of their own, to impress upon the natives the notions of a creation of the world, of the deluge and salvation of a single pair therefrom, &c., &c.--The Dominican Father Gonzalo Lucero travelled about with painted charts representing such striking events, which he displayed in confirmation of his teachings. Fray Jacobo Testera (he died Aug. 8, 1543) used similar means. Fray Pedro de Angulo, who went with Las Casas to Guatemala and was made Provincial of Chiapas in 1561, wrote three dissertations in the Zutuhil language, one on the Creation of the World, one on Adam's Fall, and one on the Expulsion of our first fathers from Paradise.--Fray Luis Cancer wrote similar pages in the language of Oajaca, previous to 1546.--Fray Domingo Vico, who was killed by the Indians of Lacandon, in 1555, wrote his "Teologia para los Indios," in the Quiché language, also a dissertation on the "Eternal Paradise," in the language of Vera-Paz.--But there is also indisputable proof that _songs were composed on the subject of the creation of the world_ and other parts of the Hebrew Genesis, in the Quiché language, which songs were used as the means of conversion of the natives of Vera-Paz in 1537. (Remesal. Lib. III., Cap. XI., p. 124.) They had been composed by Las Casas, Fray Rodrigo de Ladrada, Fray Pedro de Angulo, and probably Fray Luis Cancer. Many other similar ones were composed afterwards. Thus we see that, prior to 1550, ecclesiastics had commenced to write upon cosmological subjects with our letters and in the languages of Guatemala, and that, on the other hand, Christian cosmogony had become a text for Indian songs. The "Popol Vuh" has therefore nothing extraordinary in its origin; it is but a child of its time, like the "Memorial de Tecpan-Atitlan," by the Chief of Sololá, only anonymous,--and preceded by a cosmological introduction made up of Christian and Indian tales confusedly intermingled, and therefore apocryphal so far. These criticisms, however, apply merely to the "first part,"--the rest of the "Popol Vuh" appears to be original, and therefore of the greatest value. This however cannot be said of the translation, only of the MS. A new translation, supervised by a native, should be obtained at any price. "Grammaire Quichée, et le Drame Rabinal-Aché." Paris, 1862. Of the "Rabinal-Aché," a new translation is absolutely requisite. Mr. Brasseur, like all translators of Indian songs, has so disfigured it by the introduction of a foreign terminology, as to render it useless for any one who has no access to vocabularies, &c. JOHN L. STEPHENS. (See Yucatan), also FREDERICK CATHERWOOD. JUAN GALINDO. (See Yucatan and Chiapas.) What I have seen of his reports has left upon my mind the impression that he means to be truthful, but in his zeal and eagerness saw "too big," and again "too often." "The Ruins of Copan in Central America." Transactions of the American Antiquarian Society, Vol. II., pp. 545-550. 1836. "Notions sur Palenque," &c., &c., "transmises à la Société géographique de France," in "Antiquités méxicaines," Vol. I., pp. 73-76.--Published also in the "Bulletin" of the French Geographical Society, and in the "Literary Gazette" of London. E. G. SQUIER. "The Serpent-Symbol, and the Worship of the Reciprocal Principles of Nature in America." N. York, 1851. "The States of Central America: their Geography, Topography, &c., &c. Aborigines," N. York, 1858. "Notes on Central América, particularly the States of Honduras and San Salvador." N. York, 1855.--German translation, Leipzig, 1856.--French version, Paris, 1855.--Spanish, Paris, 1856, (two different translations.) "Honduras, Descriptive, Historical and Statistical." London, 1870. "Honduras and Guatemala." "The National Intelligencer." N. York, 1854. "The Ruins of Tenampua." Although in Honduras, they appear traditionally connected with Copan. N. York, 1853, in "Proceedings of the Historical Society of New York." "Monograph of Authors who have Written on the Languages of Central America." Albany, 1861.--A very valuable and important contribution to bibliography. * * * * * CARL SCHERZER. "Wanderungen durch die mittel-amerikanischen Freistaaten." Braunschweig, 1857.--English version, London, 1857. "Narrative of the Circumnavigation of the Globe by the Austrian frigate Novara." London, 1861. (The official reports on the results of the circumnavigation, &c., are very rare.) "Die Indianer von Ixtlahuacan." Vienna, 1856. "Ein Besuch bei den Ruinen von Quirigua." Vienna, 1855. I omit here his linguistical writings, and his publication of the "Historia del Origen de los Indios, &c.," in 1857.--See Ximenez. MORITZ WAGNER, AND CARL SCHERZER. "Die Republik Costa-Rica in Central Amerika." Leipzig, 1857.--Describes the ruins of Quirigua. MANUEL GALVAN RIVERA. "Historia de México, Guatemala, Estados-Unidos del Norte, Perú, &c." México, 1852. "GACETA DE GUATEMALA." (From 1797.) Contains interesting notices, historical and ethnological. "PERIODICO DE LA SOCIEDAD ECONÓMICA DE GUATEMALA." (Only 24 numbers published in 1815 and 1816.) 1 May, 1815, to 15 April, 1816. THE PADRES: CHICA, ABELLA, AND ESCOTO, AND AGUILAR. "Informes, al Ill'mo Señor Arzobispo de Guatemala, tocantes á la Vera-Paz." 1819 and 1820. MSS. DOMINGUEZ DE MAZARIEGOS. (See Chiapas.) DOMINGO FAJARDO. "Informe dirigido al Gobierno Supremo de México, relativo á su Mision á Vera-Paz y Peten." Campeche, 1828. ORLANDO N. ROBERTS. "Narrative of Voyages and Excursions on the East Coast and in the Interior of Central America." Edinburgh, 1827. CARL HERMANN BERENDT. "Report of Explorations in Central America." Smithsonian Report, 1867. "Collection of historical documents on Guatemala." Smithsonian Report, 1876. "Die Indianer des Isthmus von Tehuantepec."--Zeitschrift für Ethnologie. Berlin, 1873, Vol. V. "_Analytical Alphabet_ for the Mexican and Central American Languages." Published by the American Ethnological Society. New York, 1869. "_Cartilla en Lengua Maya_ para la enseñanza de los niños indigenes." Mérida, 1871. _El Ramie._ Tratado sobre el cultivo y algunas noticias de esta planta. Mérida de Yucatan, 1871. (Ed. de la Revista de Mérida.) _Los Escritos de D. Joaquin Garcia Icazbalceta._ Ed. de la Revista de Mérida. Tomo II., 1870. "_Articulo sobre El México_," se halla en el "Deútsch Amerikanisches Conversations Lexicon, barbeitet von. Prof. Alex. I. Schem. Lieferung 64, Band VII., Seite 261, pp. 27. (N. Y. 1872.) "_Remarks on the Centres of Ancient Civilization in Central America_, and their Geograpical Distribution." Address read before the Am. Geogr. Society, N. Y., July 10th, 1876, with map. _Zur Ethnologie von Nicaragua._ Articulo publicado en Correspondenz-Blatt der deutschen Gesellschaft für Anthropologie, Ethnologie und Urgeschichte. Redigirt von N. A. v. Frantzius in Heidelberg, No. 9, September, 1874. In "Geographische Mittheilungen" von A. Petermann, Gotha. (The above makes no pretension to be a full list of the eminent linguist's publications.) ALEXANDER VON FRANTZIUS. (See Palacio.) "San Salvador and Honduras im Iahre, 1847."--Annotated also by Berendt. GUSTAV BERNOULLI. "Reisen in der Republik Guatemala."--In "Petermann's Mittheilungen," 1874-75. BARON DER THEIL. "Le Guatemala." In "l'Explorateur," Vol. III. 1876. J. LAFERRIER. "De Paris au Guatémala." Paris, 1877. GEORGE WILLIAMSON. "Antiquities in Guatemala." Smithsonian Reports, 1876. (Very interesting and of great value for archæological studies.) J. W. BODDAM-WETHAM. "Across Central America." London, 1877. ADOLPH BASTIAN. "Die Monumenta in Santa Lucia Cozumalguapa."--"Zeitschrift für Ethnologie," 1876. "Die Culturlaender des alten Amerikas." (See Yucatan.) GUSTAV BRÙHL. (See Yucatan.) H. W. BATES. "Central America, West Indies, and South America." London, 1878. A. BONCARD. "Le Guatèmala."--In "L'explorateur," 1878. No. 23. FRANCISCO PIMENTEL. (See Yucatan and Chiapas.) MANUEL OROZCO Y BERRA. (See Yucatan, &c.) S. HABEL. "The Sculptures of Santa Lucia Cozumalguapa."--Smithsonian Contributions, No. 269.--Washington, 1878. In closing this list, I must again distinctly state, that it is very imperfect,--and that no one acquainted with the literature of Central America can fail to notice many omissions.--But I had neither time, nor opportunity to do better, owing to the state of my health. In conclusion, I wish to advert to a few books of an exclusively bibliographical tenor, which every student of American history must at least attempt to consult.--Some of them are, unfortunately, extremely rare: NICOLÁS ANTONIO. "Bibliotheca Hispana Nova, &c." 1st edition, Rome, 1672. 2d edition, Madrid, 1733-38. JUAN JOSÉ DE EGUIARA Y EGUREN. "Biblioteca Mexicana." México, 1755. Incomplete: only the first volume published. ANTONIO DE ALCEDO. "Biblioteca americana." MS. Original belonged to Mr. Jared Sparks. México, 1807. J. MARIANO BÈRISTAIN DE SOUZA. "Biblioteca Hispana Americana. Septentrional." México, 1816 and 1819, 3 volumes. (Exceedingly rare.) BRASSEUR DE BOURBOURG. "Bibliothéque méxico-guatemalienne." Paris, 1871. * * * * * I forbear quoting here at length the bibliographical works of Harrisse, Rich, Ludewig, Ternaux-Compans, Sabin, and others.--They are deservedly well known, and of easy access to any student. OAJACA. ("Huaxyacac.") _Writers of the Sixteenth Century._ HERNAN CORTÉS. (2d letter.) BERNAL DIEZ DEL CASTILLO. (Casual notice.) FRANCISCO LOPEZ DE GOMARA. ("Conquista de México.") FRAY TORIBIO DE PARADES, SURNAMED MOTOLINIA. ("Historia de los Indios de la Nueva-España." See bibliography of Yucatan.)--This is probably the earliest mention of the ruins of Mitla, which were, however, inhabited at that time. Motolinia has been entirely overlooked by Bancroft, although his description of Mitla is truly excellent. GONZALO FERNANDEZ DE OVIEDO Y VALDÉS. (Casual notice.) CODEX CHIMALPOPOCA. Now in process of publication, in the "Anales del Museo Nacional de México." Vol. II., by Mendoza, Sanchez Solís, and Chavero. JUAN DE TOBAR. "Códice Ramirez,"--published by S^r J. M. Vigil, as an anonymous chronicle, in 1878. Also "Historia de los Indios Mexicanos." Original in possession of the Estate of Sir Thomas Phillips, at Cheltenham, England. Copy of a fragment, privately printed, at the Lenox Library, New York. (Written between 1579 and 1589.) DIEGO DURÁN. "Historia de las Indias de Nueva-España, é Yslas de Tierra firme."--(Written between 1579 and 1581, but only the first part of it printed, at Mexico, 1867, by S^r José F^r Ramirez.)--Very important; mentions again Mitla as a settlement inhabited about 1450. "Apéndice" por Alfredo Chavaro, México, 1880. FERNANDO DE ALVARADO TEZOZOMOC. "Crónica mexicana."--Written 1598. Printed for the first time in Vol. IX. of Kingsborough, and again (though not complete) in the "Biblioteca mexicana" of S^r Vigil, with notes by S^r Orozco y Berra.--A French translation has been made by Ternaux-Compans, under the title of "Histoire du Méxique, par Alvarado Tezozomoc," Paris, 1853, 2 vols. It is utterly unreliable. FRAY GERÓNIMO DE MENDIETA. (Copies textually from Motolinia.) FRAY BERNARDINO SAHAGUN. "Historia universal de las Cosas de Nueva-España," in Vols. 6 and 8 of Kingsborough.--The same book, under the title of "Historia general, &c., &c." appeared at Mexico, in 3 vols., 1829, edited by C. M. de Bustamante. Only very slight and casual mention of Oajaca. _Writers of the Seventeenth Century._ AUGUSTIN DÁVILA-PADILLA. JUAN DE TORQUEMADA. (Important.) ANTONIO DE HERRERA. (Important.) GREGORIO GARCIA. (Important.) FRANCISCO DE BURGOA. "Palestra Historiale de Virtudes y Exemplares Apostólicos." México, 1670. "Geográfica Descripcion de la Parte Septentrional del Polo Artico de la América." México, 1674. This work is regarded (especially by such as have not seen it), as the leading work on Oajaca.--I have never even seen it--it is exceedingly rare. _Writers of the Eighteenth Century._ MARIANO VEYTIA. F. X. CLAVIGERO. ANTONIO DE ALCEDO. LORENZO BOTURINI BERNADUCCI. JOSEPH JOAQUIN GRANADOS Y GALVEZ. "Tardes americanas." México, 1778--A work considerably over-estimated,--containing casual mention of Oajaca,--fluently written. _Writers of the Nineteenth Century._ I forbear mentioning here _all_ the writers on Oajaca,--more particularly avoiding all the general works,--those excepted which contain plates of special value. The first who called attention to Mitla was certainly ALEXANDER VON HUMBOLDT. "Vues des Cordilléres et monuments des peuples indigénes de l'Amérique." Paris, 1810. Royal folio.--Same, 2 vols. 8^o Paris, 1816. English version, by Helen M. Williams, London, 1814. "Essai politique sur la Nouvelle-Espagne." (See "Yucatan.") MATHIEU DE FOSSEY. "Le Méxique." Paris, 1857.--Very fair. EDUARD MÛHLENPFORDT. "Versuch einer getreuen Schilderung der Republik Mejico." Hannover, 1844. 2 vols. ARTHUR VON TEMPSKY. "Mitla, a Narrative of Incidents and Personal Adventures." London, 1858.--Of small scientific value. GUILLERMO DUPAIX, AND CASTAÑEDA. (In "Antiquités Méxicaines," also in Lord Kingsborough's "Antiquities of Mexico.") DÉSIRÉ CHARNAY. (Saw the ruins in 1859. His photographs are very important.) JOSÉ MARIA GARCIA. (Visited Mitla in 1855, according to "Boletin de la Sociedad Mexicana de Geografia y Estadistica." Vol. VII., pp. 271 and 272.) BRANTZ-MAYER. "Mexico as it Was and as it Is." New York, 1844. Very fair. "Mexico, Aztec, Spanish and Republican." Hartford, 1853. Very good. "Observations on Mexican History and Archæology." (Smithsonian Contributions. No. 86, Washington, 1856.) Contains Sawkins' drawings of Mitla. J. W. VON MÜLLER. "Beitrage zur Geschichte und Ethnographie von Mexico." Leipzig, 1865. "Reisen in den Vereinigten-Staaten, Canada, and Mexico." Leipzig, 1864. CARLOS MARIA DE BUSTAMANTE. "Memoria estadística de Oajaca, y descripcion del Valle del mismo nombre." Vera-Cruz, 1821. MURGUIA. "Estadistica antigua y moderna de la Provincia de Guajaca." "Boletin, &c." Vol. II. JUAN B. CARRIEDO. The writings of this author are, unfortunately, but little known.--In the "Ilustracion Mexicana," Vol. II., he has given an essay on "Los Palacios Antiguos de Mitla."--But he has published other papers and even books on the same subject. "Estudios históricos, y estadísticos del estado Oaxaqueño." Oajaca, 1850. The Astor Library of New York has an incomplete copy of a work of Carriedo on Oajaca, with colored drawings by him,--unfinished. Copious notes by the author's own hand accompany the text. In historical questions Carriedo mostly follows and cites Burgoa. FRANCISCO PIMENTEL. "Cuadro descriptivó de las Lenguas Indígenas de México." (See Yucatan and Chiapas.) MANUEL OROZCO Y BERRA. In "Geografia de las Lenguas."--Reference is made to a number of very important papers on Oajaca, the title of one, among others, "Estado que comprende el número de Parroquias de la Diócesis de Oajaca, con expresion de sus nombres, Estado ó Territorio en que están situadas, número de pueblos, &c., &c." Further, certain official reports are quoted,--the originals of which are in the hands of my friend S^r J. G. Icazbalceta,--S^r Orozco mentions the following: PEDRO DE LEDESMA. "Relacion de Oajaca, por el alcalde...." 1579. HERNANDO DE CERVANTES. "Relacion de Teotzacualco y Amoltepec...." 1580. AUGUSTIN DE SALAZAR. "Relacion del vicario de Chilapa." JUAN LOPEZ. "Relacion del Corregidor...." 1579. Finally, I must call attention to a linguistical work, known to me only through S^r Orozco y Berra's citation, and through references given by S^r Pimentel--to wit: ANTONIO DE LOS REYES. "Arte en lengua mixteca." México, 1593. Numerous grammars, vocabularies, "doctrinas," sermonaries, &c., &c., were written in the course of the 16th century, of and in the language of Oajaca. EMILIO HÉRBRÜGER. "Album de vistas fotográficas de las antiguas Ruinas de los Palacios de Mitla." Oaxaca, 1875. Text and valuable photographs. * * * * * In conclusion, I would merely beg to add,--that there can hardly be any doubt as to the fact that Mitla was _inhabited_ when the Spaniards first visited the place. It therefore becomes a point of special interest. 
39914	----	INDIAN NOTES AND MONOGRAPHS EDITED BY F. W. HODGE VOL. IX [Illustration: Logo] No. 3 A SERIES OF PUBLICATIONS RELATING TO THE AMERICAN ABORIGINES REPORTS ON THE MAYA INDIANS OF YUCATAN BY SANTIAGO MENDEZ, ANTONIO GARCÍA Y CUBAS, PEDRO SANCHEZ DE AGUILAR, AND FRANCISCO HERNANDEZ EDITED BY MARSHALL H. SAVILLE NEW YORK MUSEUM OF THE AMERICAN INDIAN HEYE FOUNDATION 1921 This series of INDIAN NOTES AND MONOGRAPHS is devoted primarily to the publication of the results of studies by members of the staff of the Museum of the American Indian, Heye Foundation, and is uniform with HISPANIC NOTES AND MONOGRAPHS, published by the Hispanic Society of America, with which organization this Museum is in cordial coöperation. Only the first ten volumes of INDIAN NOTES AND MONOGRAPHS are numbered. The unnumbered parts may readily be determined by consulting the List of Publications issued as one of the series. REPORTS ON THE MAYA INDIANS OF YUCATAN BY SANTIAGO MENDEZ ANTONIO GARCÍA Y CUBAS, PEDRO SANCHEZ DE AGUILAR AND FRANCISCO HERNANDEZ EDITED BY MARSHALL H. SAVILLE CONTENTS PAGE Preface 139 THE MAYA INDIANS OF YUCATAN IN 1861, by Santiago Mendez 143 Customs 143 Women 177 Dress 190 Language 192 Stature, Physiognomy, Color 192 Savage Tribes 194 Note by Antonio García y Cubas 196 NOTES ON THE SUPERSTITIONS OF THE INDIANS OF YUCATAN (1639), by Pedro Sanchez de Aguilar 202 OF THE RELIGIOUS BELIEFS OF THE INDIANS OF YUCATAN IN 1545. Report of Francisco Hernandez 209 Glossary 216 Bibliography 221 Notes 223 PREFACE So little has been written in regard to the ethnology of the Maya Indians of Yucatan, and especially concerning their beliefs, which persist to the present time, that we publish here a translation of an important and practically unknown account of this subject. This report was printed in Mexico in 1870, but it is buried in a study by Antonio García y Cubas entitled "Materiales para formar la Estadistica General de la Republica Mexicana," in _Boletin de la Sociedad Mexicana de Geografia y Estadistica_, segunda epoca, tomo II, pp. 352-388. It is on pages 374-387, bears the date Mérida, October 24, 1861, and was written by Santiago Mendez, who states that he was governor of Yucatan during the years 1841-42. In connection with a study of this report, so far as it relates to the beliefs of the Maya, it will be profitable to consult the paper by Dr Daniel G. Brinton on The Folk-lore of Yucatan, printed in the _Folk-Lore Journal_, London, vol. I, part viii, 13 pp., August, 1883. We have also had translated the notes on the superstitions of the Indians of Yucatan contained in the work of Pedro Sanchez de Aguilar, 1639, published by the Museo Nacional of Mexico in 1892 (pp. 83-84), and the report of Francisco Hernandez on the religious beliefs of the Yucatan Indians, which was sent to Bartolomé de las Casas, evidently while Bishop of Yucatan in 1545, and is given by him in chapter cxxiii (pp. 328-330) of his Apologetica Historia de las Indias, a work which did not appear in print until 1875-76, the first complete edition of which was edited by M. Serrano y Sanz, and printed at Madrid in 1909. The information contained in the Mendez report is strikingly similar to that given by Bartolomé José Granado Baeza on Los Indios de Yucatan, an account written in 1813 but not published until 1845, when it appeared in the _Registro Yucateco_, tomo I, pp. 165-178. This report of Baeza is one of the principal sources used by Brinton in his study. The editor has incorporated a few Gbrief notes, and has prepared a glossary of the Indian words and a short bibliography of the subject. MARSHALL H. SAVILLE. THE MAYA INDIANS OF YUCATAN IN 1861 BY SANTIAGO MENDEZ _Report on the Customs, Labor, Language, Industry, Physiognomy, etc., of the Indians of Yucatan, made by the Agent of the Department of Public Works, who signs this report, in obedience to orders of February 6, 1861._ CUSTOMS The character of the Indians of Yucatan is such that, were they to be judged only by their customs and their habits, we would have to qualify them as stupid and devoid of reason. It seems indifferent to them to be in the shade or exposed to rain or to the scorching rays of the sun, even though they could avoid it. It does not matter to them whether they go dressed or naked. They never try to obtain commodities they see other races enjoy, even though the trouble or sacrifice it would cost to get them might be but small. In order to rest or to chat with their companions they hardly ever sit down: they squat, it being quite indifferent to them that they do it in a sun that scorches them when they might perhaps have shade two steps from where they are. Reward does not encourage them, nor does punishment admonish them; in the first place, they think they deserve more,--perhaps because they were always accustomed to be made use of,--and in the second case they consider punishment as a kind of fatality from which it is quite useless to try to deliver themselves: hence they do not reform. So long as their hunger is stilled, it is quite indifferent to them whether their meal is exquisite and varied, or whether it consists only of tortillas and chile, devouring their food in either case with astounding voracity. When they find themselves driven by utter necessity, they will work in order to remedy it, but they never do so with zeal or with the desire to improve their fortunes. They are so improvident that they may squander in one day the earnings of a week, in an exaggerated amount of dainties or in superstitious practices, and above all by intoxicating themselves, leaving their families without bread and clothing. Or, they remain idle until whatever they earned by the sweat of their brow is gone. They cultivate a cornfield and gather a good harvest from it, and even though they do not need to do so, they will sell the corn with considerable loss in order to squander the money in splendid repasts and superstitions, both of which always go together. This harvest might insure the subsistence of their family for a whole year, but their improvidence will reduce them within a few days to having to sell themselves for work (peonage). The love of the parents for their children, of the children for their parents, and between husband and wife, is barely lukewarm, and not at all passionate, if we are to judge from their absolute lack of signs of sympathy, pity, or condolence. They contemplate dry-eyed and rather indifferently the suffering of their nearest, and even their demise, without allowing this to change their demeanor or letting it interfere in the least with their general customs of life. Although some of them can read and write, they use it very little, either because they are very slow and clumsy in the exercise of both, on account, no doubt, of the lack of practice, and also because there is but little written in their own language. Their children have usually no other education than that which they receive from the curates, priests, choirmasters, and teachers of the catechism, which education was formerly given to them at the church doors or in the mansions of the large ranches and farms, and they were compelled to assemble every morning from seven to eight to learn the catechism. At the present day, as it is not possible to force the parents to send their children to learn even this, there are but few who learn at all, especially among the boys. When the writer of this was governor of this state in the years 1841 and 1842, he succeeded in establishing primary schools in almost all the villages, and although averse to anything that looks or sounds like despotism, he authorized, nevertheless, the mayors, justices of the peace, and chieftains (_caciques_[1]) to use it in order to force parents to send their children to the said schools. Unfortunately, in 1842 came the invasion by the forces of general Santa Anna, and in the effort to resist them, all the resources of the state were spent for many years in advance. Then followed our own senseless revolutions and the almost general uprising of these same Indians against the other native races, consequently these schools passed out of existence without it having been possible until this day to reëstablish them. Hence this remains an unsolved problem and it is difficult to calculate the profit they might have brought (once the tenacious and persistent opposition of the Indians overcome), leaving them convinced of the advantages it might mean to further their knowledge even in the manual labor they perform. Generally they train their children from a very early age to help in their agricultural labor such as their forefathers did before the conquest, or else they teach them light manual labor, such as weaving little mats or matting in general, making small bags, baskets of all kinds and sizes, leather bands such as are used by the native porters, sacks, hammocks, ropes, to prepare henequen from agave fiber, to make straw hats, and so forth. In some villages they are taught to make common pottery, and in places near the coast they are shown how to extract salt, to fish, and seamanship in general. It is very rare that they are taught other arts and crafts or trades, with the exception perhaps in cities or principal towns, where, especially when they have been reared and educated in the households of white people, they may become efficient in the art of quarrying stone, though quite primitively, or they qualify as masons, shoemakers, tailors, muleteers, drivers, and cowboys. They also provide the town with firewood, charcoal, and fodder. With regard to their marriage customs, there is little else to say except that the daughter-in-law goes to live in the house of her father-in-law, and the son-in-law goes to live with his wife's parents, which is at present the most usual way, because an episcopal edict had to be issued prohibiting the first-mentioned to avoid the very frequent abuses committed on the bride by her father-in-law and brothers-in-law. At a very early age young men marry, without repugnance, women who are much older, widows, and even girls who have children born out of wedlock. To remonstrances made by those who wish to dissuade them in view of such conditions, they will reply, "Why should I care? This happened before my time!" It is to be supposed that conjugal fidelity is not regarded very scrupulously by such couples. Their most common diseases depend largely on the seasons, and recur regularly. During summer and fall, when fresh food is abundant, the Indians are very immoderate in its use, consequently they suffer from diarrhea and vomiting. In spring and summer they have _tabardillo_, which is a burning fever, and dysentery, both of which are caused by too much exposure to the hot sun; and in winter obstinate constipation, colds, and affections of the throat and lungs. Their curative methods consist merely of abstinence and of bleeding, which they perform with a thorn or a fish-bone, and they cool their blood by drinking sour _pozole_ or boiled lemonade, or else a decoction of a plant called _xhantumbú_. They never use emetics nor cathartics. Ordinarily they eat two meals a day, one on rising and another in the evening. If they go to work in the field, after having breakfasted on tortillas and _atole_, they take with them a large lump of _pozole_ which they use as a refreshment at noon by diluting it in water. At sunset they leave work, and, returning home, eat the second meal, generally after having taken their bath. Their usual food consists of boiled vegetables seasoned with salt, chile, and sometimes with the juice of oranges (the sour orange is used for this) or of lemons. On Sundays, if they are able to do so, they buy beef or pork; these are the only days when they eat meat, except when they kill a wild bird or a creature of the woods while hunting. Such meat they cook by baking it in a special way in the earth, or else in _pib_. The very poor among them live all the year round on tortillas and chile, and a bowlful of _pozole_ or _atole_. Even the wealthiest content themselves with only one dish. This does not interfere with their being big eaters, nor devouring all they can get when it does not cost them anything. Their usual beverage is called _pitarrilia_, consisting of the bark of a plant called _balché_ which they put in soak in fresh water and honey and let it ferment. After fermentation it becomes strong enough to be intoxicating. They are also very fond of liquor, and there are very few among them who do not become intoxicated occasionally, at least on Sundays. Experience, and to a certain extent tradition, are their only guides for telling the different seasons of the year; they have not the slightest remembrance of their ancient calendar system. They are accustomed to hear clocks strike where such exist, but otherwise, simply from the course of the sun, moon, and stars, they are able to regulate the hours of the day and night, more or less. They also know when an eclipse of the moon is approaching, attributing this phenomenon to an intention of the sun to destroy his satellite, and they therefore are prepared to make a fearful racket with sticks, _mitotes_, whistles or horns (_fotutos_[2]), shotguns, and other instruments during the eclipse, believing that by so doing they can avoid the catastrophe. They sleep from early evening until four o'clock in the morning. Their working hours, if it is at all necessary for them to go to work, last from sunrise to sunset. If they are paid, they walk or travel at all hours, even with a load. There are a few among them who are trustworthy and faithful in their contracts, and know how to keep their word and promises; but there is a greater number who absolutely lack all of these virtues, with the exception, perhaps, of the solemn promises they make to their saints, in the fulfilment of which they are scrupulously punctual. They lie easily and very frequently, although they are aware that lies are prohibited. Generally they evade, whenever possible, a truthful answer which is to the point and fully satisfies the question. Their principal vices are lasciviousness among both sexes, and drunkenness among the men. To do them justice though, we might as well acknowledge that it is more than probable that if other races and tribes had to live as they do, almost naked, in the complete liberty and isolation of country places, all members of one family, males and females, grownups and minors, the married and the single ones sleeping together in those little huts without any, or at best, very scant, knowledge of religion, of modesty and honor, without any fear of the consequences of unchastity to the women, without any intellectual enjoyment, reduced to the merest essentials--to satisfy hunger, thirst, sleep, and the intercourse of the two sexes, might they not be guilty of worse crimes? They are generally accused of being inclined to theft, but as a rule they steal small things of little value, and they are not known to recur to violence or murder to satisfy this tendency. The wealthy are free money-lenders to members of their own tribe and even to those of a different stock, so long as they are satisfied they are not going to be cheated. As in almost all of the most populated part of the Yucatecan peninsula, it is impossible to use the plow for tilling the fields; labor is reduced to clearing the tropical growth by burning it in the height of summer and sowing corn or vegetables when the rains commence, to fencing in the fields and weeding them, etc. In order to be able to cultivate at one time as much as possible of their extensive lands, the wealthy Indians pay their day-laborers and volunteers exceedingly well, either in money or in its equivalent in provisions at a price below its actual market value, especially in times of scarcity. They are guided in this by the rule, "This is sweat of my brethren and it is not right that they should pay it too dearly." If those workers are servants of some large ranch and live on the place, they are called _Luneros_,[3] because they give their master their day's work on Mondays in exchange for the land he gives them to cultivate for themselves and for the water he allows them for irrigation of their fields. If they do not, for one reason or another, go to work on that day, he receives one real in silver instead. The customary amount of work they really are compelled to do for their master per year is twenty _mecates_ of clearing of untilled land and another twenty of already previously tilled fields. Had the owner to pay for hired labor, this would amount to 12 pesos, 4 reals. In addition to this they have to give him two hours on Saturdays for what they call _fagina_,[4] which means work around the house of any kind their patron should order them to do. On some of the ranches the obligatory field-work is reduced to half, but in this case they have to pay their real for Mondays, and always have to do the Saturday's _fagina_. Any other service or work they may be called on to do is paid or put to their account. By _milpa roza_,[5] the first clearing of a field by felling trees, cutting and burning undergrowth, etc., is meant; while the _milpa caña_[6] is the clearing of fields that have already been tilled the year before, where the cornstalks are to be split and burnt in order to plant again. Those who are employed as cowboys on stock-farms receive a fixed wage, and are not subject to the Monday service nor to the usual field-work. They have to look after the cattle and horses, and they have charge of the draw-wells, the tanks, and drinking pools. They have to attend to irrigation, weeding, and sowing of the truck gardens and orchards, and in general to do all work performed on such ranches either for their conservation and improvement or else in personal service to the owners or for the advantage of its products. It is also their duty to rasp a certain amount of henequen fiber from the agave each day. Their wage is from eight to twelve reals per month and five _almudes_[7] of corn per week. Yet neither this latter nor the salary are paid to him as his earnings, but credited to his account against what he draws in provisions or money, so that he actually is always indebted. This, however, is the aim of the owners, in order to hold the man quite secure, even though they know very well that, should the man die in their service, they would lose that amount. They see to it, however, that he never owes too much. This really constitutes a kind of slavery (peonage) which the men try to avenge by serving as poorly as they can, even to such masters as aim to make their lot easy and agreeable by frequent gifts or bonuses. As a rule the Yucatecan Indians are regarded as being meek, humble, and not easily stirred to ire and cruelty, basing such an opinion on the fact that the most customary punishment among them was a whipping applied with moderation. This kind of punishment did not offend them, if they were informed of the reason why it was meted out to them, nor did they consider it degrading. This characteristic is still noticeable among those who have remained submissive and attached to the white people. It is quite different with those among them who have had to suffer the cruel, atrocious, and protracted martyrdom inflicted by the rebels. They are merciless to those who have fallen and still fall into their power, not only those of other tribes, but even of their own, in case they refuse to follow their tracks. They have no pity on either age or sex. The chieftains (_caçiques_) of today, as well as those who were in office in the past, and the most prominent or wealthy Indians, live just as simply as the rest, without the slightest variation. They all are respected by their subordinates, whom they do not oppress to their own advantage, nor do they demand any services from them without compensation. The Indians are generally gay, light-hearted, gossipy, and fond of tricks, in which they can display strength, agility, and adroitness. They are also very fond of music and song, although not very gifted or talented in the execution of the former especially. At their feasts and dances, which usually are rather tumultuous and poorly organized, they still use some of the old songs in their own language, to the accompaniment of a little raucous flute, the carapace of a turtle (_hicotea_), upon which they beat the time with a hart's horn, and of the _mitote_ or _taukul_. The _mitote_[8] is a solid piece of wood of cylindrical shape, one yard long and a third of a yard or a little more in diameter, open at one side almost from one end to the other. This opening is made for the purpose of hollowing out the piece of wood until it is reduced to one inch or a little more in thickness. On the opposite side of the mouth, or opening, they fasten two oblong wings, which, starting at both ends, meet in the center and are separated from one another by a serrated edge. In order to play this instrument, they place it, mouth downward, on the ground, so that the wings remain on the topmost side, and they hit them with two short sticks whose points are covered with an elastic resin that makes them jump, so as not to deaden or confound the sound, which is of such resonance and force that it may be heard at a distance of two leagues. Notwithstanding the fact that they regard death almost with indifference, they are timid and cowardly. They never attack the enemy unless they are far superior in number. Still, they are very astute or cunning to plan ambushes and to take advantage of every occasion to surprise their foes, and then fight with great advantage, always accompanying the fighting with frightful shouting. They are generally good marksmen, and they handle the machete[9] with admirable skill. Whenever they see that they cannot resist the onslaught, they disperse in the woods, but almost instantly come together again at a previously designated meeting-place. They are very fleet of foot and good racers, and of an almost incredible endurance for walking long distances, even with a load of six to eight arrobas [150 to 200 pounds][10] on their backs. They also can stand a long time without food or drink. They do not excel in writing or in learning to write, although not a few have studied the same length of time and the same subjects as white men, but they are generally clownish and slow of understanding. It happens very often that after they have been given a clear and oft-repeated order, they will manage to execute it the wrong way, and their memory is so short that, although they attend catechism daily from the age of six or seven until they are twelve or fourteen years of age, there are very many among them who have never been able either to learn it or to commit it to memory. Those, however, who do not evade those lessons and who furthermore attend the preaching of the gospel in their own language, have obtained Catholic ideas about eternity, the last judgment, the glory of God, purgatory, and hell. As the climate of the peninsula is so hot that it exhausts our physical strength and energy, as well as reduces the needs of man who can live almost nude and in the open air and feed himself sparingly, we cannot expect that the Indian should be particularly inclined to work. We had the same experience among the other native races, although perhaps their social standard may impose greater necessities. A hut of six or seven yards in length by three or four in width, he builds himself; its walls consist of rows of sticks (which sometimes are covered with a coat of clay) and thatched with palm-leaves or grass, with a door frequently made of reeds twined together. Two or three roughly-woven hammocks of henequen, a machete, perchance a hoe, perhaps a hatchet, and, very rarely, a poor shotgun, are all his furniture. A _metate_ to grind his corn, an earthen pot to boil it, another pot to cook the vegetables and the _atole_, a _comal_ or flat earthenware plate to cook the corn-cakes or tortillas, a pitcher for water, one or two _jicaras_ of _gúero_,[11] an equal number of gourds cut in halves to make drinking vessels and for other purposes, are the eating utensils. A roughly-made, circular stool of half a yard in diameter and about as much in height, and which is used for shaping the tortillas as well as for a table at which they eat their meals, etc. Fifteen to twenty yards of cotton cloth for the man's clothes, for the wife's, and for the children's, which costs a real per yard, supposing the woman does not spin and weave this herself; two or three coarse needles, a reel of cotton thread, a straw hat, sandals, a handkerchief and a cotton belt; a large straw basket or hamper, a _mecapal_, and a sack of henequen, complete the list. A trough in which to wash clothes and to bathe themselves; a few pounds of corn which he sows himself, as well as chile, beans, calabazas,[12] _camote_ [sweet potatoes], and _jicama_,[13] a bunch of bananas, the leaf of which is used to shape the tortillas, and perhaps a sour orange. His wood he himself cuts in the forest for cooking his meals and also for the fire which he keeps all night in the center of the hut; and lastly a little salt. This is the entire inventory of the necessaries of life an Indian family of Yucatan needs, and which suffices even to the wealthy ones in the larger towns and principal cities. A great many of them live even without some of the things enumerated. They substitute for corn and vegetables (in case they cannot have them either for not having sown or for having lost the harvest), fruits, roots, and indigenous plants which grow wild all over their country, and which are edible and nourishing. Shall we still ask why the Yucatecan Indian is so indolent, when he has such few and such modest necessities, all of which are so easy to obtain even in the midst of the forests and at a great distance from any other human habitation? He instinctively hates the superiority of the white race, and even of the mestizos, to whom institutions both of long ago and of the present day, customs, greater civilization, and above all the allotment of land, give so many advantages. His almost irresistible inclination carries him into isolation, almost exile, in order to escape from the torment of seeing them and from social duties. He retires where the land is free, where he can till his field wherever he pleases. This accounts for the often very small settlements of perhaps only a couple of families in the thickets of the forests, provided they find a spring or at least a watering place, even though they might have to travel a considerable distance to provide themselves. But even those who live in larger settlements, in towns of white people, will invariably select the most retired spots in streets in the outskirts (far away from the center of the town) where to build their huts. This isolation in the big forests is the principal cause of his becoming more and more brutish, and it grows with the facility which those same isolated places afford him to satisfy the one and only desire he has acquired--drunkenness. It is there he finds _balché_ and wild honey to brew his _pitarrilla_. And there are ever some of his own race or mestizos who bring him liquor in exchange for the little corn he may have stored. He gives this up with an improvidence which seems innate, though perhaps we might attribute it to ignorance. The Indian never sees the crucifix or a simple cross or the image of some saint displayed anywhere, without going to kneel before it in reverent devotion, nor does he ever meet a priest without raising his hat or hurrying to his side to kiss his hand. He spends half of his earnings in devotional offerings which in the end degenerate into perfect orgies of religious fervor. And yet, in spite of all that, he does not feel the slightest scruple to take as concubines his sisters or even his own daughters. He does not profess half as much love and devotion to God as he shows toward the images of Saint Anthony of Padua or to the crucifix, both of which are the only ornaments he has in his little hut. He enters a church without bowing to the Holy Sacrament on the main altar, but he goes and kneels before the cross or before Saint Anthony or Saint Francis of Paula, or to any other image to which miracles are ascribed, no matter how poorly executed or how defective such an image might be. On rising from his prostrate position, he bends over to kiss the altar, to touch its board with his cheeks or forehead, then touches the image itself, if such is possible, at least with a twig of some aromatic herb or a flower which he carries home as a relic, paying it the utmost reverence. In addition to this he offers a certain amount of money for candles which he lights before the image of his saint at certain times; he pays for a determinate number of "Salve Reginas" to be sung either in the church or during street processions for his sake, and he offers prayers for the souls of departed relatives. He believes that the souls of the departed return to earth, and he therefore marks with chalk the road from the cemetery to their former abode, that they may not get lost. He has just as deep-rooted a belief in witches and elves, and he is in very great fear of witchcraft. It is impossible to eradicate from his mind the idea that there are men who especially dedicate themselves to inflict this dreadful art on others. He fears and respects at the same time an ideal being whom he calls _Balám_ and who, so he says, is the lord of the fields. They all are therefore convinced that these fields cannot be tilled without danger even to their lives if they do not offer him sacrifices before beginning work, such as _horchata de maiz_ (orgeat), which they call _sacá_; a stew made of corn and turkey, which they call _kool_; the tortilla with beans, called _bulihuah_; pitarrilla, and fumes of copal which they use instead of incense. It may safely be stated, therefore, that they adore him like God, but they are always careful that the white people do not see or notice this sacrificial offering for fear of being considered as idolators. _Alux_ they call certain apparitions which they believe to exist in the ancient ruins and on the hills, and they say that as soon as it grows dark in the evening these apparitions or ghosts commence to walk around the houses, throwing stones, whistling to the dogs and lashing them when they get near them, which leaves the poor beasts with a cough that kills them. They pretend that these ghosts can run with great speed, as well backward as forward; that they do not terrify those who look at them. They are wont to enter into the houses to annoy and tease people who are abed in their hammocks, not letting them sleep. They assure us that on ranches where sugar-cane is grown, and just as soon as the grinding machine for the cane is set up, they will go and turn it or they will drive on the horse attached to it, to make it trot around. They say these apparitions are of the size of a little Indian boy of four or five, and that they appear naked, with only a little hat on their heads. This belief is the cause of incalculable loss to antiquarians on account of the almost daily destruction of articles found in the ruins. The Indians will destroy without pity or regard, notwithstanding they may be offered a good price for them, all the images in clay and other objects found on the hills or in subterranean passages, because they are convinced that these objects are the ones that become alive at night and come out to walk around. They attribute to the _alux_ or to their influence, all the diseases they have, as they consider their touch malignant. They say that if these apparitions find anyone asleep they will pass their hands over his face so lightly that the sleeper does not even feel it, but this causes him a fever which incapacitates him for a long time. They also believe in the existence of the _Xtabay_, the _Huahuapach_, and the _Xbolontharoch bokolhahoch_. The first of these apparitions or ghosts may be seen, according to them, in the most isolated spots of a village or settlement in the shape of a woman dressed as a mestizo, combing her beautiful hair with the fruit of a plant they call _xaché xtabay_. She runs away as soon as anyone approaches. She quickens or retards her flight, either disappearing or allowing the one who pursues her to reach her side. This latter is the case if the one who pursues her is some amorous fellow who thinks her to be a beautiful maiden. But as soon as he reaches and embraces her, he finds that he holds in his arms a bundle filled with thorns, with legs as thin as those of a turkey, and this gives him such a terrible shock that he has fainting spells and high delirious fevers. The _Huahuapach_ is a giant who may be seen at midnight in certain streets, and he is so tall that an ordinary man barely reaches to his knees. He amuses himself by blocking the traffic, opening his limbs and placing one foot on either side of the street. Should anyone inadvertently try to pass between his feet, he quickly brings his legs together and so closely presses the throat of the poor victim that he finally chokes him. The two other specters or ghosts confine themselves to repeating during the night the noises that have been prevalent in the daytime, and especially the noise made by the spindle-wheel the women use. The other one makes a subterranean noise which sounds like the chocolate-churner, but both these noises terrorize those who hear them. There is no end of superstitions among the general mass of the Indians, and the most customary form of fortune-telling is performed by means of a piece of a certain crystal which they call _zaztun_, which means a clear and transparent stone, and this enables them to see hidden things and also to divine the cause of maladies. Those who arrogate to themselves the title of a diviner are freely consulted, and they receive presents and live a very easy and carefree life. By means of their tricks and great cunning they make the simple and ignorant Indians believe, when they are ill and go to consult them, that through the _zaztun_ they (the sorcerers) have discovered that some ill-intentioned enemy has bewitched them, and that in order to discover the malicious spell, they will have to wake for three nights with an abundant provision of pitarrilla, and aguardiente, food, and lighted candles. Of course, during these three nights they give themselves up to high living and immoderate drinking. While the others, their patients if we may so call them, are sleeping, or off their guard, they bury within the house or in its immediate vicinity a little wax figure pierced by a thorn through that part of the body where the complaint of their patient lies. When everybody is awake after the last night of vigil, they start certain ceremonies with the _zaztun_, and finally they go to the spot where they had buried the figure and take it out within sight of everyone, making them believe that that was the witchery. Then they start their treatment of the patient with the first and any herbs they can find, and if by mere chance these cure the ailment, they have naturally made for themselves a great reputation among the ignorant. They also perform a "healing" incantation by offering certain prayers in which they mention the diseases and the different winds to the influence of which they attribute them. They will repeat the Lord's prayer over their patient, the Ave Maria, and the Creed, and sometimes also the prayer to Saint Anthony which is included in the Mexican prayer-book. On other occasions they will resort to the _kex_, which means exchange, and consists in hanging around the house of their patient certain food and drink for the _Yuncimil_, or Lord of Death, and they believe that by so doing they are able to save, for the time being, the life of the patient by barter. To prevent bees from abandoning the hives and to make them bring home ample honey, and also that their owners may be free from sickness, they will hang in the beehives chocolate cups with _sacá_ or _horchata_ of corn. They also perform the _misa milpera_ (mass on the cornfield), which they call _tich_, which means offering or sacrifice, and which is celebrated in the following manner: On a barbecue or roast made with little sticks of equal length they place a turkey, and the one who officiates as priest opens the bird's beak and pours pitarrilla down its throat. Then they kill it, and the assistants carry it off to season it. In the meantime they have been cooking in the earth some large loaves of corn-bread which they call _canlahuntaz_, which is made of fourteen tortillas or broken bread filled with beans. When all is well flavored and cooked, they place it on the barbecue with several cups filled with pitarrilla. Now again the one acting the part of priest begins to incense it with copal, invoking the Holy Trinity; he repeats the Creed, and, taking some pitarrilla with a holy-water sprinkler, he flings it to the four winds, invoking the four _Pahahtunes_, lords or custodians of rain. He then returns to the table, and, raising one of the jicaras aloft while those surrounding him kneel, he places the jicara to each one's mouth for a sip. The feast then proceeds and terminates by general eating and drinking, most of all by the one who "officiated," who furthermore takes home with him a goodly supply. They say that the red _Pahahtun_, who is seated in the east, is Saint Dominick (_Santo Domingo_); the white one in the north is Saint Gabriel; the black one in the west is Saint James; the yellow _Pahahtun_, said to be female and called by them _Xanleox_, is seated in the south, and is Mary Magdalen. They very readily take their new-born babies to the baptismal font, and they never refuse to bury their dead in the cemetery. WOMEN It is quite astounding how in this climate woman in general passes very rapidly from childhood into womanhood, but this development is still more remarkable in the case of the native Indian woman, prompted no doubt by their mode of life and native customs. It is quite usual to see a little Indian girl of three trot daily to the woods with her parents to help cultivate the fields; very often her excursions extend to neighboring villages, and she seems to make those trips of four and even six leagues with the greatest ease, on foot; and after she has reached five or six years, she even carries her little bundle tied on her back. They also journey day after day out into the fields in search of firewood, small sticks perhaps not thicker than an inch or a little more, which they call _moloch_. They search for the wood themselves; they cut it and tie it with two reed or rattan rings, so that they can carry it on their backs. Then they go for water in the morning and again in the evening, having to draw it from wells forty and sixty yards deep, in buckets made of tree-bark. After they have reached the age of eleven or twelve years, they always present themselves for this particular errand, as clean as possible. They take great care to be well-washed and their hair carefully combed, almost as if they were going for a pleasure walk or to some meeting. This is particularly the case on the ranches and farms, and in almost all the villages where they have to provide themselves with water from the communal wells. Between the ages of six and eleven years the little Indian maiden attends, either at the church door or, on big haciendas, in the main building, to the teaching of our Christian religion. She goes there with bare head and with her hair hanging loose over her shoulders. All a mother teaches her daughters is how to cook, grind the corn, and shape the tortillas; to make _atole_ and _pozole_; to wash clothes,--and this very poorly,--at all events. Or rather the girls learn all those things by themselves through mere observation and by helping their mothers in their daily tasks. Some mothers, however, will teach them to spin and weave their rough cotton cloth, to sew their garments, and sometimes even to embroider in a very primitive way. They are usually accompanied by a _criada_, or housemaid, who is a kind of guardian angel and remains by their side wherever they go. When they meet the man they love, they bow their heads and look down; when speaking of their love, with the big toe of one foot they will draw lines on the ground. While they are within their homes they wear only a skirt or petticoat of white cotton cloth, which covers them from the waist down to their knees, and in this way they will also present themselves to visitors, unless it is someone absolutely unknown to them, in which case they cross their arms over their breasts to hide them from the stranger. If one meets them in the fields or lies in wait for them over the walls of unmortared stones, they hide immediately, apparently to run away from the presence of a wayfarer, notwithstanding they are all exceedingly curious, and the love of gossip is one of their main characteristics. They are tender-hearted and desirous of pleasing, but rather in an uncouth manner, in keeping with what little education they have received. Anyone who asks them something in the name of God is welcome to their compassion and to whatever they can afford to give. Their bodily cleanliness almost borders on superstition, for they consider a person who does not wash her body everyday as not quite sane or reasonable. For their daily bath they heat a stone they call _sintun_ in the fire, and when it is well heated they throw it into the water they have prepared for their bath. It is very seldom that they are happy in their love affairs, because it is generally their parents who choose their husbands. After the choice is once made, the parents of the prospective husband come to ask for the girl's hand, and if accepted they present an offering of two pesetas, which is known under the name of _pochat tancab_ or _buhul_. One peseta is for the bride-to-be, the other for her mother. From the day following this ceremony the bridegroom-elect has to furnish daily a fagot of firewood to the house of his future parents-in-law. On her wedding day the bride is dressed in a _hipil_ or loose garment over a petticoat or skirt, the border of which is adorned with ribbons of deep purple; while another wide ribbon of the same shade is tied around her hair. Her head is covered with a cloth of white muslin. She also has to wear shoes, a rosary around her neck, earrings and finger-rings with big cheap stones. All this jewelry may be borrowed from someone. Once the religious ceremonies over, they all proceed to the banquet, at which the newly married couple and their godfathers (sponsors) are assigned a prominent place. If the girl is not to continue living with her parents, she returns there, nevertheless, and remains for eight days, after which time the godparents come to get her and turn her over to her husband. The husband is the recipient of all the attention and care of his wife. She sews, she washes, and she grinds the corn and makes the tortillas, the _pozole_, the _atole_, and all the rest of his food with her own hands. She does all the work of her household; she has to prepare his bath when he comes home from work in the evening. These are her daily duties. In the evening, by the light of the home fire or in the pale light of a tropical moon, she sews or mends his clothes and hers and those of her children. Whenever the husband leaves home to go on a journey to some neighboring town or hacienda, the wife has to follow him; she is never allowed, however, to walk by his side, but behind, in his footsteps so to speak. If this husband gets drunk, which occurs rather frequently, and he should fall by the roadside, it is the wife's duty to remain by his side and take care of him until he is able to continue on his way. Neither the scorching sun, nor heavy rains, nor thunderstorms, nor any other danger of the road has power enough to take her away from his side. Even the fact that a woman has just been delivered of a child does not serve as an impediment to her going with the husband; she simply carries the new-born baby with her, either in a piece of cloth on her back or else mounted on one of her hips. If the husband, for one reason or another, is called before a court of justice, he appears accompanied by his wife, simply because it is her duty to go with him and to act as his defender. She does this wonderfully well; she speaks with such warmth and so fluently, with such courage and enthusiasm, absolutely free from her usual bashful shyness, that one cannot help but admire her. And this absolute devotion on her part to the service of her consort does not weaken even with the ill-treatment she receives at his hands in return, for whenever he is intoxicated he treats her to a liberal whipping--he beats her with his bare hands even, or with a stick. Under such circumstances marital fidelity on the part of the women is not, nor can it be, very deep-rooted, and frequently her seducers triumph over her virtue. However, if the husband surprises them and the woman succeeds in escaping him, he denounces her to the next court of justice and demands that she be given a certain number of blows. She invariably receives them quite resignedly, and after the ordeal returns peacefully to her domestic duties. If the woman is the offended one, she also goes before the judge and demands that her rival be treated to the same punishment. Any sickness that might befall them after this misadventure, they unfailingly attribute to witchcraft instigated by their offenders. Witchcraft enjoys such wide popularity among Indian women that there is hardly one among them who cannot relate one and even many cases of the black art in her family. To their minds superstition and credulity go hand in hand, and if one tells them of some strange occurrence ascribed to enchantment, they believe it as readily and as firmly as if it had happened to themselves or as if they had witnessed it. And if one immediately afterward asks them whether it is day or night, they will answer doubtfully, even after having looked at the sun--so wrapped up in the tale have they become. They are very fond of dancing and of music, but they do not perform the former either gracefully or freely, nor have they any variety or art in its execution. They have no talent or gift for playing an instrument either. They are wont to sing in their idle moments or even while at work, but sadly and in a monotone. The woman who finds herself pregnant works until the very last moment before the child is born, and resumes her tasks immediately afterward, as soon as the baby is attended to. They leave their children so much to themselves, and give them so little care, that they are forever creeping around on the floor in all the mire and dirt, and always completely naked. A diaper and a tiny _hipil_ are all they get for the first few days of their life. Around wrists and ankles they occasionally will tie tiny cords made of blue cotton to protect them, so they say, from epilepsy. Those who can afford to do so will hang a little rosary of beads interspersed with wooden honey-berries around their necks and put tiny earrings in their ears. A pregnant Indian woman will not go outdoors during an eclipse, in order to avoid her child being born with spots or ugly birthmarks on its body; nor do they visit women who have just given birth to a child, because it is their belief that the babies would become ill with pains in their bowels. As soon as the child is six months old they name a godfather and a godmother for the ceremony of opening the baby's limbs for the first time. To this end they set a table with some kind of pottage, and the godfather makes nine rounds of the table, with the baby placed astride one of his hips, which is the way in which it will be carried thereafter by its mother. Then they place in the child's hands, if it is a girl, a needle, a spindle, and the implements with which they weave their cloth; if it is a boy, he is given a hatchet, a machete, and other implements he is expected to use when grown up. These godparents enjoy the same distinction as those at the christening. The women do not care about knowing their own age, and they keep track of the age of their children only until they have attained about six or eight years; after that they forget it. Although they grow into young manhood or womanhood very quickly, really old age comes late, except in the appearance of the women, who at the age of thirty-five look like women of forty-five. Their most common diseases are pleurisy, intermittent fevers, and jaundice, while fits, fainting spells, and hysterics are exceedingly rare. As a rule the women are abstemious, economical, and very hospitable. They love work, and are fond of raising chickens and turkeys, which they sell in order to enable them to buy what they most need, or else they prepare such fowl for banquets, marriages, christenings, the day of All Souls, or for the novenas which they celebrate for the Holy Cross or the saint of their special devotion. They do not fancy all manner of necessities, nor do they pretend to live on the work of their husbands; rather they work constantly in order to dominate them, and in this they succeed generally, at least to a certain degree. They will upbraid them if they undertake anything without asking their advice. They do not forget offenses they may have received until they are avenged. In their old age they are liable to commit small insignificant thefts, and they especially seem to like to become mendicants, even though they do not need to be. They seem to do this as a kind of compensation for what in their earlier days they may have given to the poor. Sentiments of gratitude do not last long. However, we must in this case always except those who were reared in the homes of white people. With few exceptions (when perhaps poor methods or little care in their education, or perchance bad example and ill-treatment dominated), these Indian girls are virtuous, assiduous, disinterested, and very well-disposed toward all the different branches of service and ready to learn whatever they are taught. They are modest, and are fond of dressing themselves nicely and decently. They are so affectionate, true, and grateful, that many a time they grow old in the service of one family, and if this family meets with misfortune and perhaps becomes impoverished, they will go to work outside to help support them, of which I could mention many cases. Just the opposite happens with the men, who, although they were educated in a white family from early childhood, and many a time with the same care as the white children, the cases are rare that they do not gradually drift apart, become estranged, give themselves up to vice, and finally forget their benefactors entirely. DRESS The ordinary costume of the men consists of a shirt of white cotton like ours, worn outside the white drawers of the same material, which are wide and reach to the calf of the leg; a belt, white or in colors, is worn around the waist under the shirt; a kerchief; a straw hat, and sandals consisting of only soles which are adjusted to the foot by cords of agave fiber, complete his costume. While at work in the field they take all their clothes off and wear only a loin-cloth, which they call _huit_, consisting of a piece of cotton cloth fastened around the hips, the points passing between the thighs to be fastened to the belt below the navel. From this belt hangs the sheathed machete on the left side. When they go out, the Indian women wear on their heads either a piece of cotton cloth of about half a yard in width by two and a half yards in length, the ends of which hang down the back, or else they tie a red kerchief around the head, a very bright red being their favorite color. A _hipil_ of cotton is fashioned like a wide sacque-coat, with an opening in the center to put the head through, fitting around the neck, having openings on the two sides for the arms. This _hipil_ reaches to about the calf of the leg, falling on a skirt or petticoat, also of white cotton, three or four fingers longer. It is fastened around the waist under the _hipil_, which falls loosely over it. The hem of both the skirt and the _hipil_ are very often roughly embroidered in blue or red thread. For traveling they wear sandals like the men. LANGUAGE The Indians of Yucatan speak the Maya language, though somewhat adulterated through contact with Spanish. Several Spanish expressions have gradually crept into their idiom, especially in cities and principal towns where the Indians are in almost constant intercourse with whites and mestizos. Many among them can speak Spanish perfectly well, but as a rule they avoid it, and will answer in Maya to those who speak Spanish to them. STATURE, PHYSIOGNOMY, COLOR Generally speaking, the Indians of Yucatan are of about the same stature as all intertropical races, of a round face, straight black hair, rather coarse, not very pronounced eyebrows, very little beard or none at all, a low narrow forehead, black and expressive eyes, a somewhat flat nose, small but outstanding ears, protruding cheekbones, a regular mouth with thin lips and beautiful teeth, a stout neck, broad chest and shoulders, arms, thighs, and limbs of robust and muscular build. Their hands and feet are small, and the toes of their feet stand closer together than the heels. They have no hair on their bodies except on the head. Their color is a copper-brown, darkened through constant exposure to the sun, especially as they go about almost totally naked. The color of the women is therefore much lighter, and this is also the case with such men as have been reared from childhood in homes of the white people. Among the women there are some very pretty ones, slender in form, with an airy but graceful carriage, and a very sweet voice; but the hard work to which they are subjected from early childhood causes them to lose their beauty at an early age. There are also some truly fine types among the men. SAVAGE TRIBES Of real savage tribes there are none in Yucatan. After the greater part of the peninsula, cities as well as villages, had been reconquered from the possession of the Indians who had taken them during their insurrection in 1847, which was general, the most tenacious and unruly ones among them settled in the eastern part of the peninsula, where they have built several towns, the principal one being Chan-Santacruz. From these fastnessess they frequently sally forth to attack and even to raze our absolutely defenseless villages. These attacks cause frightful suffering not only to members of other tribes and races, without regard to sex or age, but they are at times even greater among those of their own race, who at one time or another have either absolutely refused to join their ranks, or, after following their lead for some time, have deserted, and returned to live in peace among the white people. Another and by far the most numerous band of those rebellious Indians went to settle in the south of the peninsula, and by virtue of the treaty they celebrated with General Vega have given up all hostilities, although they remain in complete independence of national as well as of state authorities, and in peaceful business intercourse with this city (Mérida), and also with Campeche and other points in close proximity to their abodes. Colonel Juan Sanchez Navarro drew a map, which he presented, together with his report, before the government of Yucatan on April 12 of the present year, on which map he gives an approximate idea of the localities on the peninsula still occupied by rebellious Indians who maintain a hostile attitude and those who have agreed to peaceful intercourse. The first mentioned he calls the eastern group, and the last named the southern one. SANTIAGO MENDEZ. Mérida, _October 24th, 1861_. NOTE BY ANTONIO GARCÍA Y CUBAS After having written about several groups of aborigines who inhabit the central part of the republic, I wish to extend these notes with the aid of documents in my possession to the Indians of Tabasco and Chiapas. The customs, habits, and inclinations of all those Indians in general do not, with any certainty, evoke any hope for the improvement of their race and their subsequent utility and usefulness to the nation. The task I have set for myself is a very delicate one, and there may exist a great many people who will attribute to lack of patriotism the frank statement of many defects in our population; but I observe that our nation is not moving toward its aggrandizement with the alacrity and speed which the progressives among the authorities wish to see. Therefore I consider it necessary to study and point out the defects. I do not wish it to appear as if the conceptions expressed in these lines were imputations of my own imagination, and I wish to state, therefore, that whatever is said in this report is extracted from official documents in my possession. The aborigines living in the towns and villages of the district of Jalpa, and the same may be said of the rest of the Indians of Tabasco, despite their docility, prefer the wild, uncivilized life of the mountains to the advantages of communal life, if by so doing they are able to evade all public responsibilities and duties. They come together only for their religious festivities, and on all such occasions they are given to drunkenness and gluttony to such a degree that they contract very serious diseases which in a great many cases hasten their demise. With very few exceptions they live in complete vagrancy, and they propagate without respecting any degree of blood relationship. They insist on curing their diseases with all sorts of roots and plants, which, however, mostly impair their health, causing great mortality, especially among children. This may be regarded as the principal cause why very few among their number reach the age of fifty years. The aborigines who inhabit the borders to the river Usumacinta and its tributaries are for the greater part natives of Yucatan, and are like all the rest of their kind, very fond of drinking. The Indians of Tenosique, about forty years ago, were known as very honest and trustworthy, but their intercourse with the rebels and emigrants from Yucatan have demoralized them to a great extent. These and other defects, with but a few honorable exceptions, are revealed in the documents treating of the Indians of the district of Comitan, state of Chiapas, which, however, I am not going to enumerate, so as to avoid repetitions, and by so doing make this article altogether too long. All the above mentioned shows the decadence and general degeneration of the aborigines, as compared with the very scant elements of vitality and vigor that might help in the movement toward progress in our republic. The same customs, the same reserve and diffidence which characterized the Indian of colonial days is manifestly still his today under the so-called protective laws of the republic, which barely give him the title of citizen. Yet, as I have stated before, I do not belong to those who despair of his ultimate civilization, and I believe that the most efficacious means of effecting this is by crossing his breed or race by way of colonization, introducing other nations and elements to come in contact with him. That this efficacious means of stopping the infinite defects which retard, if they do not hinder, the natural progress of our nation, has not been attained, to my idea, lies in the fact that so far no protective laws have existed which, founded on prevision, afford guaranties and procure work for colonists. There are no laws that fix the boundaries of the immense stretches of waste-land within our country, nor a careful study of climate, geology, and production. There is not, to my knowledge, any report establishing the best methods of making all our territory productive either through sales or the renting of all lands that cannot be tilled by their original owners. Our own elements, as we have tried to demonstrate in this article, are either heterogeneous or too scarce and insufficient to accomplish the task of carrying the nation onward on the road of aggrandizement. Hence it is, according to my idea, colonization, and colonization alone, that may serve as the final remedy for our national ills. If we had today laws such as I have had reference to, we would at this very moment see European colonists arrive continually, attracted by hopes of a splendid future which our fertile soil and our salubrious climate offer to the industrious and enterprising man. Our population would increase daily at the same pace with the United States of Brazil and Buenos Aires, where European immigration forms an element of prosperity. It remains for our government to fix in the most decisive way the answer to this question in the interest of the future of our country. ANTONIO GARCÍA Y CUBAS. Mexico, _May 1st, 1870_. NOTES ON THE SUPERSTITIONS OF THE INDIANS OF YUCATAN INFORME CONTRA IDOLORVM CVLTORES DEL OBÍSPADO DE YVCATAN. MADRID, 1639 BY PEDRO SANCHEZ DE AGUILAR The abuses and superstitions in which those Indians of Yucatan believe and the abuses which they cherish are mostly inherited from their forebears, and are as numerous as they are varied in kind. I am including in this report all I was able to investigate, so that they may enable the curates to disapprove them publicly, and in their sermons to reprimand the Indians on account of them. They believe in dreams which they try to interpret to suit the occasion. On hearing the cawing (or cackle) of a bird they call _kipxosi_, they interpret it to mean poor success to whatever enterprise they are engaged in at the time. They consider it as a bad omen or foreboding, as the Spaniards do with the female fox or the cuckoo. If, while the Indian is traveling, he stumbles over a big stone among a pile which had been dug up to build or level a road, he venerates it by placing on the top of it a little twig, brushing his knees with another one in order not to get tired. This is a tradition of his forefathers. If he happens to be traveling near sunset, and he fears that he will arrive late or even at night at the village he is bound for, he will drive a stone into the first tree he finds, believing that this will retard the setting of the sun. Another superstition to the same effect is the pulling out of some of his eyelashes and blowing them toward the sun. These are superstitions that came down to him by tradition from his forebears. During lunar eclipses they still believe in the tradition of their forefathers to make their dogs howl or cry by pinching them either in the body or ears, or else they will beat on boards, benches, and doors. They say that the moon is dying, or that it is being bitten by a certain kind of ant which they call _xubab_. Once, while at the village of Yalcobá, I heard great noises during an eclipse of the moon which occurred that night, and in my sermon the next day I tried to make them understand the cause of the eclipse in their own language, according to the interpretation from the Philosopher: "The lunar eclipse is the interposing of the earth between the sun and the moon with the sun on top and the moon in the shadow." With an orange to represent the sphere of Sacrobosco, and two lit candles on either side, I explained to them plainly and at sight what an eclipse really was. They seemed astonished, and quite happy and smiling, cured of their ignorance and that of their forefathers. I gave orders to their chieftain (caçique) that he should punish in the future all those who made a noise on such occasions. They also call certain old Indian shamans when a woman is in labor, and, with words of their former idolatry, he will enchant her and hear her confession. They do the same with some other patients. I could not find out all about this, for which I am very sorry. There are some Indian medicine-men who, with similar enchantment, are supposed to cure the bites or stings of snakes, especially of the rattlesnakes, of which there are a great many here. The victims of such bites are sometimes delirious, and often the flesh around the wound will decay until they die. The remedy the wizards give them, according to what I heard, is to make them eat human excrement or drink the juice of lemons, or else they will take a domestic fowl and place its beak on the wound, and have it suck in this way the poison of the snakebite. The hen or chicken will of course die, and they immediately replace it by another live one, and repeat that until all the poison is absorbed. When they build new houses, which occurs every ten or twelve years, they will not inhabit nor even enter them unless the old wizard has been brought even from a distance of one, two, or three leagues to bless it or consecrate it with his stupid enchantment. This, however, I have only heard, and I am now sorry never to have recorded it personally. They are fortune-tellers, and they perform this feat with a heap of grained corn, counting always two and two grains, and if it comes out in even numbers, the fortune-teller will continue counting one, two, or three times over until it comes out uneven, bearing all the while in mind the main facts or reason for which he had been called on to tell the fortune, _vera gratia_. Once a girl ran away from home, and her mother, like any true Indian woman would have done in a similar case, immediately called one of those fortune-tellers, who drew lots on all the different roads until the fortune told of or pointed to a certain road the girl had taken and where she would be found. They sent out to look for her and found her in the village to which that road led. I punished that wizard, who was a native of a village at one league from Valladolid, and while I examined him with patience and slowly, I found that all the words he used in that so-called fortune-telling, while he counted the grains of corn, were no more than "Odd or even, odd or even" (_huylan nones, caylan pares_). He could not even tell me whether those words were meant as an invocation to Satan. In fact, he seemed not to know what they meant, for this particular wizard was a very great simpleton, almost imbecile. In this city of Mérida it is publicly known that there exist several Indian sorceresses (witches), who by using certain words can open a rosebud before it is time for its opening, which is given to the one they wish to attract to their lascivious desire. They let him smell of it, or they place it under his pillow; but should the person who gives it to him smell its perfume, she is said invariably to lose her mind for a long while, calling to the one she expected to inhale it, and in whose name the rose was opened by the witch--a worthy matter which serves as medicine as well as punishment, especially if it hits the double mark. It has also been assured that the Indian women of this city are wont to throw a certain enchantment into the chocolate which is ready for their husbands to drink, and by it they become bewildered. This I only heard however, and I could not vouchsafe its truth. I will also note here what I saw as a child, and that is that they used to drown in a hole young puppies of a breed of dogs they raise as pets as well as for food. These are a kind of dogs, with but little or no hair at all, which they call _tzomes_.[14] It is an old Jewish dogma of _cosher_. See the Apostle, _ut abstineant se a suffocatis_, etc.--that they abstain from the food of animals dying by smothering or any kind of natural death. OF THE RELIGIOUS BELIEFS OF THE INDIANS OF YUCATAN IN 1545 REPORT OF FRANCISCO HERNANDEZ When our people discovered the kingdom of Yucatan they found crosses there, and one cross in particular which was made of stone and mortar, of a height of ten palms, and was erected in the center of a court or enclosure, very prominent and fair, and crowned with battlements; it stands alongside of a sumptuous temple and is very much frequented by a great number of people. This is on the island of Cozumel, which lies near the mainland of Yucatan. It is said that this cross was really adored as the God of Water or Rain; as often as there was a drought they went to sacrifice quail before it, as will be told later. When asked whence or through whom they had first heard of that sign, they replied that a very handsome man had once passed through their country and that he left it with them, that they might always remember him by it. Others, it is said, answered that it was because a man more resplendent than the sun had died on that cross. This is referred to by Peter Martyr in chapter I of his Fourth Decade. I shall refer to another tale or report which is very unusual and new regarding the Indies, and which until now has not been found in any other part of them. As this kingdom, on account of its close proximity to it, comes within the jurisdiction of my bishopric of Chiapa, on one of my visits I disembarked and remained at a very healthy port. I met there a clergyman, good, so it seemed, of mature age and honest, and [one] who knew the language of the natives from having lived there several years. As it was necessary for me to return to my episcopal residence, I nominated him as my vicar, and ordered and entreated him to travel inland and visit the Indians there and preach to them in a certain way in which I instructed him. After a certain number of months (I even believe it was one year), he wrote to me that on his trip he had met a principal lord or chief, and that on inquiring of him concerning his faith and the ancient belief all over his realm, he answered him that they knew and believed in God who was in heaven; that that God was the Father, the Son, and the Holy Ghost. That the Father is called by them _Içona_,[15] and that he had created man and all things. The Son's name was _Bacab_,[16] who was born from a maiden who had ever remained a virgin, whose name was _Chibirias_,[17] and who is in heaven with God. The Holy Ghost they called _Echuac_.[18] They say that _Içona_ means the great Father. _Bacab_, who is the son, they say killed _Eopuco_,[19] and flagellated him, crowning him with a crown of thorns, and placed him with arms extended on a pole, not meaning that he should be nailed to it, but tied (and in order to show him how, the chief extended his own arms), where he finally died. He was dead for three days, but on the third day he returned to life and went up to heaven, and he is there with his Father. After this immediately came _Echuac_, which is the Holy Ghost, and he filled the earth with all it needs. When asked what _Bacab_ or _Bacabab_ meant, he said it meant the son of the great Father, and that _Echuac_ meant merchant. And very good merchandise did the Holy Ghost bring to this earth, for he filled men with all their faculties, and divine and abundant graces. _Chibirias_ means mother of the Son of the great Father. He added, furthermore, that at a certain time all men would have to die, but he did not seem to know anything of the resurrection of the flesh. When asked how they came to know all these things, the chief replied that the lords taught their sons, and in this manner it descended from one age to another. They also assert that in olden times, long ago, there came to the land twenty men (he gave the names of fifteen of them), but because they were very poorly written, and furthermore as they do not have great importance for this report, I do not copy them. Of the five others the vicar says he could not obtain their names. The principal one was called _Cocolcan_,[20] and they called this one the God of all kinds of fevers. Two of the others are the Gods of fish, still another two the Gods of farms and homesteads [landed properties], still another was the God of Lightning, etc. They all wore long gowns or mantles, and sandals for their feet. They had long beards, and wore nothing to cover their heads. These men ordained that the people should go to confession and should fast, and some people fasted on Fridays because on that day _Bacab_ had died. The name of this day (Friday) is _Himis_,[21] and they honor it in their devotion on account of the death of _Bacab_. The chiefs (caçiques) know all the particulars of those things, but the common people believe only in the three persons, _Içona_ and _Bacab_ and _Echuac_, and in _Chibirias_, the mother of _Bacab_, and also [in] the mother of _Chibirias_ called _Hischen_,[22] whom we consider to have been Saint Ann. All this above stated is from information I have received in a letter from that reverend father whose name is Francisco Hernandez, and I still have his letter among my papers. He also stated that he took the said chief to a Franciscan friar who lived near there, and that the caçique repeated all he said before the friar, and they remained both greatly surprised at it. If all those things just stated are true, it would seem that that part of the land had been (long ago) informed about our Holy Faith, for in no other part of the Indies have we ever found such news. It is true that in Brazil, which belongs to the Portuguese, it was stated that traces of the wanderings of Saint Thomas the Apostle had been discovered, but such news could not very well fly over through the air, and furthermore it is quite certain that the country and kingdom of Yucatan give us more special and singular cases to ponder over, and of far greater antiquity, if we think of the great, exquisite, and admirable way the most ancient buildings are constructed, also of a certain lettering in queer characters which are not found anywhere else. Finally these are the secrets which only God knows. GLOSSARY _Alux_, _h'lox_, or more fully _h'loxkatob_. According to Brinton the meaning is "the strong clay images." He writes in his paper, The Folk-lore of Yucatan, that "the derivation of this word is from _kat_, which, in the Diccionario Maya-Español del Convento de Motul (MS. of about 1580), is defined as 'la tierra y barro de las olleras,' but which Perez in his modern Maya dictionary translates 'ollas ó figuras de barro'; _ob_ is the plural termination; _lox_ is strong, or the strength of anything; _h'_ or _ah_, as it is often written, is the rough breathing which in Maya indicates the masculine gender." _Atole._ Nahuan _atolli_, or _atlaolli_. Corn-meal gruel. _Balám._ Tiger or mountain-lion. The word was applied also to a class of priests and to kings as a title of distinction. _Balché._ A fermented liquor made from wild honey and the bark of a tree. _Buhul_, _buuhul_. A section of a stick of wood split lengthwise in the middle. _Bulihuah._ Tortillas made of corn-meal and beans. From _bul_ or _buul_, beans; _uah_, tortilla. _Caçique._ Antillean word meaning a lord or chief. _Camote._ Nahuan _camotl_, a kind of sweet-potato. _Canlahuntaz._ Large loaves of native bread. From _canlahun_, fourteen; _taz_, tiers, or layers. _Comal._ Nahuan _comalli_, clay griddle. _Hipil._ Nahuan _huipilli_, a woman's chemise. _Huahuapach, ua ua pach._ According to Brinton (op. cit.) it means giant crab. _Huit_, _uith_. Loin-cloth. _Jicara._ Nahuan _xicalli_, corrupted into _jicara_, a calabash. _Kex._ To barter or change; also used as a name for ex votos placed on altars. _Kipxosi_, _kipchoh_, _cipchoh_. "A diviner bird among the Indians." _Kool._ A dish prepared by cooking corn with chicken. _Mecapal._ Nahuan _mecapalli_, leathern band used over the forehead for carrying burdens. _Mecate._ Nahuan _mecatl_, rope or cord made of maguey fiber. _Metate._ Nahuan _metatl_, a stone on which corn is ground. _Milpa._ Nahuan _milli_, cultivated land; _pan_, a postposition. _Mitote._ Nahuan _mitotli_, a dance. _Moloch._ Brush-wood or kindling. _Pahatun_, _pah ah tun_. The four _pa ah tunes_, the lords of rains, are, according to Brinton, "identical with the winds, and the four cardinal points from which they blow.... The name _pahatun_ is of difficult derivation, but it probably means 'stone, or pillar, set up or erected.'" _Pib._ An underground oven. _Pochat tancab._ According to the author of this report the phrase has the same signification as _buhul_: the offering made to a girl by a prospective bridegroom. The words seem to be: _poc_, to wash or rub; _hat_, numerical termination serving to count split-wood; _tancab_, outside the house, or in the patio. _Pozole._ Nahuan _pozolatl_, or _poçol atl_, a drink of cooked corn. _Sacá_, _zacá_. Orgeat of corn; from _za_, corn gruel; _cá_, or _caa_, duplicative particle. _Sintun_, _zintun_. A heated stone for heating water for bathing purposes. From _zin_, to haul, girdle or encircle; _tun_, stone. _Taukul_, _tunkul_. A wooden drum. _Tich._ A mass celebrated in planted fields. See Brinton, op. cit. _Xaché xtabay._ According to the author, the name of a plant. The first word, _xaché_, is evidently _xach_ or _xachah_, to comb. _Xtabay_ may be _x-_, a prefix, indicating feminine gender; _tabal_, to deceive. _Xanleox_, _x'kanleox_. From _x-_, prefix denoting feminine gender; _kan_, yellow; _lox_, to strike with the closed fist. Brinton simply gives "yellow goddess" as the equivalent. _Xbolonthahroch bokolhahoch_, _X bolon thoroch bokol_ (or _bookol_) _h'otoch_. From _x-_, prefix denoting feminine gender; _bolon_, nine; _thoroch_, sound of a spindle revolving in its shaft. Brinton says, "The name therefore signifies 'the female imp who magnifies the sound of the spindle." _Bokol_ or _bookol_, to stir; _h_ or _ah_, to indicate the rough breathing which in Maya denotes the masculine gender. _Xhantumbú_, _xkantumbub,_ or _xkantun bub_. A small plant used for medicinal purposes. _Xtabay._ See etymology under _xaché xtabay_. _Xulab._ Spelled by Sanchez de Aguilar _xubab_. An ant which attacks beehives. _Yuncimil_, _Yumcimil_. The God of Death; from _yum_, universal father or lord; _cimil_, death. _Zaztun._ A quartz crystal; from _zaz_, clear; _tun_, stone. BIBLIOGRAPHY 1845 BAEZA, BARTOLOMÉ JOSÉ GRANADO. Los Indios de Yucatan. Informe dado por el cura de Yaxcabá D. Bartolomé del Granado Baeza, en contestacion al interrogatorio de 36 preguntas, circulado por el ministerio de Ultrámar sobre el manejo, vida y costumbres de los Indios, que acompaño el Illmo. Sr. obispo á la deputacion provincial. _Registro Yucateco_, Mérida, tomo I, pp. 165-178. This account was written in Yaxcabá, April 1, 1813. It is one of the principal sources of information used by Brinton in his paper, The Folk-lore of Yucatan. G. C. El Indio Yucateco, carácter, costumbres y condicion de los Indios de Yucatan. _Registro Yucateco_, Mérida, tomo I, pp. 291-297. This report is dated Mexico, December 30, 1843. 1846 CARRILLO, ESTANISLAO. Papeles sueltos de P. Carrillo. Fantasmas. _Registro Yucateco_, tomo IV, pp. 103-106. The material in this article was used by Brinton in his paper, op. cit. HERNANDEZ, JUAN JOSÉ. Costumbres de las Indias de Yucatan. _Registro Yucateco_, Mérida, tomo III, pp. 290, 298. This report is dated Mérida, April 24, 1846. 1865 CARRILLO, CRESCENCIO. Estudio historico sobre la raza indigena de Yucatan. Vera Cruz, 1865, 26 pp. 1882 BANCROFT, HUBERT HOWE. The native races of the Pacific states. 5 volumes, San Francisco. In the several volumes of this work Bancroft has assembled most of the early accounts of the manners and customs of the Maya of Yucatan. He was unaware of the existence of the report by Mendez which forms the basis of our publication. 1883 BRINTON, DANIEL G. The Folk-lore of Yucatan. _Folk-Lore Journal_, London, vol. 1, part viii, pp. 1-13. This study is based largely on the report of Baeza, with additions from the article of Estanislao Carrillo, and manuscript notes of several other persons, notably those of Carl Hermann Berendt. CARRILLO Y ANCONA, CRESCENCIO. Historia de Welinna. Leyenda Yucateca. Segunda edición, Mérida, 52 pp. The first edition was printed in 1862. 1895 BRINTON, DANIEL G. A Primer of Mayan hieroglyphs. _Publications of the University of Pennsylvania, Series in Philology, Literature, and Archæology_, vol. III, no. 2. 1905 REJÓN GARCÍA, MANUEL. Supersticiones y leyendas Mayas. Mérida, 1905. NOTES [1] For the meaning of this and of other Indian words, consult the glossary. [2] _Fotuto_ is a musical instrument used by the Carib Indians and also by the negroes of the Antilles. [3] _Luneros_ are Monday-workers. [4] _Fagina_--_faena_, manual labor. [5] _Milpa roza_ is, literally, field cleared of underbrush and ready for planting. [6] _Milpa caña_, literally cane field. [7] An _almud_ is a dry measure equivalent to twelve English bushels. There seems to be an error in the quantity here. [8] The author here seems to have confused the meaning of the word _mitote_ (see glossary). In Yucatan the instrument he describes is called _tunkul_. [9] The _machete_ is the large knife which the Indian men of Yucatan invariably carry with them. [10] The _arroba_ is the Spanish measure of twenty-five pounds. [11] We have been unable to find the meaning of the word _güero_. [12] _Calabaza_ is the Spanish for pumpkin; but the Mexican pumpkin is different from that raised in our latitudes. [13] _Jicama_ seems to be a local word not in the dictionary. [14] _Tzomes_, according to Sanchez de Aguilar, is the name applied to hairless dogs. The common appellation is _kúkbil_, or _kikbil_. _Tzom_ in Maya means a horn, also a proboscis. The word _tzomes_ is close to _tzimin_, pl. _tzimines_, the name of the tapir, which has an elongate snout. Alonzo Poncé who was in Yucatan in 1588, speaks of tapirs being called by the natives _tzimines_, and further states that they call horses by the same name, a definition to be found in the Maya dictionary of Pio Perez. [15] The names to which we call attention in notes 15 to 22 represent, with a single exception, in misspelled form, well-known Mayan deities. It is interesting to note the early influence of the Spaniards on the religious beliefs of the Maya, as evidenced by the interpretation given to Father Hernandez by the old caçique. There is a curious mixture of old and new in the account. Dr Seler has identified the various deities spoken of, and a description of their attributes will be found in Brinton's Primer of Mayan Hieroglyphs. Içona is _Itzamna_, chief of the beneficent gods, the personification of the East. According to Brinton the name means "the dew or moisture of the morning." Brinton writes, "He was said to have been the creator of men, animals, and plants, and was the founder of the culture of the Mayas. He was the first priest of their religion, and invented writing and books." [16] According to Brinton the _Bacabs_, or _Chacs_, were the offspring of _Itzamna_ and his consort _Ix-Chel_ (spoken of by the caçique as _Hischen_). [17] _Chibirias_ is identified by Seler as _Ix-chebel-yax_, who, according to Brinton, was "the inventress of painting and of colored designs on woven stuffs." [18] _Echuac_ is _Ek Chua_, said by Landa to be the god of the cacao planters, hence, as cacao-beans were the medium of exchange, the god of merchants, as here related. It is difficult to understand the confusion by which this god has been interwoven in Christian beliefs as the Holy Ghost. [19] _Eopuco_ has been interpreted by Seler as_ Ah uoh puc_, or _Ah-puch_, the God of Death, or God of Evil. Brinton believes that "these words mean the Undoer, or Spoiler, apparently a euphemism to avoid pronouncing a name of evil omen." In modern Maya he is plain _Yum cimil_, lord of death. [20] _Cocolcan_ is _Cuculcan_, or _Kukulcan_, the same as the Nahuan _Quetzalcoatl_. _Kukulcan_ was the feathered or winged serpent god, a deity of culture and kindliness. [21] _Himis_ is _Imix_, the name of the first day of the twenty-day month of the Maya calendar. [22] _Hischen_ is _Ix-Chel_, the consort of _Itzamna_. Brinton states that the word means "rainbow," and that the goddess was also known as _Ix Kan Leom_, "the spider-web" which catches the dew of the morning. Her children, according to Brinton, the _Bacabs_ or _Chacs_ were "four mighty brethren, who were the gods of the four cardinal points, of the winds which blow from them, of the rains these bring, of the thunder and the lightning, and consequently of agriculture, the harvests, and food supply. Their position in the ritual was of the first importance. To each were assigned a particular color and a certain year and day in the calendar." 
43519	----	PAPERS OF THE PEABODY MUSEUM OF AMERICAN ARCHAEOLOGY AND ETHNOLOGY, HARVARD UNIVERSITY VOL. IV.--NO. 2 COMMENTARY ON THE MAYA MANUSCRIPT IN THE ROYAL PUBLIC LIBRARY OF DRESDEN BY DR. ERNST FÖRSTEMANN TRANSLATED BY MISS SELMA WESSELHOEFT AND MISS A. M. PARKER Translation revised by the Author CAMBRIDGE, MASS. PUBLISHED BY THE MUSEUM OCTOBER, 1906 * * * * * NOTE ---- In pursuance of the plan of publishing translations of valuable contributions to the study of the Maya hieroglyphs, the Museum Committee on Central American Research has the pleasure of offering the following translation of Dr. Ernst Förstemann's important Commentary on the Maya Manuscript in the Royal Library of Dresden, generally known as the Dresden Codex. The translation by Miss Selma Wesselhoeft and Miss A. M. Parker was made under the direction of Mr. Charles P. Bowditch of the Museum Committee. In the original German edition, published in 1901, Dr. Förstemann used the Arabic numerals to designate the days, but in this translation, with the consent of the author who has kindly revised the translation, Mr. Bowditch has substituted the corresponding Maya names of the days, in uniformity with the general use of students in this country. It is needless to call attention to the importance of this paper by Dr. Förstemann whose long-continued study of the intricate system of hieroglyphic writing by the ancient Mayas makes all he writes of great value to students engaged in this most interesting research. F. W. PUTNAME. HARVARD UNIVERSITY, October, 1906. * * * * * PREFACE. -------- Some of those who examine this book will say, that it is too early for a commentary on the "Dresdensis," since Maya research is yet in its infancy, and this opinion is certainly justified inasmuch as a final explanation of that remarkable monument is, of course, impossible at the present time. On the other hand the accounts of the numerous investigations and discoveries which have been made thus far are so isolated and so scattered in the shape of a hundred short magazine articles, that it is certainly desirable to have what we know and what we have still to learn gathered together under one head. This book is intended, therefore, to give an idea of the state of our knowledge in this department of research at this time, when the nineteenth century is passing into the twentieth, with the definite expectation that this work will soon be far outstripped and will possess an historical value only. The contents of the following pages are of very little value, unless the student can compare them with an edition of the manuscript. My first edition was published in 1880 at Leipsic and the second at Dresden in 1892. The edition in Lord Kingsborough's "Mexican Antiquities" (in Volume III of that work, London, 1831) is still of practical use. And since in this work I must premise a knowledge of the elements of the subject, I would recommend, as additional aids to the comprehension of the following pages, my "Erläuterungen zur Mayahandschrift der Königlichen öffentlichen Bibliothek zu Dresden" (Dresden, 1886), and also Brinton, "A Primer of Mayan Hieroglyphics" (in the publications of the University of Pennsylvania. Series in Philology, Literature and Archaeology, Vol. III). I would also mention the very valuable work by Paul Schellhas, "Die Göttergestalten der Mayahandschriften" (Dresden, 1897), which I follow in the designation of the various gods by letters of the alphabet. It need hardly be pointed out, that the numerous pioneer articles by Edward Seler offer abundant instruction to the student in this field as well as in that of Aztec remains. I wish to express heartfelt thanks to Mrs. Zelia Nuttall and Mr. Charles P. Bowditch, who have aided my work in various ways and have thus rendered possible the publication of this book. E. FÖRSTEMANN. CHARLOTTENBURG. * * * * * FIRST PART. Pages 1-45. Page 1. As the first page is almost entirely effaced by abrasion, we know very little of its contents. Like the second, however, it was doubtless divided into four parts. The two pages have this also in common, that, for lack of space, their contents are not expressed in full, but abbreviated as much as possible. The top section (a) of page 1 may have been filled with a sort of frontispiece, perhaps a face with a few signs around it. The three lower sections (b, e, d,) with the three lower of the second page doubtless formed a whole. Each of these sections contained a normal Tonalamatl of the commonest kind, which was introduced on the left by five day-signs having a difference of 12 and was thus divided into five sections of 52 days each. In sections b and d, at least, these periods seem to be divided into equal halves of 26 days each. In d alone we recognize the initial week day, VII, of the Tonalamatl. In each of the three divisions there were two figures of gods, but we can recognize only the first of these in section d as the god D. Page 2. This page contains four much abbreviated Tonalamatls. In the following I will represent each Tonalamatl by setting down in a vertical line those of the twenty days with which the principal divisions of equal length of the Tonalamatl begin, in a horizontal line with Roman numerals the days of the week of thirteen days on which the separate subdivisions begin, and with the Arabic numerals the distance between these days. I will also remark that the position of the Tonalamatls in the "Dresdensis" is not connected at all, as in the Aztec, with certain places in the year, and that no rule for this proceeding can be found. It is curious, however, that no Tonalamatl in this codex begins with the day IX or Eb, which is the more important in the last pages of the Dresden Codex. 2a. This first Tonalamatl has the following form:-- XIII 5 V 12 IV 11 II 12 I 12 XIII Cauac Chuen Akbal Men Manik. The hieroglyphs and the figures show that preparations for a human sacrifice are treated of here and that the subject is, therefore, closely connected with page 3a, where the sacrifice itself is represented. There are but two pictures of persons, which refer, therefore, only to the first or to the first two subdivisions and which, for lack of space, are wanting for the others. On the left walks the person doomed to sacrifice, his arms are bound on his back, his head is barely visible and his eyes are apparently torn out. There is an object in front of his breast resembling a wreath. Behind this figure crouches a second, who holds an object in his hand which probably represents a rattle. The parallel passage in Cod. Tro. 2b shows the bound prisoner with an axe behind him. Then follows in Tro. 3b the prisoner without a head and behind him the black god with gory lance. The hieroglyphs--four for each of the five subdivisions--are arranged in the following order:-- 1 2 5 6 9 13 17 3 4 7 8 10 14 18 11 15 19 12 16 20. Of these 9, 13 and 17-20 are wholly effaced and 14 for the most part. The very first group refers to human sacrifice, for 1 is a head with an axe affixed to it, 2 contains the hand (_i_) which so often appears as the sign of grasping, especially in representations of the chase; here it has the same superfix as on page 22a, which on pages 4a-10a and 11a, b, appears as prefix. 3 is the head of god H, perhaps given here as a symbol of wounding (serpent god?). I am unable to explain the meaning of the dot between two crosses in front of this head; perhaps the sign denotes the day Kan, which is here arrived at by calculation. We find the same hieroglyph on page 3. Sign 4 signifies the death-god A = Cimi, who appears again in 12. In like manner 2 is repeated in 6 and 14. 7, 11 and 15 (probably also 19) are, however, the familiar cross _b_; 8 is the head of E with a prefixed knife; the intention here may have been to show that human sacrifice would be likely to have an auspicious influence upon the harvest. 10 and 16 are another unknown head. In 5 we see the familiar Kan-Imix sign, which, for the present, I am inclined to regard as denoting a feast or a sacrificial meal. 2b--c. These two sections have something in common. First, 2b (as also 2d) is divided into but two parts and 2c into only three parts. Second, in 2b and 2c the scribe intended to draw the hieroglyphs for 10 days each, instead of 5 each, but only drew the outlines of the second five, since they could not be used for these Tonalamatls. Third, the persons represented here are all engaged in the same occupation, each holding in his hands an object which looks like a frame for a net or web, and also a large needle with an eye through which a thread has been passed. A very similar representation is found in the Codex Troano 34a, 33a and 23*c, and also in the Sahagun Manuscript of the Bibliotheca Laurentiana at Florence. This can hardly mean anything else than the knotting of cords, which was the only method of casting lots current among the Mayas; compare Seler, "Altmexikanische Studien II" (1899), p. 31, and "Zauberei im alten Mexiko" (1900), p. 90, by the same author. This clearly indicates the use of these Tonalamatls in soothsaying. Fourth and last, each of the five hieroglyph groups of 2b and 2c begin with the same sign, which must, therefore, denote the casting of lots. The Tonalamatl 2b runs thus:-- XI 34 VI 18 XI Oc Ik Ix Cimi Ezanab. The pictures are of three persons. At the left two sit facing one another and at the right is the god A. Of the first two, the one at the left is probably feminine, but with an old face. I am inclined here, in spite of the sex, to recall the bald-headed old god (N, according to Schellhas), whom I am inclined to consider, for the present, the representative of the 5 Uayeyab days at the end of the year. This would account for the sign resembling an 8 lying on its side, which appears on the god's head and which usually represents the change of the year (compare pages 38a, 41b, 52b, 68a and 72c). I cannot explain the person sitting facing this god further, than that from his hieroglyph he is either H or allied to H. Of the 8 hieroglyphs 1 2 5 6 3 4 7 8. the first, as stated, seems to refer to the casting of lots, 2 is the sign for H, 3 denotes the female figure pictured beneath it, and 4 is the sign _q_ with the Ben-Ik on top of it. In the second group 5 is the same as 1, 6 is the cross _b_, and 7 and 8 are the hieroglyphs for A. 2c contains the following Tonalamatl:-- III 20 X 17 I 15 III Oc Ik Ix Cimi Ezanab. There are illustrations for only the first two of the three subdivisions; the two figures composing them are engaged in the occupation mentioned under 2b. At the left sits a deity, who is probably E, whose head develops into a second, which is that of an animal; on the right sits the god D. The three groups of four hieroglyphs each are arranged as follows:-- 1 2 5 6 9 3 4 7 8 10 11 12. Of these hieroglyphs 1, 5 and 9 are the head already numbered 1 and 5 on 2b; 2, 6 and 10 are the cross _b_; 3, 7 and 11 are three different heads, all, as it seems, having the Akbal sign, and 11 having also the numeral 6. 4 is again (see 5 on 2a above) the Kan-Imix sign, 8 a Kin with suffix (the east?) and the numeral 16 as prefix; finally 12 is Cimi (A). Do the numbers 16 and 6 refer to the 16th and 6th of the 17 and 15 days standing below them? The beginning of this Tonalamatl III Oc seems to me to fall on an especially auspicious day (hieroglyph _a_). 2d has the following Tonalamatl:-- XIII 28 II 24 XIII Lamat Ahau Eb Kan Cib. This refers probably to the section devoted to women, pages 13-23. For the picture on the left is a woman sitting and holding an unknown object in one hand; on her right stands the death-god A holding in his hands what may be an apron or breech-clout; there is a similar representation in Cod. Tro. 29*b. The hieroglyphs are 1 2 5 6 3 4 7 8. Of these 1, 6 and 8 are one of the signs of A, 7 another, and 4 may be a third, recalling the Moan, which, as on page 14c, rests on a hand held beneath it. 2 and 5 seem to signify a carpet or other fabric (or a lying-in bed?), on the one hand suggesting the occupation of the figures in 2b and 2c, and on the other the checkered hieroglyph, which is so common in the Palenque inscriptions. Finally 3 is the woman pictured beneath. Page 3. We come now to the sacrificial scene proper, which practically fills the upper half of the page. The victim, a woman, lies bound hand and foot, on the sacrificial stone, just as in the Cortes. 41-42; the incision above the stomach is already made and the eyes are closed. Behind her rises the tree of life with a bird (vulture?) sitting in its branches, which holds in its bill one end of an object, resembling a ribbon (entrails) issuing from the eyes of the victim, just as in Tro. 26*a and 27*a. This picture is surrounded by four gods, who, however, differ very much from the other four in the second sacrificial scene, page 34a. At the right above is K, who, I think, is the storm-god; the figure at the left above is almost entirely destroyed, and its hieroglyph wholly; I prefer to consider it a rain deity, so that these two gods shall signify the productive season. The two gods below may refer to the blessing upon the harvest and chase resulting from the season and the sacrifice. For, at the left below, we see the maize deity E, holding a dish of fruit, while her head-ornament contains a second head. At the right below sits the serpent deity H and in front of him is an animal with the noose still around its neck, with which it was caught. The hieroglyphs are in the following order:-- 1 2 5 6 9 10 13 14 3 4 7 8 11 12 15 16 17 18 21 22 19 20 23 24. Of these, 1-5 are wholly effaced and also the most essential part of 6. Of these hieroglyphs four (1-4, 13-16, 17-20 and 21-24) clearly belong to each of the four deities, for 15, 18, and 22 (the last again with the dot between two crosses as on page 2a) certainly belong to the picture. From this it seems to follow that Hieroglyphs 5 to 12 refer to the sacrifice itself. As a matter of fact 9 and 11, which are directly above the sacrifice, also refer particularly to that part of the representation. I wish also to call special attention to the two signs 8 and 16 which seem to correspond to one another. They are the two which I have designated with _q_ and _a_, which are met with here for the first time (aside from the _q_ with the Ben-Ik, which is not in question here) and which, I think, denote the good and evil days, _q_ referring to the sacrifice and _a_ to its results. In regard to the rest of these hieroglyphs, 7 and 9 are Cimi; 10, 14, 17 and 24 the cross _b_ and 11 and 23 the hieroglyph c. 12 is the head with the Akbal eye, having for its prefix the uplifted arm, which is joined thus to the most diverse signs, and which also occurs in the Tro-Cort. 13 is a similar head, 19 again Imix, 20 the sign _o_ and 21 a hieroglyph, which is without doubt a simplified head. Here, too, we have a Tonalamatl, and one beginning on an especially ceremonial day I Ahau, which seems to play the same role in celestial affairs as IV Ahau does in terrestrial matters. On the sacrificial stone we read the days Ahau, Eb, Kan, Cib and Lamat, and I think it likely that the same days occur in the passage of the Cortes. referred to above; the passage evidently contains some errors. The subdivisions of this Tonalamatl are not known to us, for here the manuscript is somewhat confused. I propose to read it as follows:-- I 10 XI 4 II 15 IV 9 XIII 14 I but Cyrus Thomas, "Aids," p. 294, has I 4 V 8 XIII 11 XI 15 XIII 14 I. Either reading is dubious. The scribe divided the lower half of page 3 into two parts, and drew in each the outline of five days; but then he saw that, to continue his work, he needed a long surface extending from left to right, and he therefore omitted filling in these two sections. Pages 4a--10a. We have here a normal Tonalamatl, which, however, was evidently meant by the author to serve a very special purpose, since he divided the first section of 52 days into no less than 20 parts of 2, 3 or 4 days. I give the following arrangement here, remarking, at the same time, that in one doubtful case (between the third and fourth groups) I deviate from my former plan:-- X 2, XII 4, III 3, VI 2, VIII 4, XII 2, I 2, III 4, VII 2, IX 2, XI 2, XIII 4, IV 2, VI 3, IX 2, XI 3, I 2, III 3, VI 2, VIII 2, X. Since the five sections on page 4a begin with the days Imix, Ben, Chicchan, Caban, and Muluc, we have resulting from this and from the intervals specified, the following days:-- X Imix, XII Akbal, III Manik, VI Oc, VIII Eb, XII Cib, I Ezanab, III Ahau, VII Kan, IX Cimi, XI Lamat, XIII Oc, IV IX, VI Cib, IX Cauac, XI Imix, I Kan, III Cimi, VI Muluc, VIII Chuen, X Ben. Now, however, in the "Globus," Vol. LXXIII, in my two articles entitled "Die Tagegötter der Mayas," I have expressed the opinion that there is good reason to believe that the scribe has made a grave mistake here. I assume that the scribe simply transferred the so-called month days from the year just past to the year in which he was writing, in doing which they were, of course, moved five days on (since 365 = 20 × 18 + 5), but he did not bear in mind, that the pictures and the hieroglyphs could then no longer correspond. Hence the days must be not Imix, Akbal, Manik, Oc, Eb, Cib, Ezanab, Ahau, Kan, Cimi, Lamat, Oc, Ix, Cib, Cauac, Imix, Kan, Cimi, Muluc, Chuen, Ben, but Cib, Ezanab, Ik, Chicchan, Manik, Chuen, Ben, Men, Cauac, Imix, Akbal, Chicchan, Muluc, Chuen, Ix, Cib, Cauac, Imix, Kan, Cimi, Lamat. Let us now consider the 20 groups, disregarding the first (really zero) which has no figure and no hieroglyphs. We will leave out of the question also the first two hieroglyphs of each group, which are the same twenty times and form, as it were, merely a superscription, in which the first sign is a head, also occurring elsewhere (4b-5b), with suffix and affix, and the second is the hieroglyph _i_, which might readily denote a sacrifice. Thus only the usual four signs remain for each picture. 1. Day 15 = Ezanab; Aztec Tecpatl, flint, lance point. The figure of the god does not correspond with this at all; it is a god in a gala cloak, holding before him a serpent and bearing a quetzal bird on his back. This figure, which resembles none other in our manuscript, strongly recalls Kukulcan, who, in fact, is often placed by the scribes at the head of the 20 Maya gods (cf. Dres. 36) in which manner he appears in this place quite without reference to the day and the hieroglyphs. In this interpretation I follow Seler, in the main, who in his treatise "Quetzalcouatl-Kukulcan in Yucatan" (1898) expresses this opinion on page 403 of the separate edition. But possibly the ear-ornament may refer to Ezanab. Of the hieroglyphs, 1 and 2 are the familiar sign of the serpent deities H or I, though here they are not drawn exactly alike. They also appear together on page 6a. 3 ( = _r_) I think is the sign for the week of 13 days, which recurs in groups 5, 11, 14 and 16, and hence is distributed 4 times, though not regularly, among the 4 × 13 days. Sign 4 is the death bird. 2. Day 19 = Ik; Aztec Ehecatl, wind, air, breath. The deity pictured is B, the god who is found the most frequently, and with the most varied attributes, of all the gods in our manuscript. He is the god proper of breathing and living and was, perhaps, the local god in the region where this manuscript originated. The second hieroglyph is his sign; the first, with a prefixed 9, is _p_ the third _q_ and the fourth _a_ with the usual 3 before it; their relations to B are still unknown. 3. Day 3 = Cimi; Aztec Miquiztli, death. The deity with a black line about the mouth is certainly the bald-headed old god N, whom we shall find on pages 12c, 14b, 17a, 21c, and 37a. His hands are much deformed; perhaps indicating the bite of a serpent? Of the hieroglyphs, 1, 2 and 4 are effaced; 3 is surely the sign of the god, differing, it is true, from his usual hieroglyph, but recurring with a 4 also on pages 21c and 24. This 4 might refer to the four kinds of years, but here, perhaps, to the fourth of the five Uayeyab days, and would thus agree with the 24th day of Cumku, which should lie here (in the year 9 Kan), if I have begun the Tonalamatl correctly. 4. Day 4 = Manik; Aztec Mazatl. The significance is stag or roe, game or the chase. The first picture on page 5 is one of the forms of F, which seems to stand here not merely for human sacrifice, but also for war and the chase, and especially for the act of killing in general. Of the hieroglyphs, unfortunately only the fourth can be read in full (the sign _c_), the upper part of the second is the cross _b_ and the lower part the sign Ahau; the number 11, which is peculiar to the god F, probably stood before the second sign. Did this god rule the eleventh of the 13 months of 28 days, as Moan ruled the thirteenth? 5. Day 8 = Chuen; Aztec Ozomatli, ape, then probably the constellation of Ursa Minor, and hence belonging to the god C. The figure is unquestionably his, and the first hieroglyph is surely his sign. The other three are the familiar _a_, _o_ and _r_. 6. Day 10 = Ben; Aztec Acatl, the fundamental significance of which is reed, rush, etc. The connection between this day and the god B pictured here must be left undecided. Of the hieroglyphs, the first points rather to the sun-god G, the second, with the numeral 7 as a prefix, is entirely destroyed, the third is the sign _u_, and the fourth, which is half obliterated, was _q_. 7. Day 12 = Men; Aztec Quauhtli, eagle. The figure to which the first hieroglyph with the numeral 11 belongs, is a form of the god F, but has the nose-ornament of the sun-god G. Hieroglyph 2, which we shall find again on 22c, may refer especially to the eagle; the third is the sign of the day Caban with a prefixed 3, and the fourth is the sign _o_. 8. Day 16 = Cauac; Aztec Quiahuitl. The meaning in the different languages points to rain, storm and summer, of which the tortoise and serpent are special symbols. I shall not venture to decide positively upon the deity pictured here; perhaps the object in his hand may be a tortoise; Seler, "Quetzalcouatl-Kukulcan" (1898), p. 403, calls him the young god. In the hieroglyphs we find the serpent sign Chicchan twice, just as in the first group on page 4; then follow _a_ and Kan-Imix. 9. Day 18 = Imix; Aztec Cipactli. In my treatise on the day-gods, I have referred to the variations in the significance of this day. The Mayas connected with it the idea of the female breast, of drink, and, in particular, of the intoxicating beverage pulque. The deity pictured here, which is certainly a female deity, has a kind of vessel in her hand, from which the serpent resting on her head appears to be drinking. Hieroglyphs 2 and 4 are wholly obliterated, and 1 partly; there is a lock of hair, the sign of femininity, before 1 and 3. It is to be noted further that 3 is the sign of the death-god and that the deity pictured here has the death-sign on its cheek. Can this possibly suggest deathlike intoxication? 10. Day 20 = Akbal; Aztec Calli. The meaning is that of darkness, night, dark hole, then that of house as an artificial cave or as a place of shelter at night. The first picture on page 7, the black deity L with the beard fits admirably here. The black paint still visible proves that the first hieroglyph, which is almost effaced, was his sign, and the second may be a head more definitely identifying him. The third was the sign _q_, the fourth is an Ahau, perhaps intimating that Akbal belonged to the days beginning the Uinal sections of 20 days, and to the lords of the same. In addition to appearing with these 5th, 10th, 15th, and 20th days, an Ahau is found with the 1st, 6th, 11th and 16th as regent of the year, and lastly, but especially, with the 17th, which bears the name Ahau, and with the god D belonging to it. 11. Day 2 = Chicchan; Aztec Cohuatl, serpent. With this would agree also the third and fourth hieroglyphs (the latter _r_), which are the two we found in the first representation on page 4 belonging to the deity holding the serpent. But what is the meaning here of the dog-head of the figure, and of the first two hieroglyphs corresponding to it? And what does this creature hold in its hand? The lightning? The hieroglyphs seem to correspond to the seventh day, as if the scribe had recognized his mistake and referred here to the present and not to the past year. 12. Day 6 = Muluc; Aztec Atl, water, cloud. With this corresponds the image of the storm deity K and his two hieroglyphs 1 and 2, the first of which occurs frequently, and the second is found on pages 20 b and 47, while 3 (Ahau) designates the day as regent of the year and 4 is the hieroglyph a. The curious sign 2 is also given on Cort. 32 b. 13. Day 8 = Chuen; Aztec Ozomatli, ape. There is no agreement at all here, but everything points to the day 3 lying 5 days back, the picture of the Cimi as well as the hieroglyphs, even the third with the Akbal sign and the uplifted arm (as on page 36a), also the fourth (_c_) which is generally thought to be the death-bird. It even seems here as if the scribe had had the preceding year in mind; possibly he did not want to repeat the fifth group. 14. Day 11 = Ix; Aztec Ocelotl, jaguar. Here there is an admirable correspondence between the figure and the first hieroglyph, which on page 26, top, also refers to the jaguar represented there; the other three hieroglyphs are _r_, Kan-Imix and _q_. 15. Day 13 = Cib; Aztec Cozcaquauhtli, vulture. The bird is actually pictured here and its sign is the first hieroglyph; the third is _q_, the second and fourth are obliterated. 16. Day 16 = Cauac; Aztec Quiahuitl, meaning, as in the eighth group, rain, storm, summer. The figure, the first on page 9, seems, however, to indicate the day Ahau, as does also the second hieroglyph, which is Ahau; the first and third are effaced and the fourth is _r_. Perhaps the scribe did not wish to repeat the eighth group. 17. Day 18 = Imix; Aztec Cipactli, as in the ninth group. Here the allusion to pulque is still plainer than it is there. The picture is that of a woman with bound eyes and uncertain position of the hands, and here too with the death-sign, and on her head a bee from whose honey the beverage was prepared. I shall not venture to explain the first two hieroglyphs; the second with uplifted arm appears again on page 8c. The third is Cimi and the fourth _q_. 18. Day 1 = Kan; Aztec Cuetzpalin, denoting maize with the Mayas. The representation consists of the maize deity with the Kan sign on her head, the first hieroglyph is hers, then follows Kan-Imix, which I am inclined to interpret as meaning a meal, next the sign _a_ and finally a head, which is uncommon and undetermined, with the leaf-shaped prefix as on pages 4c, 6c, 9c, 34b, 61a, 67b and 69a. 19. Day 3 = Cimi; Aztec Miquiztli, death. The first figure on page 10 is a deity with the head of the death-bird Moan and above the head is the death-sign. As has long been known, the first and third hieroglyphs unquestionably belong to this god, also the fourth with the Akbal sign agrees with it, and the second likewise recalls the Moan. 20. Day 5 = Lamat; Aztec Tochtli, meaning rabbit in the latter language. Neither the figure, which represents Cimi, death, nor the corresponding hieroglyphs, excepting the second one agree with this day. This second hieroglyph has both in front and above it the number 6. Two numbers added thus to the common Uinal sign usually designate the Uinal period plus days, as is so very common on the inscriptions, so that the sign appearing here would denote 6 × 20 + 6 = 126 days. The hieroglyph here, however, is _not_ the usual sign for 20 days. On the contrary, it has in the centre a straight line and on either side of it a parallel line ending in a little knob (or loop?). I propose to regard these lines as representing the ecliptic and the moon, which takes its course now to the north and now to the south of the ecliptic, and the sign as a whole as signifying the lunar month of 28 days. This is confirmed on pages 51, 55, 56 and 57. In that case this hieroglyph would denote 6 × 28 + 6 = 174 days. Now bear in mind that in this passage the day X Lamat, which equals the Aztec Tochtli, is referred to. In the year named after this day, and indeed on the 174th day of the same (1 Cipactli), in February 1502, the emperor Ahuitzotzin died; compare especially Brinton, "Essays of an Americanist" (1890), pp. 274-283. Should this association in our manuscript of Cimi = death, X Tochtli and the numeral 174, be considered accidental? Or did the scribe, writing in the year after the event, actually record it in the year 1503 and, departing from his real subject, immortalize it in this place at the end of the greatest Tonalamatl? I will not refrain from expressing the conjecture I have long entertained, though I am quite prepared for differences of opinion. Seler attempts to explain this series of 20 gods in another way; see his "Monumente von Copan und Quirigua" (1899), p. 729. (Cf. his collected papers p. 781.) Pages 4b--5b. It is my opinion that the Tonalamatl just now discussed connects with another, which is recorded directly below the beginning of the first, and which also differs from all the other ordinary Tonalamatls. It likewise divides the first 52 days into a large number of small parts (14) and has the following form, if we adopt Seler's correction in the last member:-- XII 4 III 4 VII 4 XI 3 I 4 V 3 VIII 4 XII 3 II 6 VIII 3 XI 4 II 4 VI 4 X 2 XII Ix Cimi Ezanab Ik Oc. The two days Ik and Oc should be read Oc and Ik. There is only one picture here:--a scaly green monster with the head of the principal god D. There are six hieroglyphs on its body, the first is that of Eb and the second that of Cimi, the fourth is the sign c. The others I shall not venture to determine. According to a conjecture expressed verbally by Dieseldorff, this figure may represent the god who continually recreates himself. We are reminded here of the two-headed serpent (Seler, "Tonalamatl der Aubinschen Sammlung," 1900, pp. 65-66). There are two rows of hieroglyphs above the monster, the upper contains 8 and the second 6, but the second hieroglyph in the upper row belongs in the lower. Thus there are 14 hieroglyphs corresponding to the subdivisions noted above. The upper seven signs are all alike and are also identical with the one, which, in the great Tonalamatl, recorded above, begins the heading of all the 20 groups; this likewise points to a close connection between the two Tonalamatls. The remaining 7 hieroglyphs should be considered as only 6, for it is improbable that C occurs twice in this series. They are the gods D, C, H, N, A and B, to which perhaps an E or F or G is to be mentally added in place of the second C. They are all principal gods with the exception of N (as always, according to Schellhas's nomenclature). This N, an old man, denotes, as it seems, the five Uayeyab days at the end of the year, as he does also on page 21c. This sign with the number 4 has already been seen on page 4a. If in 4b this sign signifies the last day of the year, then this Tonalamatl falls in the year XIII Kan. The sign 5 Zac also appears in the Tro-Cort., _e.g._, Cort. 29 c, Tro. 9*b and 28*b. Now I shall proceed to examine all that has not yet been discussed to the end of page 12, taking up first the remainder of sections a and b and then all those of 4c-12c. Pages 10a--12a. XI 12 X 8 V 12 IV 8 XII 12 XI Lamat Ahau Eb Kan Cib. The period of 52 days is thus divided into five sections of 12 and 8 days each, alternating regularly. A deity and four hieroglyphs belong to each of these sections, viz:-- 1. D sitting, with his right hand pointing upward and his left downward; on his head is the Akbal sign as on page 15c. The hieroglyphs are destroyed with the exception of the third, which is the sign of D (Ahau). The fact that the 12 days happen to end with the day belonging to D (Ahau) is accidental. 2. R, a human figure with the head of the Moan (as on page 7c and 10a) and with the copal pouch around his neck. Of the hieroglyphs only the fourth, one of the common signs of Moan (_c_), is legible. 3. H, or, according to Seler, "the young god," as on 12b and 14b, with nose-peg and copal pouch. On his (her?) head sits a bird with an object, which I do not recognize, in its bill; compare page 12b. Of the hieroglyphs, the first is destroyed, the second is the unmistakable sign of H, the fourth is the common _a_, and the third I cannot as yet decipher. 4. A, with the usual design issuing from his mouth (the expiring breath of life?). Of the hieroglyphs, the first is a double Manik with prefixes, which probably denotes violent death; the other three are very common symbols of A. 5. E, holding a vessel containing plants (agave?) and with the cross _b_ on his head-ornament. The first hieroglyph is an unexplained compound design apparently referring to the Moan, an Imix and two prefixes, the second is the monogram of E, whom the third hieroglyph, Imix-Kan, designates as dispensing nourishment, and the fourth, Ahau, as a leading deity. Page 12a. The scribe evidently wishing to carry out his material in some conclusive form in the top, middle and bottom sections of page 12, found insufficient space in the top section. He, therefore, condensed two independent unconnected Tonalamatls, by arranging them in such a manner, that the period of 52 days was divided, for the sake of brevity, into only two parts, viz:-- VIII 27 (IX) 25 (VIII) Ahau Oc Eb Ik Kan Ix Cib Cimi Lamat Ezanab. I have supplied the two numbers enclosed in parentheses; they are wanting in the Manuscript. The hieroglyphs 1 2 5 3 4 6 7 8. are sufficient for the two figures one expects to see here; but they are, in fact, intended for four figures--two for each of the two Tonalamatls. For the first of the two Tonalamatls we have only one figure, God K, who, however, from the dish held in his hand, probably containing honey (compare 10b), seems to stand here also in place of E. In agreement with this, Hieroglyph 2 and probably also 1 (_s_, which occurs again on page 13a, and also on page 10b) refers to K, while 3 clearly refers to E and 4 is the sign a. Hieroglyphs 5-8 belong to the second of the two Tonalamatls. The first two of these hieroglyphs, which are entirely erased, refer to an unknown deity, and the last two unquestionably relate to A. Pages 5b--6b. I 16 IV 9 XIII 25 XII 2 I Manik Cauac Chuen Akbal Men. Four hieroglyphs belong to each of the four subdivisions:-- 1 2 5 6 9 10 13 14 3 4 7 8 11 12 15 16. These four parts, however, form a whole, inasmuch as they all relate to making fire, as it is also represented in the Troano 6, 19 and 14*c. Hence the upper row of hieroglyphs contains signs which are repeated. 1, 5 and 9 are the same head, the last two cases have the sign for darkness (Akbal); this Akbal appears again in the parallel passages of the Tro. and in 13 it is somewhat enlarged simply owing to the absence of a head. The act of making fire seems to be denoted here rather by the second sign (2, 6, 10, 14), which I designate by _k_ and which, originally, doubtless consisted of two hands (double Manik sign); the prefix is the same in 6 and 14, and different in 2 and 10. The eight lower hieroglyphs are merely the monograms of the four gods making the fire. The first deity is F, the second either A or one of the black deities L or M, the third D and the fourth apparently F again, but conceived as feminine. In the third picture there is a second object, apparently a head (of D?), below the piece of wood in which the fire-stick is being whirled. Hieroglyph 11 belonging to this deity has an Akbal as a prefix. Pages 6b--7b. X 13 X 13 X 13 X 13 X Kan Cib Lamat Ahau Eb. This Tonalamatl is divided, by way of exception, into four equal parts, which all begin with the same week day X. Here too, as in the preceding Tonalamatl, there are four subdivisions, and also 16 hieroglyphs arranged in the same way. And here too the upper line is a condensation of the whole, the same two signs being repeated four times. The first of these is _q_, which is still a problem and which occurs inverted also on Cort. 20d-21d (where there are figures with bird-heads); there too it is the characteristic hieroglyph. The second, however, is again the double Manik sign referring to activity of some kind, as in the preceding Tonalamatl. But the occupation of the four deities represented here is of very different kinds and altogether problematical. E, conceived as feminine, occupies the first place, with a Kan sign on her head and holding in her hand a vessel exactly like the one held by the figure just above on the same page. The third hieroglyph is hers and the fourth is the sign a. The second figure is A with a hook-shaped object hanging around his neck. His hands also seem to be deformed, as are those of the third and fifth figures of the great Tonalamatl (on pages 4 and 5). His two hieroglyphs are among those usually belonging to him. The third god is D sitting, by way of exception, on some object (stone?). Something resembling the pestle of an ordinary mortar is hanging down in front of his headdress, and he is holding a very similar object to his mouth. His two hieroglyphs are also those which usually refer to him. The most striking figure is that of the fourth god, whom I do not recognize. He seems to be attracting to himself a bird flying down from above, whose bill almost touches his mouth. His hieroglyph has the sign Yax (strength) for a prefix and the fourth hieroglyph is c. Page 8b. VIII 26 VIII 26 VIII Manik Cauac Chuen Akbal Men. Again we have a Tonalamatl divided into equal parts, this time, however, into but two, and it seems thus to be closely connected with the preceding. While hitherto four hieroglyphs have usually belonged to each figure, we find here ten in all and in the following order:-- 1 2 5 6 3 4 7 8 9 10. There are two figures here, which stand in some relation to one another,--two persons sitting facing each other. The one at the left is certainly D, the one at the right can hardly be the old woman, whom Schellhas designates with O, but rather N, the old god of the Uayeyab days. The former seems to be about to take something from the hand of the latter. I surmise that it is one of the prophetic weaving implements. which we found on page 2. The two hieroglyphs _e_ and _h_ must refer to this; they are repeated, as usual, in the two groups, _e_ in places 2 and 8, and _h_ in 1 and 6. Signs 3 and 4 refer unquestionably to D and hence 5 and 7 (the first _q_ with Ben-Ik, and the latter unknown) must be the designation of the person sitting on the right. We shall meet the latter sign again on pages 15b and 18a, with the same person, and on pages 27a and 39b with entirely different persons. Sign 7 is an object, which also appears on 15b and 18a, held in the hands of women and may denote some special sacrificial offering; on 9b Kan-Imix appears in place of this sign, and on 39b beside it. It should be noted that sign 7 stands here in exactly the same proximity to 1 and 6 as on page 27a. The hieroglyphs 9 and 10 stand outside the two groups, and since, as we know, they belong to the god A, this prophecy must concern death, as is more clearly indicated by the corresponding hieroglyphs on page 9b. Page 9b. Here, for the first time in this manuscript, we have a Tonalamatl in which the 260 days are not divided into five fifths of 52 days each, but into four quarters of 65 days. This may be represented as follows, if we supply the III, which is wanting at the beginning:-- III 33 X 32 III Muluc Ix Cauac Kan. In the first place, the close connection of this Tonalamatl with that recorded on page 8b, just now discussed, is striking, for 1. Here too we find a division into two equal parts is intended, but which, of course, as the number is 65, cannot be mathematically exact. 2. Here too we not only find 10 hieroglyphs, but we find them in the same order as on page 8b, and here too the sign _e_ stands in places 2 and 8, and _h_ in 1 and 6; again 3, 4 and 9 are exactly the same hieroglyphs here as there, so that only 5, 7 and 10 are different. 3. The picture is again that of two persons sitting facing each other. Here D sits on the right and facing him is the grain deity E. D is speaking to E as is indicated by the sign before his face and by the position of his right hand. The signs belonging to E are Hieroglyphs 5 and 7, while those of D are 3 and 4. It seems, therefore, that D is announcing to E the prophecy contained in the preceding Tonalamatl. 4. Two hieroglyphs, 9 and 10, are again added, both relating to death--9 to god A and 10 to F. Now what especially distinguishes this passage from the preceding one, is the fact that the four days are the so-called regents of the year, Muluc, Ix, Cauac and Kan, above which, perhaps to emphasize this circumstance, there is a particularly elaborate Ahau. Seler ("Einiges mehr über die Monumente von Copan und Quiriguá," p. 210), however, thinks that this sign is the hieroglyph for the numeral three, which should stand here. The fact that the tenth sign, which is the last, is 13 Moan in the preceding Tonalamatl, while here it is 11 F, will be of special significance in deciding the interpretation. Page 10b. The manuscript gives the following:-- XIII 22 III 22 Oc Ik Ix Cimi Ezanab. This cannot be correct, for 22 + 22 is not 52, and from XIII to III is not 22 days, while the last Roman numeral is wanting. I, therefore, propose to make a 6 of the numeral 2, which occurs twice, by changing the lower dot into a line, and to change the III into a XIII by the addition of two lines. This gives the series the form XIII 26 XIII 26 XIII. Then by its division into three equal parts, this Tonalamatl accords with the three preceding ones, which it also resembles in other respects. For here too we find two persons pictured; this time, however, they do not face each other, but are placed one behind the other. The first is B, the god of life strictly speaking, the second is F, who is represented by his hieroglyph in the preceding Tonalamatl, and who is the god of the chase and probably of death by violence. Both hold offerings in their hands, which have been presented to them, and this also seems to be suggested by the two pendent copal pouches. The dish in B's hand probably contains honey, while F holds a plant (agave?)--the very same articles, which we find on page 12a in the hands of other gods. It looks as if the gods had been propitiated and as if this were the conclusion of a drama running through four Tonalamatls. Again the two death-hieroglyphs, which were added on pages 8 and 9, are wanting here, and we find only the usual eight signs:-- 1 2 5 6 3 4 7 8. Of these, 1, 2 and 5, 6 are the usual comprehensive heading; 1 and 5 are the Manik sign, which must denote the offering, while 2 and 6 are the characters, which perhaps, not incorrectly, has been thought to denote a repetition, a kind of plural; we have already seen it on pages 12a-13a. 3 is the monogram of B, yet it looks more like a fist with the thumb prominent--a figure I have frequently found in the inscriptions of Palenque. It must also refer to the sacrifice offered to B, which is confirmed by the _a_ added to it in 4 and probably denoting a good day. 7 is the hieroglyph of F to which the sign in 8 corresponds, while the prefixed arm in 8 seems to refer to the presentation of the sacrifice. Pages 10b--11b. VIII 8 III 9 XII 9 VIII 10 V 16 VIII Chuen Akbal Men Manik Cauac. I have corrected the 15 in the manuscript by making it 16. 20 hieroglyphs correspond regularly to the five sections in the following order:-- 1 5 6 9 10 13 17 2 7 8 11 12 14 18 3 15 19 4 16 20. This section seems to refer chiefly to the harvest. First the Muluc sign with suffix and affix, which is repeated in 1, 5, 9, 13 and 17 at regular intervals, suggests rain as a preliminary condition of the harvest. Next in 2 the hieroglyph of K, the wind-god, is added to this Muluc sign, and K is the patron of the day Muluc. Then the signs _a_ and _o_ follow in 3 and 4. There is no picture belonging to this group; it ought to be the god K. The second group adds to the Muluc in 6 the glyph of the sun, which is the second preliminary condition of the harvest. This is followed in 7 by the sign _u_ apparently denoting wind and cloud and having the prefix of the storm-god, and in 8 is the sign, which, strange to say, stands also in the last Tonalamatl in the eighth place. I am not very clear in regard to this sign. The sun-god G with copal pouch and a vessel containing grains of maize is appropriately represented with this group. With equal fitness the third group contains E, the harvest-god proper, with copal pouch and grains of maize, and, as usual, a Kan sign on his head, but also with a parrot, probably as an enemy of the harvest. Sign 10 is E's hieroglyph, to which, as is so often the case, sign 11 (Imix-Kan) is added and in 12 the double Manik (_i_). The last two groups are without figures of deities; the double Manik (14 and 18), possibly a repeated summons to sacrifice, is common to both groups. There seems here to be a further reference to the _enemies_ of the harvest, for 15 is the hieroglyph of the vulture, 16 that of the death-bird and 19 that of the night-god, after which this section closes with the quite universal sign a. If space had permitted, the vulture and the night-god would have been represented here. Page 12b. I 13 I 26 I 13 I Ix Cimi Ezanab Oc Ik. This is again a regular arrangement, half of the 52 days being in the middle and a quarter each at the beginning and end. The first four days refer to the purport of the prediction, Ix, the tiger, Cimi, death, Ezanab, the wounding lance point, and Oc, the lightning dog. The 12 hieroglyphs indicate the connection with the foregoing Tonalamatl, for 1, 5 and 9 contain the same Muluc sign which we found there in the same places. The three figures, it seems to me, signify the approach of death, the wound occasioning death, and the arrival of death. The first picture represents the god probably as feminine, with which the illustration on page 9c should be compared. The lock of hair before sign 3, the death hieroglyph, agrees with this as do also the familiar signs 2 and 4. The god is making sounds, which is indicated by the figure issuing from his mouth. Is the snail in his head-ornament to be understood as the sign for retarded motion? The second figure is the wounding serpent deity H, likewise represented here as feminine, with a lock of hair; the copal pouch hangs from her neck, her nose-peg resembles a flower as on page 19a. A bird is sitting on her head and is devouring a piece of an animal's body; we have already met this representation in the preceding Tonalamatl. Hieroglyph 6 designates the deity H, 7 (Imix-Kan) probably denotes the devouring of the flesh and sign 8, which is an Ahau with a prefixed knife, may also refer to this. Finally, the third picture is again the death-god, who is clad in a gala cloak and, in contrast to the first picture, where the deity is sitting on some object, is squatting on the ground. The three hieroglyphs 10, 11 and 12 fit here admirably. We will now turn back to page 4 and consider the lowest section (c) of pages 4 to 12, which like pages 5b-12b (I omit 4b here because its contents are of an entirely different nature) contain 7 Tonalamatls, that is, five ritual years of 364 days. If, however, we add 4b to these and bear in mind that 10c-11c contain a double Tonalamatl, we will have 9 Tonalamatls. We find a group of 7 Tonalamatls also on pages 51a-52a. Pages 4c-5c. XII 10 IX 22 V 11 III 9 XII Cauac Chuen Akbal Men Manik. The incorrect 10 of the manuscript has been changed to 9. The hieroglyphs are as follows:-- 1 2 5 6 9 10 13 14 3 4 7 8 11 12 15 16. and there are four figures of gods. The sign of the rising Moan with its usual prefix and superfix (_d_) forms the principal part of this section, the meaning of which, however, is not yet very intelligible. This sign appears not merely as the 1st, 5th, 9th and 13th hieroglyphs, but all the four gods hold it in their hands. Placed after each of these signs are hieroglyphs 2, 6, 10 and 14, which are the double Manik or hand sign denoting a sacrifice (_i_). The first god portrayed here is G, the sun-god, and the third hieroglyph is his sign, which is rendered yet more unmistakable here by the laterally elongated head _q_, the meaning of which is not yet wholly determined. The second god is D with his two signs in 7 and 8. 7 designates him rather as night and moon-god and 8 more as the old god and lord of the gods. The third god is the serpent deity H or Seler's "young god." His sign is hieroglyph 11, with which, to be sure, the unusual sign 12 (_v_) appears as a not very intelligible determinative. The fourth god is A and his usual signs are given in 15 and 16. Pages 5c--6c. This is the second example in our manuscript of a Tonalamatl divided into four parts:-- XII 29 II 11 XIII 18 V 7 XII Ezanab Akbal Lamat Ben Ezanab. The repetition of the 15th day at the end is superfluous. Here, then, we have the four days with which the 18 Uinals can begin; in the Tonalamatl on page 9b, the four regents of the year were given instead. Now, whether the beginning of these periods of 20 days was celebrated by a banquet or not, at all events, a feast is suggested by the sign Imix-Kan, which is repeated in hieroglyphs 1, 5, 9 and 13. The four vessels in the hands of the four deities, two of whom are sitting and two standing, would agree with the idea of a feast. The first vessel is a cup filled apparently with foaming pulque, and the other three are larger vessels meant to be hung up. The first deity is D with a snail on his head. Compare page 12b. His hieroglyphs are 2 and 3, and sign _a_ is added as fourth. The next deity is A with his usual signs in 6, 7 and 8. C follows with his hieroglyph in 10 and lastly F with the sign 14 which belongs to him. There still remain as the 11th and 15th signs, the elongated head _q_ with the Ben-Ik superfix belonging to C and with another superfix belonging to F (with which he likewise appeared as sign 4 in the preceding Tonalamatl). The 12th sign (_v_), which occurs in exactly the same place in the preceding Tonalamatl, is no more intelligible to me here than there. Pages 6c--7c. I 17 V 19 XI 6 IV 10 I Chuen Akbal Men Manik Cauac. Four sitting gods with the regular 16 hieroglyphs. There is no collective sign, however, among these. It seems exactly as if the intention had been to represent the _different_ offerings usually presented to the various deities. At all events the sacrifices are designated by hieroglyphs 1, 5, 9 and 13, and the same objects are also held in the hands of the four gods respectively, although they are clearly recognizable only in the case of the second and third gods. Now what are these four different sacrificial gifts? The principal part of the first looks like the sign of the month Mol. In excellent agreement with its appearance is the fact, that this word signifies egg in the Quecchi language. The god receiving the sacrifice here is A. Hieroglyph 2 is his monogram and 3 is that of his companion F and 4 fits both deities. The second figure is D and his signs are hieroglyphs 6 and 7 to which 8 is added quite superfluously. The sacrifice proper is denoted by 5, which, I think, is a sign of multiplicity and which was originally the fin of a fish. In the manuscripts and inscriptions, when this sign is added to the sign for 360 days, it enhances the value to 20 × 360 = 7200 days. The third picture represents the god with the bird-head of the Moan and his signs are hieroglyphs 10, 11 and 12. One of these, signifying rising birds, is also the offering in 9. Lastly, the fourth picture is, according to Schellhas, the serpent deity H, and, according to Seler, the "young god," with the snail on his head. His sign is hieroglyph 14. Added to this is the sign _a_ in 15, and in 16 it is _q_ again with the same superfix as in sign 15 of the preceding Tonalamatl. The sacrifice in 13 is represented by a Kan sign, which is equivalent to maize, maize bread or tortilla. Repeatedly, as on page 23b or 29b-31b of our manuscript, we see a portion of game (deer), a bird, a lizard and a fish represented as sacrifices. With this the fish and bird in our second and third pictures agree very well. I shall not venture to explain the other two in the first and fourth pictures. Perhaps future explanations of the curious head-ornament of the four gods will shed further light on the subject. Page 8c. III 9 XII 9 VIII 9 IV 9 XIII 9 IX 7 III Cib Lamat Ahau Eb Kan. The horizontal line should be read in this order; in the manuscript the numbers are in a somewhat unusual order. An attempt has been made to divide the 52 days into sections of 9 days each, and in doing this the sixth subdivision has fallen short of two days. Since this passage has but two pictures, six of the 12 hieroglyphs must belong to each of the figures. I read the hieroglyphs in the following order:-- 1 2 5 7 8 11 3 4 6 9 10 12. Each of the two pictures contains a building and a deity in front of it, each of whom seems to have placed another deity in the building. In the first picture D is putting C inside and in the second F is doing the same to A or the Moan. I will add also, that the day belonging to C (Chuen) is actually 9 days distant from that of D (Ahau). I am uncertain in regard to the other two. In the back of each building we see a cross. A similar association of two gods appears again elsewhere, as on page 35a, where D lies on a building in which C is sitting, thus showing an association of the same two gods as in our first group. In both groups the first two hieroglyphs form the common heading, since 1 corresponds in general to 7 and 2 to 8. In the first group 3 and 4 are the hieroglyphs of D and 5 and 6 are the signs _q_ and _v_; does one of these last signs refer to the god C? In the second group 9 is the sign of F, who stands in front of the house and 10 that of the god in the house, as perhaps is also 11, when we consider the closed eye; this is one of the many hieroglyphs having an uplifted arm as a prefix. On page 9a we find exactly the same sign. The last sign is the hieroglyph _q_, which sometimes seems to be used merely to fill space; it corresponds, but with a different superfix, to the fifth hieroglyph of the first group. The last three parts of this section of the manuscript all differ appreciably from the usual form (5 × 52 = 260 days). Page 9c. Here for the first time the manuscript contains a Tonalamatl, which is divided into 10 × 26 days. It is true the position of both the days and numbers is quite irregular. The manuscript presents the following order:-- III III VI VIII 3 2 Cauac Ben XI II Chuen Chicchan 3 4 Akbal Caban VI VII Men Muluc 4 1 Manik Imix. I III 7 2 I read it thus:-- III 3 VI 2 VIII 3 XI 4 II 4 VI 1 VII 7 I 2 III Cauac Chicchan Chuen Caban Akbal Muluc Men Imix Manik Ben. Two figures and eight hieroglyphs are given here. I do not venture to decide whether each of the two figures with its hieroglyphs relates only to a period of 26 days or to the half of the whole, 130 days. I think the latter is more likely to be the case. The sign Imix-Kan, which I am inclined to refer to a sacrificial meal, is common to both groups and connects them. The two gods seem also to have a sign pertaining to a meal in their hands; this may be a cup. The first deity is D or I, but with a female breast and with a serpent on his head. His signs are 2 and 3. The second god is A with a snail on his head and his signs are 6 and 7. In addition to these, sign 4 of the first group is _v_ and sign 8 of the second group is c. Pages 10c--11c. I 3 XIII 1 I 5 VI 10 III 13 III 15 V 8 (in error 9) XIII Imix Cimi Ben Ezanab Chicchan Oc Caban Ik Muluc Ix. Here we have two independent Tonalamatls as on page 12a. There are subdivisions only for the second; the first should be regarded either as entirely invalid or else its division has merely been omitted. 6 gods with 4 hieroglyphs each are represented on these pages:-- 1 2 5 6 9 10 13 14 17 18 21 22 3 4 7 8 11 12 15 16 19 20 23 24. Here too Hieroglyphs 1, 5, 9, 13, 17 and 21 are the common factor; they have the form of the month Mol, but here, as on page 6c, they probably designate the particular object constituting the sacrifice. The following details are to be noted regarding the six divisions:-- 1. The god A with his two signs in 2 and 3. 2. D with the signs 6 and 7. 3. F with the signs 10 and 11 (the latter _c_). 4. E with the signs 14 and 15, having on his head a structure, which is compounded apparently of a Kan sign, a snail and the suggestion of the maize plant. 5. G, clad in the gala cloak and the copal bag. His sign is 18, while 19 suggests rather the Moan or K. 6. B, his headdress displays the little circles, which often occur in connection with him, _e.g._, pages 30c, 40a and 41a, and which may suggest the starry sky. His sign is 22; the hieroglyph _m_ is added to it in 23 as a determinative. As usual, the fourth sign of each group is the most puzzling. 4 and 12 are Imix with the uplifted arm as a prefix, as on page 13a, 8 is the hieroglyph _o_, 16 is _a_, 20 is _c_ and the principal part of 24 is _r_. This sign _r_ seems to me to suggest the week of 13 days (see above the explanation of page 4a); four weeks of this kind end here. It is to be noted further that all the six gods are holding one hand outstretched:--A downward, B upward and the four in the centre forward. Page 12c. XIII 26 XIII 26 XIII 13 XIII Chuen Cib Imix Cimi Chuen. This is another Tonalamatl divided into 4 × 65, the subdivisions being transferred to the end of the second, fourth and fifth weeks. The Chuen at the bottom is superfluous. The twelve hieroglyphs standing here according to rule are grouped together in fours by the three pairs of the first row. Of these 1, 5 and 9 are the fist, familiar from the inscriptions, and which we also see on page 10b of this manuscript, where, to be sure, it occurs with the sign of B, as often happens, but here it has the closed eye of the death-god A. On the other hand, 2, 6 and 10 are the sign Kin = sun, with merely a dotted outline, and the three gods pictured below all hold the same Kin sign in their hands. This passage, may refer to the dying sun, the winter solstice. The first god is D, who, however, has B's head on top of his own. An object like a spyglass projects from the eye of B, which one could hardly venture to pronounce a nose-peg. The sign 4 (Ahau) refers to D; but what is the meaning of 3, the hieroglyph of the serpent deity H? Is the sun wounded? The second god is the baldheaded old deity, whom Schellhas designates as N. The hieroglyph 7, apparently referring to the five Uayeyab days, is his sign; we found it on page 4b and shall again find it on page 21c, and this time likewise with the old man. What is the meaning of the grain-goddess E denoted by sign 8? As N is connected with the close of the year, so E seems to be in various ways connected with the beginning of the new year. The third picture is unmistakably the sun-god G with the copal pouch hanging from his neck. His sign is 11, while sign 12, which suggests the wind-god K and balled-up clouds, is as difficult to explain here as it was on page 11c. The signs 8 and 12 seem, therefore, to refer to one another, and, if I do not see too much, look like a promise of rain and harvest. On page 12 the Tonalamatls of the three sections of the page come to an end and a new part of the manuscript begins. Page 13a. I shall here group together pages 13 and 14, the top third of 14 encroaches a little upon page 15. 13a has the following Tonalamatl:-- Imix Ben Chicchan Caban Muluc. I have supplied the first day, which is effaced. The week days are wanting. The 52 days are divided into halves of 26 days each. Of the 8 hieroglyphs the fifth seems to be the same as the destroyed first; aside from the prefix, it is the sign _s_. The two halves of the period have two gods, the first is B with a very singular head-ornament, and the second A, perhaps with the symbol of a snail on his head. Both hold a plant (agave) in their hands, as on pages 10b and 12a. Hieroglyph 2, which is mostly destroyed, must have been B's monogram, 4 has the Ahau as its determinative, and 3 is the elongated head _q_ with Ben-Ik. In the second group 6 and 8 are the signs of A, and 7 is an Imix with the uplifted arm prefixed, as on page 10c. Pages 14a--15a. VIII 13 VIII 13 VIII 13 VIII 13 Ahau Eb Kan Cib Lamat. The month days 13 and 5 have changed places in the manuscript. The initial day VIII Ahau will prove to be of especial importance in the second part of the manuscript (compare page 70). Here, as in the preceding Tonalamatl, the period is divided into equal parts. Little can be said of the hieroglyphs, 16 in number, since 6, 9, 10, 12, 13, 14, 15 and 16 are wholly or mostly destroyed. 3, 7 and 11 seem here to be a comprehensive element, as is also probably 15, but I am unable to refer this head to a particular god; 2, 6, 10 and 14 may also be alike, but this is very uncertain. 1, 5, 9 and 13 may have denoted the four cardinal points, at least 1 suggests the south and 5 the north. Thus we have left for the four deities E, H, A and G, only the signs 4, 8, 12 and 16; 4 surely belongs to E, and 8 to H, but the other two are erased. Pages 13b--14b. VI 13 VI 9 II 7 IX 7 III 7 X 9 VI Ahau Eb Kan Cib Lamat. There are 24 hieroglyphs for the 6 divisions:-- 1 2 5 6 9 10 13 14 17 18 21 22 3 4 7 8 11 12 15 16 19 20 23 24. Of these the upper row again contains the comprehensive signs, and the lower the discriminating characters. The closed eye in 1, 5, 9, 13, 17 and 21 suggests A, who also appears below as the first of the six gods, and the superfix of these signs suggests the south. 2, 6, 10, 14, 18 and 22 are the Kan sign, and we also find this sign in the hand of each of the six gods. Thus the subject of this passage seems strictly speaking to be harvest or food. The six gods are A, E, C, L, F and D; the second, third fourth and fifth have a bird on their heads. The first and fourth birds are eating, as on pages 11a and 12b, and thus probably represent enemies of the harvest. The first is of a different species from the other two. The four gods in the centre have the copal pouch about their necks. Signs 3 and 4 are the common hieroglyphs for A; 7 that for E, to which _o_ is added as a determinative; 11 is C's hieroglyph with an _a_ added to it, and L is undoubtedly denoted by sign 15; 16 is _r_ (equal to 13 days; it is meant here for the day III Cib). F appears quite according to rule in 19, which is appropriately followed by the sign _c_ in 20. Finally the hieroglyphs for D in 23 and 24 are the usual ones. We come now to the large section extending to page 23, which, owing to the numerous pictures of women, forms a section quite by itself. It is not likely that this contains anything else than oracles relating to pregnancy; in fact, the period of 260 days represented here with great frequency is in excellent accord with this subject. In the Codex Tro-Cort. there is also a section devoted to women, which corresponds to this chapter and particularly page 19* of the Troano affords remarkable parallels to the Dresdensis, even in details. Pages 13c--14c. II II 7 IX 3 XII 3 II 13 II Men Chicchan Imix Chuen Manik Caban Ben Akbal Cauac Muluc. The second of the two vertical rows on the left should be considered as immediately joined to the first. Thus we have here the second example in this manuscript of a Tonalamatl of ten parts; the first was on page 9c. The entire representation on 13c and 14c looks like an introduction to the following section, as though treating in general of the relation to one another of pairs of animals, of human beings and of deities. Corresponding with the Tonalamatl, there are four pairs of this kind represented. The hieroglyphs belonging to these pictures are distributed among the four sections as follows:-- 1 2 5 6 9 10 11 15 16 17 3 4 7 8 12 13 14 18 19 20. Apparently, the first two pictures have only 4 signs each, and the other two 6, but this is equalized by the fact, that hieroglyphs 1, 3, 5, and 7 are clearly each composed of two signs. The comprehensive sign appearing in 2, 6, 9 and 16, is, properly speaking, the sign _t_, which may denote coition, and, not unsuitably, contains in its centre two black figures side by side. Passing now to the separate four groups, I think the male figure is always on the right and the female on the left. In the first and second groups the two face each other, and in the other two groups the male is behind the female. 1. The female figure is an animal, perhaps a deer, the male is a black and white spotted deity having a human form and his head appropriately embellished with horns. The hieroglyphs belonging to these are:--1, a combination of Manik and Chuen with a prefixed 4, just as on page 21b; 3, likewise a compound sign, with a prefixed 7, which occurs also on page 46c on the left, and which I do not venture to explain, but which seems to denote horns, and lastly the hieroglyph c. 2. The female figure is an animal (on page 19a the female is represented more in resemblance to the human form) with a bird-head, to which belongs the compound sign _s_, still unexplained; the male figure is a barking (or howling?) dog, as on page 21b. Hieroglyph 7 is composite and contains first the sign generally belonging to the dog and suggesting a skeleton, which also represents the 14th month, and secondly, a Cimi closely related to it, precisely the same as in the parallel passage 21b. The well-known _q_ follows in the 8th place. 3. The god D holds in front of himself an animal, which may be a rabbit. His signs are hieroglyphs 11 and 12, while 13, the principal part of which is a grasping hand, clutching a Moan sign, seems to refer to the animal in the picture. 10 is _b_ and 14 is a. 4. Lastly, two beings in human guise, showing thus a closer connection with what follows. They are the black god L with his hieroglyph in 18 enlarged by an Imix, and a woman holding a Kan sign in her hand, hieroglyph 20 likewise showing the ordinary combination of Imix-Kan. Sign 15, however, refers to the woman, and lastly 17 and 19 are the signs _m_ and _r_; I note that _r_ ends a period of 13 days. The contents of the following seem to suggest that we should first read page 15 (including the middle section of 16) from top to bottom, then pages 16-23, partly from left to right and partly from top to bottom, according to the subject. Page 15a. V 34 XIII 18 V Ahau Eb Kan Cib Lamat. There are two pictures with 4 hieroglyphs each. The two pictures represent D and A, the latter probably as feminine. Both are falling headfirst, and both have leaves about them as if they were falling from a tree and a cry is issuing from A's mouth. The common element is given in hieroglyphs 2, 3 and 7, which are all signs of D. Further, 4 is the Chuen sign, the ape (as the animal living on trees?), its prefix is hieroglyph _r_, which I regard as denoting the week of 13 days and which falls here exactly on the day XIII. And the same Chuen sign is repeated in the second group as the first part of sign 6, the second part of which is illegible. 8 is the sign of A and 1 is effaced. Pages 15b--16b. I 13 I 31 VI 8 I 13 I Ik Manik Eb Caban Ik. That is 4 × 65 = 260 days. Hence the sign of Ik repeated at the bottom, as is usual in such cases, is superfluous. The Tonalamatl contains 4 figures, of which 1 and 2 form one pair and 3 and 4 another. As on page 15a, the pair at the left are falling down and also have leaves about them. They are god B, who holds a Kan sign in his hand, and a woman, whose eyes are closed and who holds the sign of death before her breast. B is falling down in a similar fashion in Cort. 17. Hieroglyphs 1-8 belong to this pair. Of these, 1, 5 and 8 and also 7 refer to death, 3 with the determinative sign, 4, added (which is the sign _q_ with a Ben-Ik), refers to B, while signs 2 and 6 belonging to god D, who occurred in the preceding Tonalamatl, should be noted. The pair at the right on the other hand is _seated_, the woman apparently on the curved handle of a vessel. The head-ornament and hieroglyph of the female figure prove that she is the serpent deity H, while the male figure is the rare black deity M, whom we find again with his sign on page 43a for example; he holds a bone in his hand. Hieroglyphs 9 and 13 agree. The lower part of these hieroglyphs is the fist with the thumb unfolded, the sign at the top seeming to be merely an empty outline (Muluc?) and thus, like 1 and 5 of the preceding group, they seem to refer to a sacrifice offered to the death-god. 10 and 14 are again, strange to say, like 2 and 6 of the preceding group, the sign of D. 11 is the hieroglyph of H, who is represented below as feminine, and that 12 is a complement of 11 is proved by the upper part of this uncommon hieroglyph, which corresponds to the object in H's hand, and which is repeated on page 18a with the same figure; compare also page 8b. 15 is surely the hieroglyph of M, who is pictured below, as in the Tro. 2a and 22*a where the same M appears with the same hieroglyph, and to him belongs in 16 the sign _r_, which I am inclined to consider the week of 13 days, and which here, as on 14c, ends a section of 13 days. Page 15c. III III 12 II 14 III Lamat Ix Ahau Cimi Eb Ezanab Kan Oc Cib Ik. This is a Tonalamatl of ten parts, the days are to be read in the following order:--Lamat, Ix, Ahau, Cimi, etc. There are two figures, A probably conceived as feminine and D with the same head-ornament as on page 10; both hold in their hands a Kin = sun. Hieroglyphs 2 and 6 are also the Kin sign, while 1 and 5 have the closed eye of A, but differ in their secondary parts, the sign suggesting the south being a suffix in 1 and a superfix in 5; 1, however, has an affix, while 5 has as a prefix a sign differing from the affix in 1. 3 and 4 are the signs of A, 7 that of D, next to which in 8 one would expect to see an Ahau, but instead of this there is again the sign of H (borrowed from page 15b?). This seems to end the subject of coition; now, in natural course, follows the subject of pregnancy, to which I believe the following Tonalamatl is exclusively devoted. Page 16a. Kan 21 31 Cib Lamat Ahau Eb. There are no red numerals, hence the Tonalamatl seems to apply to any one of the initial week days. Two women are portrayed, both of whom are stretching a hand forward and upward. There are 8 hieroglyphs of which, however, the top row is almost entirely obliterated; 3 and 7 in the lower row are just alike, being the usual sign for woman. There is a decided contrast between the two figures, which might suggest barrenness and fruitfulness. Observation of their physical differences would give us that idea. Furthermore, the first carries on her back an unfamiliar head, perhaps A's, while the second has the Ahau, Imix and Kan signs, from which plants seem to be sprouting. The first is represented in the fourth hieroglyph by the sign _c_, which is closely allied to the death deities, while the second woman is denoted by hieroglyph 8 which is the sign of the deity E, the grain-god. Pages 16a--17a. In the following I will group together all the pages from page 16-23 as follows:--First, I shall discuss the top thirds, then the middle and lastly the lower thirds. The sense, however, often seems to require that the first third should connect with the second, and the second with the third; but I find it impossible to determine exactly the intended order. On pages 16a-17a, we find for the first time in this manuscript not a Tonalamatl, but in its stead all the twenty days arranged in four columns, each of which ends with one of the regents of the year:-- Men Ahau Chicchan Oc Cib Imix Cimi Chuen Caban Ik Manik Eb Ezanab Akbal Lamat Ben Cauac Kan Muluc Ix. This seems to establish the fact that the day of its birth was of importance to a new-born child. Between each column and the next there is a picture and above each picture four hieroglyphs, which, however, are mostly destroyed, so that much of the meaning of this passage is lost to us. The first is an old man walking, who beyond doubt is N, the Uayeyab god, with a staff in his hand and the signs Imix and Kan on his back. He is looking upward and is also pointing upward with his right hand. Of his hieroglyphs only enough of the fourth is visible to enable us to recognize in it the regular sign of N, 5 Zac. The second picture is again an old man walking with a stick, he is baldheaded and hence is probably also N, as on page 12c. His hieroglyph might be the fourth of those written above him, the other three are entirely unrecognizable. He has a carrying-frame on his back, but it is uncertain whether he is carrying anything upon it. The third figure is a woman who is pointing upward with one hand and with the other holding the bundle on her back, which I am unable to explain (does it refer to the 14th Uinal--the end of pregnancy?) and from which rises an object resembling a flame. Her sign is in the fourth place and _q_ is in the third. 1 and 2 are not legible and perhaps may be supplemented by the third picture on page 19c. Finally, the fourth figure is F, who is sitting and has a Cimi sign on his back. His monogram is the second of the hieroglyphs above him, the third is very appropriately _b_ and the other two are not very clear to me. The first two pictures might designate a male birth, the first indicating wealth and the second poverty, the third might denote a female birth and the fourth a still birth. But who can positively assert this! Pages 18a--19a. VIII 12 VII 12 VI 9 II 10 XII 9 VIII Ik Ix Cimi Ezanab Oc. This is a Tonalamatl of five parts with 20 hieroglyphs, which unfortunately are so much injured that no signs comprehending the whole can be distinguished. There are five women in a sitting attitude. The first woman corresponds exactly to the third figure on page 15b. She is sitting on a bench, the same implement is in her hand and there is also a serpent on her head, for which reason she likewise reminds us of H. The third hieroglyph is hers, and the 4th sign is an Ahau. The second woman holds in her hand the Kin sign; above it is the Yax sign and above this a little cross between two dots (the numeral 18?). Compare pages 18c, 19c and 27b, and in the second part, 46b and 50c. I shall venture no opinion regarding the hieroglyphs. The third woman with the copal pouch hanging from her neck has nothing in her hand. She is pointing upward with her right hand. Her hair seems to be wound in the shape of an 8 in horizontal position and above her is a sign denoting the union of two parts. The hieroglyphs are entirely destroyed. Does this represent the birth of twins? The eyes of the fourth woman are closed, she is pointing forward with her hand and there is a bird on her head. Nothing is left of the hieroglyphs. Finally, the fifth is distinguished by a large nose-peg, which, as on 12b, resembles a flower. Her hand is extended forward. The fourth of the hieroglyphs above her is her sign. There is nothing to be said regarding the three others. Are these five women engaged here in presenting their thankofferings and prayers of thanksgiving for the birth which has taken place? Pages 19a--21a. XI 13 XI 13 XI 13 XI 13 XI 13 XI Ahau Chicchan Oc Men Ahau. Instead of Men the Manuscript has incorrectly Eb. Ahau in the fifth place is superfluous, since we have here a Tonalamatl divided into four equal parts. The hieroglyphs are so nearly obliterated that we can no longer distinguish a common sign. There were in all six signs for the first picture, of which the first two are above the day-signs, while the figures from the second to the fifth have only four signs each, as follows:-- 1 2 5 7 8 11 12 15 16 19 20 3 4 6 9 10 13 14 17 18 21 22. All that can be distinguished here is that the 4th and 13th have the same cross _b_ and that 6 and 10 probably contain the same head. Each of the five pictures contains a woman sitting. In the first representation she sits opposite a male figure, who bends down to her with his bird-head, which we have already seen on page 13c. In the other four pictures the woman is holding the figure of a god on her lap. I do not recognize the god in the first picture on page 20. In the second and third pictures he is related to A or the Moan and the first figure on page 21 may represent the god D. These can only be new-born children represented by the gods under whose signs they were born. It should also be noted that the second woman on page 20 has a serpent on her head and the third a bird. The bird's head resembles that on page 16c. Pages 21a--22a. The Cimi and Eb of the second column have changed places in the Manuscript. Instead of the X there is an erroneous 2 and there is no initial VII. VII VII 3 X 2 XII 7 VI 9 II 3 V 2 VII Oc Ahau Cib Cimi Ik Eb Lamat Ezanab Ix Kan. We have here a Tonalamatl consisting of 10 × 26 days, and the 26 days are subdivided into six parts. I have just assumed that the 2 is wrong and the initial VII is wanting over the first column, yet the 2 followed by the laterally elongated head _q_ might here, perhaps, be explained in some manner as the sign of the day VII Oc. Apart from this sign which occupies an entirely exceptional position, we have here 24 hieroglyphs, _i.e._, 4 for each of the six groups. The fourth sign in the first five groups is in each case a Chuen combined with the cross _b_ and the suffix, which seems to be a knife, and also with a numeral, which, however, is not recognizable in the first group; in the second it is a 3, in the third a 7, in the fourth a 5 and in the fifth a 3. What can these numbers mean? 3 + 7 + 5 + 3 = 18, and Chuen with the meaning of 20 (especially in the inscriptions) would be 18 × 20 = 360. In the fourth place of the sixth group there is a compound character, the main part of which (top, right) seems to be the sign for the thirteenth month, Mac, and which may also, as we shall see on page 24, denote the entire Tonalamatl. It is again compounded with a Chuen, an uplifted arm and a kind of suffix, and hence might denote the end of a Tonalamatl. The remaining 18 signs are in the main destroyed. In the second of the fourth group we recognize the lock of hair denoting a woman, in the third of the second group the superfix suggesting the south, which we find above the Cimi sign, for example on page 13b. Lastly, the other third signs are in the third group Imix-Kan, in the fourth group the head _q_, in the fifth the bird c and in the sixth a Manik sign with prefix and superfix resembling the sign _i_; in a few places (24, 39a, 53a, 56b, 58b, 61a, 61c, 68c) the prefix might have the meaning of 20. Since the intention was to close this section on the next page, the space had to be used as economically as possible, and instead of the six pictures to be expected, there is only one and that is the first. It is a woman in whom I observe nothing characteristic except that she has a kind of cloak, which has fallen down over the lower part of her body, and who therefore remains unexplained. Pages 22a--23a. II II II II 2 IV 8 XII 7 VI 10 III 12 II Men Cib Caban Ezanab Chuen Eb Ben Ix Manik Lamat Muluc Oc Akbal Kan Chicchan Cimi The Tonalamatl is no doubt to be read in this way after the correction of a few inaccuracies in the Manuscript. The 20 days, all of which occur again here as on pages 16a-17a, should be read from the right top to the left bottom, since they form but one series. As a matter of fact Ezanab is distant 19 days from the future Caban, but 39 days distant from the desired weekday of the same name (see my "Erläuterungen," p. 24). Thus we have here a period of 20 × 39 days = 780, _i.e._, a three-fold Tonalamatl. The three Tonalamatls represented on the pages between the preceding passage (pages 16a-17a), where all the 20 days appear, and this, are of three _different_ kinds (5 × 52, 4 × 65, and 10 × 26). This in itself is very remarkable. Furthermore a fourth kind of Tonalamatl seems to be introduced here, which embraces, as it were, these three Tonalamatls. The hieroglyphs, which are mostly destroyed, were arranged in groups of four for each subdivision, in the following order:-- II II II II 1 2 5 9 13 17 3 4 6 10 14 18 7 11 15 19 8 12 16 20. Of the above the third hieroglyph of each group, _i.e._, 7, 11, 15, 19 (probably also 3) is always the same and is the sign of D, the moon and night-god. In detail we should expect to find five pictures here, but owing to lack of space only the first of these is given. It represents a deity with a Kan sign in its hand and a serpent on its head, who is probably E, and he is falling down here in exactly the same manner as the four deities on page 15 at the beginning of this section. Now, which were the other four deities? Signs 8, 12, 20 refer to A, H and C. 16 is the laterally elongated head _q_, to which Seler is inclined to refer the day Men, and Schellhas an undetermined deity I. On account of its frequency this sign must have besides a more general significance. In addition, however, we have in 14 and 18 the signs of F and B. 6 is uncertain, 10 is probably C, and the top row is entirely illegible. If to these deities is added the D repeated five times in the third row, it will be seen that all the important gods are grouped together here on the last page of this section. Pages 16b--17b. I will now attempt (for it cannot be more than an attempt) to separate into three parts, according to their contents, the middle and lowest thirds of pages 16 to 23. The first part, 16b to 18b and 16c to 20c, contains six Tonalamatls with pictures of women, each of whom carries on her back the figure or symbol of a deity. This deity can hardly be any other than the one to which the horoscope of the child especially refers. The first of these Tonalamatls, on pages 16b-17b, runs as follows:-- Muluc 13 4 35 (or 20 15) Imix Ben Chicchan Caban. The red numerals are wanting and were probably forgotten. The hieroglyphs stand thus:-- 1 2 5 6 9 13 3 4 7 8 10 14 11 15 12 16. Of these 3, 7, 11 and 15 are the sign for women, 2, 6, 10 and 14 are likewise all the same sign, which is repeated in the same places on pages 17c to 18c. I do not understand its meaning; it may have reference merely to the carrying-frame. Instead of the four women, whom we should expect to find here, only the first two are portrayed. The first carries B, whose sign is the first hieroglyph, while the fourth hieroglyph is the sign _q_. The second woman carries A to whom hieroglyphs 5 and 8 refer. The third woman would have carried D, which is plainly proved by hieroglyphs 9 and 12, and the fourth, F, as follows from sign 13 and probably also from 16 (_q_). Pages 17b--18b. Eb 11 7 6 16 8 4. Kan Cib Lamat Ahau. Here again there are no red numerals. The 24 hieroglyphs of the six divisions stand thus:-- 1 2 5 9 13 14 17 18 21 22 3 4 6 10 15 16 19 20 23 24. 7 11 8 12 Again, six women should be portrayed here, but there are only four; the second and third are wanting. The signs for the women are given in 3, 7, 11, 15, 19 and 23, but in 15 and 19 the prefix is different from that of the rest. As from here on the women repeatedly carry a bird, the signs for this are 2, 6, 10, 14, 18 and 22, which are the symbol of a rising bird, as in the sign of the 15th Uinal (Moan), which in my opinion generally coincides with the 13th month of 28 days. The women pictured here have nothing in their hands, which they hold stretched forward, as is usually the case in this section. The first woman carries a vulture on her head. Compare 8a. In regard to it see also Schellhas, "Göttergestalten," p. 31. The hieroglyph of the vulture, which we find repeated on page 17c, 24, 37b, 46, 50, 65, is here hieroglyph 1, usually regarded as the sign of the bat deity, and near it in 4 is _q_. The second woman would have carried the black deity L (hieroglyph 5), to which _q_ is added in 8. The third would have had the dog, _i.e._, the lightning dog, which we find in hieroglyph 9 and in the month sign Kankin; an _a_ is added to them in 12. The fourth woman carries A, as is proved by his signs in 13 and 16. The fifth carries nothing; according to the hieroglyphs 17 and 20 she ought to carry D. Lastly the sixth carries the Moan as is proved by signs 21 and 24. Pages 16c--17c. Muluc 8 13 13 13 8 10 Ix Cauac Kan Muluc. This is a Tonalamatl of 4 × 65 days. The Muluc at the bottom is, therefore, superfluous. I have been obliged to correct the 12 in the last column of the Manuscript by changing it into a 10. The red numerals are again wanting. This passage admirably continues the one in the preceding Tonalamatl containing the women carrying birds, and is also divided into six parts. The hieroglyphs stand thus:-- 1 2 5 6 9 10 13 17 21 3 4 7 8 11 12 14 18 22 15 19 23 16 20 24. Signs 3, 7, 11, 14, 19 and 23 (14 and 15 have changed places) denote women. Of the six women only the first three are here portrayed. The first carries the Moan with which signs 1, 2 and 4 agree perfectly. The second and third carry two birds, which may be parrots of a different species. They are very seldom represented elsewhere and hence their hieroglyphs, 5 and 9, with the added determinative 10 are unfamiliar. In 8 and 12 the well-known determinatives _a_ and _c_ are added. Judging by sign 13 the fourth woman would have carried the same vulture, which we see in the middle section of this page; 15 and 16 are again signs _c_ and _q_. The fifth woman would have carried an unknown bird of prey, the signs of which are 17 and 18, and 18=10; 20 is again _q_, but with a superfix different from that in 16. Finally the sixth woman, like the third in 17b, seems to have carried the dog, as is proved by sign 21, but in 22 the symbol of a bird is again added. This passage ends in 24 with the well-known Imix-Kan. Pages 17c--18c. IV 15 VI 33 XIII 4 IV Ahau Eb Kan Cib Lamat. Here we again find the regular red numerals (Roman in my transcription of the text), which were wanting in the last three Tonalamatls. That they were not added until after the black script and drawings were completed, is evident in several passages of our Manuscript and also in this one, where they have been faintly indicated in black by the scribe (or corrector). The absence of red numbers in the passages 17b-18b and 16c-17c is an evidence that I was right in proceeding directly from the former to the latter. Of the 12 hieroglyphs, 2, 6 and 10 have again the form which we found on pages 16b-17b, and which seems to refer to a carrying-frame; compare, however, the explanation of pages 25-28 below. The women themselves are designated by hieroglyphs 3, 8 and 12. The first woman carries the god A and hieroglyphs 1 and 4 are his regular signs. The second woman has on her back a Kin sign, above that a Yax, and this combination overtopped by a cross between two dots also forms hieroglyph 5; compare the upper section of the same page. That this hieroglyph is nothing else than a designation of god D follows from hieroglyph 7. Finally the fourth woman carries a figure, which has a Moan sign for a head and to which hieroglyphs 9 and 11 certainly refer. Pages 18c--19c. XIII 32 VI 20 XIII Ahau Eb Kan Cib Lamat. The first woman carries the god A, who is denoted by hieroglyphs 4 and 1, though somewhat irregularly by the latter. 2 is the carrying-frame and 3 the woman herself. The second woman has again the Yax-Kin sign on her back as in the preceding Tonalamatl, and hieroglyph 5 is also a combination of these signs, but here in 7 we find, not the sign of D, but that of E, to which also the Imix-Kan in 8 corresponds. 6 is again the carrying-frame, though, as is also the case in 2, more indistinctly drawn than in the earlier Tonalamatls. Pages 19c--20c. XIII 11 XI 11 IX 11 VII 10 IV 9 XIII Ahau Eb Kan Cib Lamat. This is a Tonalamatl divided into five parts, to which 20 hieroglyphs belong. The hieroglyphs are in the following order:-- 1 2 5 6 9 10 13 14 17 18 3 4 7 8 11 12 15 16 19 20. At places 2, 7 (6 and 7 have changed places), 10, 14 and 18 we find again the sign which we think means a carrying-frame, while signs 3, 6, 11, 15 and 19 are those of the five women. The first carries a figure with a Moan head and agreeing with this is the second death-god F in hieroglyph 1 and his determinative in 4. The second woman, who is seated, carries the same object regarding which I am still uncertain, which is carried by the standing woman on page 17a. This object is denoted by hieroglyph 5 (_w_). Its determinative is probably 8. It may perhaps be a step in the right direction to point out that this sign suggests the god K. The third, like the first, has a figure with a Moan head, with which a female form of A in 12 and hieroglyph 9 accord. The fourth woman carries the maize deity E. 13 is his sign and the food hieroglyphs, Imix-Kan in 16, agree with it. The fifth woman seems to carry the somewhat indistinct form of D, if this may be inferred from the Ahau of the 17th sign. 20 is the universal sign a. This ends the six Tonalamatls, which are represented in what I have called the section of the burden-bearing women. Five other Tonalamatls follow, which again suggest the idea of conception, which we met once before on pages 13c-14c. Page 19b. X 29 XIII 23 X Ik Ix Cimi Ezanab Oc The most frequent sign in the five Tonalamatls, which I have grouped together, is the cross _b_, which plays the most important part in all the Tonalamatls, excepting the third, which differs from the rest also in other respects. It is essentially the sign for union, referring in the case of the stars to their conjunction and here to sexual union. In this Tonalamatl we see the cross in hieroglyphs 1 and 5, the sign for woman in 2 and 6, and their determinatives in 3 and 7. The first woman has a deity facing her who is devoid of all characteristic marks, and sign 4 is also nothing but the universal a. The second woman whose eyes are closed, sits facing A, whose hieroglyph is in 8. Pages 19b--20b. VI 28 VIII 24 VI Cib Lamat Ahau Eb Kan. The arrangement of this Tonalamatl is very similar to that of the preceding. Hieroglyphs 1 and 5 are again the cross, and 2 and 6 the signs for woman. The first picture is wanting; hieroglyph 3 with the number 7 as a prefix denotes a deity with whom I am not familiar. The same sign is found on page 50, left, middle; in 4 the usual head _q_ is added. Beside the woman in the second group--not facing her--is the serpent deity H, again, as on pages 11c and 12b, with the nose-peg resembling a flower. His sign is 7 to which in 8 the familiar Ahau is again added. Page 20b. II 20 IX 19 II 13 II Cauac Chuen Akbal Men Manik. The hieroglyphs stand thus:-- 1 2 5 9 3 4 6 10 7 11 8 12. The subject now passes into the province of astronomy. This is already proved by sign 1, which represents the clouds, between which the sun or moon is usually pictured; the sun is probably omitted here merely owing to limited space. Sign 3 suggests the storm-god K (compare pages 7a and 47 left) to which in 2 the Ahau might be appropriately added, inasmuch as it rules the year here under consideration as on pages 25b to 26c. On account of the Ben-Ik sign I see in 4 one of the months of 28 days as a more exact determination of time. Below the Ben-Ik a head is represented with eyes apparently closed, and this head is repeated in 6 and 10, though, probably for lack of space, without the Ben-Ik. In each of the three places a sign is used as an affix which might readily be the year sign, contracted laterally. The two similar hieroglyphs 5 and 9, which have the following form, are especially worthy of consideration:-- [Illustration] The part on the right recalls by its trisection the sign _r_, which I regard as the week of 13 days and, in fact, the interval between the two hieroglyphs is 13 days. On the left is the inverted figure of a person in a squatting attitude, the head surrounded by stars as on pages 57b and 58b and a sign on the back which may be a suggestion of the sun-glyph. In this figure, which occurs also in the Tro-Cort. and in the inscriptions, I see the planet Mercury and I believe that that planet's retrogression (which lasts 17-18 days) or disappearance into the light of the sun during this week, is the subject of this passage. 7 and 8 are the sign for D with the usual Ahau, and 11 and 12 are the hieroglyphs of the death-god A. Instead of three pictures there is only one here, viz:--a woman with nose-peg, sitting on a mat and apparently waiting for something. We also find figures sitting on mats elsewhere, for example on pages 7b and 68b. Page 21b. VII VII 7 I 7 VIII 7 II 5 VII Oc Ahau Cib Cimi Ik Eb Lamat Ezanab Ix Kan. This is also a Tonalamatl of 10 parts (10 × 26). The first column should be read first from top to bottom and then the second. The days are exactly the same as on page 21a, and here too Cimi and Eb have changed places. The hieroglyphs run thus:-- 1 5 6 9 13 2 7 8 10 14 3 11 15 4 12 16. The signs forming the hieroglyphs into groups are, in addition to the cross in 2, 6, 10 and 14, the heads in 1, 5, 9 and 13 with an Akbal sign (indistinct in 9) which, by the lock of hair in 5, 9 and 13, refer to a woman. This lock of hair is replaced by a hand in 1. Sign 3, with which _m_ in 4 is associated as a determinative, shows that the first group ought to have a picture of the black god L grouped with a female figure. The second group is the only one with a picture. On the right there is a female figure, which, judging by the headdress, we have already met on page 19a. Opposite her sits the dog which we saw on page 13c. Here (in sign 7), as on page 13c, the hieroglyph of the dog is combined with a Cimi sign, and this hieroglyph is repeated in 8 with the sign _c_, which is so closely allied to Cimi. For the third group the god A should have been represented with the woman, as is proved by sign 11 so peculiarly combined with _r_ as a superfix. To this hieroglyph _a_ is added, doubtless referring to the good days, as if merely to fill space. The hieroglyphs of the fourth group do not, I think, convey a clear idea as to which deity belongs here. His sign is 15, which is compounded of Manik and Chuen with a superfix, nor does the Cimi added in 16 shed light on the subject. As for 15 we have already found it on page 13c with the prefixed 4, which I find prefixed in this way in at least 12 different signs. Pages 21c--22c. Caban 5 21 16 10 Muluc Imix Ben Chicchan. This is a Tonalamatl of five parts in which the red numerals are wanting. The hieroglyphs are in the following order:-- 1 2 5 6 9 11 13 3 4 7 8 10 12 14 15 16. Among these are hieroglyphs which are common to all the groups:--the cross in 1, 5 and 9 and the woman in 3, 7 and 15. In 13 this cross is replaced by another sign, perhaps that for the year of 360 days, and in 12 the sign for woman is replaced by the universal a. Each of the three pictures contains a woman facing a deity. I will consider first the second picture in which H is the deity, as is proved by hieroglyph 6 to which an Imix is added in 8, with the uplifted arm prefixed as in 10c and 13a. Between the first and third pictures there is some confusion. The first is D, for while his type inclines more to that of N, the other old god of the Maya Olympus, comparison with 23c clearly shows that D is intended here. But the year-sign on his head also suggests in some measure the Uayeyab god N and moreover this sign does not belong to D and only occurs again with him on page 23c. Further, there is no hieroglyph at all for D and instead we find in 2, 5 Zac, the regular sign of N. Also sign 4 fits N better than it does D. Furthermore this passage relates to the day Ik, which might very well be the last day of the year. On the other hand the third picture contains, unquestionably, the figure of N. I look for his sign in the 11th hieroglyph, which is the head of an old man with a prefixed 4, referring to the four different forms of N in the Kan, Muluc, Ix and Cauac years. The Ahau in 12, however, does not fit N, but D. This confusion can only be adjusted by transferring D from the first group to the third and also, perhaps, the sign of the woman in 3, which applies to all the three groups, and by transferring to the first group N and the 11th sign of the third group. The fourth group has no picture. It should have, as hieroglyph 14 shows, the god F, who represents death by violence in human sacrifice and the chase. The hieroglyph Cimi in the 16th place is a suitable sign for this deity. Pages 22c--23c. II 10 XII 12 XI 9 VII 6 XIII 7 VII 8 II Oc Ik Ix Cimi Ezanab. The hieroglyphs are arranged in the following order:-- 1 2 5 6 9 13 14 17 18 21 22 3 4 7 8 10 15 16 19 20 23 24. 11 12 This Tonalamatl, the fifth and last of this section, presents much that is irregular and puzzling. It can hardly be said that there are comprehensive hieroglyphs here, forming the heading of the six groups. The sign for woman occurs only in 2, 8 and 24, and the cross _b_ only in 14 and 18, but it is sufficient to make it clear that here, too, connection with a woman is the principal theme. Let us pass, therefore, directly to the single groups. The first group contains A and a woman. The god, however, is not facing the woman but sits beside her. The Cimi sign in 1, the familiar _c_ in 3 and the unknown sign in 4 (=6) hardly explain this particular proceeding. The second group contains two persons who sit facing each other, but the representation is so obscure and peculiar that it is difficult to determine which is the male figure and which the female. The hair of the person sitting on the right stands up in a manner not found elsewhere. It forms a figure similar to that which is issuing from the mouth of the dog on pages 13c and 21b. The Cimi sign in 5 and the sign _c_ in 7 are familiar, but the infrequent 6=4 remains a puzzle. Uncertainty regarding the third group is increased by the fact that there is no picture belonging to it. The well-known signs, 10 (Cimi) and 12 (_q_) afford no explanation, nor does the head with the uplifted arm in 11, which we find with the same hieroglyph on pages 8a and 36a. The most puzzling is the 9th sign, which is composed of two crouching persons leaning back to back, and who also appear in the astronomical sections of the Manuscript on page 68a, not merely in the form of a hieroglyph, but also carried out in a picture. In my article on the Maya chronology published in the Zeitschrift für Ethnologie of the year 1891, I attempted to explain this Janus picture as meaning the change of the year, but that interpretation would make no sense here. The fourth group contains the woman opposite D, who is clad in the gala mantle and has on his head a bird and apparently the sign for a year, and is designated by the Ahau in 16, while Imix-Kan in 13, _b_ in 14 and _a_ in 15 are rather meaningless. The fifth group represents the woman united with A, who is designated by the Cimi sign in 17. 18 with its _b_ and 19 with its _q_ display little that is characteristic, _r_ in 20, which I think is the sign for the week of 13 days, invites further study. The sixth picture, which is the last, is very peculiar; it represents three women sitting side by side denoting perhaps the virgins who still remain. Sign 21 as Imix-Kan, 23 as _a_ and 24 as sign of femininity supply nothing in the way of explanation. As 6, 9 and 20 are the characteristic signs in the preceding groups, so here the characteristic sign is 22--an open hand holding the day Ben--which perhaps designates these virgins by referring to the house in which they are held fast by the hand. Cf. Tro. 23* d. Now of the entire woman section closing with page 23 only the two Tonalamatls on pages 22b-23b remain. These Tonalamatls again display very many peculiarities and seem to be but loosely connected with the five Tonalamatls last discussed. Page 22b. III 13 III 13 III 13 III 13 III Akbal Men Manik Cauac Chuen. This is a regular Tonalamatl, in which the 52 days are divided into four equal parts. The hieroglyphs are in the following order:-- 1 2 5 6 9 10 13 3 4 7 8 11 12 14 15 16. An Ahau is added here as the 17th sign, which is very unusual. We find elements here forming the hieroglyphs into groups in three different ways. 1. The signs 1, 5, 9 and 13 designate the four cardinal points as they so often stand together in this Manuscript in the order of East, North, West and South, _i.e._, in the sequence of the annual and not of the diurnal course of the sun. 2. The hieroglyphs 2, 6, 10 and 14 are all alike and are the head with the Akbal eye, which in 6 is closed. 3. The three persons pictured here all carry a Kan sign in their hands, probably as the offering they have received. Similarly we found the Kan sign held in the hand twice on page 16b. The first picture is B; his sign is the third with the _q_ in 4 as a determinative, which has above it a Ben-Ik sign. The second figure is a goddess with a serpent as head-ornament, though we find in the 7th sign, not her hieroglyph, but merely the one generally used to denote a woman. 8 is the usual _a_, which in my opinion is the sign for the _good_ days, to which also the Kan sign refers in the hands of the three personages. The third picture is that of the sun-god G; his hieroglyph is the 11th, to which in 12 is added the sign _q_, the sign for the bad days, with a superfix. The fourth picture is wanting. According to the 15th hieroglyph it should be the maize deity E. My theory that 16 is the sign for the week of 13 days is supported by the fact that the division into 4 × 13 days is the prevailing one. Page 23b. VIII 12 VII 12 VI 12 V 12 IV 12 III 5 VIII Kan Muluc Ix Cauac Lamat. This is a Tonalamatl of 4 × 65 days divided as evenly as possible into 5 × 12 + 5. The 5th day added after the 16th must be a mistake (suggested by the 5th day of the last section) for it is usually the first of the days, which is repeated superfluously. The hieroglyphs are:-- 1 2 7 11 15 19 23 3 4 8 12 16 20 24 5 6 9 13 17 21 25 10 14 18 22 26. Contrary to practice the first section has six hieroglyphs, and the other five but four each. As the characteristic hieroglyph we find in 1, 7, 11, 15, 19 and 23 a sign, the meaning of which is still undetermined and which we shall meet again on page 60, where it may refer to darkness. The groups have in common, furthermore, the head without an underjaw and the hair gathered up in a tuft in 4, 10, 14, 22 and 25 (in 18 perhaps represented by _q_, the evil days). We shall find this sign on pages 25, 28, 30-35, 42-44 and 65-69, repeated a number of times in many instances. I consider it the sign for fast-days. It appears also in the Tro-Cort. Associated with this sign here as in other passages are the four sacrifices derived from the animal kingdom:--a haunch of venison, a bird, an iguana and a fish. The fish is beyond doubt denoted by 3, the mammal by 21 and the bird by 13, and I believe, therefore, that the iguana with its spiny back is denoted by 9. We find the four animals, though in a different order, also on pages 29b-30b, 30b-31b and 40c-41c, as well as in Cort. 3-6 and 8, for example. They seem to have a certain reference also to the four cardinal points. Only the first of the six groups has a picture (I?). This represents a woman with a serpent in her hair, holding in her hand a dish containing a fish. The woman is denoted by the fifth hieroglyph and the fish by the third. The 6th sign is an Ahau, which is not quite intelligible here. Sign 2=5 Zac is very remarkable; it is the hieroglyph of the Uayeyab days and of their god N. If this Ahau refers, as it often does, to the god D, it suggests the relation between D and N, which follows from page 21c. According to the 8th sign, the second group might refer to the serpent deity H, and the 9th sign would not improperly denote the iguana. In the same way sign 12 in the third group probably denotes the storm-god K, with whom the bird in 13 accords very well. In the fourth group both the animal and the sign of fasting, belonging to it, are wanting, while 16 and 17 as well as the unlucky day in 18 clearly refer to the death-deity A. The fifth passage belongs, as sign 20 shows, to the maize deity E and to this is added the haunch of venison in 21. In the sixth group we recognize Imix-Kan, the sign for food derived from the vegetable kingdom. It stands beside the grain-deity E of the fifth group. I do not understand the vulture-head in 26. The five deities specified here may be compared with those on page 24, which are denoted by hieroglyphs 21-25 of the second column, though the agreement is not perfect. This ends the first great section of the Manuscript, in which Tonalamatls are represented in uninterrupted succession. We come now to a page which stands quite alone, being the first which treats of astronomy and which ends the front of the first part of the Manuscript. Page 24. In my article "Zur Entzifferung IV" I discussed this remarkable page in detail and in what follows I shall conform to that treatise, though omitting many things which since then have become the established possession of science, and shall endeavor to shed a still clearer light upon other points. This page presents in brief the subject which is more fully treated of on the front of the second part of the Manuscript (pages 46-60). The first problem it presents is to find periods in which the solar year (365 days) is brought into accord with the apparent Venus year (584 days). This takes place in a term of 2920 days = 8 × 365 = 5 × 584. Sequent to this is the still higher aim of bringing the Tonalamatl (260) into harmony with this period, which is accomplished in 37,960 days (= 146 × 260 = 104 × 365 = 65 × 584). The revolution of the moon (28), the ritual year (364 = 28 × 13) and the apparent revolution of Mercury (115) come in question as secondary matters. I will now give an approximate reproduction of the page:-- Hieroglyphs. 1 17 29 151,840 113,880 75,920 37,960 2 18 30 (4 × 37,960) (3 × 37,960) (2 × 37,960) (13 × 2920) 3 19 31 I Ahau I Ahau I Ahau I Ahau 4 20 32 185,120 68,900 33,280 9100 5 21 33 I Ahau I Ahau I Ahau I Ahau 6 22 34 35,040 32,120 29,200 26,280 7 23 35 (12 × 2920) (11 × 2920) (10 × 2920) (9 × 2920) 8 24 36 VI Ahau XI Ahau III Ahau VIII Ahau 9 25 37 23,360 20,440 17,520 14,600 10 26 38 (8 × 2920) (7 × 2920) (6 × 2920) (5 × 2920) 11 27 39 XIII Ahau V Ahau X Ahau II Ahau 12 28 40 13 11,680 8,760 5,840 2920 14 (4 × 2920) (3 × 2920) (2 × 2920) VII Ahau XII Ahau IV Ahau IX Ahau 15 16 2,200 1,366,560 1,364,360 IV Ahau I Ahau I Ahau 8 Cumhu 18 Kayab 18 Zip. First let me observe that I have restored the four large numbers at the top, which are almost entirely effaced, as follows:-- 1 15 10 5 1 16 10 5 1 6 16 8 14 0 0 0. 0 And furthermore, at the right, bottom, I have substituted the third month for the second of the Manuscript, which proceeding will be justified later on. The least difficult portion of the contents of this page is the first series consisting of 16 members, each being a multiple of 2920. It begins with the date I Ahau (which is always concealed in these series), regularly stops at the month day Ahau (since 2920 = 146 × 20), but necessarily advances in the week days by 8 days each (since 2920 = 224 × 13 + 8), until 37,960 is reached, when the day I Ahau again appears (since 37,960 = 146 × 260). According to my method of filling in the numbers, the top row of the page consists only of multiples of 37,960. On the other hand, the four numbers of the second row from the top are more difficult. They are, it is true, all divisible without remainder by 260, but otherwise they seem to be without rule, and they give one somewhat the impression of a subsidiary computation such as one might jot down on a slip of paper in the course of some important mathematical work. Nevertheless, the following remarkable results are obtained when the first and third and the second and fourth numbers are combined by addition or subtraction:-- 1) 185,120 + 33,280 = 218,400, which is just 600 years of 13 × 28 = 364 days, 280 Mars years of 780 days, 840 Tonalamatls of 260 days or 7800 months of 28 days. 2) 185,120 - 33,280 = 151,840, _i.e._, precisely the highest number of the top row, = 416 solar years of 365 days each or 260 Venus years of 584 days each, _i.e._, the product of the days of the Tonalamatl multiplied by the Venus years. We shall again find the 151,840 on page 51, and Seler ("Quetzalcoatl and Kukulcan," p. 400) finds this same period on a relief of Chichen Itza. 3) 68,900 + 9100 = 78,000, _i.e._, 100 Mars years or 300 Tonalamatls. The half of this number, or 39,000, we shall find again on pages 69-73 by computation; also the whole 78,000. 4) 68,900 - 9100 = 59,800, _i.e._, 520 Mercury years of 115 days, or 230 Tonalamatls, or five times the period of 11,960 days, in which these two periods are united. By computation again we find the 59,800 on page 58. This period of 11,960 days is, however, to the period of 37,960 in the proportion of 23:73, _i.e._, 23 × 520:73 × 520. 23 is the fifth part of the apparent Mercury year, as 73 is of the solar year. Let us now turn to the numbers, which form the bottom of my transcription, but only the left hand lower corner in the Manuscript. Here, in the latter, we find the following (with the correction already mentioned of the second to the third month):-- 2200 1,366,560 1,364,360 IV Ahau I Ahau I Ahau 8 Cumhu 18 Kayab 18 Zip. The first thing to be done is to arrange and fill out these numbers to suit our purpose. The 2200 is clearly nothing more than the difference between the two high numbers. We can therefore dispense with it. Further, we find by the usual computation, that the second number belongs to the first date and the third to the second. Hence the number corresponding to the third date is wanting from lack of space. This number can be calculated from that date; it is 1,352,400. It would suit this date equally well if the number were higher or lower by 18,980 or a multiple of 18,980; but it will be seen directly that it agrees with the other two numbers only at the value given above. Now, if we add to this passage the years in which the dates must lie, they are in the case of the date on the left, the year 9 Ix, in the case of the middle date, the year 3 Kan, and of that on the right hand, the year 10 Kan. Then if we arrange the three numbers with the dates and years belonging to them, according to the value of the first, this part of the page will run as follows:-- 1,352,400 1,364,360 1,366,560 I Ahau I Ahau IV Ahau 18 Zip 18 Kayab 8 Cumhu 10 Kan 3 Kan 9 Ix. Let us now consider the properties of the three numbers individually. 1) 1,352,400 = 28 × 48,300 and = 115 × 11,760, hence it is divisible by the month days of the year of 364 days and by the Mercury year. At all events this is the least important of the three numbers. 2) 1,364,360. This looks as if it referred particularly to the moon and to Mercury; to the latter since it is equal to 115 × 11,864, and to the former if we assume that the lunar revolution has been fixed at 29-2/3 days, in which case this number is exactly equal to 46,000 such lunations. If this last number be again divided by 115, the number of days required for a revolution of Mercury, the quotient is 400, which is a round number in the vigesimal system and which was therefore denoted by a single word, by Bák in the Maya (according to Stoll) and by Huna in the Cakchiquel (according to Seler). 1,364,360, therefore, is a Huna of lunar revolutions multiplied by the number of days in the Mercury period. Later on we shall find the lunar revolution fixed at 29-2/3 days. 3) 1,366,560. This is the most comprehensive number of the entire Manuscript, for it is divisible into each of the following periods:--Those of the Señores de la noche or Lords of the Cycle (9 × 151,840; this is, however, the first number of the top row), the Tonalamatls (260 × 5256), the old official years (360 × 3796), the solar years (365 × 3744), the Venus years (584 × 2340), the Mars years (780 × 1752), the Venus-solar periods (2920 × 468), the solar year-Tonalamatls (18,980 × 72), the Venus, solar, Tonalamatl periods (37,960 × 36), and the periods which are generally designated Ahau-Katuns (113,880 × 12). We have next to consider the intervals which elapse between the three dates. 1) From 1,352,400 to 1,364,360 is 11,960 days, which period we have already found once on this page by computation. 11,960, however, is equal to 104 × 115 and 46 × 260, _i.e._, the Mercury revolution and the Tonalamatl combined. 11,960 is again equal to 32 × 365 + 280, and from the year 10 Kan to 3 Kan it is actually 32 years, and from the date 18 Zip to 18 Kayab it is, in fact, 280 days. The day I Ahau must be common to both dates. 2) From 1,364,360 to 1,366,560 is 2200 days, as the Manuscript expressly states. 2200, however, is equal to 8 × 260+120, and the distance from the day I Ahau to IV Ahau is in fact exactly 120 days. Further 2200=6 × 365+10; from the year 3 Kan to 9 Ix it is 6 years and from the date 18 Kayab to 8 Cumhu it is 10 days. 3) From these two statements the third follows. The distance from 1,352,400 to 1,366,560 is 14,160. This contains first the 14040, in which both the Tonalamatl and the old official year of 360 days meet, and second 120, which is again the interval between I Ahau and IV Ahau. But 14,160 is also equal to 38 × 365 + 290, and the interval between 10 Kan and 9 Ix is of course 38 years, and from 18 Zip to 8 Cumhu it is 290 days. The numbers with which we have had to do here will again occupy our attention further on, especially the 2920 and the 37,960 on pages 46-50, the 11,960 and 115 on pages 51-58, and the 14,040 on page 73. That these computations are not confined to the Dresden Manuscript is proved by the cross of Palenque, where we find in signs A B 16 precisely the date I Ahau 18 Zotz, a Tonalamatl before 18 Kayab, in D 1 C 2 exactly the difference 2200 and in D 3 C 4 the date IV Ahau 8 Cumhu. This is in favor of the theory that our Manuscript did not originate far from Palenque. Now, the question finally arises as to what may, strictly speaking, be considered the significance of these numbers, dates and differences. In the first place, I would recall the fact that the dates of the monuments of Copan and Quirigua, which doubtless refer to present time, are in the neighborhood of 1,400,000. The high numbers of our Manuscript, so far as they are in question here, form first a group, which extends from about 1,200,000 to 1,280,000, and then there is a blank, and next a large group extending from about 1,350,000 to 1,480,000, then another blank and lastly a group extending from about 1,520,000 to 1,580,000. If we assume that our Manuscript belonged to about the same date as these inscriptions, then the three numbers discussed here would extend over a past period lying about 160-170 years back, when a new period of importance had begun probably dating from the immigration of the Aztecs into Mexico, which they placed in the first half of the 14th century (see "Weltall," Vol. 5. pp. 374-377). Now, however, the number 1,366,560 contains the statement that 3744 years ago (each year having 365 days) an event must have occurred, which can hardly be anything other (according to the belief of the Mayas) than the creation of mankind. Hence all the _historical_ dates of the Mayas were computed from this starting-point. But how did this event come to have the date IV Ahau 8 Cumhu? In my opinion this date is to be regarded only as the result of the far more important date I Ahau 18 Kayab, lying 2200 days earlier. Day 17, Ahau, belongs, without doubt, to the chief of the gods, and as the first week day it must have been especially sacred. The prophecies of the Tonalamatl preferably begin with the Ahau and with the I. The series on the page under discussion, constructed with the difference 2920 as a basis, begins with I Ahau, and the three series on pages 46-50 also have the same day as the zero point of departure. I Ahau is therefore the starting-point of the astronomical computations as IV Ahau is of the historical. Now, however, all the periods of 260 days end each time with I Ahau. Why is precisely this day chosen here, which is the 18th day of the month Kayab, therefore in the year 3 Kan, and lying 2200 days earlier than the historical date? Day 18 Kayab is our June 18th. In my treatise "Schildkröte und Schnecke in der Mayaliteratur" (1892), I have sought to prove that the tortoise served as symbol of the summer solstice, that the sign of Kayab was the head of a tortoise, and that probably the 18th of June was regarded as the longest day. The middle one of the three series on pages 46-50 begins with exactly this date, I Ahau 18 Kayab. But whence come the 2200 days? I will offer a suggestion which may serve until a better theory is propounded. Let us assume that each of the five principal planets had in succession regulated its time of revolution by this astronomical starting-point, thus:--sun 365, moon 356, Mercury 115, Venus 584, and Mars 780 days, these numbers added together give exactly 2200. It will scarcely excite surprise that I should set down the lunar year at 356 days (and not at the usual 354 days) for there are 12 × 29-2/3 lunations in a year and we thought we had already found this period on this page, while discussing the number 1,364,360; also on pages 51-58, in addition to the half lunar year of 177 days, we shall find one of 178 days. Were the planets therefore created 2200 days before the appearance of mankind? Jupiter and Saturn, of course, with their 397 and 380 days are probably not considered here, because their periods of revolution so nearly correspond to that of the sun, and on pages 51-60 they are also treated as of secondary importance. I confess I am quite unable to discover what may have happened 11,960 days before the creation of the stars--possibly the birth of one of the principal deities. Perhaps one of my fellow-students may succeed in finding an answer in one of the creation myths. We come now to the 40 hieroglyphs on the left half of the page. These are intended simply to familiarize the reader with those signs which are of importance in the calendrical-astronomical portions of the Manuscript. Since no phonetic system of writing existed, we cannot, of course, expect that the scribe should have explained these signs. Signs 1-4, which are mostly destroyed, can hardly denote anything other than the four quarters of the globe, at least we can still recognize in 4 the sign for the east, which has also the fourth place in pages 46-50. They stand thus together five times in the middle of the left side of pages 46-50, which pertain to this subject. 5 to 9 are the sign for Venus repeated 5 times, probably denoting the four parts of its revolution as on pages 46-50 and also the revolution as a whole. In connection with this first appearance of the Venus sign, I would mention that the same hieroglyph also occurs in the Tro-Cort., _e.g._, Cort. 25c, though this Manuscript contains little else that is astronomical, yet it also has the rectangular heavenly shields. 10. This is a well-known form of the Moan sign. In the Globus, Volume LXV, 1894, I sought to make it appear probable that the Moan also denoted the Pleiades, with whose disappearance and reappearance the beginning of the years seems to be connected. Likewise on page 50, where the 2920-period ends, the Venus and Moan signs appear at the top on the right-hand side. 11 and 12 are the same sign, being that of the 13th Uinal (Mac), with which 260 days of the year end, and hence this sign is also used as the sign of the Tonalamatl. The repetition seems to show, that not until the 73 Tonalamatls of the period of 18,980 days are doubled--thus obtaining the number 37,960 of such importance here--are the sun and Venus periods brought into unison (with the whole system). 13. The Kin sign (sun, day) with the superfix, which in all probability expresses conjunction, union, and which, in my opinion, we also see on page 51, combined with Kin and Imix, as the sign for 18,980 days, is used here after the two Tonalamatls to denote the doubling of this period. 14-18. If the preceding signs led us to the Venus-solar period and to the continuation of this subject on pages 46-50, these five hieroglyphs bring us to the Mercury-lunar period and later, on pages 51-58, which are devoted to the same period, we shall find a parallel especially on the last page. First comes 14, which, as has been acknowledged, is the sign for 20 × 360 = 7200 days. 15, a hand holding a rectangle divided by a cross into four parts, is, I believe, the sign for the period of 20 days augmented to 21 by the 1 in front of it. The much more distinct form of sign 16 on the middle of page 58 and also at the top of page 53, should be compared with the sign as given here. The top part is the familiar Ben-Ik sign denoting the 10th and 19th days, and the bottom is the sign of the 14th division of 20 days, which make up the year. Now, however, the 10th day, when it becomes the 19th of the next 20 days, is distant from the first 29 days. The prefix consists of two parts:--First two small circles joined by a zigzag line, which I think denotes the division of a day into halves; the sign would then equal 29½ days, _i.e._, very nearly the true lunar month. Second, of two vertical lines, which might denote a doubling. The whole would then be equal to 2 × 29½ = 59. I admit that this interpretation is very artificial and I should be very glad if a better explanation could be found. On the other hand the 17th hieroglyph becomes quite clear when it is compared with the parallel passage on page 58; it is 13 × 360 = 4680 days, a third of the remarkable period of 14,040 days. Thus we have Hieroglyph 14 = 7200 " 15 = 21 " 16 = 59 " 17 = 4680 ----- 11960, which is exactly the lunar-Mercury period. The sign Xul = conclusion, end, is fittingly added in 18 to the end of this period, as also on page 58. This sign is very common on pages 61 and 62 at the end of the long periods. From signs 19 and 20 we see that the four parts of the Venus year are also about to be treated of here, that is, the periods of 236, 90, 250 and 8 days respectively, which are discussed on pages 46-50. For 19 is the sign for Venus, and 20 is a hand with a knife as a superfix, which divides the Venus revolution. This hand appears 20 times in like manner on the pages mentioned above. Signs 21-25 represent five gods, who in all probability are N, F, H, the bat-god and A. These are the same signs which are repeated twice on the left-hand side of pages 46-50, both times at the beginning and end of the period of 236 days, that is, the period during which Venus is the morning star and which is under the dominion of the east. The fact that there is a 4 with N has reference to the four forms which this Uayeyab god assumes. Now we ought to expect a similar treatment of the periods of the planet, which are under the rule of the south, west and north, but there is no room for this. Instead, we find in 26, 27 and 28 three different signs plainly belonging together, the first of which is the day Caban, _i.e._, the earth; the second may be Muluc denoting rain and water; the third is Chuen (the ape) which fittingly denotes the north, for Chuen denotes the little bear, as I have proved in my treatise on the day-signs of the Mayas. The Chuen sign in 28 also has a prefix, which probably refers to the night-god D. I find exactly the same combination in signs 8 A and 8 B of the inscription on the Cross of Palenque, but I must leave to others the task of connecting 26 and 27 likewise with the north, which is very evident in 27 (Muluc). Sign 29 is entirely effaced. Nevertheless, I am positive that it represented the day IV Ahau, the beginning of Maya chronology, for 30 may still be identified as 8 Cumhu belonging to IV Ahau, and sign 31 is the same sign as 18, _i.e._, the sign Xul = the end, and denoting here the end of the long period. The comprehensive hieroglyphs, 29-31, stand here in the wrong place. A more suitable position for them would be before 19 or just after 35. For they are intended to specify the periods during which Venus is in the west and south, _i.e._, the time during which it is the evening star and the period of its inferior conjunction. Sign 32 is the black deity, L according to Schellhas, here denoting the west, and 33 is the Venus sign with the prefix denoting division. In the same way we find these two signs together on page 46 at the right in the middle series, where presumably the four Venus periods are specified in close succession. The black deity is also found on page 50 in the middle of the page in the beginning, at the end of a period of 250 days. On page 24 it has as a prefix the sign Imix with three rows of dots proceeding from it. Imix, however, among the Mayas and Aztecs (as Cipactli), under some circumstances often, and under others always, denotes the first of the 20 days. Hence this sign may mean:--here begins the Venus period of 250 days. 34-35. The sign for the south still remains to be found. Sign 35 is again the Venus hieroglyph. In 34 we should expect to find one of the five gods of the south, which are found on pages 46-50, _e.g._, the Moan, who is represented on page 47 as the regent of this cardinal point. But there is no figure of a god here, and in place of it we find set down here, as on page 47, middle, right-hand, an actual date as the beginning of this short southern period of only eight days. It is the date 10 Zip (third month), the month sign of which does indeed suggest a hieroglyph of the Moan. Now, if we recall that in hieroglyph 21 the god N is designated in exactly the same way by an actual date, viz:--4 Zac (11th month), then we see that the interval between 4 Zac and 10 Zip of the second year following, is exactly 236 + 90 + 250 = 576 days, and this corresponds exactly to the interval of time from the beginning of the period when Venus is in the east to the beginning of the period when she is in the south. If we knew in what years the morning star made its first appearance on February 4th and disappeared as the evening star on the 3d of September, we should make some progress in the comprehension of this subject, but not much, since these events fall approximately on the same dates after each period of 8 years. 36-40. The last five of the 40 signs appear in the same order again on pages 46-50, _one_ sign on each page, in the middle group of the right-hand half of the page at the beginning of the third line, but with this difference, that on page 24 each sign has the same prefix, which is wanting on pages 46-50, where a similar hieroglyph always _follows_. From their position on pages 46-50 it follows that these are hieroglyphs of five gods, each of whom belongs to a whole Venus year of 584 days. I am not very sure in regard to these gods. I prefer to call 36 K, 37 F, 38 E and 40 A. Sign 39 with the person crouching, I am obliged to leave entirely unsettled. We shall find this hieroglyph again, _e.g._, on pages 47 and 49 right, middle. Let it suffice that in these five signs we have a repetition of the Venus-solar period of 2920 days, with which we will end the discussion of this page. Only F and A have already been met with among the five gods denoted by hieroglyphs 21-25. Pages 25--28. As these four pages, which are the beginning of the back of the first part of the Manuscript, not only belong together, but also display a parallel arrangement of their separate parts, the corresponding parts will be considered together as a whole. There are seven of these parts on each page, viz:--the column of day-signs on the left hand; the top, middle and bottom pictures, and lastly the top, middle and bottom groups of hieroglyphs; but I will consider the pictures and hieroglyphs of the same section as belonging together. 1. The Columns of Day-Signs. On the left-hand side of each page two days are repeated 13 times. They are as follows:--On page 25 Eb and Ben, on page 26 Caban and Ezanab, on page 27 Ik and Akbal, and on page 28 Manik and Lamat. Cyrus Thomas first made the important discovery that these pages represent the transition from one year into the next, but held the erroneous opinion that the last two days of each of the four kinds of years were treated of on each page. While Seler, on the other hand, found that we have here to do with the last day of one year and the first of the following year, and that, therefore, Ben, Ezanab, Akbal and Lamat are the beginnings of the years and thus of the 20-day periods. The years, however, were always named after their second day (_i.e._, Kan, Muluc, Ix and Cauac years), since the New Year's Day was considered unlucky and it was the practice of the Mayas to conceal the real starting-point. These four pages, therefore, extend over 13 × 52 years, that is, over a period of 18,980 days, after which period all the calendar dates are repeated. A list of all these dates is given in "The Maya and Tzental Calendars" by William E. Gates (Cleveland, 1900). The transition from the Muluc to the Ix years is represented on page 25; from the Ix to the Cauac years on page 26; from the Cauac to the Kan years on page 27, and from the Kan to the Muluc years on page 28. The Ix years are represented first, because the beginning of the historical chronology lies in an Ix year (IV Ahau; 8 Cumhu). This section treats of ceremonies, especially of the setting up of the idols at the changing of the year, which I can pass over here since they have already been described by Diego de Landa and in our own day by Cyrus Thomas in his "Study of the Manuscript Troano," and elsewhere. 2. The Top Pictures. The principal representation on all the four pages is a priest, but disguised as an animal with the head of a beast of prey as a mask (always the same one) and also with a tail. He is pictured with the same three articles in each of the four representations, viz:--First, in his right hand, the staff of office with the hand at the top, which, according to Seler, "Mittel-Amerik. Musikinstrum.," p. 112, is the rattle-stick, second the incense-pouch, _i.e._, for copal, and third in his left hand a rattle, or, according to Schellhas, "Vergleichende Studien" (1880), a fan. There is one point, however, in which the first two pages differ from the other two; on the first two the priest is walking on dry land and on the second two through a stream of water. Was the city, to which this calendar especially refers, bordered in two directions by water, so that the road led across it? On all the four pages, however, the priest carries on his back a different deity, and I cannot find out by what rule these gods are connected with one another, or with the one which is represented below them, or with the years. On page 25 the god is B, on 26 he has the form of a jaguar (Ix), on 27 he is undoubtedly E, and on page 28 he is the god A, Cimi. Now to the left of the priest on each page there is one of the familiar Chuen bundles, such as are also frequently found in the the Tro-Cortesianus. Here, on pages 25-28, there are always three of these Chuen signs in a bunch. If Chuen really denotes the eighth day (which, of course, is only possible when Kan = 1), and at the same time the period of 8 days, then in this passage these three Chuen signs would properly designate the 24 days which elapse _before_ the last day of the year, which is the last day of the 18th month. In the same way we shall find the Chuen bundle appropriately given this meaning on pages 42c-45c. Likewise the simple Chuen sign at the top of page 52 seems to denote 8 days. But what do the Chuen bundles in the Tro-Cortesianus mean, some of which are much larger? In close proximity to these Chuen bundles we find numbers as follows:--on page 25 numbers 8 and 9, on 26 number 13, on 27 number 2 and on 28 number 13. I can offer no opinion, which would be even approximately acceptable in regard to the meaning of these numerals, but we shall discuss them later. 3. The Top Hieroglyphs. I shall discuss these glyphs in this place, although each group seems to relate not merely to the top picture, but to the whole page. There are 16 on each page, and arranged as follows:-- 1 2 9 10 3 4 11 12 5 6 13 14 7 8 15 16. Unfortunately, the writing at the top is obliterated, which makes it impossible to understand not merely this passage, but also those on all the rest of these pages. Of the 16 signs in the top line only one is legible, and that is the first on page 28. This is the usual cross _b_; as a comprehensive heading it perhaps occupied places 1 and 9 on each page, alternating with another sign in 2 and 10. In spite of this obliteration there are a few points which can be profitably discussed here. I would call attention first to signs 7 and 8 on page 25. The first seems to contain twice repeated the figure, which is thought to represent eagle feathers, and which we found on pages 10b and 13a, for example. As this double character is also used to change the 360-sign into a 7200-sign, so it may also combine the 52 years of this passage. The 8th sign on page 25 is the head with the tuft of hair and no underjaw, which I think refers to fast-days, such as might properly occur at the transition point of one long period to another. The sign for the year stands five times on the other three pages, which is in keeping with their contents. On page 26 it appears three times. This page treats of the transition of the Ix to the Cauac years. In the 6th place the Ix sign seems actually to be used as a prefix, in 7 the prefix is plainly the Kin-Cauac sign, just as on page 37a, and in 5 the prefix is probably Ezanab, the beginning-day of the Cauac years. At this last place the suffix is the same as that which we often see with the year sign on pages 13c-14c. On page 27, in the 7th place, the year sign has a prefix and a suffix, which seem to indicate that here it was intended to represent 365 as separated into 5 × 73 or 360 + 5. Lastly, on page 28 the 8th sign can be explained as meaning that the ritual year of 364 days is separated into 4 Bacab periods of 91 days each. Resembling the year sign in form, and placed near it on these pages, is the following sign:-- [Illustration] This sign frequently appears on pages 8b-9b, 16b-17b, 17c-20c. We find it with slight variations once on each of the four pages 25-28. It is the 6th on page 25; the 8th on 26; the 6th on 27; the 6th on 28. Its lower part, especially the (phallic?) sign added at the left, suggests the hieroglyphs of the Bacabs, as we find them on pages 52, 55, 56, etc.; they might refer to the separation of the ritual year of 364 days into 4 × 91 days. On the other hand it has been considered simply as the reproduction of the carrying-frame pictured below it (compare above under page 17c.) While the hieroglyphs, hitherto discussed, demonstrate the connection between the parts on the left of the four pages, two other signs prove the connection of the portions on the right. One of these looks like the Ik sign surrounded by a dotted circle; it occurs on page 25 as the 13th sign, on page 26 as the 15th, on page 27 as the 14th and on page 28 as the 15th. To this sign are prefixed successively the numbers 9, 7, 11 and 6. The second is unquestionably the hieroglyph for the numeral 20 or for the moon. It is effaced on page 25 and on pages 27 and 28 has a prefix, which on page 26 is used as a superfix. This sign is the 14th on page 25, the 16th on page 26, the 15th on page 27 and the 16th on page 28. The prefixed numbers are 7, 16, 5 and 6. The meaning of these two signs and that of the apparently irregular numbers is still a mystery. The latter will be discussed presently. The 4th sign on all the four pages seems to refer to a period like the one hitherto discussed. On page 26 the sign resembles that for the 13th Uinal (Mac) and hence appears to refer to the Tonalamatl, as in the first column on page 24. Above it is the sign for the south. The corresponding hieroglyphs of the other pages are obliterated, but strange to say the vestiges suggest that they too had _below_ them the sign for the south. Now the south and the Bacab of the south preside over the fourth quarter of the year from which ensues the transition to the new year in question here. Among the signs on the left side we should expect to find those of the gods to whom the expiring year belonged. On page 25 it ought to be B. Sign 5, however, though it can with difficulty be identified, points rather to god K. Sign 3 on page 26 corresponds better; this is the hieroglyph of the tiger already known to us, which is carried by the priest in the upper section of page 8a; here its prefix is the sign for the west. On page 27 we ought to see the grain-god E carried by the priest; his hieroglyph may be destroyed, but sign 5, which is Kan-Imix (food and drink) is his determinative. Finally the 5th sign on page 28 is, just as we should expect, the hieroglyph of A and, in addition, we find his determinative in 7. But what is to be said of the fact that the tiger appears again on page 28 in sign 3, and this time with the sign for the east? The Ahau on page 27, sign 16, refers to the god D of the middle section. There maybe some reference here to sacrifice, thus:--the 11th sign on page 25 is Kan-Imix, the 12th on page 27 is Kan, which is followed in the 13th sign on page 27 by another one with a Yax and a suggestion of a second Kan-Imix. Also the curious sign in the 8th place on page 27, which we have already discussed under page 8b, is used to denote the sacrifice on pages 18a and 15b. Here its position with reference to sign 6 is the same as on page 8b. On page 26 the prefix of sign 13, which is half destroyed, may be recognized as a serpent. Signs 12 and 15 on page 25 are unintelligible. Unfortunately the following signs are entirely effaced:--Sign 1 on pages 25, 26 and 27, as well as 2 on all the four pages, 3 on page 25, 9 and 10 on all the four pages, 11 on pages 26, 27 and 28, 12 on pages 26 and 28, 13 on page 28, 14 on pages 26 and 28, and 16 on page 27. 4. The Middle Pictures. On each page at the right there is a house, the back wall of which is always marked with the cross often met with. In front of the house with his back turned towards it, sits a deity. Each of the four deities has the front of his body covered with a gala mantle. Now we know that the god of the new year was set up before the house of the chieftain. On page 25 the god is K with his eyes apparently destroyed, and on page 26 it is B with a Kin sign on his head covering, hence designated here as a sun or day-god. On page 27 the god is D, and on page 28, A with the cross-bones on his robe, his own hieroglyph on his cheek, and the Akbal sign on his forehead. Only on the last page, therefore, and apparently by mistake, the god in the top picture is the same as in the middle picture. At the left of each page, _i.e._, opposite the house and the god, is a flaming altar, bearing the sign Ix equivalent to fire. The centre, between the gods and the altars, is occupied by vessels of which there are two on each of the first three pages and but one on the fourth; they contain food, without doubt intended for the sacrificial feast. On page 25 the lower vessel contains Kan (maize) and the upper probably a food prepared from Kan. Or are the spines on the back of the iguana indicated on this vessel? (Compare 40c and Cort. 8 and 12c). The contents of the lower vessel on page 26 are still unknown (birds?). The upper vessel contains a Kan, but the sign has a superfix, which corresponds to the sign for the west. On page 27 the lower vessel contains a fish and the upper the sign for the south. Lastly, the single vessel on page 28 contains the cross-bones (mammal?) and above them the Kan sign repeated three times. Finally here on the last three pages, we find some numbers, which are still undetermined; on page 26 there is a 7 with the lower vessel, and on page 27 with the upper vessel two dots with a cross between them (perhaps this may mean 20 - 2 = 18, which is used in place of the usual clumsy numeral?). On page 28 we see above the vessel a 6, and below it, in place of a second vessel, a double Chuen sign, as in the upper section of the page, therefore it can hardly be the Akbal sign resembling Chuen. 5. The Middle Hieroglyphs. On each page these signs consist of but _one_ line containing 5, 6, 3 and 3 glyphs respectively. The first of these signs in all of the four places is the same (_o_), which very suitably refers to the change in the year. The second sign is always the hieroglyph of the god represented in the middle section:--K on page 25, B as the sun-god on page 26, and D on page 27. The second sign on page 28, which is the head without an underjaw and with the prefixed four, probably referring to four fast-days, must, therefore, be an uncommon sign for A, who was similarly designated on page 25 in sign 8 of the upper section. If the gods in the top thirds are those of the past year and those in the middle the gods of the year just beginning, we should expect to find in each top third the deity who is represented in the middle of the preceding page. But this does not hold good. For then we should expect to find K on page 26 and not the tiger, on page 27 B or G and not E, on page 28 D and not A, and on page 25 A and not B. Hence there is some confusion here. Yet it seems to be in the nature of a correction, that on page 26 the third sign, next to that of the sun-god, is actually the sign for E who is in the top section on page 27, and that the sixth sign is Kan-Imix belonging to this god. On pages 25 and 26 this line also refers to the past year, _i.e._, to the year set down in the top third. The fourth sign on page 25 is a Manik, _i.e._, originally a grasping hand denoting taking away, disappearance, and the fifth sign on this page is a Muluc, which seems to denote the ending of the Muluc years. The fifth sign on page 26, is, in fact, the tiger pictured above. The lunar hieroglyph as the third sign on page 25 and the _a_ as the fourth on page 26 are strange and unaccountable. Both appear to be almost without significance here and seem almost like mere points between the names of gods in groups of two each. The Ahau as the third sign on page 27 is the usual determinative of D, whose hieroglyph stands beside it. On page 28 the main part of the third sign corresponds to the sixth of the upper section. I do not know, however, how to explain either the upper part suggesting a mat or the familiar leaf-shaped prefix. 6. The Bottom Pictures. In the left-hand lower corner of each page we see the sign for the year of 360 days, which at the same time designates the heap of stones, on which the stelae were erected, the two thick black lines indicating the two columns of hieroglyphs usually found on them. A tree is growing out of this sign, having on its trunk an abbreviated Cauac sign, at least, on pages 26, 27 and 28, which probably refers to rain as the most desired event of the year. The tree on page 25 has no leaves, but the top is carved into the shape of the head of the god B. In the other three cases it has leaves, but instead of ending in the god's head the tree is draped with a mantle and a breech-clout, and a serpent is coiled about it denoting a period of time (here, the year). Furthermore there are foot-prints on the trunk or the drapery of the tree, which represent it as the goal of a pilgrimage. If the top and middle thirds refer to the mere transportation of the idols, the bottom thirds refer to the feasts connected with this act, or, at any rate, to those dedicated to the _new_ god. For we see here on page 25 the god B, on 26 the god K, on 27 A and on 28 D, _i.e._, the same deities as in the middle sections, yet so placed that the first two and the last two have changed places. Each of the four deities hold in one hand a hen with its head cut off; "degollavan una gallina" is the statement made by Landa concerning these feasts. Perhaps all four gods, at any rate the last three, are scattering grain; this was one form of divination; we found the other on page 2. There are besides, on every page, several small objects between the two pictures, just as in the middle section. On page 25 the object is probably an altar, but instead of the flame it has the number 19. Above this is the sign for the west (the Ix days) with that for the sun, and on top of them the sign which we found in the middle section of page 26 as the contents of the lower vessel. On page 26 we see a vessel containing a bird, then another whose contents are indicated by Yax and a double Kan sign. Above it is the sign for the moon or for 20 with a prefix, and above this a 9. At the bottom of page 27 there is a vessel containing two Kan signs and a fish; above this another vessel the contents of which are the same as we found in the vessel in the middle section of page 26 and in that of the lower section of page 25. Above these is again the sign for the moon or 20 with a superfix, which is the same as the prefix on page 26, and beside it is a 16. Page 28 has the usual haunch of venison (Landa:--"una pierna de venado"), above this is a vessel with a bird and Kan and above this again the sign for the moon or for 20 with the same superfix and the numeral 15. I shall discuss below the numbers scattered over these four pages. 7. The Bottom Hieroglyphs. These hieroglyphs also form but _one_ line on each page and each line contains six hieroglyphs. The _first_ of each line is always the same (_p_). It consists of a surface divided into four quadrants thus suggesting the four cardinal points, the four Bacabs presiding over them and the four kinds of years. The superfix seems to be the abbreviated hieroglyph of the north; the sign for the north, however, is Muluc and these four pages begin with the Muluc years. The _second_ sign is the head of D as the supreme god; to this a Yax is joined on pages 26-28 as the symbol of strength, and on page 25, but probably by mistake, the abbreviated sign for the west. The _third_ sign always represents one of the four cardinal points:--on page 25 the east, on page 26 the south, on page 27 the west and on page 28 the north; here then the usual order is reversed and the signs are set down according to the diurnal instead of the annual course of the sun, probably occasioned merely by exchanging the sign for the west (Ix), which belongs on page 25, with that for the east (Kan), which belongs on page 27. The other three signs do not stand in the same order on every page. The _fifth_ sign on pages 26 and 28 and the _fourth_ on page 27 show correspondence most clearly. This sign is always a head, undoubtedly that of the god pictured in the bottom third. But on page 25 it is the hieroglyph of E, who is pictured on the top of page 27, instead of that of B. In the same way the 6th sign on page 25, the 4th on page 26, the 5th on page 27 and the 4th on page 28 have something in common. One element of the hieroglyph is always the sign for the year of 360 days, combined on page 25 with cross-bones and the Cauac sign, on 26 with Yax and Kan, and on 27 and 28 simply with Yax. The most puzzling and divergent of these hieroglyphs are the remaining ones. The 4th on page 25 has an oblique cross (or bones?) and the abbreviated glyph for the west, the 6th on page 26 is the head of E, the 6th on page 27 is the 360-day sign combined with Kin and Cauac, and the 6th on page 28 is the usual Kan-Imix sign. Here, too, there seems to have been a displacement. Before I leave the four pages 25-28, I will glance at the numerals, which are scattered over them and which apparently have no connection with one another. I have discussed these numerals in my article "Die Mayahieroglyphen" in Volume LXXI, No. 5, of the Globus, and the following is borrowed therefrom. First of all, I believe that I proved there, that the sign composed of two dots with a cross between them is an abbreviation for the usual clumsy representation of the numeral 18 and designates it like a duodeviginti by 20 - 2. Next, that in this passage as on pages 18a, 18c, 19c, 46b and 50c, the sign is combined with the hieroglyphs Yax-Kin. Third, that it is closely related to the god D, inasmuch as it stands on page 27b close beside the picture of that god. Assuming this as a known fact, we find scattered over these four pages the following numbers:-- 25: 9, 7, 8, 9, 19, 26: 7, 16, 13, 7, 9, 27: 11, 5, 2, 18, 16, 28: 6, 6, 13, 6, 15. It is very remarkable that the sum of the numbers on each of the first three pages is equal to 52, and as an accidental freak it would be most surprising; somewhere on the fourth page six units may have been omitted; but perhaps the 6, which stands above the _two_ Chuen signs in the centre, is to be counted twice. The 52, however, designates the very 52 years, which are treated of on these four pages. As yet I know no reason to account for the fact that the 52 is here separated into these apparently very irregular numbers. The discovery of this reason would be an important step in advance. Or does it means 52 _days_, perhaps those which follow a Tonalamatl coming in the middle of the year? Page 28 is followed in the Manuscript by three empty pages. The scribe's object in reserving them is beyond our ken; possibly they were intended to represent the period of 8 years. Pages 29-45 (_i.e._, to the end of the first part of the Manuscript) all belong together. After the Maya manner there is very little system displayed in their arrangement, and though here and there there may be occasion to consider the three parts of each page consecutively, I will discuss them here as follows:--First, the top thirds, which are most difficult owing to the destruction of a large portion of them; then the middle, and last the bottom thirds. They all consist in great part, with a few interruptions, of representations of the regular Tonalamatl, such as we find represented from the beginning of the Manuscript to page 23. The element which these pages have in common is the fact that the god B, who can hardly be Kukulcan or Quetzalcoatl, occurs on almost all of them. He is the god of wind, fire, breath, _i.e._, the true god of life and is here represented in his relation to the most varied manifestations and activities of a human being, so that this section bears a certain resemblance to the Tro-Cortesianus. With this is closely connected his relation to all four cardinal points, which so often occur. He may have been the local god of the region from whence this Manuscript came; in the Tro-Cort. It seems rather to be C who lays claim to this office. Pages 29a--30a. XI 13 XI 13 XI 13 XI 13 XI 13 XI Lamat Ben Ezanab Akbal. This is a Tonalamatl of 4 × 65 days, each part subdivided into 5 × 13 days. The four days written on the left are those which may begin the year. In each of the five sections B is pictured in a sitting posture, the first four times on a tree (the tree of life rather than the sacrificial tree). In the first picture he holds in one hand the haunch of venison, so often occurring as an offering, the last time on page 28; the object above it is probably the Kan sign. There is a vessel at the god's feet, probably a receptacle for the venison, bearing the hieroglyph of the 13th day Cib, which, however, refers rather to a bird. In the second picture an animal with a protruding tongue lies on its back at the feet of the god, who kneels upon its stomach. This probably represents the lightning-dog as vanquished. The same animal is pictured on the next page and also on page 40b and perhaps on page 60. There are a number of small dots around B's head, which on page 11c we attempted to interpret as the starry sky. I can find nothing of special importance in the third and fourth pictures, but in the fifth, B is sitting in a house, which is marked repeatedly with the sign Caban (ground). Here the god is holding the hatchet (machete) in his hand, as if prepared for some terrestrial activity. Four hieroglyphs in the usual order belong to each of the five pictures. They are almost entirely destroyed, but the vestiges show that the fourth sign was always that of B, while the third sign with the first picture had the abbreviated hieroglyph of the west as a prefix; with the second picture it had that of the south, and therefore with the third and fourth it must certainly have had the signs of the east and north. We should expect the signs with these prefixes to contain references to Ix, Cauac, Kan and Muluc, but they are not distinguishable. Thus B is represented in pictures 1-4 as ruler of the four cardinal points and in 5 as the ruler of the earth in general. Pages 30a--31a. This passage looks like an amplification of the middle picture on page 29a. Here B is represented with the hatchet in his left hand and holding aloft by the tail with his right hand the animal, which is spitting out something upon a stepped pyramidal structure, probably the pyramid of a teocalli. That this is probably meant to represent lightning is rendered almost a certainty by the picture on page 40b. In this passage there are several red and black numerals scattered around the animal in an irregular manner, which we find nowhere else in our Manuscript, but with which the Tro-Cortesianus has made us familiar. The sum of the black numbers still legible is 23, probably a 3 is effaced and the sum should be 26, the sum which so often occurs in the Cod. Troano 8-13 with the animal represented there. The red numbers likewise do not admit of exact determination. This passage also contained hieroglyphs, four standing side by side on each of the two pages. The legible portion is limited to the Cimi sign in the third place, perhaps an Imix in the second, and possibly an Ahau in the first. Pages 31a--32a. In my article "Zur Entzifferung, etc., VI," published in the year 1897, I discussed this passage more in detail, and the following will be in continuation of what I stated there. The real aim of the computation on these pages is to find a number in which the following periods of time are united with the Tonalamatl of 260 days:--1. The ritual year of 364 days, and consequently also a quarter of it, the Bacab period of 91 days. 2. The period of 104 days, being the number of days which remain after a Tonalamatl has been deducted from a ritual year. The hypothesis advanced by Mrs. Zelia Nuttall ("Note on the Ancient Mexican Calendar System," Stockholm, 1894) and also the entirely different opinion held by Mr. Charles P. Bowditch ("The Lords of the Night and the Tonalamatl of the Codex Borbonicus" in the American Anthropologist, N. S., Vol. II, New York, 1900) prove the existence not only of merely arbitrary Tonalamatls for the purpose of prediction, as those in our Manuscript, but also of Tonalamatls having a fixed position in certain years. But after the manner peculiar to priestcraft, the number sought is found only by an indirect and mysterious process. In the first place we find on page 32a all the days set down in the following manner:-- XIII XIII XIII XIII Manik Cib Chicchan Ix Chuen Ahau Muluc Ezanab Men Kan Ben Ik Cauac Lamat Caban Cimi Akbal Eb Imix Oc. That is to say, a series counting from the day XIII Akbal, the New Year's day of the year I Kan, recurring every 52 years, furthermore a series which shows the same difference of 91 from the day XIII Akbal to XIII Ix, XIII Chicchan, etc., and finally ends with XIII Akbal again, after it has run through a period of 20 × 91, _i.e._, 1820 days = 7 Tonalamatls, like a similar representation of 7 Tonalamatls on page 51. Above these 20 days, and to the left of them, numbers are set down rather irregularly, which begin with 91 and are multiples of that number. The signs of the days corresponding to these numbers are joined to them; but they are omitted with the numbers of lowest value. Hence we have:--91, 182, 273, 364 (4), 455 (5), 546 (6), 637 (7), 728 (8), 819 (9), 910 (10). Then with a bound follow 1456 and 1820; with the last number Akbal is reached in the natural way, which day the scribe had erroneously set down again with 1456 in place of Cauac. The number 728 already united the numbers 91, 104 and 364, but did not include the number 260. This inclusion is accomplished by the number 3640 on page 32, quite on the left where we find the numbers 10 and 2, under which only a 0 has been omitted. With the usual hiatuses this series seems to end on page 31, where I think the numbers 4, 0, 16 and 0 ought to stand, but they are almost wholly effaced; this would then be 320 × 91, 280 × 104, 112 × 260, 80 × 364 = 29,120. We have thus gone far in advance of the first problem, but a second always presents itself in these series, it is that of using these periods for larger numbers, which refer to a not too remote past or to a future not too distant. The first numbers are, as a rule, in the neighborhood of 1,252,680, the close of the eleventh Ahau-Katun, and the latter in the neighborhood of 1,480,440, the close of the thirteenth Ahau-Katun. The Manuscript presents the following:-- 1,272,544 1,268,540 1,538,342. XIII Akbal XIII Akbal XIII Akbal 121 17 51,419 IV Ahau IV Ahau 8 Cumhu 8 Cumhu IV Ahau. In connection with this it should be noted first that I have restored the 8 in the statement of the months, and second that the two numbers on the right were found with the aid of page 63 only by an easy conjecture. For with the reading of the Manuscript 10, 13, 3, 13, 2, I do not agree, but read instead 10, 13, 13, 3, 2; the number below, however, is given in the Manuscript as 7, 2 and then a black 14 joined to a red 5; I read this 7, 2, 14, 19. The three numbers nearest the bottom have red circles around them, indicating subtraction, or, according to my present point of view, addition. Now let us see how the computer arrived at the large numbers. Day XIII Akbal, the New Year's day of the 1 Kan years, is given; also the differences of the series 91 and 104, therefore also in the proportion of 7 to 8. If we combine these last two numbers by addition and then by multiplication with 260, the result is (7 + 8) × 260 = 3900. If, however, 7, 8 and 3900 be combined by multiplication the product is 7 × 8 × 3900 = 218,400 = 2400 × 91 = 2100 × 104 = 840 × 260 = 600 × 364 = 1120 × (91 + 104). We have already met with the 218,400 on page 24, which was obtained by the addition of 33,280 + 185,120. My opinion is as follows:--First 11 Ahau-Katuns = 1,252,680, were taken as a point of departure, and to this sum was added 15,600 = 4 × 3900, and 243 as the interval between the normal date IV Ahau and XIII Akbal. The result was 1,268,523. The position of this day, however, is XIII Akbal 11 Xul (1 Ix). Then the 3900 mentioned above was added to this number and the result was 1,272,423 = XIII Akbal 16 Pop (12 Muluc). Then to the 1,268,523 was added the 218,400 and the sum was 1,486,923 = XIII Akbal 1 Kankin (1 Kan), the very place in that year where a Tonalamatl ends. The following numbers were thus obtained:-- 1,272,423 1,268,523 1,486,923. These numbers are suppressed in the Manuscript. But if the encircled numbers are added to them, viz:--121 (interval between XIII Akbal and IV Kan), 17 (interval between XIII Akbal and IV Ahau), and 51,419 (= 197 × 260 + 199; 199, however, is the interval between XIII Akbal and IV Ik), the result is the three large numbers set down in the Manuscript, which have the following properties:-- 1) 1,272,544 = IV Kan 17 Xul (12 Muluc). This number = 13,984 × 91 = 12,236 × 104 = 3496 × 364. It also = 4894 × 260 + 104, the interval between IV Ahau and IV Kan. 2) 1,268,540 = IV Ahau 8 Mol (1 Ix) = 4879 × 260 = 3485 × 364 = 74,620 × 17. 17 is the interval between XIII Akbal and IV Ahau. 3) 1,538,342 = IV Ik 15 Zac (12 Muluc). It also = 5916 × 260 + 182. The 182, however, the half of the ritual year of 364 days, is the interval between IV Ahau and IV Ik and between IV Ik and IV Kan. The fact that the interval is the same in each case is clearly the reason for the choice of the days IV Kan and IV Ik, which are otherwise not at all prominent. It is remarkable that the third number is obtained by the addition of 51,419, _i.e._, of 197 × 260 + 199 (there are 199 days between XIII Akbal and IV Ik). But it was evidently desirable to obtain as large a number as this. On page 63 a number of nearly similar value is associated with it, viz:--1,535,004. It is set down almost in the middle between the 13th and 14th Ahau-Katuns, for it is 57,902 days greater than 1,480,440, and 55,978 days less than 1,594,320. Now, however, the Manuscript presents in the last column but one of page 31 a number, 2,804,100, which occupies a very unique position, since it is nearly twice as great as all the other large numbers, with the exception of those in the serpents. It must refer to the year 9 Muluc, and to the date IV Ahau 13 Mol. It has many remarkable properties, for it is:-- 1) = 10,785 × 260 2) = 17,975 × 156 (156 = IV Kan - IV Ahau). 3) = 35,950 × 78 (78 = IV Ik - IV Ahau and IV Kan - IV Ik). 4) = 719 × 3900. We have already met with this 3900 above. Now, however, the 2,804,100 by virtue of its magnitude creates the suspicion that it may be composed of two ordinary large numbers. It might be 5) 1,308,580 + 1,495,520, therefore 14,380 (91 + 104). 6) 1,380,600 + 1,423,500, therefore 3,900 (354 + 365). That is to say, the important 3900 multiplied by the days of the lunar year and also by those of the solar year, hence the 719, referred to under 4, separates into these two parts. The lunar year of 354 = 6 × 29 + 6 × 30 days was not unknown to the Mayas. We shall find its half, 177 days, several times on pages 51-58. We might also use the two important numbers 14,040 and 18,980, the first of which is divisible by 260 and 360, and the second by 260 and 365, without remainder. Then we have the large number desired:-- 7) 147 × 18,980 + 14,040. 8) 200 × 14,040 - 3900. What future student will penetrate more deeply into the meaning and purpose of these numbers? We might now expect to interpret also the upper right-hand corner of page 31, but here almost everything is in a deplorable state of obliteration. In the first three of the five columns over each of the three large numbers there was a date consisting of a numeral and a hieroglyph, but these admit of no certain nor even probable determination. Four hieroglyphs still remain in the fourth column, respecting which compare my treatise "Zur Maya-Chronologie" in the Berliner Zeitschrift für Ethnologie XXIII, pp. 141-155. In the top sign I recognize an Imix with a prefix and probably also a superfix. I think this denotes the period of 18,980 days. I am forced to pass over the second entirely, inasmuch as a red 6 inserted in it remains a mystery (6 × 18,980 = 113,880?). As I stated in the above-named work, I think the third is three times the sacred period of 2920, _i.e._, 8760 days. Finally, the fourth sign certainly denotes the period of 7200 days. Whether or not there was a fifth sign above the one now at the top is as uncertain as the meaning of the whole. The most remarkable thing about it is that in three other passages of this Manuscript these three signs appear in close proximity to another. On page 61 we find the third in the 11th place in the second column, the first in the 12th place in the same column, and the fourth in the 14th place in the first column. Page 70 has the first sign in the middle of the 4th column; the second somewhat lower down in the 3d column and the 4th two places below. Finally all three signs appear in succession on the top of page 73 in the same order as on page 31. The fifth column on page 31 may have contained another numeral belonging to the series, the loss of which is not so serious a matter, but there may have been one or two hieroglyphs above it, the obliteration of which is greatly to be deplored. Pages 32a--39a. This is a large section extending over eight pages, which is difficult of interpretation owing to the prevailing disorder and because a large part of the hieroglyphs are effaced. Here, too, the principal subject is the god B, who is represented in manifold activity. A series of numbers extends through the entire representation. I read them as follows:-- I 11 XII 28 I 12 XIII 26 XIII 12 XII 19 V 5 X 1 XI 20 V 12 IV 6 X 8 V 5 X 7 IV 12 III 5 VIII 8 III 11 I. There are thus 18 divisions, the different lengths of which reveal no rule. They embrace 208 days, _i.e._, 2 × 104, which may well be considered as a continuation of the computation in the preceding section, of which the 104 was so important a number. The red numbers are entirely lacking in the beginning, then they are very slightly indicated, and finally they are distinctly written out on pages 36-39. I assume that the scribe has set down the 4th, 3d and 2nd numbers from the end, one too little. The last number has been entirely omitted. I have supplied these omissions though in a manner somewhat different from that adopted by Cyrus Thomas, "Aids," p. 28. I would note in addition that a period such as this, consisting of 208 days = 16 weeks, might be explained in an entirely different way, if there were a column of five days at the left having a difference of 8 days; then the whole would signify four Tonalamatls. But there is no such series of days. Another point of view presents itself, however. If we take cognizance of the fact that a group of four hieroglyphs usually belongs to a picture, then it is evident that here there are such groups not for 18, but for about 22 subdivisions. It may, therefore, be assumed that about four subdivisions averaging 13 days are not specified, in which case this passage would extend not over 208, but over 260 days. The very irregularity in the arrangement of these numbers is an argument in favor of this hypothesis; it may be occasioned by the fact, that the pictures do not correspond exactly to the subdivisions. For the present, however, we shall discuss the single pictures assuming that there are 18 subdivisions. 1. Pages 32a-33a. Here at the very beginning it is uncertain whether the signs at the end of page 32 and at the beginning of page 33 are to be regarded as a single group of 8 hieroglyphs, as seems to follow from the numbers, or as two groups of 4 hieroglyphs each. At the end of page 32 we see two persons facing one another, one of whom, to be sure, is barely visible. The other wears a head-covering like a man's silk hat, similar to that worn by the priests on the inscriptions of Palenque. It is a remarkable fact that of the four hieroglyphs above these figures, 1, 2 and 4 (the last probably the god C) seem to have the sign for the west as a prefix, while the prefix of 3 (Imix) suggests the usual representation of the tortoise head. Below the persons there is a Kan sign, the prefix of which is also the sign for the west. On page 33, B is represented walking and carrying the Caban sign in his hand. The first of the four hieroglyphs is the sign for B, the second is Imix, probably again with the sign for the west as a prefix, the third is an Akbal sign with Kin, and the fourth is the cross-hatched sign with Kan. 2. The rest of 33a is occupied by two persons, one of whom is clad in a gala mantle, but neither admit of further identification. They are occupied in fishing, inasmuch as they are sitting on the shore of a body of water and are either casting a net or drawing it in. There is a fish between them and above it is a vessel with something apparently cooking in it. Of the 8 hieroglyphs belonging to this picture, only the following are distinguishable:--the 1st containing an Akbal, the 3d, which is the common cross _b_ with a 9, the 4th, an Imix also with 9, and of the 7th only the prefix Yax. The 3d and 4th appear again on page 35a, 28 days later. 3. Page 34, like page 3, represents a human sacrifice. The victim, very vaguely drawn, lies on a step-shaped sacrificial stone, or on the pyramid of a teocalli. There is a Caban (earth) sign between the sacrifice and the pyramid, and also on the walls of the buildings; the shrieking of the victim is plainly indicated. As on page 3, there are four persons in the form of gods surrounding the sacrifice, but here they are different ones. The one at the left above is the black god (L?), holding the rattle-stick (Seler, "Mittelamer. Musikinstrumente," p. 111), and at the right, above, F, the companion of the death-god, is sitting with a rattle in his hand. Below, the two have changed places, F is on the left and L on the right. The former is beating the drum and the latter blowing a wind-instrument. The sounds emitted by the two instruments are represented by drawings. This may, therefore, be regarded as an instrumental quartette. The following objects are also in this picture:--at the left above is a vessel the contents of which are cooking; at the left below, another vessel with three Kan signs, and at the right above, a Kan sign with a bird's head and below the food known to us from pages 27b and 29b. These four objects refer to the sacrificial feast. Lastly, at the bottom on the right there is a ladder, probably intended for scaling the pyramid. Ten hieroglyphs in the upper line belong to this picture:--the first, which is effaced, is followed by a Cauac, then comes the cross _b_, then a Cimi appropriate to the sacrifice, and lastly a head with an Akbal eye, probably D's. The first sign in the lower row is likewise destroyed, the second sign is a Kan, the next is the cross _b_, both having a different prefix, then here too is the hieroglyph of B with Yax as a prefix, and the last is an unknown sign. 4 and 5. Page 35a. According to the numbers there are two sections here, but neither the pictures nor the hieroglyphs can with certainty be assigned to either. On the left is a house in which C sits holding a Kan sign in his hand; on the roof, as if guarding him, and also holding a Kan sign, lies the god B. In the Cort. 24b-25b, there are six gods lying on houses, within which other gods are also represented in a recumbent position. Then follow two vessels, again denoting the sacrificial feast, the contents of which are probably cooking, and which, from the sign on the second, are probably liquid. Above these are three others, one with the Cimi sign (human flesh?), one with a bird and the third with the haunch of venison. At the right of these is an implement, which is unfamiliar to me and is similar to that held in the god's hand on pages 5c and 6c. And quite on the right sits B with foot-prints pictured below him and on his clothing. The hieroglyphs on page 35, when they were all legible, numbered 14 and were arranged in two rows. 4 of the upper row are preserved, the lower part of the first is a year-sign (?), similar to that which often appears on pages 25-28, the upper element is the cross, and the prefix is the one resembling a leaf, which occurs so frequently. The second sign is an Imix with a prefixed 9, the third a cross and the fourth a head (probably D's) with Akbal. In the second row there is a cross with a prefixed 9 (sign of the second or third month?). These two signs with the prefixed 9 are perhaps to be read as a calendar date IX Imix 9 Zip (1 Ix), as on page 33a. Ix, however, belongs to the west, which is the predominant cardinal point from 32a onward. The second sign is a compound of Kin and Akbal (day and night) which often occurs here, the third is the compound of the Moan and Caban signs with the number 1 above each, and the fourth is the hieroglyph of B. The fifth sign is unfamiliar to me. The sixth contains an Imix with the sign for the west as a prefix, and the seventh is effaced. At this point the representations begin to display a more orderly arrangement. 6. Page 36a. Here the head of B forms the head of a serpent (cf. pages 61 and 62) represented in pouring rain, while on page 35b it is emerging from the water. Of the four hieroglyphs 1 and 2 are entirely and 3 for the most part destroyed, and 4 is the usual Kan-Imix. 7. The lightning-beast with flames pouring forth from his forepaws and tail, is plunging down from the rectangle, which primarily designates stars and then the sky in general. This rectangle occurs for the first time here, but will often be met with later. Here it may be a combination of Mars and Venus. Of the four hieroglyphs, 1 is effaced, 2 is a compound of Kan and Kin, 3 a head with Akbal and Kin (D?) with the uplifted arm as a prefix, and 4, corresponding with the picture, is the compound of the rain sign Cauac with the prefix of the storm-god K. 8. Here B himself is the bringer of lightning. In one hand he holds a burning torch and flames are bursting from his carrying-frame. The third hieroglyph is his sign. It is doubtful whether the fourth is the hatchet (machete) or is not rather intended for an ear pierced for the purpose of ritual blood-letting, as on pages 44b and 45b; the first and second signs are rather indistinct. 9. Page 37a. Unless I am entirely mistaken, B is here represented with his arms bound behind his back. Cf. the pictures on page 2, top, and 60, bottom. Are the ends of the rope fluttering in front of the god intended to render this still more plain? Hieroglyph 1 contains the sign _t_, which resembles, but is not the same as, the year sign. This sign has already occurred frequently, especially on pages 25a-28a, and the last time on page 35 in the first hieroglyph. As on page 35, hieroglyph 4 is the compound Kin-Cauac, but here it is joined to the year-sign, _i.e._, it denotes the Kin-Cauac year, just as it does on page 26a. 3 is again Cauac and 2 is the hieroglyph for B. 10. Rain is falling from the heavenly shield, already seen on page 36, here however designating different planets (Mars and Mercury?) and the figure represented in the rain is the one which we have already seen on pages 12c, 17a and 21c. It is that of the old Uayeyab god N with a hatchet in one hand and an unfamiliar object in the other like the one on page 39a, and with another unknown object on his back shaped like a shield marked with a Kin. That this figure is really meant to represent N follows from the fourth hieroglyph (which, however, is not his regular sign 5 Zac), which is repeated on the head of the figure. The lower part of the hieroglyph is replaced by the year-sign just as it is in the hieroglyph on page 47, left, middle. The third hieroglyph contains 2 Caban signs, the first and second cannot be clearly identified. 11. This is a deity which I hardly think appears elsewhere. It has an animal's head resembling that of a bear, thus recalling page 7a, and it also has the paws of a bear. Of the hieroglyphs only a Kin-Akbal is recognizable. 12. Page 38a. Here we have another heavenly shield (Mars and Venus?) and under this shield B is represented seated and strangely enough facing himself, the figures not being back to back as on page 68a. Hieroglyphs 1 to 3 are wholly and 4, which is a head, is for the most part destroyed. 13. B is here represented in very close connection with a female figure. Cf. pages 21c-23c. The representation on page 68b is a still closer parallel to this passage. The first hieroglyph is destroyed for the most part, the second is B, the third is probably only a determinative of the latter, but has the sign for the west, and the fourth is Kan-Imix. 14. B holding a Kan sign is sitting on an object, which may be meant for the stone on which the idols were set up at the change of the year. Of the hieroglyphs the third is again B, and the fourth is probably the frequent sign a. The first sign is the most remarkable. In the Zeitschrift für Ethnologie, Vol. XXIII, p. 147, I stated that this was the sign for the change of the year, which is its meaning on pages 41b, 52b and 68a. The Kan year follows here after the Cauac year of page 37. The prefix of the sign is the hieroglyph for the east to which the Kan years belong. The Kan sign in B's hand also corresponds to this. The second hieroglyph is destroyed. 15. Page 39. The picture represents the lightning-beast with two flaming torches walking under the heavenly shield (Mercury and Jupiter?). Of the hieroglyphs the third belongs to B, the fourth has as a prefix the sign of the storm-god K, but otherwise admits as little of determination as do the first and second. 16. Here we see B in the rain holding in one hand a machete, and in the other a strange implement similar to that on page 37a. Of the hieroglyphs the second was the god's sign, the third is _a_, and the fourth may be an Akbal sign with Kin. The first sign somewhat suggests the sign for the Moan; its prefix is curious. 17. Here in place of the picture and the superscription, owing perhaps to lack of space and in order not to omit the last picture, we have a vertical row of seven hieroglyphs interrupted between the sixth and seventh by the red and black numeral belonging here. The top sign is effaced and the second is B's. I will not venture to determine the third, which contains a Yax. Could it belong to the serpent deity H? The fourth is probably Kan-Imix and the fifth is indistinct. And the same is true of the sixth, the prefix of which we have already met with as the sixteenth hieroglyph on page 24, and shall meet with again on pages 53, 56, 58, 61, etc. The seventh sign, which is quite at the bottom, consists of a vessel with a foot-print beneath it; it seems to be in the place of the picture. 18. The entire section ends with a picture of B, who carries the hatchet and probably the copal pouch. The hieroglyphs are wholly obliterated. Pages 40a--41a. The following Tonalamatl, one of the form of 10 × 26, has suffered much from the carelessness of the scribe and from injury. I have attempted to restore it as follows:-- X X 7 IV 4 VIII 4 XII 2 I 1 II 8 X Ahau Oc Cimi Cib Eb Ik Ezanab Lamat Kan Ix. The first row should be read from top to bottom, and then the second in the same order. The six subdivisions all refer to some activity of B. Among the 6 × 4 hieroglyphs his sign occurs five times as the fourth and only in the last group as the third. Let us now examine the six groups individually. 1. B is traversing the water in a canoe, as on pages 29c and 40c, with the paddle in his hand. All the hieroglyphs belonging to him are obliterated. 2. B is sitting on the laterally elongated head _q_, which here, as on page 69, is enlarged and drawn with special care. Seler ("Charakter der aztekischen, etc. Handschrift" in the Zeitschrift für Ethnologie, 1888, p. 83) discusses this sign in connection with the day Men. It seems to me to denote unlucky days, the influence of which may here be checked by B. B holds in his hand a hatchet. The head (_q_) is repeated in the third sign, perhaps also in the second, and the superfix of these two signs is probably the same as that of the sign beneath the picture of B. The first sign is mostly destroyed. 3. As on pages 30a and 31c, and again just as on page 69a, B is sitting on the tree of life or sacrificial tree. A branch of this, which he grasps in one hand, ends in a serpent-head, and the root of the tree also represents B's head. Around the god's head are again the familiar dots, probably signifying stars. Of the hieroglyphs, the first is probably _f_, the second is destroyed, the third may be a variant of _a_, although it recalls the sign which, I believe, has the meaning of 73 days on pages 46-50; the prefix of 1 also suggests this meaning. 4. B's head is again surrounded by stars and he holds in one hand the outline of a hieroglyph. He is sitting on a peculiar ornamented structure resembling the crenelations of a wall. This wall displays the spiral which we found also on pages 33b-35b, and which in the treatise, "Zur Maya-Chronologie" (Zeitschrift für Ethnologie XXIII, p. 147), I regarded as an abbreviation for a serpent and hence as a symbol of time. It is further to be noted that B is wet with rain and with this the third hieroglyph is in keeping, if it is actually intended to denote the rainy season and not the week of 13 days ("Zur Entzifferung" V, 6); still the red numeral 13 below is more in keeping with the second meaning. The second sign is an Ahau with the leaf-shaped prefix, which also appears in the first sign of the third group. The first is effaced. 5. B, represented with a gala mantle hanging down in front and with the copal pouch, is sitting on a head, which looks like his own, especially as to the eyes, but which notwithstanding probably belongs to D and is marked with Ik (wind) and Cauac (cumulus clouds). Of the hieroglyphs the first and second do not admit of positive identification, and the third is Kan-Imix. 6. The god is sitting on a mat in a house. All the hieroglyphs except his own are obliterated. Pages 42a--44a. Another Tonalamatl of the form of 10 × 26; I have restored the effaced day-signs as follows:-- XIII XIII 3 III 2 V 2 VII 6 XIII 2 II 2 IV 2 VI 7 XIII Oc Cib Ik Lamat Ix Ahau Cimi Eb Ezanab Kan. Thus the month days are the same as in the preceding Tonalamatl, but should be read in a different order:--Oc, Cib, Ik, Lamat, etc. Here each of the 8 subdivisions has 6 hieroglyphs, and the order is as follows:-- 1 2 3 4 5 6. A few of these signs are common to all the groups. Thus the first sign (_v_), as far as what remains is distinguishable, seems to occur in all the groups. It has the leaf-shaped prefix, but I cannot understand the rest of it; we shall find it again several times on pages 29c-41c. Again the sign in the sixth place, as far as we can see, is always the head without an underjaw and the tuft of hair tied up on top of it (O, according to Schellhas), which we found above on page 25 and which we shall meet again on pages 65-69 no less than 13 times, with regular intervals of 6 signs between them. Indeed that passage is a remarkable parallel to this one. That the sign for B, who here too plays the most important part, occurs often, is self-evident. It appears in the fourth place, in the 1st, 3d, 4th, and 7th groups, and in the third of the 8th group; in the 6th group it is destroyed. In the 2nd and 5th groups B has neither picture nor sign. The hieroglyphs of the cardinal points I shall mention in connection with the separate groups. They are especially conspicuous in this section, being sometimes represented in full and sometimes in an abbreviated form as mere prefixes. 1. B with arms crossed sits above a serpent denoting time, and holding in its coils the cross _b_, which so often refers to astronomical conditions. Above the head of the serpent is the vessel with the three Kan signs, which we have already found several times on pages 25-28. It is remarkable that the flourish, which usually appears as the nose-ornament of the sun-god G (_e.g._, pages 11b and c), is added to these Kan signs. As the stars are again indicated on B's head, he plainly denotes a time-god here. The third hieroglyph, the sign of the east, corresponds with this meaning, and the Kan sign, which we see in the fifth hieroglyph probably combined with Ahau, also belongs to the east; the prefix of the fourth hieroglyph is the sign for the west. 2. A deity whom we shall probably have to call F, the god of human sacrifice, is sitting on a stepped pyramidal structure (a teocalli as a place of sacrifice?). He holds something in his hands, resembling a long and broad scroll, joined to which is the head of the god of the north, C, and in the third hieroglyph of this group the sign for the north also appears, prefixed to the head of F, who seems to be repeated in the fourth hieroglyph. The fifth hieroglyph with an Imix is unintelligible to me. 3. Page 43. B is sitting in the water, the copal pouch hangs from his neck and the hatchet is raised as if ready to attack. The second hieroglyph clearly denotes water, while the third is the sign for the west and the fourth is the sign for B, its prefix being the sign for the east abbreviated; the order of the cardinal points is thus exactly the reverse of that in the first group. The fifth hieroglyph is not clear to me, but it appears to be repeated in the same place in the next group. 4. B is sitting here astride a sort of bench again holding the hatchet in his hand. Belonging to this picture in the third hieroglyph is the sign for the south, which is repeated in an abbreviated form in the fourth hieroglyph. The fifth is Kan, joined to what appears to be the same sign as the one found in this place in the preceding group. The second sign is indistinct. 5. This is an aged deity, probably M according to Schellhas, seated on an indefinite object. In front of the deity is a Cauac sign, which contains exactly the same cumulus clouds as those in the sign 5 Zac, which belongs to N. Cauac, however, belongs to the south, and therefore corresponds with the north of the second group on page 42. Sign 5, a Kan, corresponds exactly with the same sign in the fifth place of the preceding group. 6. Page 44. B seems to be in a state of collapse. Behind him is a second person, who is either trying to support him or to pull him up by some kind of a sling. I think the second person is E, the grain-deity, if it is not Seler's young god. If the hieroglyphs were not completely effaced, they would probably shed some light on this interesting passage. 7. Here we see B, holding a fish in his hand, and sitting on a hieroglyph, which is compounded of Imix and a prefix, which resembles the tortoise head and which appeared once before in this combination on page 32a. This passage recalls page 40a, where B is seated on the laterally elongated head _q_. Nothing more can be said of the hieroglyphs, than that 6 is the head without an underjaw. 8. B is sitting here in a house; his sign in the third place has Yax as a prefix. Hieroglyph 5, with the number 4 prefixed, recalls the one which we found on page 21c belonging to the baldheaded old man. Hieroglyph 4 is the common Kan-Imix. Page 45a. The last page on the front of the first section of this Manuscript is used for a series, which presents itself as a second improved edition of the series which was found on pages 31a-32a. The very fact that the writing is so much better proclaims it an amendment. The chief aim of both series is the same, viz:--to bring into unison the numbers 91, 104, 260 and 364. But the two series gain this end by different means. On page 32 the series begins with 91, and at first has only 91 as a difference, until with 728 a multiple of 104 and 364 is obtained, then it returns to the simple difference 91, in 1456 it obtains again the 104 and 364, loses these two last numbers once more in 1820 and finally in 3640 obtains the desired multiple of all four numbers, which is retained in 7280, 14,560, 21,840 and 29,120. The series on page 45a proceeds much more briefly. It begins at once with 728 (91, 104, 364), loses the 104 in 1092, gains the 260 and loses the 104 in 1820, arrives at divisibility by all four numbers in the 3640, loses the 104 again in 5460, but then comes to a standstill after having obtained the same multiples (double at that) of 3640, which I mentioned just now in the preceding series. Indeed it can be seen from what is legible in the third column above, that the series went still further. But so much is obliterated that I have obtained the numbers 14,560 and 21,840 in both series only by conjecture. In the earlier passage the starting-point of the series is the day XIII Akbal and in the one before us it is the day XIII Oc. In the former the days specified were 91 days apart from each other, and here they are separated by 104, _i.e._, XIII Ezanab, XIII Ik, XIII Cimi, XIII Oc. The initial days of the two series, XIII Oc-XIII Akbal, are separated by 13 days, and the reversed series, XIII Akbal-XIII Oc, by 247 days. Hence the subject of both passages is essentially the week of thirteen days, _i.e._, the year of 364 (28 × 13) days. Now this series is also accompanied by a number amounting to millions. It is in the second column of page 45; only, in order to understand it, we must add a zero as the bottom figure; then it becomes 1,278,420. XIII Oc stands below this number as the beginning of the series. The first column has 30 as an encircled number and below it the normal day IV Ahau. The large number must have been formed as follows:-- The point of departure was 230, the interval between IV Ahau and XIII Oc, to this was added 98 × 260 = 25,480, the sum being 25,710. The result of this number added to 11 Ahau-Katuns = 1,252,680, was 1,278,390, which number is not revealed in the Manuscript. It is concealed in XIII Oc 3 Mol (2 Muluc). But 1,278,390 = 42,613 × 30, _i.e._, it is divisible by the interval XIII Oc-IV Ahau. Now if we add to this large number the 30 set down in the Manuscript, the result will be the above-mentioned 1,278,420. This number in the Manuscript has the date IV Ahau 13 Chen. (2 Muluc). It is, of course, divisible by 30 and by 260, hence = 42,614 × 30 and 4917 × 260. It corresponds not merely in this respect with the largest number on page 31a, viz:--2,804,100, but also with regard to its divisibility by 78, 156, 195, which are all multiples of 13. On page 45a, top left, there were doubtless five hieroglyphs, of which the two topmost ones are effaced. First we see only the sign of the eleventh or twelfth month, Zac or Ceh, with an uncertain number prefixed, then the signs for beginning and end are distinctly legible. Ceh begins and Zac ends the year of 364 days; see page 4 of my treatise "Zur Entzifferung V." Pages 29b--30b. We come now to the middle section of pages 29-45, in which we shall not be so hampered by obliteration in our attempts at interpretation, as we were in the upper section. We have here first a Tonalamatl of the usual kind, arranged as follows:-- III 13 III 13 III 13 III 13 III Ix Cimi Ezanab Oc Ik. That is to say, the 52 days divided into four equal parts. To these four divisions, as on page 23b, belong the four usual forms of animal food, which are joined in three places to Kan (bread) and probably denote sacrifice. They are, first a mammal, which, however, is erroneously represented by a fish; second, a fish, third an iguana and lastly a bird. I would add, that in the hieroglyphs above, the east, north, west and south correspond in turn with these representations of food. The hieroglyphs are arranged as follows:-- 1 2 5 6 9 10 13 14 3 4 7 8 11 12 15 16. Of these, 2, 6, 10 and 14 are the cardinal points just mentioned; 4, 8, 12 and 16 are the sign for B, and 1, 5, 9 and 13 are the head with the tuft of hair and the Akbal eye to which I attribute the meaning of _beginning_. Likewise the remaining four signs, 3, 7, 11 and 15, although they are not exactly alike, have something in common, the 15th being a distinct Imix; they are not yet wholly intelligible to me. Four pictures of B belong to these hieroglyphs. In the first the god is seated with crossed arms on two of the ordinary astronomical signs (Jupiter and Mars?). In the second, where he is pointing forward with his hand, there are footprints on his seat, as, for example, on page 35a. In the third the seat contains the usual cumulus clouds in clusters. Finally, in the fourth, he is seated on the tree of life or of sacrifice, the hatchet is in his hand and he is clad in the gala mantle; cf. pages 31c, 40a, 69a. Pages 30b--31b. This passage is in some respects closely related to the preceding Tonalamatl, but in other respects it differs significantly from this and from what is usual, for the Tonalamatl is divided here into only four principal divisions of 65 days each, which begin very regularly with the days VIII Oc, VIII Men, VIII Ahau and VIII Chicchan. There are neither subdivisions nor the usual pictures belonging to them. But on the other hand each of the longer periods of time written down here have eight hieroglyphs for each section in the usual order. B's sign occupies the places 6, 4, 4 and 4; from this it follows that here too he forms the principal subject. Here, as in the preceding Tonalamatl, the first place in each group contains the sign denoting beginning, while the eighth sign is invariably the head without an underjaw, which seems to me to refer to _fasting_, as if a fast-day fell at the end of every 65 days. In the fifth place we see in succession the four animals, which in the preceding Tonalamatl are not included in the groups of hieroglyphs. Here they stand in the order of mammal, bird, amphibian and fish, but the bird in the second group is replaced by the sign which usually occurs with the dog (lightning-beast). The signs in the second place are those of the cardinal points, and they are given in the same order as in the preceding Tonalamatl, _i.e._, east, north, west and south, so that they do not belong to the same animals as they do there. The third signs are the cardinal points again, but in the abbreviated form discovered first by Schellhas, and in a different order:--west, north, east and south, and always joined to the head of C around which everything revolves as around the polar star. The Kan sign with different accompanying signs occupies the seventh place in the first group, and the sixth in the other three. Four signs still remain:--the fourth of the first group I am inclined to consider the abbreviated sign for the sun; the seventh of the second, rain with the sign for the west as a prefix; the seventh of the third, Caban, ground, with the sign for the east as a prefix; the seventh of the fourth is Kan with the Yax sign above it, probably denoting the vegetable kingdom. Pages 31b--35b. This entire passage is devoted to a single Tonalamatl, which is divided and written out in an unusual manner. Like the preceding it is divided into four parts of 65 days each, but the remarkable thing about it is that these divisions of 65 days are each subdivided into two periods of 46 and 19 days, and the 46 days again into eight unequal parts, which are exactly the same each time, while the 19 days run their course without further subdivision. On pages 33, 34 and 35 this 19 is always on the left at the bottom, on page 32 it is wanting, probably because it was self-evident and there was no suitable place for it. We shall next discuss the division of these four periods of 46 days each. This division is indicated with especial exactness on these pages, since not merely the length of the separate divisions and the week days are specified, but also the month days. This representation has the additional peculiarity, that the two columns on each page must be read from bottom to top, and of each group of two days standing side by side, the one on the right is to be read first and then the one on the left. If the Tonalamatl were written in the usual manner, it would have the following form:-- X 9 VI 9 II 9 XI 2 XIII 4 IV 9 XIII 4 IV 19 X Ben Ezanab Akbal Lamat. Instead of this we read in greater detail as follows (the pages and the stated _length_ of time are in parentheses):-- (31) X Ben (9) VI Ik (9) II Chuen (9) XI Ahau (2) XIII Ik (4) IV Cimi (9) XIII Men (4) IV Cauac (19). (32) X Ezanab (9) VI Manik (9) II Cib (9) XI Chicchan (2) XIII Manik (4) IV Chuen (9) XIII Ahau (4) IV Kan (19). (33) X Akbal (9) VI Eb (9) II Imix (9) XI Oc (2) XIII Eb (4) IV Cib (9) XIII Chicchan (4) IV Muluc (19). (34) X Lamat (9) VI Caban (9) II Cimi (9) XI Men (2) XIII Caban (4) IV Imix (9) XIII Oc (4) IV Ix (19). In spite of the seemingly wholly irregular division of time, the following relation, which is certainly not accidental, results from this arrangement:--the first of the eight members of each row is one of the days which may begin the year and the months, and the eighth, on the other hand, one of the four regents of the year. The remaining six members are the remaining 12 of the 20 days repeated twice and the second always corresponds with the fifth of its own series, and the third to the sixth and the fourth to the seventh of the following series. Two pictures of god B belong to each of these periods of 65 days, the first of these pictures referring to the divided period of 46 days and the second to the undivided one of 19. It is also in agreement with this that on pages 61 and 62 the fourth, sixth and eighth pictures represent the god as rising from the jaws of a serpent--the serpent being represented each time as lying in water which invariably contains the number 19. As the hieroglyphs belonging to the periods of 46 days are allied to one another, and as this is also true of those belonging to the periods of 19 days, I will first consider the hieroglyphs of the first period by themselves, then those of the second, and the pictures shall be treated in the same manner. Therefore, let us first examine the four pictures (1, 3, 5 and 7) on the right side of the pages:-- 1. The first page shows the god walking with the official staff in his right hand, in his left the hatchet raised for a blow and with the copal pouch hanging from his neck. 2. He is walking and holding a flaming torch reversed in his right hand, in his left the hatchet is raised aloft, the pouch hangs from his neck, the mantle is indicated and around his head are the little circles which are so frequently his adjuncts and probably signify stars. 3. He is walking and holding the reversed torch in his left hand and the hatchet in his right. 4. He is walking and holding a torch in each hand. He wears on his head the head of K. He seems to be bringing storm and fire. Now let us examine the hieroglyphs, which I have numbered thus:-- 1 3 5 2 4 6. The first hieroglyph on each page certainly represents one of the cardinal points. They are in the usual order:--east, north, south and west. 2 is the same sign on each page. I take it to be the sign for Xul = end, denoting, it may be, the end of the period of each cardinal point. In each group 3 is the head with tuft of hair and the Akbal eye; probably the sign denoting _beginning_. This beginning and end occur most distinctly repeated on page 63, and the end alone eight times at the bottom of pages 61-62. On page 31, 4 is B's sign, on page 32 B's with the prefix of the north, on page 33 it is B's sign again and although quite indistinct its is plainly joined with the east. On page 34 there is another indistinct sign which may be that of the serpent deity H. Owing to indistinctness I do not venture to determine the fifth sign on pages 31 and 33; on page 32 it is the laterally elongated head _q_ with the Ben-Ik superfix, and on page 34 the ordinary Kan-Imix. The sixth sign varies as much as the fifth; it seems here to denote four different gods, perhaps the four given on pages 25-28. On page 31 it is a Cauac, the prefix of which here, however, suggests K, on 32 it is certainly the hieroglyph of E and on 33 possibly of A, on 34 it most resembles Muluc of the day-signs, but also suggests the line crossing F's face from top to bottom. We come now to the four pictures 2, 4, 6 and 8 and to the hieroglyphs belonging to them, which are on the left side of the pages and belong to the periods of 19 days. 1. B is pictured walking, raising the hatchet in his right hand, and holding an uncertain object in his left; the serpent with the 19 set down in its coils does not appear here. The 2nd, 3d and 4th pictures belong together. In each picture on these three pages there is a serpent with water in its coils and the number 19 in the water, denoting the number of days belonging here. As on pages 61 and 62 B is emerging from the open jaws of the serpent. In each case he is brandishing the uplifted axe in his left hand. The difference in the three pictures consists, first, in the fact that only in the 2nd and 3d B wears the copal pouch, second, that only in the 3d and 4th he has an implement in his right hand (the two implements differ somewhat but are both, apparently, adapted for hanging up) and third, that only in 3 the whole picture is painted blue, which means that the entire scene is enacted under water. The hieroglyphs are as follows:-- The first in all four cases is a Manik, _i.e._, originally a grasping hand, perhaps referring to the chase; on page 32 it has a prefix and on pages 33-35 a superfix corresponding to the first. The second sign on each page is simply B's. The Cauac sign in the third refers in all four cases to the water represented at the bottom of pages 33b-35b. On page 32 it has an Akbal as a superfix, on 33-35 a prefix, which is familiar and in keeping with the sign and probably also the same suffix, though it is indistinct on page 34. The fourth sign shows, as do several other things, that the representation on page 32 differs from that on pages 33-35. On the first of these pages we see an Imix with a puzzling 1 prefixed. If the numbering of the days really begins with Kan, as is probable in this Manuscript, then Imix is the 18th day and 1 + 18 might denote the 19, which is not set down here. On pages 33-35 this sign contains the spiral, which refers to the serpent in the picture below (and probably therefore to time). A curious element, however, is the numeral 9 prefixed three times to the spiral. This number is rarely a prefix, but it occurs, for example, on pages 33a and 35a before the cross _b_ and on page 60 right, middle, prefixed to Xul (= end). The interval 9 occurs in this Tonalamatl 16 times, including therefore 117 of the 260 days. The fifth sign each time contains the head without the under jaw, just as it recurs regularly in the preceding passage, pages 30-31. The sixth sign in each group is the not uncommon compound of Caban and the sign, which resembles Muluc and which we saw before in the sixth place among the hieroglyphs on the right side of page 34. Pages 35b--37b. I 11 XII 6 V 9 I 4 V 7 XII 9 VIII 6 I Caban Muluc Imix Ben Chicchan. That is, a regular Tonalamatl of five parts, 5 × 52. That the 52 days are divided into two halves (11 + 6 + 9 = 4 + 7 + 9 + 6), may only be accidental. I will designate the hieroglyphs of the seven divisions thus:-- 1 2 | 5 6 9 10 13 14 | 17 18 21 22 25 26 3 4 | 7 8 11 12 15 16 | 19 20 23 24 27 28. I will first consider those signs, which are repeated and by means of which the sections seem to be brought into connection with one another. But I shall attend in detail to those hieroglyphs which contain characteristic references to each picture, when I discuss the latter. The first place both among the pictures and among the hieroglyphs again belongs unquestionably to B. He is plainly designated in the 10th, 17th, 21st and 26th hieroglyphs, but, for an unknown reason, C's sign is joined to B's in the 16th, probably also in the 6th and perhaps in the 9th, and in 20 and 28 C's sign forms an integral part of a hieroglyph. Now in discussing the great Tonalamatl, pages 4a-10a, I attempted to make it appear probable that C belongs to the eighth day (Chuen) and in that case the Chuen sign in the thirteenth hieroglyph may be probably set down here. Further, in discussing pages 25 to 28, I expressed the conjecture that this Chuen sign might simply mean eight days, if we begin with Kan as the first day, for which proceeding there is some warrant in the "Dresdensis." Now, in hieroglyphs 8 and 24 we find an 8 inscribed; in hieroglyph 8 it is joined to an Imix, exactly as on page 39c; on page 65a it is joined to Kin, and on 67a and 68a to a hand. Is it possible that here also the 8 is intended as a sign for Chuen = C? Then the familiar Kin-Akbal sign (day and night) is in the fourth place as well as in the eleventh and nineteenth. The other signs which appear but once, I will discuss in connection with each of the seven pictures:-- 1. A serpent in the water, with B emerging from its head, exactly as on pages 36a, Tro. 26 and Cort. 10. The third sign, that of the serpent-deity H, refers to the serpent. The first sign is the one which I think may be Caban-Muluc, while the second, owing to its indistinctness, eludes interpretation. 2. This also represents a deity sitting in the water, whom we are probably safe in calling H, for the top of his head changes into a serpent, ending, however, in a bird's bill holding a fish. The deity holds up both hands. The union of serpent and bird should be noted in connection with the fourth picture. The deity is represented in the fifth sign; the sixth, seventh and eighth signs have already been discussed. 3. B is traversing the water in a boat, exactly as on pages 29c, 40a and c, and 43c. Here, however, there is a person beside him (probably a woman) whom, from the ninth hieroglyph we recognize as the deity E, unless this sign is C's. In 12 we see with Kan a sign which may suggest the usual hieroglyph denoting a year. 4. A serpent is pictured here, with a bird sitting upon it. We met with the same bird on page 17b. Schellhas, "Maya-handschr.," p. 51, has already expressed the opinion that this is probably a rebus for the name Quetzalcoatl or Kukulcan, and this theory is certainly worthy of consideration. In this connection I would call to mind that it is probably also Kukulcan with serpent and bird who occupies the first place on page 4a. The bird appears again in the fourteenth sign, while the thirteenth is a Chuen, which, according to the statement made above, may be connected with the C in the sixteenth. The fifteenth sign is the cross _b_, which probably denotes the connection between the thirteenth and sixteenth or else between the bird and serpent. Or is Chuen intended here to represent the serpent and not the ape? 5. This picture represents B carrying a burning torch, with the copal pouch hanging from his neck. His left hand touches a strange object, a kind of frame, the top of which ends in the head of a bird of prey. The eighteenth sign is obliterated and the twentieth is a curious combination of Caban, C and the front part of K. 6. B is walking, with the hatchet in his left hand and in his right an object which looks like the representation of sounds issuing from musical instruments, as on page 34a. Perhaps B is represented here as the air-god. The twenty-second sign is the familiar Kan-Imix. The twenty-third sign (_w_) is not intelligible to me; it occurs on pages 19c, 40b, 58, on the right, with a superfix suggesting K. 7. Water, in which a small human being seems to be emerging from a snail (the symbol of birth). Above the water is B, grasping a serpent which is in the water, as if to protect the new-born being from the serpent. The twenty-fifth (with Kin) is the so-called bat-god, who on page 50 at the left ends the series of twenty gods. The twenty-seventh sign (with Yax) is still undetermined. Pages 38b--41b. VI 16 IX 8 IV 11 II 10 XII 1 XIII 12 XII 6 V 12 IV 11 II 11 XIII 6 VI Cauac Akbal Manik Chuen Men. The sum of the black numbers is 104, the whole is, therefore, a double Tonalamatl = 5 × 104 = 520. While the series on pages 31a-32a primarily brought the 91 and the 104 together, and the series on page 45a accomplished the same result with the 104 and the 364, here, though the process is a different one, the 104 is combined with the 260 in another number. It is characteristic of this part of the Manuscript, that the astronomical rectangles, which are very rare in the preceding pages, appear here in no less than five of the eleven divisions and six of them represent showers of rain. One is very readily, therefore, led to infer that the 104 days have reference to the rainy season and to its dependence upon the position of the planets. I will now analyse the eleven sections separately. 1. Rain is streaming down from two astronomical signs (Mars and Jupiter? Day and night?) and in the rain stands a black human form, grasping an implement with the right hand held downward and pointing upward with the left. It has the vulture head which occurred on pages 8a and 13c. Hieroglyphs 1 and 2 represent the sun and moon, both surrounded by half white and half black envelopes, which must denote clouds. The third sign is Imix, which just here might refer to the rainy season productive of nourishment. The fourth sign is the vulture head of the picture. 2. B is walking in the rain and holds in one hand a stick pointed at the lower end. This is doubtless a farming implement, likewise occurring frequently in the Tro-Cort., which was used for making furrows or holes in the ground. The second hieroglyph is B's, the first is Caban = earth, the fourth might be a compound of Caban and Muluc, referring to the rain, and the third is the familiar Kan-Imix, which, as the designation of food and drink, would be especially appropriate here. 3. B is apparently resting from tilling the soil, since he is sitting on a support consisting of the signs just spoken of, _i.e._, Caban and Muluc (?). The latter signs are repeated in the second hieroglyph, while the third is B's with the sun-glyph (?) prefixed; the first is the head apparently open on top with the Akbal eye, probably the sign for beginning, and the fourth is the familiar sign _a_, which I think signifies a good, auspicious day. 4. Page 39. This represents a violent shower of rain, which might be pronounced a cloud-burst. The old red goddess with tiger-claws and a serpent on her head is pouring water in a stream from a jug. The same goddess occurs on page 43b and on the last page, 74. Her hieroglyph is the second; it is more distinct in the two other passages. The first part of the third hieroglyph is indistinct, and the second part is the hieroglyph denoting the year. The first hieroglyph is a head with the Akbal sign, and the fourth is the usual compound of Kin and Akbal. 5. The cloud-burst seems to have destroyed the cultivation of the field, for B walks forth again with the implement for tilling the soil, as in the second picture. The second hieroglyph is B's with the prefix of the west, therefore probably denoting sunshine, the first again contains Caban and Muluc and the fourth is Kan-Imix referring again to the produce of the field. I shall not venture to explain the third sign here any more than I did in the previous passages. Compare page 8b. 6. B is again sitting in the rain and under the same astronomical signs as before on page 38. He is pointing downward (to the sprouting seed?). He has the sun-glyph on his back. The first two hieroglyphs are unfamiliar to me (Yax); the third is Imix with the sign for the west, and the fourth is again Muluc. 7. Page 40. B is plunging down headfirst from the same astronomical signs and is brandishing the hatchet. Hieroglyph 1 is the cross _b_, 2 is B's sign, 3 probably that of the grain-god E, and 4 being Kan-Imix refers to grain. Favorable weather seems to have set in. 8. The astronomical signs are not the same as those in the three preceding instances (Mercury and sun?). Below them is a deity with tortoise-head--in my opinion, the sign for the longest day--holding a torch in each hand and thus referring to the heat. Hieroglyph 1 (_w_) with the superfix suggesting K still puzzles me. 2 is the cross _b_, 3 is the tortoise-head with the number 4, which probably refers to the Kan, Muluc, Ix and Cauac years, as the 4 sometimes appears prefixed to N's hieroglyph. In exactly the same way the tortoise-head with the tortoise itself occurs frequently in the Cortesianus. 4 is the sign of the year with prefixed Kin and Cauac, _i.e._, day-Cauac-year. 9. A thunder-storm, which is very appropriate after the longest day. The lightning-beast, likewise holding a burning torch, is plunging down from the astronomical signs, which are different ones again (Venus and the moon?). The second hieroglyph contains the sign of the dog together with the cross _b_, while the third is that of the north-god C, and the fourth is Muluc. I cannot explain the first sign; its prefix, which rarely occurs, appears also on pages 23b, 25a, 37b, 63a, and possibly on pages 53b, 62-63a, 69b. 10. Page 41. Another representation of rain. There is an old deity in the rain, who is N rather than F, denoting the end of the old year. He is emerging from a snail (cf. with this page 37b), and is pointing upward; a part of the first hieroglyph is on his head. This first hieroglyph recalls the sign which, in the Zeitschrift für Ethnologie, XXIII, p. 145, I ventured to connect with the change of the year; but it also suggests the snail pictured below, hence the birth of the new year. The beginning of the year for the Mayas, although of course not for all parts of the country, is fixed, as a rule, to fall on the 16th of July. This would agree admirably with the eighth and ninth sections, which represent the time of the longest day and of thunder-storms. The second hieroglyph is B's, the fourth the cross _b_, probably referring here to a union of two years, and the third with its Cauac to the duration of the rainy season or to the god N. 11. The rain seems to fall with less violence. B is seated, clad in the gala mantle with a Kan on his head, as the sign of grain. His headdress also strongly recalls that of the grain-deity E (which is also the case of the headdress on the preceding picture.) Hieroglyph 1, the upper part of which is very like that of the first sign of the preceding group, looks like a plaited mat. Does it not suggest that the name of the first month of the new year is Pop and that this word is denoted by carpet, mat? Hieroglyph 2 is B's, 3 is the sun between a dark and a bright sky, and 4 is the common Kin-Akbal, day and night. If the seventh picture really refers to the beginning of the year, then the entire period of 104 days extends from April 15th to August 2nd, which, with the addition of the five days not counted at the end of the year, does indeed make 109 days. All this, however, is only true on the supposition that I have not seen more in these representations than they contain. Pages 41b--43b. VI 12 V 7 XII 6 V 21 XIII 6 VI. Caban Muluc Imix Ben Chicchan. Another regular Tonalamatl, and like the preceding one apparently referring to the change of the year, the tilling of the soil and the rainy season. B's sign is regularly repeated in the second place of all five groups of hieroglyphs, and moreover each of these groups has six signs. The head with the missing under jaw is in the fourth place of groups 2 and 3, in the sixth of group 5 and might perhaps be intended also in the fourth of 1 and 4. The usual Kan-Imix is in the third sign of group 2, in the fifth of 4, and the fourth of 5; possibly also in the fifth of 1; the third hieroglyph in group 3, at any rate, contains Imix. Let us now consider the five groups individually:-- 1. The rainy season seems to have been delayed; the beginning of the year draws near. B is kneeling on a kind of footstool, the hatchet is in his right hand and his left hand holds a kind of chisel with which he is carving something out of the trunk of a tree. The purpose of the work is indicated by the god's own head directly below (probably placed in front of the tree as a model?). No doubt this is intended to represent the making of the statue of the god of the new year destined for the beginning of the year, as we know it from pages 25-28. Corresponding with this is the first hieroglyph denoting the year with Yax as a superfix, and also the sixth being the sign to which in the article in the Zeitschrift für Ethnologie cited above, I attributed the meaning of change of the year. I cannot decide whether the third sign is intended for an Imix-Chuen with the sign of the south as a superfix, the fifth for a Kan-Imix and the fourth for the head without the under jaw. 2. Page 42. Prayer for rain. B (that is to say, his priest) is seated apparently on the same footstool. He is gazing upward and presenting a vessel containing an offering, the nature of which is uncertain. The vessel ends in a tube; cf. page 67b. The first, fifth and sixth hieroglyphs are not finished, and the third is Kan-Imix. 3. The rain-goddess promises aid. B is seated opposite the old red goddess, who is holding intercourse with him. The god is seated on the Caban sign (earth) and the goddess on Muluc (rain?). The first, fifth and sixth hieroglyphs are also unfinished; the third is Imix with its meaning intensified by the prefixed Yax (the luxuriantly growing grain?). 4. B is again tilling the ground in the manner already familiar to us. Under him lies his own head with the Imix-Kan sign, denoting food and drink, as a superfix. The first hieroglyph is the sign of the eighteenth month Cumhu, _i.e._, of the end of the year. The third is a Kin-Akbal, the fifth a Kan-Imix, the sixth is not finished, and the fourth may be intended for the head without the lower jaw, but it is carelessly drawn. 5. Page 43. The solicited rain begins. The goddess with the serpent on her head is pouring streams of water from her vessel. The first hieroglyph repeats the month Cumhu, denoting the beginning of rain, before the close of the year; the third is the sign of the goddess met with on page 39b, here also with the sign for the west as a prefix; the fifth is her determinative, the serpent, and the fourth is Kan-Imix. If the first sign in the first group is not regarded as the sign of the year, but as that of the sixteenth month (Pax) resembling it, and the fact is taken into consideration that there is an interval of 34 days between the second and fourth groups and of 40 days between the second and fifth, this would be found to correspond with the interval between the months Pax and Cumhu. Pages 43b--44b. This is the fourth and last series of the first part of the Manuscript; the first is on page 24, the second on pages 31a to 32a, and the third on page 45a. The first series is quite by itself, but the second and third are similar in form to this fourth, though their initial days are different from those of the latter:--XIII Akbal, XIII Oc and III Lamat. All three begin with differences which are divisible by 13:--91, 104 and 78, equal to 7, 8, and 6 × 13. All three aim and arrive at numbers which are common factors of 260, 104 and 364, and therefore also of 3640, which last number is written out in the other two series, while in this series it can only appear later on and then, increased by multiplication. Since this series has the difference 78, the week day numbers remain the same, while those of the month days must advance by 18 each, that is, from the hidden starting-point III Lamat they go on to III Cimi, III Kan, III Ik, III Ahau, etc., until the tenth member of the series is 10 × 78, _i.e._, 3 × 260 and thus comes again to the day III Lamat. From 780 onward this number is itself always the difference of the higher terms of the present series. At the same time 780 days are the duration of the apparent revolution of Mars, which is here supplementary, as it were, since page 24 treated of the revolutions of the sun and of Venus, and also of those of the moon and of Mercury. Hence in the present passage we find the numbers 1560, 2340, 3120 and 3900, always accompanied by the day III Lamat. The larger numbers require a few corrections; I read them 13,260 (17 × 780), 15,600 (20 × 780), 31,200 (40 × 780), 62,400 (80 × 780) and 72,540 (93 × 780). The very largest again are correctly set down; first 109,200 equal to 140 × 780, but here also equal to 1050 × 104 and 300 × 364, so that in this series the goal aimed at is not reached until later than it is in the two preceding series. Then follows 131,040 = 168 × 780, 1260 × 104, 360 × 364, but finally 151,320, which number = 1455 × 104 and 194 × 780, but is not divisible by 364. Detached in the usual way from this series on the left of page 43 is the number 1,435,980. Above and below it is the day III Lamat, further down IV Ahau, and between them is 352 in a red circle. This number seems to have been obtained in the following way:--The writer began with the distance between III Lamat and IV Ahau, which is 92, added to it 172 × 260 = 44,720, and subtracted the result 44,812 from 13 Ahau-Katuns = 1,480,440. The remainder was 1,435,628, which number would correspond to the date III Lamat 6 Zotz (4 Kan), which, however, is suppressed in the Manuscript. The 352 = 260 + 92 was added to this sum, and the result was the 1,435,980 written out in the Manuscript, _i.e._, a day IV Ahau 13 Zip (5 Muluc). Now this number is the one sought; it is 5523 × 260 = 1841 × 780 = 3945 × 364, and hence must also be equal to 263 × 5460, since the 780 and 364 are united in 5460. According to our present knowledge, it would seem to lie in the future, but not far from the present; the solar and Mars revolutions are united in it. There is but a single hieroglyph here, the hieroglyph of the animal which is the chief subject of the next section; from which it appears that the two sections are closely connected. Pages 44b--45b. This section supplements the pictures and hieroglyphs belonging to the series just examined. Therefore it likewise extends over 78 days and divides them as follows:-- III 19 IX 19 II 19 VIII 21 III. These five days are plainly intended to be the days III Lamat, IX Manik, II Cimi, VIII Chicchan, III Cimi. With regard to the real purport of this section, it is my opinion that it has reference to the time of the shortest day and also to the four winds and that this section therefore forms, in a measure, a contrast to pages 38-41, where attention was called to the rainy season, the longest day and the thunderstorms. We see here in the first place four of the ordinary heavenly shields, with two astronomical signs each. I cannot decide, at present, whether these are 1st, the moon and Saturn, 2nd, Mars and Mercury, 3d, the moon and Mars, and 4th, Jupiter and Venus. From each of these shields hangs a figure not unlike an heraldic beast. It cannot be the canine lightning-beast; it has no flames, it is cloven-footed and with the upper lip bent upward and the lower lip curved downward suggesting the storm-god K, and therefore probably represents the four winds; this wind-beast repeated four times also occurs on Cort. 2. Six hieroglyphs belong to each picture. Those in the first place are pierced ears and refer therefore to the ritual bloodletting, which may have been performed at this season. In Tro. 5*b we also find the pierced ear; a pierced _tongue_ (Tro. 17*b), however, does not occur in the Dresdensis. The second place always contains the sign of the beast like the one instance on page 43. The third place seems to be devoted to the four cardinal points, _i.e._, to the four winds. First we see Akbal-Kin, _i.e._, the transition from night to day, the east. The north-god, C, is here in the second group; in the third we see Kin and beside it in the fourth place Akbal, both enveloped by clouds denoting the transition from day to night, the west. The fourth group, it is true, has the year-sign here, but with the compound Kin-Cauac prefixed, and Cauac always belongs to the south. I believe I have found a distinct reference to the season of the year in two other places. The fourth hieroglyph of the second group and the sixth of the fourth both have the familiar prefix suggesting K, the storm-god. The first of the two contains the month Mol (December 3d-22nd); the second might very well be the month Yax (January 12th-31st). This is quite in keeping with the distances 19 + 21 = 40 set down below. In my "Tagegöttern der Mayas" (Globus LXXIII, 10) and above in my discussion of the great Tonalamatl under pages 4a-10a, I have assigned the day Chuen to C, and Muluc to K, _i.e._, the first to the dark north and the latter to the wind, which are both under consideration here. In fact, we find the Chuen sign in the fifth place of the fourth group with the same prefix that C has in the second group. The Muluc sign, however, seems to occur three times:--1st, group 1, sign 6, where it may be joined to the month Mol belonging here; 2nd, group 3, sign 5, joined to the Akbal, which also belongs here; 3d, group 4, sign 4, with a usual prefix. In the second group it may be included in the very similar month sign of Mol. Four hieroglyphs remain:--1st, Akbal in group 1, sign 5, hence probably denoting the darker time of the year in general; 2nd, A in 2, sign 5; 3d, E in 2, sign 6; _i.e._, probably referring to the death of the grain (I do not know to what extent this expression may be used in relation to the Maya country); 4th, Kan-Imix in 3, sign 6, perhaps expressing the hope of new harvests. This finishes the middle sections of the pages of the first part of the Manuscript, and we must now turn back again to page 29 in order to examine the lower sections. Pages 29c--30c. III 16 VI 16 IX 16 XII 17 III Ix Cauac Kan Muluc. Here is a Tonalamatl of four quarters, 4 × 65. In the Manuscript 16 is again erroneously set down for 17 and the III following it is omitted. The initial day is exactly the same III Ix, as in section 29b above it, to which in other respects the passage now under consideration shows a great likeness, since the four familiar animals occur here as well as there. But in spite of beginning in the same way the days here are different ones, being the four regents of the year, as on page 9b. The four parts are grouped together by the sign, which always occupies the first place in each part; I have denoted this sign by _f_, and I think it must have a very general significance, since from pages 29c to 40c it always begins the groups. The connection between the four parts is further shown by the four cardinal points in the second place:--the north in the first group, the west in the second, the south in the third and the east in the fourth. In the third place these cardinal points are again indicated by their usual abbreviations; the east is erroneously set down in the second group. These abbreviations are here invariably joined to the head of C as the representative of the north, the first of the cardinal points occurring in this passage; the others revolve about the north pole. As B's sign always occurs in the fourth place, there is nothing further to be said concerning the hieroglyphs. We now come to the pictures:-- 1. B is rowing a boat, as we have already seen him several times (36b, 40a, _c_, and 43c). To the left of his head there is a bird's head and in the left, bottom, corner, a pot in which apparently a soup of fowl is cooking, emitting bubbles. The Cib sign on the pot refers to the cooking or bubbling. 2. B, with his head surrounded by the familiar stars, is seated in water, in which are represented the iguana over a Kan sign, and the familiar spiral probably denoting a serpent. He is painted black (perhaps corresponding to the west?) and holds in his hand an implement not yet determined. Perhaps it may be intended for a tree, _past_ which the water is flowing. 3. The god is seated, holding in one hand the spiral with a Kin sign over it and a Yax on top of that, and in the other hand something which looks like a bird's feather or a fish's fin. Above him is a fish with a Kan sign, as on page 27, where the fish and Kan are also combined. 4. Holding a hunting-spear, he is sitting on an animal slain in the chase, as on page 45c. Finally, I have remarked that pages 42c-45c, the last part of the first division of the Manuscript, look like an enlargement or amendment of the section just considered. Pages 30c--33c. To begin with, the day signs are set down in the following order:-- XI XI XI XI Ahau Chicchan Oc Men Caban Ik Manik Eb Ix Cauac Kan Muluc Chuen Cib Imix Cimi Lamat Ben Ezanab Akbal. Here then, as is frequently the case in this Manuscript, all the twenty days are specified. But in order to obtain equal periods of time, the left column should first be read from top to bottom and the following ones should be treated in the same way. Then each succeeding day is 17 days distant from the preceding, but in reality the interval is 117 days, since the same week-day is always implied. The hieroglyphs seem to indicate that these 117 days are divided into three distinct parts, 52, 39 and 26. 117 days, however, are equal to 9 × 13 and hence in what follows we find a black 13 set down 9 times as the interval between the days, and a red XI being the number of the week-day an equal number of times. Now, since the whole series extends over 20 such sections of 117 days, the duration of this calendar is 2340 days or 9 Tonalamatl. Consequently we find nine pictures of the same god B. In five of them (in Groups 1-4 and 9) he is sitting before or on a sacrificial tree or tree of life; cf. 30b. It is probably not accidental that in these five cases the hieroglyphs refer to the cardinal points. In the eighth group the god is surrounded by the suggestion of one or more trees; he is sitting in water as if in a forest; or in a cave bordered by trees? In the remaining groups, 5, 6 and 7 he is seated on various supports, in 5 on an object, which is not completed and which cannot, therefore, be explained, in 6 on astronomical figures (Mars and Venus?) and in 7 on agave leaves. In 1 and 3 his head is again surrounded by those dots suggesting stars, in 4 there seems to be a bird (quetzal?) seated upon it and in 2 it bears what may be the Kin sign. In 1 and 5 he has the pouch for incense in his hand, while in 3 alone he wears the gala mantle and is painted black, just as he appears in connection with the same hieroglyphs on page 29c. He carries a hatchet in repose in 2, 6 and 9, and raised for a blow in 1 and 7. In 7 he also holds the Imix sign. The hieroglyphs form nine groups of four signs each. The first hieroglyph, as is always the case in this part of the Manuscript, is the sign which I have denoted by _f_, and the second is always B's hieroglyph. The cardinal points are everywhere specified by two signs each; in places 3 and 4 of group 1, the west comes first and beside it is the sign for the east, erroneously used for that of the west (a like error occurred in the preceding Tonalamatl); in group 2 there are two signs for the north; in group 3 that for the east with the sign for the west beside it erroneously given for the east, and in group 4 two signs for the south. In groups 5, 6 and 7 we find in the 4th place the head of C, and the same sign in group 7 in the 3d place, where it is joined to another head, which may be that of a woman. The 3d sign of group 5 is incomplete and cannot be determined. The 3d sign of group 6 displays a repetition of the astronomical signs represented below. There still remain the 3d and 4th signs of groups 8 and 9. Of these the 3d in group 8 is _w_, which is as yet unexplained. The 4th might be interpreted either as Oc (day 7) or as Xul (end). Its prefix is a Yax sign. Finally, in group 9 the 3d sign is Manik (day 4), the 4th the elongated head _q_ with the Ben-Ik superfix, which Seler assigns to Men (day 12). Pages 33c--39c. The beginning of this Tonalamatl is indicated by a large red dot on page 33. It resembles the Tonalamatl almost exactly above it on pages 31b-35b, inasmuch as its arrangement is an unusual one. I will here, as I did above, give it the form in which it would present itself if it were set down in the usual order:-- XIII 9 IX 11 VII 20 I 10 XI 15 XIII Ahau Chicchan Oc Men. In this passage as in the earlier one, instead of employing the above concise order, a preference has been shown throughout for carrying out the whole series in such a manner that the week days are set down each time and not merely in the left column. It, therefore, has the following form in the Manuscript:-- XIII Ahau (9) IX Muluc (11) VII Ahau (20) I Ahau (10) XI Oc (15) XIII Chicchan (9) IX Ix (11) VII Chicchan (20) I Chicchan (10) XI Men (15) XIII Oc (9) IX Cauac (11) VII Oc (20) I Oc (10) XI Ahau (15) XIII Men (9) IX Kan (11) VII Men (20) I Men (10) XI Chicchan (15) I have arranged the whole series in four parallel periods of 65 days each, for the 65 appears throughout the computation, although the entire Tonalamatl is written out in _one_ continuous line. On the right of page 35 the scribe seems to have wished to erase an entirely incongruous 4, and in writing the last 15, on page 39, he began to use the red paint prematurely, so that the top one of the three lines is red. Attention should also be called to the fact that the second of my vertical columns contains the year-regents, the others only the days following immediately after them, while 12 month days do not occur at all. Also the intervening periods 9 + 11 (= 20), 20, 10, 15 doubtless reveal some design. In order to avoid repetition, I think it proper to mention first, that in the twenty groups of four hieroglyphs each, the sign _f_ always stands in the first place, but the hieroglyph of B, who is represented 20 times, usually appears in the second place, in the first and second groups in the third place, and in the 18th and 19th his sign does not appear at all. I will discuss the remaining hieroglyphs in their place in each of the 20 groups. 1. B is sitting in a house and holding the Kan sign in his hand. The second hieroglyph is apparently meant for the Ahau sign (referring to the 17th day), which usually does not belong to B. This hieroglyph, which certainly bears a resemblance to Ahau and with which we have become very familiar in the inscriptions, occurs again in this Manuscript on pages 46b, c, 50b, 54b, 65a and 66a. The fourth sign is a combination of Cauac and Manik. 2. B is seated on what may be a tree, below him is the cross _b_, and he holds the hatchet in his left hand. The second sign with an emphasized 6 as a prefix (cf. the same sign with the 6 on page 48, bottom, left, below the gods), has the usual Ben-Ik superfix, perhaps to denote that a lunar month has now elapsed, for this passage extends from the 20th to the 40th day of the Tonalamatl. The rest of the hieroglyph is unintelligible. In the 4th place we see a vessel with Imix, probably denoting pulque. 3. B is sitting in water, the hatchet raised in his right hand and his face turned upward. The 3d hieroglyph is again Imix and the 4th a compound of Ik and Muluc:--wind and clouds. 4. B is seated on a reproduction of his own head or D's, beating a drum with his hand. The 3d hieroglyph denotes the serpent-god H with the number 3 as a prefix. The 4th hieroglyph is a Chuen with the sign for the south prefixed,--at any rate the upper part of that sign. 5. B is standing in the pouring rain and looking backward. The 3d sign here is a Caban apparently in a vessel. Following this in 4 is the hieroglyph which I have proposed to interpret as the sign for _beginning_ (Globus, Vol. LXVI, page 79). This sign occurs again in groups 7, 12, 15, 17 and 19, and must therefore be connected with the principal idea embodied in this Tonalamatl. 6. B with folded arms is sitting in a house. Aside from the usual leaflike prefix, the third sign is composed of two parts. The upper part looks like a plaited mat and suggests that the word for the first month of the year (Pop) is expressed by mat. The lower part is the sign, which occurs frequently especially on pages 25-28, and which very much resembles the familiar sign for a year of 360 days. We shall meet it again in the continuation of this Tonalamatl on pages 36 and 38. The three passages refer to the 74th, 139th, and 204th days of the Tonalamatl, and hence are 65 days apart. The 4th sign is the cross _b_, with possibly the sign of the east as a prefix. 7. B is seated on the cross _b_, which is here undoubtedly meant for an astronomical sign. He holds a Kan sign in his hand and there is an Ahau sign on his back. The naked crouching personage, pointing upward, should have especial mention here. The same figure recurs above as a prefix to the 4th hieroglyph. We have already seen it in the 39th hieroglyph on page 24, and shall meet it with especial frequency in the second part of the Manuscript. It is placed sometimes, as in this case, _before_ a sign, sometimes _after_ a sign and again two of these figures are placed back to back as on page 22c, and one of them is even placed upside down before another sign, where it seemed to me to be a sign for Mercury ("Zur Entzifferung VII," p. 11). This figure is represented independently only on the right of page 58. In the passage under present consideration this personage appears again on page 38. The two figures are connected one with the 85th and the other with the 215th day, and are, therefore, divided by exactly half a Tonalamatl or 130 days. Here we find it as a prefix of the supposed sign for _beginning_ of which mention was made in discussing the 5th group. The 3d sign is the same astronomical one, which we saw below under B. It might refer to the Moan and to the change of the year, and thus indicate that a Mercury revolution was coincident here with the beginning of the solar year. 8. B is walking in the rain, both arms are stretched upward, and the pouch hangs from his neck. At the left top there is a black spot suggesting those which usually occur beside the sun and moon. The 3rd sign is Manik, with a prefix. The 4th is an indistinct head, which may be C's, with an Imix sign as a prefix. 9. B is walking with the pouch hanging from his neck, and the hatchet in his hand. The 3d sign, which is unusual, is very obscure, but suggests the fish on page 44c or that on page 36b. The 4th sign with the prefix of the north is very indistinct. 10. B is standing in _water_, his face turned upward while water is pouring from a cloud. The third sign is very complex. The top, left, suggests a serpent, the right a hand, the bottom, left, a Chuen and the element at the bottom, right, may be intended for a bird's head. Exactly the same sign, with the 4th part merely indicated, occurs 65 days later on page 38. The 4th sign is the familiar compound Kin-Akbal. 11. B is sitting in a tent, on the roof of which there is a vessel containing food of some kind. The third sign, which is very complex, is indistinct. The 4th sign likewise consists of four parts, the left, bottom, part is probably the vessel, above it is a spiral (which usually means serpent or time). The right, bottom, is again the sign resembling the year-sign which was spoken of in discussing group 6. The component at the right, top, is indistinct. 12. B is sitting here on no less than four astronomical signs, he has the hatchet in his hand and the design on his back may be a shield or the elaborately ornamented sun-glyph Kin. The third sign (denoting _beginning_?) has already been discussed in connection with group 7, which is 65 days earlier. The fourth is the sign of the year of 360 days or the month Pax with the Ben-Ik as a prefix. These signs are here suggestive of the beginning and end of the year. 13. _Above_ B are astronomical signs (Jupiter and Mercury?) and also the sun and moon. The rain is pouring down upon the god, and a fish is placed beside him. He seems to have the same chisel in his hand which we saw him using on page 41b in connection with the beginning of the year. This again would correspond to the date indicated in the preceding picture. The shield (?) also is the same here as in the preceding group. The third sign ought to represent the fish; the drawing seems to have been unsuccessful and the sign looks more like a bird and also resembles the third sign in the ninth group on page 36. The fourth sign is a Kin-Akbal. 14. B is seated on the elongated head _q_, which has an ordinary prefix. He is pointing upward with his right hand and the left looks as if opened to receive something. The third hieroglyph contains a _q_ like the one under the god, the fourth is an indistinct head (C's?) with an unintelligible prefix. 15. B is standing in water while rain is again pouring down upon him. He holds the hatchet raised in his left hand, while the fingers of the right are extended upward in an unusual manner. This is repeated in the third hieroglyph. The third hieroglyph, however, is the same as the third in the tenth group 65 days earlier, only here the hand is more distinct, while the element below it is vague. The fourth sign is again the one denoting beginning. Compare the fifth group (130 days earlier). 16. B with arms folded is sitting in a house with the Cauac sign below. The third and fourth hieroglyphs contain the sign resembling that for the year, which was mentioned in discussing the sixth group (130 days earlier). In the third a Kin is prefixed to this sign, while the superfix of the fourth is what I take to be a mat, which also occurred in the sixth group. The prefix is a figure suggesting the serpent-deity, which we have already met with in the tenth and fifteenth groups. 17. B, holding the hatchet, is seated on a Moan head, and the third sign is probably intended to represent the same Moan head, in front of which we find the same crouching person met with in the seventh group, 130 days earlier. The fourth hieroglyph is again the sign for beginning, which we have already often met with, as, for example, 65 days earlier in the twelfth group. 18. B is sitting in the pouring rain under astronomical signs (Mars and Mercury?) to which those of the sun and moon are added. The god's face is upturned and he holds the hatchet in his hand. The third hieroglyph may be the vulture head, to which a part of the unintelligible second hieroglyph may also refer. This second sign stands in the place of B's hieroglyph, which is wanting here. The fourth sign contains the enigmatical numeral 8, which we found on pages 36b and 37b, and has the Imix sign as a prefix, as in the first of these two passages. The same compound appears on pages 67a-68a. 19. B is seated here on his own head, as in the fourth group he is sitting on D's. His hands are empty. The second sign is again the vulture head instead of B's hieroglyph. The third is probably the head of the lightning beast, and the fourth is again the sign supposed to denote beginning. 20. B is sitting in water and holding in his hands a vessel with a Kan sign upon it. The water (with Imix prefixed) is denoted by the third sign, while the fourth represents a head (with what is probably a hand pointing to the right above it), which I should prefer to consider the grain-deity E. In conclusion I would call attention to the remarkable fact that every four pictures, which are separated from each other by four of the other pictures, _i.e._, after every 65 days, correspond in certain respects with one another, _viz_:-- 1. Pictures 1, 6, 11 and 16. In all, and _only_ in these, B is sitting in a house or tent, in 6 and 16 with his arms folded. 2. Pictures 2, 7, 12 and 17. In the first three the god is seated on astronomical signs and in the fourth on the Moan head, which I think refers to the Pleiades. 3. Pictures 3, 8, 13 and 18. Here in the last two B is sitting _beneath_ astronomical signs. In all four pictures water, clouds and rain are represented. 4. Pictures 4, 9, 14 and 19. In the first and fourth the god is seated on D's head and on his own, and in the third on the elongated head _q_. 5. Pictures 5, 10, 15 and 20. Like the third of these five classes, these pictures are likewise distinguished by water, clouds and rain. Now the first set of pictures is between the week days XIII and IX, the second between IX and VII, the third between VII and I, the fourth between I and XI, the fifth between XI and XIII, while the month days are quite different. Hence the conjecture is but natural that the pictures and week days bear some relation to one another, though that relation is still shrouded in obscurity. Pages 40c--41c. I 10 XI 10 VIII 10 V 10 II 3 V 9 I Ahau Eb Kan Cib Lamat. This is a Tonalamatl of the most ordinary kind, in which an unsuccessful attempt has been made to divide the subdivisions into equal parts. In the groups of four hieroglyphs each, which belong to each of the six parts, the sign _f_ always occupies the first place, and B the third. Let us now examine the six parts separately. 1. B is sitting in a boat and rowing (as on the top of the same page). Around his head there is again the suggestion of what may denote the starry sky, and in this picture his nose-peg is unusually large. The second sign is an Imix, but it might also denote the thirteenth month Mac and therefore the Tonalamatl (13 × 20). The fourth sign is a fish forming a connecting link between the water represented below and the rest of the group. 2. B is seated on the Caban sign and his arms are apparently resting on an altar standing in front of him, on which fire is burning, indicated by the Ik sign, while the moon is placed below the altar. The Caban sign below is repeated in the second hieroglyph, combined here as usual with a sign which may be Muluc. The fourth sign is a head. I think the scribe meant to set down an 8 before it, but as there was not sufficient space for the heavy line _after_ the three small circles, he indicated it by a black dot _below_ the circles. Now, if we call the head D's, which of course cannot be asserted positively, this would be day VIII Ahau, and this, in fact, is twenty days from the beginning day I Ahau, as it is meant to be in this passage. There is no representation of food; can this have been a fast day? 3. B is seated on four astronomical signs. He wears the gala mantle and holds a serpent in his hand. The second sign is _b_, and at the same time one of the astronomical signs. The fourth is the iguana prepared as food, recognizable by the spines on its back, as on page 25b. It is drawn in precisely the same curious fashion in Cort. 8 and 12c; hence it is represented in the picture by the serpent. 4. B is falling down from above headfirst. I believe that the numerous footprints below him are only intended to represent swift motion. The descent from above may only be intended here to bring the god into closer relationship with the head of the bird of prey in the fourth sign. That this head is again as usual joined to Kan, may refer merely to the fact that it was the Maya custom to eat bread with animal food. Compare page 27b. The second sign might be the abbreviation for the south. 5. B is seated on a mat with his hand extended as if to receive something. He is wet with water. The second sign contains the mat, with what may be the sign below it, and the leaf-shaped prefix probably denoting the plant from which the mat is plaited. The very same combination is given on page 35c and a similar one on 38c. The fourth sign has the prefix of the west followed by two Kans, as if on this day (V Akbal) it had been the custom to eat tortillas without meat. 6. B is standing holding the hatchet. The fourth sign must denote venison, the fourth article of animal food. The second seems to represent the day Eb, with which the remaining 52 days begin, and if the prefixed 9 indicates nothing more than that the ninth day of the month is here meant, it is further evidence that the "Dresdensis" began the days with Kan and not with Imix. In the discussion of this Tonalamatl I have omitted the mention of a very peculiar feature, which as yet does not admit of explanation. I refer to the numbers below the pictures. With the first picture we find 6 + 20, with the second 20, with the third 19 + 20, with the fourth 6 + 20, with the fifth 19 + 20, and with the sixth 6 + 20, _i.e._, with the exception of the second, 26 or 39, two multiples of 13. Now the question arises, should not one of these multiples have been set down with the second picture? There was no space left for a prefixed 19. Therefore the idea suggests itself that what we took to be an altar with the sign Ik above it, is intended for nothing else than this 19, and Ik is the 19th day, if we count from Kan as the starting-point. Pages 42c--45c. This is a Tonalamatl consisting of 4 × 65 days. If written out in the usual way it would run as follows:-- XIII 17 IV 8 XII 8 VII 8 II 8 X 8 V 8 XIII Akbal Lamat Ben Ezanab. Since, however, the subdivisions are divided and the individual month days also are given for all the parts of the whole Tonalamatl, the representation follows the order which we have already found on pages 31b-35b and 33c-39c. In this place, as in the two former ones, I will reproduce in four lines what is set down in the Manuscript in one single line extending over all four pages. XIII Akbal (17) IV Ahau (8) XII Lamat (8) VII Cib (8) II Kan (8) X Eb (8) V Ahau (8) XIII Lamat (17) IV Chicchan (8) XII Ben (8) VII Imix (8) II Muluc (8) X Caban (8) V Chicchan(8) XIII Ben (17) IV Oc (8) XII Ezanab (8) VII Cimi (8) II Ix (8) X Ik (8) V Oc (8) XIII Ezanab (17) IV Men (8) XII Akbal (8) VII Chuen (8) II Cauac (8) X Manik (8) V Men (8) Thus the days Chicchan, Lamat, Oc, Ben, Men, Ezanab, Ahau, and Akbal are repeated here twice, and the others occur but once. The 4 (17 + 48) strongly recalls the 4 (19 + 46) on pages 31b-35b. The repetition of six times eight days in each quarter of the Tonalamatl is closely connected with the fact that there are six Chuen signs on each page, two of which, however, are omitted on page 44. From this it follows, as we have already found on pages 25-28, that Chuen really denotes 8 days and that the count of the days in the "Dresdensis" begins with Kan. But the numbers 12, 15, 16 and 17 are entirely unexplained. They show no recognizable order and always stand near the bundle of Chuen signs. They recall the numbers on pages 25-28, which are equally irregular and unintelligible, and upon which, it is probable, light will break at the same time as it does upon these now under consideration. We come now to the purport of this passage, which seems to be a further amplification of the contents of pages 29c-30c. The meaning is simply as follows:--every 65 days the god B discards a cardinal point and the deity presiding over it and installs another. From this point of view let us now examine the four pictures. 1. Page 42. B is represented here as a warrior with the front of his body painted red. He is aiming a blow with his hatchet at a person sunk down before him, who, from the ornament above his head, seems to be the grain-deity E, the ruler of Kan and of the east, although the contents of this passage really demand a deity of the south, a ruler of Cauac. In a very similar way on page 27, E occurs with the completed Cauac years, instead of with the Kan years just beginning. Behind B's head is the sign of the discarded cardinal point, the south, while below it is a vessel with food, clearly a piece of venison with Kan. 2. Page 43 deals not with the removal of the old cardinal point, but with the introduction of the new one. Here B is rowing in a boat, as in other passages (29c), and Muluc, the north, has certainly a close relation to water. We see here two kinds of food, while none is represented on page 45. The same bird's head, which we find at the bottom of the corresponding page 28, is placed in front of the canoe, and on 29c it is combined with the representation of rowing a boat. On the left is the picture of a vessel with Kan and the iguana. There is something resembling a net between the boat and the bird. 3. Page 44 likewise refers to the introduction of the new cardinal point, west, which is represented on page 26 by the tiger Ix. The two hieroglyphs in the middle of this passage must surely refer to an animal; the lower is the skeleton of an animal, which we so often find as the sign of the lightning-dog, but also as that of the month Kankin, and the upper I take to be a rather vague picture of the day Oc, which certainly denotes the dog. Below these two signs the fish is represented as the fourth species of animal food. The picture belonging to these hieroglyphs is very remarkable. B stands opposite a seated personage wearing an animal's snout, which somewhat resembles that of the wind-beast on pages 44b and 45b and also the nose of the storm-god K, who occurs on the corresponding pages 25 and 26 both with the coming and the departing Ix years, as he does here with the coming years. In the picture before us, the two personages seem to be throwing something resembling a rope at each other, as if these ropes were to be tied together. Is this meant to suggest the casting of lots by means of the knotting of cords, as it is represented on page 2? Or of hunting with snares? Page 45 refers to the displacement of the Ix period by the Cauac period, _i.e._, of the west by the south. The end of the former is represented here. The lightning-beast, which occurred in the preceding period, here lies on his back and B sits astride his body brandishing in each hand a burning torch as an appropriate symbol of the south. On pages 29a and 30c we already saw the god riding on the lightning-dog. Finally the six interesting hieroglyphs set down in a vertical row on the left of each of the four pages are still to be examined. I will give here in the following table what I think is a correct interpretation of them:-- Page 42. 43. 44. 45. South (1) East (7) North (13) West (9). It ends (2) (8) (14) (20) B (3) (9) (15) (21) the time of the Cauac (4), Kan (10), Muluc (16), Ix (22), while Kan (5), Muluc (11), Ix (17), Cauac (23) begins (6) (12) (18) (24). If that which is actually set down in the Manuscript be compared with this, it will be seen that in 11 of the 24 places the Manuscript corresponds to my hypothesis:--1, 7 and 19 are the familiar signs for the three cardinal points, 8 and 20 are the sign Xul = end, which I have already frequently mentioned, 9 and 21 are the sign for B, 11 is Muluc, 23 is Cauac, where the scribe has added to the correct Kin-Cauac the sign for the year, as if the Cauac _years_ were treated of here as on pages 26 and 27. Finally the two agree in 12 and 18, where the Manuscript has the compound Kan-Imix to denote beginning, _i.e._, the two days beginning the series of twenty days, one of them according to this Manuscript, and the other according to the method resembling that used by the Aztecs. The other cases have the correct signs, but set down in the wrong place, thus B is changed from 3 to 2, from 15 to 16, the north from 13 to 14, the Xul from 2 to 3, 14 to 15, the E (Kan) from 5 to 4 and 6 and Cauac from 4 to 5, _i.e._, pushed along every time to the next place. This is all in favor of my theory. As one series began at the top, the scribe incorrectly placed the sign for beginning in the thirteenth place. Strange to say in the tenth place we have the very general sign _a_ in place of Kan. In the 4th, 17th and 22nd, and probably also in the half destroyed 6th sign, the scribe thoughtlessly put down a sign for E, which is proper only with Kan and should come after 5 or 10. Finally in the 24th place he put a sign for A, as if it were the intention that this passage should end exactly like its parallel on page 28. For, as a matter of fact, the two principal sections of the first part of the Dresdensis do end in a very similar way. * * * * * PART II. Pages 46--74. The first glance at the form and contents of the second part of the Manuscript shows that it is very different from the first. The pages are no longer divided into the usual three parts and there are fewer pictures. The Tonalamatls, which form the principal contents of the first part, disappear wholly, and with them both the vertical columns of day-signs and the horizontal lines of numerals alternating between red and black. On the other hand, the large number series as well as the high numbers significantly increase and we note the appearance of the large vertical columns of hieroglyphs, which were impossible in the triple division of the earlier pages. We also find a large number of hieroglyphs which did not occur in the first part. The contents are essentially astronomical. And yet the two parts are so closely connected with one another that the idea of two independent Manuscripts must be dismissed. Especially the front side of the second part as far as page 60 is nothing more than an amplification of page 24. The contents of pages 61-74 are of a more independent nature, but special attention should be called to the relation of 31a-32a to 62-63. Pages 46--50. The entire contents of these pages must be represented as a unit, for what is in the main true of page 24 is also true of these pages, namely that they treat exclusively of the period of 2920 days, in which five Venus years of 584 days each are brought into accord with eight solar or terrestrial years of 365 days each. Each page is a direct continuation of the preceding one. Each period of 2920 days is taken 13 times, the result being 37,960 days, which are equal to 146 Tonalamatls. I will give here first a reproduction, as it were, of the left side of the five pages, omitting for greater clearness a few indifferent matters, which are intended only to fill the blank spaces, viz:-- 1. The twenty hands pointing to the right, with a knife placed over them, in the middle of the pages, which mean nothing more than that these parts of the Venus year are to be read from left to right. 2. The Venus hieroglyph three lines below, repeated twenty times with the sign of the knife, to denote the _division_ of the Venus revolution. 3. The _Akbal_ sign occurring further down, four times on each page, except on pages 46 and 47. This is the last of the day-signs, again counting forward from the day Kan, and means only that henceforth the _close_ of the four periods of the Venus year is indicated below, as the beginning is indicated above. 4. The sixteen Venus signs also occurring below, except on page 48. This sign likewise occurs in a very similar form on Altar R of Copan. With these omissions, the left side of these pages presents the following appearance:-- Page 46. III Cib II Cimi V Cib XIII Kan XI Cib X Cimi XIII Cib VIII Kan VI Cib V Cimi VIII Cib III Kan I Cib XIII Cimi III Cib XI Kan IX Cib VIII Cimi XI Cib VI Kan IV Cib III Cimi VI Cib I Kan XII Cib XI Cimi I Cib IX Kan VII Cib VI Cimi IX Cib IV Kan II Cib I Cimi IV Cib XII Kan X Cib IX Cimi XII Cib VII Kan V Cib IV Cimi VII Cib II Kan XIII Cib XII Cimi II Cib X Kan VIII Cib VII Cimi X Cib V Kan 4 Yaxkin 14 Zac 19 Zec 7 Xul North. West South East Gods. 236 326 576 584 9[1] Zac 19[1] Muan 4 Yax 12 Yax Gods East North West South 19 Kayab 4 Zotz 14 Pax 2 Kayab 236 90 250 8 Page 47. II Ahau I Oc IV Ahau XII Lamat X Ahau IX Oc XII Ahau VII Lamat V Ahau IV Oc VII Ahau II Lamat XIII Ahau XII Oc II Ahau X Lamat VIII Ahau VII Oc X Ahau V Lamat III Ahau II Oc V Ahau XIII Lamat XI Ahau X Oc XIII Ahau VIII Lamat VI Ahau V Oc VIII Ahau III Lamat I Ahau XIII Oc III Ahau XI Lamat IX Ahau VIII Oc XI Ahau VI Lamat IV Ahau III Oc VI Ahau I Lamat XII Ahau XI Oc I Ahau IX Lamat VII Ahau VI Oc IX Ahau IV Lamat 3 Cumhu 8 Zotz 18 Pax 6 Kayab North West South East Gods. 820 910 1160 1168 3 Zotz 13 Mol 18 Uo 6 Zip Gods East North West South 13 Yax 3 Pax 8 Chen 16 Chen 236 90 250 8 Page 48. I Kan XIII Ix III Kan XI Eb IX Kan VIII Ix XI Kan VI Eb IV Kan III Ix VI Kan I Eb XII Kan XI Ix I Kan IX Eb VII Kan VI Ix IX Kan IV Eb II Kan I Ix IV Kan XII Eb X Kan IX Ix XII Kan VII Eb V Kan IV Ix VII Kan II Eb XIII Kan XII Ix II Kan X Eb VIII Kan VII Ix X Kan V Eb III Kan II Ix V Kan XIII Eb XI Kan X Ix XIII Kan VIII Eb VI Kan V Ix XIII Kan III Eb 17 Yax 7 Pax 12 Chen 0 Yax[2] North West South East Gods 1404 1494 1744 1752 2 Pax 7 Pop 17 Mac 5 Kankin Gods East North West South 7 Zip 17 Yaxkin 2 Uo 10 Uo 236 90 250 8 Page 49. XIII Lamat XII Ezanab II Lamat X Cib VIII Lamat VII Ezanab X Lamat V Cib III Lamat II Ezanab V Lamat XIII Cib XI Lamat X Ezanab XIII Lamat VII Cib VI Lamat V Ezanab VIII Lamat III Cib I Lamat XIII Ezanab III Lamat XI Cib IX Lamat VIII Ezanab XI Lamat VI Cib IV Lamat III Ezanab VI Lamat I Cib XII Lamat XI Ezanab I Lamat IX Cib VII Lamat VI Ezanab IX Lamat IV Cib II Lamat I Ezanab IV Lamat XII Cib X Lamat IX Ezanab XII Lamat VII Cib V Lamat IV Ezanab VII Lamat II Cib 11 Zip 1 Mol 6 Uo 14 Uo North West South East Gods 1988 2078 2328 2336 16 Yaxkin 6 Ceh 11 Xul 19 Xul Gods East North West South 6 Kankin 16 Cumhu 1 Mac 9 Mac 236 90 250 8 Page 50. XII Eb XI Ik I Eb IX Ahau VII Eb VI Ik IX Eb IV Ahau II Eb I Ik IV Eb XII Ahau X Eb IX Ik XII Eb VII Ahau V Eb IV Ik VII Eb II Ahau XIII Eb XII Ik II Eb X Ahau VIII Eb VII Ik X Eb V Ahau III Eb II Ik V Eb XIII Ahau XI Eb X Ik XIII Eb VIII Ahau VI Eb V Ik VIII Eb III Ahau I Eb XIII Ik III Eb XI Ahau IX Eb VIII Ik XI Eb VI Ahau IV Eb III Ik VI Eb I Ahau 10 Kankin 20 Cumhu[3] 5 Mac 13 Mac North West South East Gods 2572 2662 2912 2920 15 Cumhu 0 Zec[4] 10 Kayab 18 Kayab Gods East North West South 20 Xul 10 Zac 15 Zec 3 Xul 236 90 250 8 Let us first examine the numbers which are regularly repeated in the lowest line:--236, 90, 250, and 8, and we shall find that the 584 days of the apparent Venus revolution are divided into these four periods. The number 236 denotes the time of the western elongation, when Venus is the morning star, 90 the time of the invisibility of the planet, during its superior conjunction, 250 that of its eastern elongation, when Venus is the evening star, and 8 the time of its invisibility during inferior conjunction. The disproportion between 236 and 250 is somewhat striking. These periods which need not of course be exactly equal are usually computed at 243 days. The short period of eight days is only calculated for very sharp eyes; we actually find in the Anales del Museo Nacional de Mexico II, 341 (Mex. 1882), that the Aztecs calculated only eight days for the invisibility of Venus, and this period is also mentioned in the Anales de Quauhtitlan. The repetition of the cardinal points in the 15th and 20th lines of the extract given above refer to these periods; in the upper line to their beginning and in the lower to their close. Hence in the lower line the cardinal points must advance one place and the gods belonging to them in the 16th and 19th lines must follow the same course. The numbers in the 17th line indicate to which day of the period of 2920 days the position has advanced. But now we see that the indication of days in the lines 1-13, the indication of months in lines 14, 18 and 21, and the numbers in line 17 are separated from those directly to the right of them by a number of days equal to the numbers given in the lowest line. From this it follows that each day of the thirteen top lines is joined to each of the month dates placed just below them, forming a complete calendar date. Therefore from the III Cib on the left upper corner of page 46 a III Cib 4 Yaxkin, a III Cib 8 Zac, a III Cib 19 Kayab must be formed. All the 4 × 13 × 5 = 260 day indications combined with three month indications each, show therefore that this whole passage is a huge abbreviation for 780 calendar dates and that the whole refers to 3 × 37,960 days = 113,880 days. But 37,960 which we already found on page 24, is equal to 146 × 260, 104 × 365, 65 × 584, 13 × 2920. I am inclined to think that I also found 113,880 on page 24. But the 3 × 37,960 = 113,880 days do not form the entire period treated of here. For the three periods begin and end with the days:-- I Ahau 13 Mac (10 Muluc), I Ahau 18 Kayab (3 Kan), I Ahau 3 Xul (4 Cauac). Hence these three dates, the second of which was found on page 24, prove that the three periods of 37,960 are not consecutive, but that there is an interval between them. Now between the first and second of the three dates the interval is 19 years + 85 days = 7020 days, and between the second and third, the interval is 26 years + 130 days = 9620 days. If these two periods be added to the 113,880 days, the sum is the whole period treated of here, viz:-- 130,520 = 502 × 260 days. But a truly surprising result is obtained, if, as must often be the case with series, we begin not with the upper of the three dates, but with the lower. From I Ahau 3 Xul (4 Cauac) to I Ahau 18 Kayab (3 Kan) there is a lapse of 9360 days or 12 apparent Mars years of 780 days, such as we shall find as the principal subject of page 59. 9360, however, equals 25 × 365 + 235 days. We shall meet with this 235 again as a difference on page 63. But from I Ahau 18 Kayab (3 Kan) to I Ahau 13 Mac (10 Muluc) there are 11,960 days, _i.e._, the 104 Mercury years, which we found on page 24, and which we shall find again as the principal period on pages 51-58. But this is equal to 32 years + 280 or 33 years - 85 days. Now if 113,880, 9360, 11,960 are added together, we have for the entire period under discussion here, 135,200 days, and this is equal to 2 × 260 × 260 days. Thus the Mayas seem actually to have had an idea of a second power. Finally I would call attention to a singular double connection between the numbers occurring here:-- 37,960 - 11,960 = 26,000 = 100 Tonalamatls, 11,960 - 9,360 = 2600 = 10 Tonalamatls. But if we subtract 2 × 11,960 = 23,920 from 37,960, the remainder is 14,040, _i.e._, an extraordinary number which often occurs and is equal to 54 × 260, 39 × 360 and 18 × 780. In short, a Mars and a Mercury-lunar period are inserted in the two spaces between the three solar-Venus periods. Now, let us try to gain a clearer understanding of this subject by approaching from another side. As we have seen, the beginning of the middle one of the three equal periods of 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24 furnished us with a day number for this date, 1,364,360, and from this the beginnings of the other two periods may be computed in the following way:-- I Ahau 3 Xul (4 Cauac) = 1,317,040, I Ahau 18 Kayab (3 Kan) = 1,364,360, I Ahau 13 Mac (10 Muluc) = 1,414,280. Between the first number and the second there are 47,320 days = 2^3 × 5 × 7 × 13^2, and between the second and third 49,920 days = 2^8 × 3 × 5 × 13 days. But, according to what has been stated above, 47,320 = 37,960 + 9360, and 49,920 = 37,960 + 11,960. The whole period is therefore divided as follows:-- It begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years, then the great period again followed by 8 × 13 = 104 Mercury years, and lastly, apparently about the present time, comes the third great period, which, as already stated, ends 135,200 days after the first date. The case assumes a different aspect, if we insert between the three dates the other two from page 24:-- 1,317,040 = I Ahau, 1,352,400 = I Ahau, 1,364,360 = I Ahau, 1,366,560 = IV Ahau, 1,414,280 = I Ahau. Here we have again, as examination of page 24 showed, the difference 11,960 between the second and third numbers, while there is no longer any connection with the periods of 37,960 days. Of the left halves of the pages we have now examined all except the twenty hieroglyphs of the gods. I shall mention them according to the upper place in line 16; the lower in line 19, where the hieroglyphs move forward only one place, is only referred to when the two signs differ. They offer many problems still unsolved. The first sign on page 46 is an unknown sign, which, however, is repeated several times on the right side of the pages; the second is probably an Ahau (_i.e._, D) with a prefix suggesting the snail, the symbol of birth; the third is a head also occurring elsewhere, which I have not yet determined; the fourth is A; compare page 24, hieroglyph 25. Page 47. The first sign is probably K; compare the third picture on page 7a with its hieroglyph; the second is C's hieroglyph with an Akbal appropriate to it; the third sign is Moan with the 13 belonging to it; the fourth sign is N's with a prefixed 4; the year-sign in the lower series is replaced by Zac, which agrees equally well; compare page 24, hieroglyph 21. Page 48. The first sign is Kin with the Ben-Ik superfix, perhaps denoting G; the second is a figure similar to the year-sign with a prefixed 6. This same sign in the line below has a 6, but is very different in other respects; the third is an Akbal with superfix and prefix, perhaps denoting D; the fourth is a head which might easily be F's; compare page 24, hieroglyph 22. Page 49. The first sign is B's; the second, A's; the 3d, K's; compare page 24, hieroglyph 38; the fourth is H's with a prefixed 1; compare page 24, hieroglyphs 23 and perhaps 37. Page 50. The first sign is E's; compare page 24, hieroglyph 38; the second is L, the black deity; compare page 24, hieroglyph 32; the third is an unknown hieroglyph with a prefixed 7, which also occurs on page 5a and 19b; the fourth is the bat-god; compare page 24, hieroglyph 24. I find it impossible to discover any relation between these hieroglyphs and the periods and I have as little success with the hieroglyphs apparently belonging to the same cardinal point. Perhaps we should follow Seler here (Quetzalcoatl and Kukulcan, p. 403), who thinks these passages suggest constellations with which Venus is in conjunction; this question, owing to the retrogression of the planet, raises increased difficulties. It is curious that the fourth of these signs on page 46 is like the fourteenth on page 49 (A), and perhaps the two following refer to the same god K; the first two are separated by 1494 days and the latter by 1508 days. We come now to the _right_ half of the pages. Interpretation is rendered impossible by the destruction of the top part. For we do not even know whether the upper hieroglyphs occupied three or four rows each, the latter being the case at least in part, and there may have been a superscription over the day signs in the left half. These upper signs are always followed by a picture, then three rows of hieroglyphs, then a second picture and next two rows of hieroglyphs and lastly a third picture. Let us first examine the pictures:-- At the top of pages 46-49 there is on each page a deity, who with his right arm extended is offering or receiving something. He is seated on astronomical signs; on page 46 B's head accompanies these signs. On pages 46 and 48 the deity is undoubtedly the old woman with tiger claws, who usually pours streams of water from a jug (compare pages 39, 43 and 74). I cannot identify the personage on pages 47 and 49. The object in the deity's hand seems invariably to be a cup of foaming pulque. On page 49 another object is placed above the cup, which I am unable to determine. The fifth, page 50, differs from the other four and forms the connecting link, as it were, between the upper row of pictures and the middle and lower ones. Here, too, a personage is represented sitting on astronomical signs and exhibiting symptoms of violent anger toward a second person opposite him holding the cup in his hands. Both personages are painted as warriors. The middle pictures on all the pages represent a warrior in a half-kneeling, half-crouching posture, holding spears or a shield in the right hand and brandishing a hatchet in the left. The shield on page 46 is doubtless a representation of the sun-glyph; and on 47 the Venus sign is combined with the head ornament. The hieroglyphs of these deities occupy the first place in the middle line of the three lines above the pictures. The five lower pictures represent a creature lying on the ground, pierced by arrows and spears. On page 47 it is a jaguar; at any rate it is the same animal found on pages 29a, 30c and 45c; a very similar creature pierced by arrows is given in the Cod. Vat. B.; compare also the pictures in Seler's "Venus-periode," page 371. On the other four pages this creature is in human guise. On page 50 where, differing from the other four pages, this figure is represented lying with the head to the right, it is plainly shedding tears. Seler takes this figure to be E on page 48 and the tortoise on page 49. The varying periods of time occupied by the revolution of the planets is plainly conceived of as contest. But who is the victor in this contest? The planet with the longer or with the shorter period of revolution? Owing to obliteration only a small part of the hieroglyphs of the top section is legible. On page 46 we see the Venus sign and E's hieroglyph; on page 47 the sign _c_, which occurs frequently on these pages, and is probably always connected with Moan (the Pleiades and thus with the year). The numeral 1, prefixed to an obliterated sign on page 47, is still legible, and we find it repeated on the lower part of the same page. There is rather more to be seen on page 48:--first the elongated head _q_ with the Ben-Ik superfix, then the sign _a_, beside it that for the west with a prefix, in the line below an Ahau, next, an Akbal sign with the prefix of the north, and lastly a Moan sign. On page 49 we see sign _c_ again occupying the first place, then o with Ben-Ik, and in the lower line the year sign with that for 20 or the moon as a superfix, and to the right of it the head with the Akbal eye, probably denoting D. This top part of the page is best preserved on page 50. In the third line from the bottom we see the Venus sign and beside it the Moan sign, below, a Cauac, then a Kin with the Ben-Ik superfix, then a Kan-Imix. Finally, in the first place in the lowest row there is a Kin sign and in the second place a sign resembling the year-sign, both having the same superfix, the next sign is again _c_ and the last is a half-effaced sign, of which only a Muluc is distinguishable. Our knowledge of the middle section of these pages is somewhat more definite. There are twelve hieroglyphs on each page, which I will number in the following order:-- 1 2 3 4 5 6 7 8 9 10 11 12. Unquestionably these 5 × 12 signs refer to a Venus year, more exactly to the _beginning_ of it, the period of the east. The first sign, which is a hand pointing to the right, merely refers here, as on the left side, to the direction in which this is to be read; the second sign is always the sign for the east, and the sixth invariably that for Venus. Notice should be taken of the fact that the signs of the Moan and screech-owl or death-bird are recurrent, that of the Moan appearing on page 46, sign 7; 48, 3; 49, 11; 50, 11; and that of the death-bird on page 47, sign 3; 48, 11, 49, 3, 50, 3 and 7, _i.e._, only in places 3, 7 and 11, which indicates that the 12 signs are divided each time into three times four. It is further to be noted that the five gods, who are represented on page 24 by hieroglyphs 36-40, always recur in the ninth place in the order of the pages:--the god represented on page 24 by sign 36 is the 8th on page 49; the 38th on the same page is the 11th on page 46 and the 12th on page 50; the 39th is the 12th on page 47, and the 40th may be the 5th on page 49, though this is hardly possible. On page 49 the 9th hieroglyph seems to be the 39th on page 24 joined to the sign for the month Kayab. Of the twenty gods on the left side of these pages, I have already remarked that E, who on page 24 occupies the 38th place, and the 11th on page 46, also occurs as the 9th on page 48 and the 12th on page 50. It is doubtless of special significance that the sign of the first of the twenty deities on the left side of page 46 is repeated on the right as the tenth sign on all the pages (on page 47 also in the eleventh place where it has a prefixed 3). It seems as if this sign, which is otherwise quite unfamiliar, might be connected with the sun and regarded as a contrast to the Venus sign in the sixth place. Also the 9th deity of the left side, the 1st of page 48, reappears in the 4th place on page 49; the 10th deity, the 2nd on page 48, in the 12th on page 49; the 15th deity, the 3d on page 49, in the 9th on page 46 and the 8th on page 49 (as already stated); the 18th, the 2nd on page 50, in the 5th on page 46. The 2nd of these deities is suggested by the 8th on page 47, perhaps also by the 5th on page 50; the 3d and 13th seem to be A and to recur in the 3d place on page 46. On the other hand C, the god who, as I believe I have proved, is connected with the day-sign Chuen, does not appear on the left side. Now the 4th sign on page 46 contains a Chuen, which in the 12th sign on page 48 is probably combined with a Muluc, in the 12th on page 49 with Yax and a prefixed 6, and in the 4th sign on page 50 with C's sign, _i.e._, as a rule Chuen stands in the 4th place in a line. As the gods E and K already mentioned also appear on pages 25-28 in connection with the change of the year, so we find the tiger on the top of page 26, and I believe this animal occurs again in the 7th sign on page 47. Of the day-signs I take the 4th on page 47 to be Kan, the 7th on page 48 to be Caban, and the next sign, the 8th on page 48, to be Muluc. Now if we take into consideration the fact, that of the three periods of the month signs on the left side of these pages, the 18th (the middle) line is the most important, owing to its ending, 18 Kayab, alone, if for no other reason; furthermore, that in this middle period the second Venus year always ends with a Kan year and the third with a Muluc year, one is naturally led to suppose that the illegible sign 12 on page 46 is an Ix (for thus the first Venus year ends) and that the days Cauac and Kan might have been found among the obliterated day-signs on pages 49 and 50. I shall examine the remaining signs in the order of the pages. Sign 8 on page 46 is the same compound of Yax and Kin having as a superfix the sign assumed by me to be the numeral 18, which occurs again in the lower group on page 50 and also on page 27. In the number 11 prefixed to the fifth sign on page 47, the 1 seems to be indistinct and may not belong here. If we correctly assume that this number is 10, then the sign is the same as the 34th on page 24, to the discussion of which I beg to refer my readers. Sign 8 on page 47 is an indistinct compound, the first part of which I supposed above to be the sign of the second deity on page 46. I cannot explain 4 and 5 on page 48. As yet I do not understand sign 5 on page 49, which we seem to have met before on page 22c. Sign 7 on page 49 is the moon, which is very curious here. I would like to call special attention to signs 5 to 8 on page 50. I interpret the passage thus:--At the time of the summer solstice after the reappearance of the Pleiades, the change of the Venus year takes place (this time). I have already discussed the Venus sign in the sixth place and the screech-owl so closely connected with the Moan (Pleiades) in the seventh place. Sign 5 connects the sun (Kin) with the Ahau (lord) and the cross-hatching on the left of it, which I have assigned to the tortoise and thus to the summer solstice (Zur Entzifferung III, 3). Sign 8 is recognized as very appropriate to the change of year; compare the first sign of the middle section on pages 25-28. All this points to the day 18 Kayab, of one of the Kan years, if, as I stated above, we base our computation on the middle series of dates. Now we have yet to examine the eight signs of the lower group, which we will do in the following order:-- 1 2 3 4 5 6 7 8. Regarding the beginnings of these groups, I will venture a bold surmise, which will, I hope, be improved upon by some one else. It concerns the first sign of four of these five groups, which seem to me to refer to the end of the Venus year, as those above refer to the beginning. This sign has the following form:-- [Illustration] I see in this the term of 73 days, which is the fifth part of the 365 days of the solar year and the eighth part of the 584 days of the Venus year:-- It is combined with Chuen in all four cases (pages 46, 48, 49 and 50). But I attribute the meaning of eight days to this Chuen sign, as I did on pages 25-28 and 42c-45c, though I am doubtful in these as in other cases. Page 46 contains the sign for 73 with a Chuen under it, and a 1 prefixed to each sign; _i.e._, 1 × 8 × 73 = expiration of the first Venus year. On page 48 Chuen follows the sign for 73 and each sign has a 3 prefixed to it; _i.e._, 3 × 8 × 73, expiration of the third Venus year. On page 49 the two signs again stand side by side, but the prefix is a 7 instead of the expected 4. By an error this 4 has been added to the 3 of the preceding page, but, for a wholly unintelligible reason, prefixed to the crouching person below the Chuen, as if to correct the 7. Page 50 again has the sign for 73 above and the Chuen below. A prefixed 5 would seem to be in order; instead of it, there is a 10, one 5 for the 73 and another 5 for the 8 days. In this connection let me say that I believe I have found on page 27, top left, the year of 365 days divided into 5 × 73. Page 47 differs from the others. Above two oval bodies appears the cross-hatched figure resembling a clamp, like the one in the middle group of page 50 in the fifth place, which I ventured to refer to the summer solstice. There is a 1 prefixed to it. Is this equivalent to a union of two Venus revolutions? Next we repeatedly meet here, as we did in the middle groups, with the Moan sign and that of the screech-owl belonging with it; the former is the 6th sign on page 46 and page 50, and the latter is the 3d and 7th on page 47, the 7th on page 49 and finally the 2nd and 4th on page 50. The moon is represented in the 5th sign on page 48 and in the 3d on page 49 and indistinctly in the 4th on page 48. The cardinal points occur here several times. The 3d and 7th signs on page 46 have at least the superfix of the south as a prefix; the 8th on page 47 apparently has the east, but with the familiar cross-hatched sign prefixed; the 7th on page 48 plainly has the east, the 3d on page 50 the prefix of the north prefixed to the cross _b_, and the 8th on page 50 the west, thus approximating the usual order and distribution. Of the gods I note the Akbal head, perhaps intended for D, in the 4th place on page 46, also in the 3d on page 48, and lastly in the 5th on page 49, the first two times with the Ben-Ik superfix, and in the 2nd place on page 47 the sign for A. In the 4th place on page 47 we have the tortoise as the sign of the month Kayab or of the summer solstice, in the 6th on page 47 the lightning-beast or the month Kankin with a Ben-Ik superfix; the beast itself is pictured below, and the same hieroglyph also with the Ben-Ik superfix is the 8th sign on page 49. It is hard to decide whether the sign 4 on page 49 represents the god F owing to the line through the eye, or a female by reason of the prefixed lock. Sign 7 on page 50 represents the deity whose sign began the series of twenty gods on the left of page 46 and which we have already met with several times in the centre of the right side. We recognize the prefix as having occurred in the middle group of the same page. Sign 6 on page 48 is a Kin combined with an unfamiliar sign. Sign 5 on page 50 contains a Kin with a Yax and probably with 18 as a superfix (as on pages 27 and 46 middle). Sign 6 on page 49 contains a crouching person with a 4 which is probably out of place here and to be regarded as a correction of the 7 above it. Sign 5 on page 46 contains a Mac denoting the thirteenth Uinal or a Tonalamatl, and having the sign _p_ as a superfix and a double Ik as a prefix. Sign 3 on page 46 merits special attention, because it contains the duplication of the sign, which, at the end of the first part of the Manuscript, pages 29-41, always began the groups of hieroglyphs on the lower third of the pages. I do not understand the second hieroglyph on page 46 and the 5th on page 47. In conclusion I would call attention to the fact that the last hieroglyph on page 48 is very peculiar. As on pages 51, 52, 61 and 69 it has the meaning of 18,980 days and consists of an Imix with a comprehensive superfix; its prefix is a 7. But what is the meaning here of 7 × 18,980 = 132,860? When we recall the statement made above that the whole section of pages 46-50 embraces 130,520 days, or, according to another calculation 135,200 days, it is a striking fact that 132,860 is exactly the mean of the two numbers, being separated from each by 2340 days = 9 × 260. Can it be an accident that on the next page (page 49) the fourth Venus revolution is reached, for 4 × 584 = 2336, _i.e._, almost 2340? The hieroglyph discussed here would not be so extraordinary on page 50. I will not venture to assert as to the 511 in 132,860 = 511 × 260, that it is connected with the 511 which will appear as the difference on page 58. Before leaving these pages, I will give a brief survey of the two signs of the screech-owl and the Moan (hieroglyph _c_ and the lower part of _d_) which occur on these pages with such marked frequency. In spite of obliteration, the first of these two signs is distinguishable in the top groups on pages 47, 49 and 50, in the middle groups on pages 47, 48, 49 and twice on page 50, in the lower groups on page 46, twice on page 47, once on 49, twice again on 50, making 14 times in all. A few additional cases might be added to these where the similar hieroglyph of the moon may have been set down instead of the one in question. On the other hand the second sign, always provided with the same prefix and suffix as the first, occurs in the top groups on page 48 and 50, in the middle of pages 46, 48, 49 and 50, and in the lowest on pages 46 and 50, 8 times in all. Since the subject here is astronomical, it is suggestive less of a deity or a sacrifice than of a period of time to which the allied page 24 has already referred (see page 110 of this book). The inner meaning of these pages is of course still enveloped in mystery. Pages 51a--52a. I shall begin the discussion of this very peculiar section with the remarkable fourth column on page 52, which, very possibly, the scribe ought to have placed at the beginning; for it looks like a repetition of the section on pages 46-50, while everything else on the left and right of it, apparently belongs together. If we omit the two hieroglyphs at the top, which I regard as belonging to the two rows of hieroglyphs extending over these two pages, we shall have the following result, according to my point of view:-- 1 5 Chuen 360 2 18,980. Since, as is frequently the case, the Chuen will here have the value of 8 days and the 5 with the sign for 360 may be regarded as 365, this group might denote 8 × 365 = 2920, but actually be 2 × 18,980 = 37,960. Both numbers are the basis of the section included on pages 46-50. And in the same way the 13 repeated 13 times seems to me to refer to the 13 series of days on those pages, which begin with the 13th day of the Uinal. The two rows of hieroglyphs are in the main destroyed. We can still recognize in the second and third columns of page 51 the signs for end and beginning, which we often find in the vicinity of numbers; in the second and third columns of page 52, the sun and moon; in the fourth column, the 8 days of such significance here and in the fifth and sixth, the normal date IV Ahau 8 Cumhu repeated twice. As the problem on pages 46-50 was to bring into accord the solar year with the Venus year and consequently also the Tonalamatl, _i.e._, to combine 365, 584 and 260, so the aim here is first of all to bring the Tonalamatl into unison with the Mercury year (115). For this purpose the number 11,960 is employed. This is equal to 46 × 260 = 104 × 115, including, therefore just as many Mercury years as there were solar years in the preceding section. 11,960 is also 8 × 1495, and this 8 is significant here, for, as we shall see directly, the day forming the basis of this calculation is XII Lamat, which comes 8 days after the normal date IV Ahau. The series given here is based, therefore, on 11,960 and consists entirely of multiples of this number, which, it is true, are recorded with the usual irregularity. The members of this series, representing the greatest values, which are set down in red numbers among the black, are the 31st and 39th multiples of 11,960, which are separated from each other by 8 × 11,960, viz:--370,760 and 466,440. All these numbers, of course, denote the day IV Ahau. The day XII Lamat as the actual starting-point of the Mercury revolution is not introduced until we come to the dates placed below the series. Here we find the days XII Lamat, I Akbal, III Ezanab, V Ben and VII Lamat written one below the other, and repeated seven times. Each of these days is separated from the next by 15, and the last of one row and the first of the next on the left are 200 days apart, hence the whole is equal to 7 × 260 = 1820 days. From XII Lamat begins also the Peresianus, pages 21-22. Now these dates are connected with the four large numbers, which we find on page 52, but between the third and fourth, one number corresponding to the day V Ben is omitted for lack of space. These four numbers, to which I have added the corresponding dates, are as follows:-- 1,412,848 = XII Lamat I Muan (6 Muluc). 1,412,863 = I Akbal 16 Muan (6 Muluc). 1,412,878 = III Ezanab 11 Pax (6 Muluc). 1,434,748 = VII Lamat I Muan (1 Muluc). It is curious that while the first three are separated from each other by 15, between the 3d and 4th, or rather between the missing 4th and 5th, 84 × 260 days are inserted in excess of the required 15, _i.e._, 21,855. This, however, is not accidental, but is due to the fact that between the first number and the last exactly 21,900 = 60 × 365 days have elapsed. This number is, however, = 18,980 + 2920, i. e., the sum of two very important numbers, in the first of which the Tonalamatl and the solar year accord, while both the solar and Venus years occur in the second. I must here call attention to the fact that the four numbers are not obtained without slight corrections, since in the 20-place of the third, I have put a 11 instead of 10, while in the 360-place of the fourth, I have omitted the three dots, _i.e._, set down a 5 instead of the 8. Of these four dates, which were doubtless not far removed from the time of the scribe, the three last are only the result of the first. Day XII Lamat is the most important. As the beginning of a Mercury period it should be regarded in the same way as I Ahau of the Venus period and IV Ahau of the solar period; and the very next day, XIII Muluc, will subsequently be seen to be the beginning day of the Mars period. The four dates XII Lamat, I Akbal, III Ezanab and VII Lamat are set down in the Manuscript directly below the numbers. Now in the first column on page 51 we again find a day XII Lamat, as is expressly stated beneath it. It has the number 1,578,988 and the corresponding date is XII Lamat 6 Cumhu (6 Kan). This day, however, is separated from the same day on page 52 (1,412,848 = XII Lamat I Muan 6 Muluc) by 166,140 days, that is by 8 × 18,980 + 14,300 = 639 × 260, _i.e._, by 8 so-called Katuns increased by 55 Tonalamatls. Here 58 × 260 = 15,080 seems to have been added to 252 (XII Lamat - IV Ahau) and the sum subtracted from 14 Ahau-Katuns = 1,594, 320. I could obtain this number only by substituting 1 for 0 in the 20-place. In the Manuscript the sign XII Lamat is set down above and below this number. I must leave undetermined whether the 8 directly above the number and combined with Kin and the Katun sign refers only to the 8 Katuns or at the same time also to the 8 days from IV Ahau to XII Lamat. It is also to be noted here that once before on page 24 of this Manuscript (which forms the basis of this section) 8 × 18,980 = 151,840 days was found to be the difference between 185,120 and 33,280, and that there, too, if my restoration is correct, it was the highest term of the series = 4 × 37,960. Finally, in the first column of page 51, we have the complete normal date 4 Ahau 8 Cumhu (9 Ix). But below this, between red numerals denoting the 1,578,988 mentioned above, there is set down in black the number 1,268,800. This corresponds to the date IV Ahau 3 Zip (2 Cauac). It may have been formed by adding 16,120 = 62 × 260 to 11 Ahau-Katuns = 1,252,680. It is, however, not only equal to 4880 × 260, but also to 158,600 × 8, therefore also divisible by the interval between IV Ahau XII Lamat, as well as by 104 = 8 × 13, while on the contrary it is not as we should expect, divisible by 11,960. I have changed the 11, in the 20 × 11, to 8 by omitting one line and adding two dots, for otherwise the result would not be the one required. The magnitude of the number recalls the one on page 31, which is only 260 less, and that on page 62. Finally it should be noted that the two large numbers on page 51 are separated from one another by 310,188 days = 849 years and 303 days, which corresponds exactly to the dates given for each. One may be situated as far in the future as the other is in the past, but this does not necessarily mean that the present coincides exactly with 1,423,894. Pages 51--58. Thus far we have examined only the upper halves of pages 51 and 52 and have still to consider the lower, but not until we have finished the upper parts of pages 53-58 of which the former are the continuation. We have first to consider the series, then the pictures and lastly the hieroglyphs. As on page 24 we found multiples of the number 2920 (= 8 × 365 = 5 × 584), while on pages 46-50 it was divided into four unequal parts, so on pages 51-52 we find multiples of the number 11,960 (104 × 115 = 46 × 260) while on pages 53-58 it is divided into 69 unequal parts. On pages 51-52 it was the aim to combine only the Mercury course with the Tonalamatl, but here we are confronted with the additional problem of bringing the lunar revolution into accord with these two. The lunar revolution, which we assume to be 29.53 days, of course requires fractional computation, of which the Mayas either were ignorant or which they timorously avoided; like the ancient Egyptians, who were acquainted only with fractions having 1 as numerator, or beyond these at most with 2/3 (see Hultsch, "Die Elemente der ägyptischen Teilungsrechnung," 1895, page 16). Now the Mayas had determined the lunar revolution so exactly that they perceived the incompatibility of the period of 11,960 days with a multiple of lunar revolutions. They found that 405 lunar revolutions amounted approximately to 11,958 days, which is, in fact, the largest number on the second half of page 58. In order not to drop the significant 11,960 altogether, they made use of a very shrewd artifice. They took as the starting-point the day XII Lamat, corresponding to the number 11,960, and set down XI Manik before it and XIII Muluc after it. Now if the count began with XIII Muluc and ended with XI Manik, it actually resulted in 11,958. Therefore what the Manuscript presents here is, in the first place, the series, which is this time to be read from left to right. Below it are the three days belonging to each member of the series and then a number for each member stating the interval between it and the preceding one. The members, the days and the differences must correspond with one another. It is, therefore, no longer necessary to pay especial attention to the two latter. They will serve merely to control and to correct the manifold errors. The entire period of 11,958 days was doubtless first divided into three equal periods of 3986 days. And in order still further to subdivide these shorter periods, the term of 177 days was employed as far as it would go; 177, however, is the half of a lunar year of 354 days, made up of 6 months of 30 days and 6 of 29 days, thus allowing 29.5 days in round numbers for each month. Now 177 is = 3 × 29 + 3 × 30. The average, 29.5, however, is too short for the length of the lunar revolution. In order to raise it as nearly as possible to the exact time, two other numbers were introduced at certain points of the series, viz:--148 = 2 × 29 + 3 × 30, 178 = 2 × 29 + 4 × 30. 148 = 5 months of 29.6 days, while 178 = 6 months of 29-2/3 days. Now let us see in what _proportion_ these 148 and 178 days were distributed among the periods of 177. First we see that the period of 3986 days (_i.e._, a third of the whole) was divided into 3 sections of 1742, 1034 and 1210 days, as follows:-- 1742 = 8 × 177 + 148 + 178 1034 = 4 × 177 + 148 + 178 1210 = 6 × 177 + 148 ---------------------------- 3986 = 18 × 177 + 3 × 148 + 2 × 178. This is equal to 135 months of 29.526 days each. Now the question arises how did the Mayas express this fraction? Perhaps some time in the future it will be found, that following their vigesimal system, they designated it approximately thus:-- 29 + ½ + 1/40 + 1/800. The _whole_ period of 11,958 days was divided as follows:-- 3 × 1742 = 24 × 177 + 3 × 148 + 3 × 178 3 × 1034 = 12 × 177 + 3 × 148 + 3 × 178 3 × 1210 = 18 × 177 + 3 × 148 --------------------------------------- 3 × 3986 = 54 × 177 + 9 × 148 + 6 × 178. Thus for every 6 parts of 177 days there was consequently 1 of 148 and to every 9 parts of 177, 1 of 178. Since 177 and 178 include 6 months each, while 148 equals 5 months, the entire length of the period is 405 months, which are divided into 69 periods. It was necessary to discuss all this before I could introduce the entire series itself. In the following table I have set down the numbers and added to them the differences between each number and the preceding one (to the first, the interval between it and the zero point), just as they are given in the Manuscript. An asterisk is added to show that the number has been corrected by me and is wrong in the Manuscript, owing to a mistake either in writing or in computation. The three columns correspond to the three divisions of 3986 days, and the two horizontal lines divide the periods of 1742, 1034 and 1210 days. Page 53a: | 24. 4163* 177 | 47. 8149 177 1. 177 177 | 25. 4340 177 | 48. 8326 177 2. 354* 177 | 26. 4488 148* | 49. 8474 148 3. 502 148 | Page 58a: | 50. 8651 177* 4. 679* 177 | 27. 4665 177 | Page 55b: 5. 856 177 | 28. 4842 177 | 51. 8828 177 6. 1034* 178* | 29. 5020 178* | 52. 9006 178* Page 54a: | 30. 5197 177 | 53. 9183 177 7. 1211 177 | Page 51b: | 54. 9360 177 8. 1388 177 | 31. 5374 177 | 55. 9537 177 9. 1565 177 | 32. 5551 177 | 56. 9714 177 10. 1742* 177 | 33. 5728 177 | -----------------+-------------------+----------------- 11. 1919 177 | 34. 5905 177 | 57. 9891 177 12. 2096* 177 | 35. 6082 177 | 58. 10068* 177* 13. 2244* 148 | 36. 6230 148 | Page 56b: Page 55a: | Page 52b: | 59. 10216 148* 14. 2422* 178 | 37. 6408 178* | 60. 10394 178* 15. 2599* 177 | 38. 6585 177 | 61. 10571 177 16. 2776 177 | 39. 6762 177 | 62. 10748 177 -----------------+-------------------+----------------- 17. 2953 177 | 40. 6939 177 | Page 57b: 18. 3130 177 | Page 53b: | 63. 10925 177 Page 56a: | 41. 7116 177 | 64. 11102 177 19. 3278 148 | 42. 7264 148 | 65. 11250 148 20. 3455 177 | 43. 7441 177 | 66. 11427 177 21. 3632 177 | 44. 7618 177 | 67. 11604 177 22. 3809 177 | 45. 7795 177 | Page 58b: Page 57a: | Page 54b: | 68. 11781 177 23. 3986 177* | 46. 7972 177 | 69. 11958 177 No one acquainted with the cursoriness of the Maya Manuscripts will be surprised that among 138 numbers I have declared 21 to be wrong. Furthermore the 21 errors are lessened by the fact that six of them are really only one, for in all 6 cases where the difference is 178, the scribe has overlooked this and written down the usual 177, although the numbers and the days of the series very correctly indicate 178. Again the three errors in groups 58 and 59 are also only one, for the author had confused the differences 177 and 148 and had, therefore, to write down 10,039 instead of 10,068. In group 4 the error is merely the omission of a line meaning 5. The scribe must have been at the same time the computer and therefore the actual author of the Manuscript. Furthermore I must call attention to the regular position of the differences 178 and 148. In the three periods of 1742 days the 178 always occupies the 6th place and in the periods of 1034 it is always in the 4th place. This difference appears, therefore, in groups 6, 14, 29, 37, 52 and 60, _i.e._, 8, 15, 8, 15 and 8 groups apart; but it is entirely lacking in the periods of 1210 days. And in all nine sections the 148 occupies the third place, _i.e._, directly in front of the pictures, which will be discussed immediately, therefore in groups 3, 13, 19, 26, 36, 42, 49, 59, 65, _i.e._, at intervals of 10, 6, 7, 10, 6, 7, 10 and 6 groups. But I must point out an error fraught with consequences. Groups 22 and 23 quite correctly have the difference 177, but in this single instance the scribe has written down 178 and hence has computed the three days belonging to it as VII Ix, VIII Men and IX Cib instead of VI Ben, VII Ix and VIII Men, and from here on to the close he is always one day in advance, so that on page 58 group 69 ends with the days X Cimi, XI Manik and XII Lamat, while it ought to have ended with IX Chicchan, X Cimi and XI Manik. So much for the series. Vid. on this series my paper "Zwei Hieroglyphenreihen in der Dresdener Mayahandschrift" (Zeitschrift für Ethnologie, 1905, numbers 2 and 3). Let us turn next to the ten pictures which are inserted in this series, three of which appear at the end of each period of 2920 days as on pages 46-50. Let us attempt to advance a step further in the darkness which still surrounds us here. One of these pictures, the 8th, which is on page 56b, is in the wrong place, owing to the error in computation in Groups 58 and 59 to which I called attention above. It belongs not _before_ but _after_ group 59, the first on page 56b. This is indicated in the Manuscript itself. For in group 59 the two hieroglyphs, usually placed above each group, are missing and we find instead of them the sign resembling a snail, which is doubtless a very much emphasized zero (compare my "Erläuterungen," page 29), which indicates that the section designated by a picture closes with this group. Having corrected this error we see that the ten pictures are on the following pages and come after the following numbers of the series:-- 1. 53a 502 2. 55a 2244 3. 56a 3278 4. 57a 4488 5. 52b 6230 6. 53b 7264 7. 54b 8474 8. 56b 10216 9. 57b 11250 10. 58b 11958. From this it follows that a picture is assigned to each of the nine sections composing the series. They are placed, however, not at the beginning or end of the section, but always after the expiration of 502 (= 2 × 177 + 148) days. The pictures are thus separated from one another by 1742, 1034 and 1210 days, which intervals correspond exactly to the length of the nine sections. But the last picture is separated from the preceding one by 708 days, and as it has a character quite its own, it must be discussed separately. But these 708 days with the 502 days of the beginning quite regularly amount to 1210 days, and the series is therefore to be considered as a recurring one. Now these nine pictures might very easily be regarded as forming a new series, which is inserted in the original one and which has the day 502 as its zero-point. In that case, we shall have to subtract 502 every time from the days set down in the Manuscript. This new series may be represented thus:-- 1. 53a 0 2. 55a 1742 3. 56a 2776 4. 57a 3986 5. 52b 5728 6. 53b 6762 7. 54b 7972 8. 56b 9714 9. 57b 10748. It is certainly remarkable that the last number, 10748, corresponds so closely to the time of the revolution of Saturn, which is computed at 10753 days. For owing to the slowness of its progress, the Mayas may have known not only the apparent but also the actual revolution of Saturn. Besides the apparent revolution of Saturn (378 days from one superior conjunction to the next) could not be made to coincide very well with the length of the solar year. I will immediately present a further confirmation of my theory. All these pictures have rectangles above them, of which I have spoken in my "Erläuterungen," page 16, and which always enclosed two or three hieroglyphs in which, with due hesitation, I assumed to be the signs of the sun, moon, and planets. This theory has as yet called forth no serious opposition. Now in the passages just mentioned, I indicated the following figures as the signs of Saturn:-- [Illustration] These figures actually occur in all the nine pictures with the exception of the first, which has no rectangle at all, and where in true Maya fashion, the zero-point is concealed. I go still further in my bold hypothesis. The time of the apparent revolution of Jupiter has been placed at 397 days. The Mayas, I think, computed it at 398 days. In the passage alluded to I regarded the following as the sign for Jupiter:-- [Illustration] We find these signs in pictures 4, 6, 7 and 9. The corresponding numbers reduced for the revolution of Saturn are 3986, 6762, 7972 and 10,748. I assume that the third picture, _i.e._, the number 2776, is another zero-point, in consequence of which the sign is here suppressed, and that still another is the tenth picture with the number 11,958, which has no relation to the revolution of Saturn. If we compare these numbers with the 398, _i.e._, the apparent revolution of Jupiter, we have the following:-- 3. 2776 = 7 × 398 - 10 4. 3986 = 10 × 398 + 6 6. 6762 = 17 × 398 - 4 7. 7972 = 20 × 398 + 12 9. 10748 = 27 × 398 + 2 10. 11958 = 30 × 398 + 18 The differences 10, 6, 4, 12, 2 and 18 are so small in comparison with 398, that the numbers 2776, etc., might very well have been regarded as approximate multiples of the revolution of Jupiter. And the remainders in the seventh and tenth pictures could be still further reduced. In the seventh picture, the first sign is very unusual and one which I do not remember having met with elsewhere. If it should be possible to regard it as the number of the thirteen week days, then it would follow (the Saturn sign being regarded as unimportant) that the contents of the rectangle meant:-- 13 + a multiple of 398, by which this remainder would be reduced to -1. The tenth picture has the cross _b_ as the beginning of the rectangle. This is the sign for union, very often denoting especially the union of all the twenty days. Thus we have here (aside from the middle sign to be discussed later) the formula:-- 20 + 30 × 398 - 2 = 11,958, or even 20 + 30 × 398 = 11,960. The regular progression from the 7th multiple to the 10th, 17th, 20th, 27th, and 30th multiples in the above six equations is also somewhat in favor of my theory, while the four rectangles without the Jupiter sign are by no means multiples of the Jupiter revolution:-- 1. 502 = 398 + 104 2. 1742 = 4 × 398 + 150 5. 5728 = 14 × 398 + 156 8. 9714 = 24 × 398 + 162. Let us now try to interpret the meaning of the remaining rectangles (always omitting the Saturn sign as a matter of course.) In pictures 2 and 8 the rectangle also contains the sign of the moon or of the twenty days. Beside it in picture 2 is the sign, which in my "Erläuterungen," page 16, I regarded as the sign for Mercury. Hence we have here 20 + 15 × 115 = 1745, _i.e._, only 3 units more than the required 1742. The rectangle with the eighth picture contains in addition to the moon a sign which looks as if it were intended for a whole divided into four parts. Until something better (perhaps the the sign of Venus) is proposed, I will assume that it is the quarter of the Tonalamatl, _i.e._, 65, and I take the required number to be 9714 in the form of 20 + 149 × 65 + 9. Above the third picture I see a Mercury and a Venus sign and I read 584 + 19 × 115 = 2769, which is only 7 units less than the required 2776. The fifth picture still remains to be discussed, but I do not know how to unite the Mercury revolution here with the 5728. For the present, however, I am inclined to believe that there is a mistake in this passage. We pass now from the obscure contents of the rectangles to the equally mysterious pictures themselves. Aside from the tenth picture, I find human forms in four pictures. Picture 1, page 53a, is the death-god (A) seated and pointing upward, an appropriate representation for the zero-point of the Saturn series, _i.e._, for the end of the preceding revolution. Picture 2, page 55a, contains the head of a deity, probably D's with the suggestion of a beard and the sun-sign on his forehead. The head is surrounded by a ring striped black and white. Picture 3, page 56a, is the head of B, again with a beard and with the sign Kin (sun) above. The head is surrounded by a design, the left part of which is black and the right white. Picture 6, page 53b, represents a hanged woman, which Schellhas, "Göttergestalten," page 11, takes to be the Maya goddess Ixtab, the goddess of the halter, _i.e._, of the hanged. The centre of picture 4 on page 57a, contains the suggestion of a face, perhaps in place of the Ahau sign, and on either side of it is a black and white surface. It is further important to note that four times in this section Kin (sun) forms the centre of the picture, viz:--pictures 5, 7, 8 and 9, pages 52b, 54b, 56b and 57b. In all four cases there is on either side of Kin a black and white surface, such as we have already seen in picture 4 and similar to that in picture 3. Pictures 8 and 9 are vomited up, as it were, by a serpent placed below them, in the same way as B is represented on pages 34b and 35b. In pictures 5 and 8, four objects suggesting arrows extend from the Kin in four directions and probably denote the four cardinal points or the four Bacabs, of which we shall have more to say presently. Two of these arrow-like signs also appear in picture 7, page 54b, but only on the black and not on the white surface. I will postpone discussing picture 10 until later and pass on to the hieroglyphs above the first nine pictures, about which it is true I have nothing satisfactory to say. There are always properly speaking ten of these hieroglyphs, among them the two signs for the sun and moon. But the scribe introduced the latter only in pictures 1-4, and also with the more elaborate last picture 10. With pictures 5 and 9 he omitted these signs in order to represent the other eight larger and with greater distinctness of detail. Among these hieroglyphs are several of gods, especially that of A with pictures 1, 5 and 9, and H with picture 5, and with pictures 1, 3, 5, 7, 8 and 9 there are other heads, some of them bird-heads, regarding which I am uncertain. The Ben-Ik sign, to which I have assigned the meaning of a lunar month, belongs with pictures 4, 8 and 9 and occurs twice each with pictures 1 and 10. I am inclined to see the sign for Mercury in the crouching figure belonging to pictures 9 and 10, which is drawn upside down and combined with the half Venus sign (11958 = 104 × 115 - 2). Hands grasping a hieroglyph (a sign for 20 days?) are represented in pictures 1, 7, 8 and 10. The enigmatical numbers, prefixed to the hieroglyphs, occur several times, thus a 1 with pictures 1 and 10, and a 4 twice with picture 8 and a 6 with picture 3. Now let us examine picture 10 somewhat in detail and also the signs standing above it, since both are of special significance here. This representation treats of the period of 11,960 days in which the Mercury and lunar revolutions meet. And this is proved by the ten hieroglyphs, which I will number as follows:-- 1 6 2 7 3 8 4 9 5 10. I can omit Signs 3 and 8, sun and moon, since they refer to a period of time only in a general way. Sign 1 seems to me, as I have already stated, to have reference to the revolutions of Mercury. Then follows sign 2, the upper part of which is a mat and the lower the Muluc sign. I believe this sign is intended to denote that the beginning of this period is in a Muluc year. Indeed, our examination of pages 51-52 showed that it was the year 6 Muluc. The mat (Pop) is very properly the symbol of beginning, since the first month of the year was likewise called Pop. Sign 7, it seems to me, indicates that this period should be divided into lunar months (denoted by Ben-Ik), and, as I have already demonstrated in my examination of page 24, the length of the period is stated here by Signs 4, 5, 6 and 9, but the dot before the fifth should be placed before the fourth, as is actually the case on page 24. Therefore:-- 4 = 21 5 = 7200 6 = 4680 9 = 59 ----- 11960. It is perhaps not accidental that the ninth sign is that of the fourteenth month, which signifies the expiration of the preceding lunar month, for here the month begins with the first day of the fifteenth month. Sign 10 is doubtless Xul = end, as it so often is, for example, on pages 61-62 below. But I have not solved the meaning of the two prefixes. The end would be XII Lamat 16 Yax (13 Ix). The picture represents a human form, which has in place of a head a design somewhat resembling the head of a lance. It is sitting with legs spread apart, and in this respect may be compared with god B of Cort. 9, who is represented in the same way. In the picture before us, the figure holds in its upraised hands the sun and moon signs, which are constantly repeated throughout the series. The Venus sign is placed between the outspread legs. In the rectangle above the figure, this sign is repeated in a more concise form, while on the left the cross _b_ appears as the sign of union or multiplication, and on the right that of Jupiter, whose period of revolution is here multiplied by 30 (30 × 398 = 11,940). And the two Venus signs can mean nothing more than that this period of 11,960 also serves the purpose of filling up the gap between the two large Venus-solar periods of 37,960 days, like the similar process which we saw on pages 46-50. We have examined first the series and then the pictures with the hieroglyphs belonging to them. Let us pass now, as the third step, to the examination of the two rows of hieroglyphs extending above the numbers throughout the whole section. First of all, I will again set down here the position of each of the sixty-nine groups:-- Page 51. | 52. | 53. | 54. 31.32.33.34.35.36.|37.38.39.40.| 1. 2. 3. 4. 5. 6.| 7. 8. 9.10.11.12.13. | |41.42. 43.44. 45. |46.47.48.49.50. Page 55. | 56. | 57. | 58. 14.15.16.17.18. |19.20.21.22.|23.24.25.26. |27.28.29.30. 51.52.53.54.56.57.58.|59.60.61.62.|63.64.65.66.67.|68.69. Since each group contains two hieroglyphs, this makes 138. in all. Of these, however, about 24 on the upper halves of the pages, are wholly or almost wholly effaced which very materially hinders the trustworthy determination of the context. Furthermore group 59 is entirely lacking or rather group 58, in the place of which the 59th has been set down. The eighth picture was probably already drawn, when the artist saw that there was not room enough left for the 58th and 59th groups. Hence he omitted the 58th, setting down in place of it the 59th and in the place of the latter he set down the zero mentioned above. The question now arises:--Are these hieroglyphs dependent upon the days and numbers of the series and upon the pictures, or are they entirely independent of them? I find but _one_ point in favor of the first possibility, viz:--the Venus sign in group 4b (I will designate the upper hieroglyphs by _a_ and the lower by _b_). It is placed in the period indicated in which 502-679 days elapse, and in which, therefore, Venus has finished a revolution of 584 days. It may be, that by way of exception, this significant date was intentionally recorded. On the other hand, there are many things, which favor an entirely different interpretation of these hieroglyphs. Thus I am of the opinion that the ritual year of 364 days with its four Bacab periods of 91 days each is referred to here, as we have already found it referred to on pages 31a-32a and on page 45a, and shall find it again on pages 65-69 and 71-73. In that case the single groups would be separated from one another by one Maya week = 13 days. I will now arrange the sixty-nine groups in the following order (the reason for which will become clear directly):-- I 4 11 18 25 32 39 46 53 60 67 II 5 12 19 26 33 40 47 54 61 68 III 6 13 20 27 34 41 48 55 62 69 IV 7 14 21 28 35 42 49 56 63 1 V 8 15 22 29 36 43 50 57 64 2 VI 9 16 23 30 37 44 51 58 65 3 VII 10 17 24 31 38 45 52 59 66. The groups in a horizontal row are separated from one another by 7 or a multiple of 7. If now a hieroglyph is repeated in those places, which are in the same horizontal row, then this is a confirmation of the supposition that Bacab periods are meant to be represented here. Hence I will examine each row in turn. These rows extend over the long period of 69 × 13 days probably merely for the purpose of filling up the space. I. In 39b, 46b, 53b and 60b, _i.e._, after every seven groups, perhaps also in 18b, we find the following sign, which I identified as that of a Bacab, in Globus, Vol. LXXI:-- [Illustration] Hence this denotes the beginning of the Bacab period. In 4b the sign is replaced by that for Venus. In 11b, 25b, 32b and 67b we find other signs, it is true, nevertheless the regularity stated above cannot be accidental. The upper signs of groups 39a, 46a, 53a and 60a contain an Imix and corroborate the connection. II. 5b and 26b (after 3 × 91 days) contain a head very like the preceding, which readily suggests the idea that it is merely a Bacab sign pushed one group ahead, but it also appears in 13b, 50b and 52b. Then 12b, 54b and 61b correspond, _i.e._, after six groups of 91 days and one more of the same length, but the same sign appears also in 34b, 48b and 56b. III. 41b and 69a are Xul = end and are therefore separated by 28 × 13 = 4 × 91 days, _i.e._, the length of a year. It is singular that both signs of 41 are like those of 47; if we assume that 47 was set down one group too soon, it would be in excellent keeping with the rest. The Xul also appears in 11b and 28b. 34b and 48b correspond after 2 × 91 days, as already mentioned under II. IV. 42a and 49b both contain the sign for the sun between clouds. V. 36b and 57b agree after 3 × 91 days; the same sign appears again in 10b and 20b. 15a and 36a correspond after 3 × 91 days; we shall continue the examination of this sign under pages 71-73. VI. 37a and 65a agree, _i.e._, after 4 × 91 days = a year. The sign contains a human figure stretching both arms aloft. The passing of a year was likewise indicated in III, but a year coming 52 days later than this. VII. 10a and 31a agree, _i.e._, after 3 × 91 days. The sign is composed of the crouching figure prefixed to the cross, which we also find in 12b, 35a and 65b; it is prefixed to a different hieroglyph in 30a. In 38b, 52b and 59b (58 in the Manuscript) we see bird-like heads resembling the Bacab sign. We should expect to find a familiar sign in 45, which is drawn between these, but a Moan appears there instead. These signs seem to indicate the end of the Bacab period. Does the Moan sign here, too, suggest the end of the year? In 38a, 52a and 59a we again see an Imix, and I consider it a corroboration of my theory that all the four signs of groups 38 and 39 are repeated in 52 and 53 after 2 × 91 days. I believe a further corroboration is the fact that though many of these hieroglyphs have no connection with these periods of 7 × 13, _i.e._, with the divisions of the ritual year, they do correspond with the usual divisions of the Tonalamatl, _i.e._, 4 × 13 and 5 × 13 days. After 4 × 13 or a multiple of it the signs recur in 20b, 24b, 40b, 44b-12b, 48b, 56b-16b, 32b, 64b-26b, 50b-10a, 30a-37a, 65a-15b, 51b-11b and 47b. As examples of 5 × 13 I would mention 3b, 63b-10a, 20a, 30a-5b, 50b-24b, 29b-35b, 65b-15b, 20b, 40b. Finally, I must mention two more hieroglyphs, which are limited almost entirely to these pages:-- [Illustration] In the first sign, which occurred on page 10a, I thought I recognized the lunar month of 28 days. It occurs in this section in connection with the third picture on page 56, and besides in the following groups of hieroglyphs:--16b, 32b and 64b, always combined with a Yax. The regularity of the intervals is striking, but as yet I can neither explain that, nor the crouching personage (Mercury?) in the 10th, 20th and 30th groups and again in the next, the 31st. The second sign is found _only_ on these pages and here not less than eleven times, possibly with the addition of the effaced sign in 6b and 27b which may have been the same hieroglyph. The eleven places in which it occurs are as follows:--3b, 15b, 17b, 23b, 24b, 29b, 40b, 44b, 49a, 51b and 63b. Two different prefixes are added to it; one in the first two and the last two places and also in the last but two joined with Kin, and the other in the six middle places. Of the eleven groups, 17 and 24, 44 and 51 are 7 groups apart, 3 and 17, 15 and 29, 49 and 63 are 14 groups apart, 23 and 44 are 21 groups apart, and hence 23 and 51 are separated by 28 groups or 1 year. Group 40 alone is not concerned with these intervals of seven or multiples of seven. Now, how far may all these periods of time be due to accident and how far to design? Accident _alone_ is quite out of the question. The frequent repetition of the sun-sign in groups 49, 50 and 51 on pages 54b and 55b, seems to me to refer to the conjunctions of the sun with certain stars, which occur at intervals of thirteen days. Pages 58--59. This section is also based on a series occupying the whole of page 59, which contains nothing but number and day signs. This series has the difference 78, which we found once before on page 44. There the starting-point was III Lamat, here it is the day XIII Muluc, probably coming in the year XIII Muluc, as in Cort. 40b, as I shall have occasion to suggest later. The series extends, with the usual errors and variations, in four divisions from top to bottom. The days, which are always two days behindhand, owing to the number 78, in 780 again reach the day XIII Muluc, at which point the succeeding members remain stationary, since from here on the difference is always 780 or a multiple of it. 780 days are, however, the apparent time of the revolution of Mars, which is the only planet now left to be discussed, the subject of pages 46-50 having been Venus and the sun, and of pages 51-58, Mercury and the moon with incidental treatment of Saturn and Jupiter. With 780 as its difference, the series ascends to 19 × 780 = 14,820, and then continues with this large number as its difference until the series is lost in the effaced passages. Curiously enough, however, directly under the line containing the 14,820, there is a new series composed of nine members, or ten counting the suppressed starting-point. But this starting-point is again the day IX Ik, the difference, as proved by the annexed days, is again 78 and the series ends with 780. Thus the starting-point is the only difference between the two series. The principal series contains all the even and the secondary series all the uneven days. Can the starting-point of the revolution of Mars have been determined according to different principles? Is it possible that in one case the beginning of the planet's retrogression was adopted as the starting-point, and in the other case the date on which the planet, after completing its retrograde course, again reached the degree of right ascension at which it had begun its retrogression? This is a difficult matter to decide, since the period of the retrogression of Mars fluctuates between 62 and 81 days. The interval from IX Ik to XIII Muluc is 147 and in reversed order 113 days. It can hardly be assumed that the 19 of the IX 19 or IX Ik is connected with the 19 × 780 mentioned above or with the 19 + 19 + 19 + 21 into which the 78 is divided on pages 44-45, or finally with the 19, which four times forms the principal part of the sub-divisions of 65 on pages 33-34. Numbers amounting to millions accompany this series in the usual way. Two of these are on page 58, viz:--1,426,360 and 1,386,580; but with the sign of the sixth day, which is important here, between them. Below these numbers, however, are two month dates:--first the normal date IV Ahau 8 Cumhu and, if I have correctly restored the effaced number before the month sign, which in its turn is indistinct, the second is XIII Muluc 2 Zac, which would fall in the year VIII Muluc. The encircled numbers also occur here. They are set down beside the lower number of seven figures. We find here a red 12 with a black 1 inserted, below this a black 7 and below this again, enclosed in a red band, a black 11, which I regard as also representing the value of a red number. We shall find a similar instance among the serpent numerals. Then we have here 1. 7. 11. = 511 and 12. 11. = 251. But 511 = 260 + 251 and 251 is the interval between XIII Muluc and IV Ahau. With the day XIII Muluc and the interval 9 between IV Ahau and XIII Muluc, numbers for XIII Muluc have been formed amounting to millions, which, however, have been suppressed in the Manuscript, just as they were on page 31 where, in like manner, numbers were first formed for day XIII Akbal. I assume that to begin with, 76 Tonalamatls (= 19,760) were added to this 9 and then 228 Tonalamatls (= 59,280), the 228 being = 3 × 76 and the 59,280 including 76 revolutions of Mars. The result in one case was 19,769 and in the other 59,289. If the 12 Ahau-Katuns, which are specified as 1,366,560 on page 24b be added here, we have the following numbers:-- 1,386,329 = XIII Muluc 2 Mol (3 Muluc), 1,425,849 = XIII Muluc 2 Zip (12 Muluc), and if the two encircled numbers of the Manuscript:--251 and 511 be added, the sums are 1,386,580 and 1,426,360, _i.e._, the two large numbers of the Manuscript. The dates corresponding to these numbers are as follows:-- 1,386,580 = IV Ahau 13 Muan (12 Muluc), 1,426,360 = IV Ahau 8 Muan (4 Ix). If we compare the two numbers with the normal date, the curious result follows that:-- 1) 1,386,580 - 1,366,560 = 20,020. This number is equal to 55 × 364, including therefore the ritual year of 364 days. 2) 1,426,360 - 1,366,560 = 59,800. This number is five times 11,960 days, which is assumed to be the time in which the lunar and Mercury revolutions accord. This 59,800 was found once before on page 24 as the suppressed difference between 68,900 and 9,100. Thus the separate sections (of the book) are very closely connected. If the two large numbers be compared with one another their difference will be found to be 39,780. This is equal first to 51 Mars revolutions of 780 days, and second to 4420 × 9, _i.e._, a multiple of the interval between IV Ahau and XIII Muluc. Now we must direct our attention to the seventeen hieroglyphs, which we find in the two columns on page 58, apart from the matter-of-course calendar date at the top, which is repeated at the bottom. One column contains 11 hieroglyphs and the other 6. I will here advance the following theory in regard to these hieroglyphs, which may serve until a better is found:-- Since, as a rule, the Tonalamatl is divided into 5 × 52 days, I believe that each group of three Tonalamatls treated of on page 59, is divided into 15 of these parts; that each hieroglyph, therefore, denotes 52 days and that the first three parts are separated from the others by the signs of beginning and end in the first and fifth places, so that three of these parts, which equal 156 days, always form a separate group. 156 is the 5th part of 780. With the omission of the first and fifth signs, the passage, I think, stands thus:-- 0 XIII Muluc 2 Kankin (13 Muluc). 1) 0-52 XIII Imix 14 Pax. 2) 53-104 XIII Ben 1 Pop (1 Ix). 3) 105-156 XIII Chicchan 13 Zip. -------------------------------------- 4) 157-208 XIII Caban 5 Xul. 5) 209-260 XIII Muluc 17 Mol. 6) 261-312 XIII Imix 9 Zac. -------------------------------------- 7) 313-364 XIII Ben 1 Kankin. 8) 365-416 XIII Chicchan 13 Pax. 9) 417-468 XIII Caban 25 Cumhu. -------------------------------------- 10) 469-520 XIII Muluc 12 Zip (2 Cauac). 11) 521-572 XIII Imix 4 Xul. 12) 573-624 XIII Ben 16 Mol. -------------------------------------- 13) 625-676 XIII Chicchan 8 Zac. 14) 677-728 XIII Caban 20 Mac. 15) 729-780 XIII Muluc 12 Pax. If we adopt this arrangement for the present we cannot fail to see that the author had an aim in view, when we consider the following:-- 1. The zero-point lies 15,609 days later than the normal date IV Ahau 8 Cumhu (9 Ix). This is equal to 20 × 780 or 60 × 260 increased by the interval between IV Ahau and XIII Muluc = 9. There are 86 days between 2 Kankin and 8 Cumhu _i.e._, 15,609 = 43 × 365 - 86, and from 9 Ix to 13 Muluc it is 43 years. 2. The same zero-point, 13 Muluc, lies in the year with the same name, that is, the very point where a Tonalamatl of the year ends. 3. In this arrangement the first as well as the last day of the year 1 Ix is exactly reached in the second and ninth groups. While the meaning of the second is as yet unintelligible to me, the end of the year is appropriately indicated by the ninth with its compound of Kin and the year-sign, above which there may be an Ix as a superfix, but misshapen for want of room. 4. Also the fact that it is the first of the two columns, which closes with this year-end, seems to show a purpose. 5. Several instances of similarity appear among the hieroglyphs in these groups of three:--an Akbal sign in 1 and 4 suggests the god D, the superfix and prefix of 2 and 14 the god K and 5 and 11 the screech-owl and therefore A. Little else is to be said of these hieroglyphs. C might be denoted by 3 (13 Zip) and 10 (12 Zip). Group 8, the central point of the series, has on the left and right the signs for the north and south as if the time between the north (Muluc) years and the south (Cauac) years were meant to be indicated here. I am inclined to consider the crouching personage in 12 as the revolution of Mercury, which requires 115 days:--573 is 5 × 114 + 3 or 5 × 115 - 2. Is 7 a sign, as yet unknown, for the year of 364 days? 15 looks like two signs for the month Mac, placed back to back, which here designates the Tonalamatl as it does on page 24. The superfix of three parts might denote three Tonalamatls = 780 days. The familiar sign in the fifth place in connection with the expiration of the first Tonalamatl is striking; it is the one usually identified as that of the screech-owl or death-bird. Page 60. This is the last page of the front of the second part and is divided into four sections:--at the top we find hieroglyphs, below these a picture, then hieroglyphs again and in the lowest section another picture. The upper picture contains first a rectangular elevation like a platform. Enclosed in this rectangle is the picture of the animal resembling a dog lying down, which we have often met with, the last time on page 47. In front of the dog is a hieroglyph, which, I regret to say, is still unknown and which occurred six times as a heading on page 23b. On the platform two personages are fighting; one is in war-dress holding in his left hand the throwing-stick or atlatl, and in his right probably arrows; the other figure, whose back is somewhat indistinct owing to obliteration, is apparently unarmed and is making a defensive gesture with one hand. Beside the platform, and therefore on a lower level, is a second person walking behind the armed person as if to help him. He too is in war-dress and likewise holds an atlatl. A black 3 is set down between the two combatants, and there may also have been a red 2, which is indistinct owing to the red background of the picture. Let us next examine the lower picture. A blindfolded personage is kneeling on the left. A serpent's head rises from the ground in front of him. A second serpent rises in several coils on the shoulders of the blindfolded personage and on the serpent's neck sits enthroned another personage, who is rather indistinct, holding a spear and a shield. On the right, opposite this group and facing it, is a second. A personage with arms bound and bowed head is sitting on the ground. There is a black ring around his eye. Behind him stands the victor in war-dress and again equipped with spear and shield. There is a red 11 and a black 2 between the two groups. We see that the reference here is to combat, just as it was on the right side of pages 46-50. And since the subject of these pages like that of 46-59 is confined to the revolutions of the planets, it is natural that the pursuit of one by the other, their periodical disappearance, the crossing of their orbits and the variation in the length of their revolutions should be looked upon as a contest. Therefore, since the sun, the moon and the five planets have hitherto been treated of on these pages, I look for these seven heavenly bodies in the seven personages pictured here on page 60. I will attempt to explain them, hoping that my interpretation may be replaced by a better one. The sun and moon stand on the platform in the upper picture; their combat is equivalent to the eclipses to which they at times succumb. The moon is the assailant and the sun makes only a proud defensive gesture. The person behind the moon must be Mars. The animal under the two persons is the embodiment of the eclipses, which the Aztecs interpreted as the act of being devoured by the jaguar. The hieroglyph in front looks very much like the meeting of two circles. Does it refer to the day Lamat (Aztec tochtli = rabbit)? At the left, bottom, the powerful Venus triumphs over the weak Mercury. The two planets are real chronometers by reason of the regular alternation of their appearance as morning and evening stars, and also by their disappearance twice in each revolution and finally even in the variation in the length of the two periods of invisibility. Hence they are each accompanied by a serpent as the usual symbol of time. On the right, on the other hand, Jupiter as the stronger has vanquished Saturn, whose bound arms symbolize his slowness of motion and the fact that he is confined to the same region of the sky. Should not the ring around his eye have a very special meaning? But we must guard against an excess of imagination. Jupiter and Saturn are the last to be represented, as they were of but secondary importance, on pages 51-58 and perhaps also in the 2200 on page 24. I will not deny that yet another interpretation of this page is possible. The top picture may be Venus and the moon opposing one another, and the bottom picture may represent the sun as victor over Mercury. There are some things in favor of this point of view. The correct order of the twenty-four hieroglyphs is the following, in my opinion, which is borne out by the different colors of the four groups:-- 1 2 | 7 8 3 4 | 9 10 5 6 | 11 12 ----------------- 13 14 | 19 20 15 16 | 21 22 17 18 | 23 24 These signs can have no relation to mythology. There is not a hieroglyph of a god among them, for if sign 6 could be taken for B's hieroglyph, the resemblance to the sign of the fist, familiar from the inscriptions, as well as the Imix and the cross-hatching as a prefix, makes this doubtful. The latter component would rather suggest the summer solstice. If sign 12 were intended to denote the Bacab, then it would refer to chronology rather than to mythology. Also the Cimi in 17 might equally well mean the day as the god. Indeed several things refer here to chronology and astronomy, among them the unmistakable union of numbers and month signs, which occur here repeatedly. Thus from what remains of the almost obliterated signs 1 and 2, they might denote the normal date IV Ahau 8 Cumhu, which always occupies the first place. Signs 7 and 20 are plainly the same, 9 Xul (sixth month) and sign 14 is 10 Yaxkin (seventh month). Sign 5 might be Caban combined with Uo (second month) and a ten. In sign 19 we again see Yaxkin without a number. Signs 9 and 23 are Zec (fifth month) and signs 21 and 22 may be Kankin (fourteenth month). The days occur in the same manner as the months. It is true that Kin is only a part of hieroglyph 10, the rest of which is effaced, but the familiar compound of Caban and Muluc appears in 18 and 24 and Cimi is in 17, as we have seen. In sign 13, Ahau is combined with a red number, which must lie between X and XV. But this should not be regarded as forming a calendar date with the 10 Yaxkin near by, for Ahau is never the tenth day of a month. Can 16 be the sign of the twelfth month, Ceh, combined with that for 7200? Hieroglyphs 3 and 8 are effaced and I do not understand 4, 11 and 15. There are no parallels in the kindred passages 46-50, unless it be 7 Zec on the bottom of page 49 and here in signs 9 and 23, but without a number. Cf. my paper on this page 60 in the "Weltall," year 6, pages 251-257. Page 61--64. On examining the reverse of the second part of our Manuscript, _i.e._, pages 61-74, we find an empty page on the left, the back of which is occupied by page 60. This may be explained by assuming that the scribe wrote pages 61-64 and possibly even pages 61-74 from right to left, the great series having occasioned such a proceeding, and that his material came to an end when he had finished page 61. Nevertheless, it is advisable to continue with the original numbering in order to avoid confusion. Aside from the concluding (or beginning) page 74, this whole section of pages 61-74 consists of three parts:--61-64, 65-69 and 70-73. Let us first consider the first section, which I have already discussed in my treatise "Zur Erläuterung der Mayahandschriften II." The basis of this section is a series, the beginning of which is on the bottom, right, of page 64. Its primary difference is always that which we found on pages 31-32, viz:--the Bacab period of 91 days, the quarter of the ritual year of 364 days = 7 weeks of 13 days each. It ascends by 91 until it reaches 1820, which number is a multiple of both 364 and 260 and is also divisible by 28, the number of weeks in a year. Just as on page 32 the series continues with the new difference 1820 as far as 7280, its fourth multiple, which then becomes the third difference. Indeed, I believe that even the partially effaced numbers could be so restored as to carry the series to the number 36,400 = 400 × 91, which would then become the fourth difference and the series would close at the top of page 63 with 145,600 = 1600 × 91, _i.e._, with the numbers 1. 0. 4. 8. 0. of which the 1 is entirely and the 0 half effaced. The series on pages 31-32, however, closed with 29,120 = 320 × 91, but there is still room for a higher series. Under this largest number (1600 × 91) there is on page 63 a large red number consisting of 19. 0. 4. 4. which is crowded into a very small space between the figures of 1820. I can only understand it by replacing the first 4 by a 3, for then it is 136,864 = 1504 × 91 or by addition of a zero. We shall return to this number in the examination of the serpent numerals. The series is accompanied in the regular way by five days. At the beginning of this series, page 64, right bottom, are the days III Cib, III Men, III Chicchan, III Caban and XIII Ix; the III is set down only with the first of these days and is to be supplied with the next three. Hence the actual zero point is to be found 91 days back in the days III Chicchan, III Kan, III Ix, III Cimi and XIII Akbal, the last of which is also the beginning of the corresponding series on page 32. From 1820 on, these last-named days, of course unchanged, accompany the numbers. The most important of these days are the first and last, but we shall see later in connection with the serpent numbers that the other three, which are separated from one another by 39, 130 and 52, _i.e._, 3 × 13, 10 × 13 and 4 × 13, are likewise not set down here by mere accident. We come now to the five columns, three on page 63 and two on page 62, which join this series on the left. They contain the large numbers, which invariably accompany these series. Here there are six numbers, four of which, in my opinion, refer to the past and two to the future. Two of these numbers, the two largest, are set down together in the third column on page 63, one with red numbers and the other with black. Of these black numbers, I take the second from the top to be not 8 but 13, assuming that a line is omitted. The normal date IV Ahau 8 Cumhu from which, as the starting-point, all these numbers are to be computed, is set down below at the end of each of the five columns. I now give the six numbers, first the two highest, then the other four from right to left, adding in each case the calendar date and the year in which they should be situated:-- 1,538,342; IV Ik 15 Zac (12 Muluc). 1,535,004; VII Kan 2 Chen (3 Kan). 1,268,540; IV Ahau 8 Mol (1 Ix). 1,234,220; IV Ahau 18 Kayab (11 Kan). 1,272,544; IV Kan 17 Yaxkin (12 Muluc). 1,272,921; IV Imix 9 Mol (13 Ix). The first, third and fifth numbers are already known from page 31a, and hence they need no further discussion here. As these three numbers depend on the day XIII Akbal, so the other three all proceed from the day III Chicchan in the following positions, which are again suppressed in the Manuscript:-- 1,483,585 = III Chicchan 8 Zac (5 Cauac). 1,233,985 = III Chicchan 8 Kankin (10 Cauac). 1,272,465 = III Chicchan 18 Zip (12 Muluc). The second date in the manuscript is 13 Kankin and the third is 13 Zip; hence there is one line too many in the former number and one too few in the latter. While on page 31a the origin of the numbers belonging to the day XIII Akbal seems to be quite clear, here their relation to one another is entirely concealed. I must, therefore, refrain from expressing any conjecture in regard to them. Now the numbers set down in the Manuscript are formed only by the addition of the encircled numbers also found there. The encircled number for the first expressed number is 51,419, which is the same number we found with the corresponding day XIII Akbal; the second has 235 and the third 456 = 260 + 196. The 51,419 was 197 × 260 + 199; but 199 is the interval from III Chicchan to VII Kan, just as it is from XIII Akbal to IV Ik. The 235 is the interval between III Chicchan and IV Ahau and the 196 that from III Chicchan and IV Imix. By the addition of these differences, the numbers written out in the Manuscript are obtained:-- 1,483,585 + 51,419 = 1,535,004 (VII Kan). 1,233,985 + 235 = 1,234,220 (IV Ahau). 1,272,465 + 456 = 1,272,921 (IV Imix). Keeping in mind what was said in reference to page 31a, let us now examine the six numbers and dates collectively. The fact that the days IV Ahau and XIII Akbal occur here and consequently also III Chicchan is not surprising. Nor is the choice of VII Kan and IV Ik an accident, for the interval between these days is exactly the same as that between III Chicchan and XIII Akbal, viz:--218 days. Hence the distance from III Chicchan to VII Kan is also exactly equal to that between XIII Akbal to IV Ik, viz:--199 days. Finally, the distance from VII Kan to III Chicchan is exactly equal to that between IV Ik and XIII Akbal, viz:--61 days. IV Imix and IV Kan are separated from the normal date IV Ahau by 3 × 13 = 39 and 8 × 13 = 104 days. Regarding the encircled numbers, so far as they are independent of 260, I would note the following:-- 17 = XIII Akbal to IV Ahau. 121 = XIII Akbal to IV Kan. 196 = III Chicchan to IV Imix. 199 = III Chicchan to VII Kan and XIII Akbal to IV Ik. 235 = III Chicchan to IV Ahau. In addition let me remark that 36 = VII Kan to IV Ahau, 39 = IV Imix to IV Ahau and 104 = IV Ahau to IV Kan. The following arrangement will prove that these numbers were as usual also employed to form the large numbers by multiplication:-- 17 × 74,620 = 1,268,540 (IV Ahau), 235 × 5,252 = 1,234,220 (IV Ahau), 36 × 42,639 = 1,535,004 (VII Kan), 39 × 32,639 = 1,272,921 (IV Imix), 104 × 12,236 = 1,272,544 (IV Kan). But the highest number, 1,538,342, was formed in a different way; it = 59,167 × 26; but the interval from IV Ahau to IV Ik = 182 = 7 × 26, and from IV Ik to IV Ahau = 78 = 3 × 26. If in conclusion, we now examine the twelve numbers of seven figures given in this section, we will clearly see that by twos and twos they plainly belong together in pairs:-- The three pairs of numbers found by computation are as follows:-- 1,486,923, XIII Akbal. 1,483,585, III Chicchan. Difference 3338 = 12 × 260 + 218 (VII Kan to IV Ik, III Chicchan to XIII Akbal). 1,268,523, XIII Akbal. 1,233,985, III Chicchan. Difference 34,538 = 132 × 260 + 218 (as above). 1,272,423, XIII Akbal. 1,272,465, III Chicchan. Difference 42 (which is 260 - 218); 42 = IV Kan to IV Imix. On the other hand the three pairs specified in the Manuscript are as follows:-- 1,538,342, IV Ik. 1,535,004, VII Kan. Difference 3338 = 12 × 260 + 218 as above, by reason of the encircled number 51,419 which is common to both numbers. 1,268,540, IV Ahau. 1,234,220, IV Ahau. Difference 34,320 = 132 × 260, on account of the same day. 1,272,544, IV Kan. 1,272,921, IV Imix. Difference 117 = IV Kan to IV Imix; strictly speaking 377 = 260 + 117. The upper part of the five columns just now under discussion still remains to be examined. Here are five vertical rows of hieroglyphs, the first four each containing seven, and the fifth only six owing to lack of space. The two rows at the top are as usual much obliterated, which is the more to be deplored since they consisted of five calendar dates, which would have contributed materially to the comprehension of the entire section. Fortunately, however, one of these dates is preserved complete, and we are able to see in what relation it stands to the rest. Thus we find in the third column of page 63 the date XIII Imix 9 Uo. It comes in the year 12 Ix and represents the number 1,523,921 (or a number separated from it by a multiple of 18,980). Now 1,523,921 = 4175 × 365 + 46 and = 5861 × 260 + 61. This agrees with the lower number inserted in red:--1,538,342 = IV Ik 15 Zac (12 Muluc), which comes later by 14,421 = 39 × 365 + 186 and = 55 × 260 + 121. 121, however, is the difference between both XIII Imix and IV Ik and the days XIII Akbal and IV Kan in the last column of page 62. If we set down with these two numbers, those of the normal date just preceding and the normal date next following, we have 1,518,400 = 80 × 18980. 1,523,921, 1,538,342, 1,556,360 = 82 × 18980. This is a period of 37,960 = 2 × 18,980 days. It is possible that at some future time an indication of such a transition from one Katun to the other will be found in the writings. Now these two top lines contain two dates; on page 62 we find 13 Ceh, and on page 63, 13 Xul, but nothing further is to be learned from this than that one or the other of the day-signs, 2, 7, 12, 17, must have been set down in the effaced indication of the position in the Tonalamatl. All else is obliterated. From the third to the seventh row of these five columns it is all extremely simple. The third row consists only of five signs for beginning, the fourth, of five for end, the sixth of B's sign five times and the seventh of the elongated head _q_ four times. But in the fifth, two deities alternate, one is apparently male and the other female; the god is in columns 1, 3 and 5 and the goddess in 2 and 4; the god probably belonging to the days III Chicchan and the goddess to XIII Akbal. If we look upon this series as the first story of a structure and the large numbers just now discussed as the second, then we find the third story here, as we shall find it again on page 69. In the passage on page 31, which is so closely related to the present one, a timid attempt has already been made with the number 2,804,100 to erect a third story of this kind, which however barely attained to a quarter of the height of the one which now engages our attention. If the numbers hitherto examined refer to a time not very far from the present, we now come to numbers which lie in so remote a future that they can hardly suggest anything else than the destruction of the world or a sort of twilight of the gods. Nevertheless the starting-point of the whole, the series, which is built up with the number 91, _i.e._, the Bacab period or the quarter of a ritual year, continually comes to view. Indeed, the number of serpents is suggestive of this. There are four large serpents, which fill most of the space on the left half of page 62 and the right of page 61. The two outer ones are bluish and the two inner ones white. They rise in several coils, their tails below and their heads above. A deity is represented above the gaping jaws of each of the four serpents, having apparently been vomited up. Above the first and third serpents B is represented in a fashion very similar to that which we have already seen on pages 33-35. Above the first serpent B has the pouch hanging from his neck and his hatchet is held downward; above the third he wears the pouch and the gala mantle and his hatchet is raised. Above the second fourth serpents, on the other hand, there are four-footed animals, but of a species not represented elsewhere. They might suggest a (four-footed?) walrus and a bear. We have here a double contrast, apparently referring to the four cardinal points. The veil enveloping this representation would be lifted to a considerable extent, if all the eight hieroglyphs written above each serpent, were still legible. But, unfortunately, the second group is wholly and the third almost wholly effaced, while the first is partially effaced and only the fourth is preserved in its entirety. I read these groups in the following order:-- 1 2 3 4 5 6 7 8. Of these 7 and 8 in the first and fourth groups form the date IX Kan 12 Kayab, which is in the year 4 Ix; this same date probably occurred also in the other two groups. That it is of special importance here, is shown by the two columns of hieroglyphs on the left side of page 61, where this date occurs again in the lowest place. The last three large numbers are not computed from the normal date IV Ahau 8 Cumhu, but from this very date and the other five from a similar one. The sixth hieroglyph in the first group seems to correspond to the fifth in the fourth, since both contain the elongated head _q_, though with different accompaniments. In the first group the fourth hieroglyph is the Bacab sign familiar to us from pages 51-58, suggesting that the series here is closely connected with the one which had the difference 91. The fifth sign of the same group is that for _beginning_, probably to confirm the fact that this section begins here. The third sign of the first group is probably an Imix, as it is in the first and fourth of the fourth group, combined here with the woman's head, which we saw repeated on pages 62 and 63 at the top; and over it in the second place of the fourth group is B's hieroglyph, which is also repeated on pages 62 and 63 at the top. The third place of the fourth group is occupied by a head, which may be C's and which is distinguished by the same kind of circle which on page 9b surrounded the Ahau. Eight complete dates are set down below the serpents, among which are the XIII Akbal already found with the previous large numbers, and III Chicchan (repeated three times), and then III Kan (twice), forming the beginning and end of the series (page 64), and also III Cimi and III Ix. As we shall see directly these are the end dates of the large numbers, and Xul = end repeated eight times at the extreme bottom corresponds with this. On the other hand, the starting-points must be found by computation, with the exception of the date IX Kan 12 Kayab, which is actually written down and is the point of departure for three of the numbers. I will designate the black numbers by _a_ and the red by b. Seven of the eight numbers are undoubtedly absolutely correct; but I must alter the number 1b, the red number belonging to the first serpent. I assume that a line is wanting in the lowest figure, _i.e._, it should be 8 instead of 3, and that the conspicuously large 1 further down on the page serves also as the red number, which belongs here. Only one slight change is necessary in the dates on the bottom of the pages, which were mentioned above. To the 16 in the date 4b I add a dot, and read it 17. I will now give a table of the numbers, the starting-points of the periods obtained by computation, and the ends of the latter which are indicated below the serpents:-- 1a: 12,489,781; XI Kan 12 Kankin (1 Ix); III Chicchan 18 Xul (4 Muluc). 1b: 12,388,121; XI Kan 12 Muan (7 Ix); III Chicchan 13 Pax (4 Ix). 2a: 12,454,761; IX Kan 7 Kankin (4 Cauac); III Chicchan 13 Yaxkin (2 Ix). 2b: 12,394,740; IX Kan 2 Chen (5 Kan); III Kan 12 Ceh (7 Ix). 3a: 12,438,810; IX Kan 12 Xul (3 Ix); III Ix 7 Zac (9 Muluc). 3b: 12,466,942; IX Kan 12 Kayab (4 Ix); III Cimi 14 Kayab (9 Ix). 4a: 12,454,459; IX Kan 12 Kayab (4 Ix); XIII Akbal 1 Kankin (1 Kan). 4b: 12,394,740; IX Kan 12 Kayab (4 Ix); III Kan 17 Uo (7 Muluc). See my treatise, "Die Schlangenzahlen in der Dresdener Mayahandschrift" (Weltall, year 5, pages 199-203). Several details show how this number-structure forms a definite, closely connected whole. 1. The beginning day in each case is the day Kan, which thereby indicates its position as the first. 2. The last three starting-points are the same; the first three end dates, at least, are the same in the Tonalamatl, though not in the year. 3. The two numbers 2b and 4b are exactly the same. 4. The first three numbers are each divisible without a remainder by 17, the interval from XIII Akbal to IV Ahau, which was true also of the 1,268,540 in the second column on page 63, although only this last number has anything to do with these important days, of which the other three numbers are independent. On the other hand, a notable difference between the first serpent and the other three is, that the day XI Kan is the starting-point of the first and IX Kan of the others. There are, however, 80 days between IX Kan and XI Kan. Hence the numbers 2a and 1b are separated from each other by 66,640 = 256 × 260 + 80, although they have the same end III Chicchan. Further it is to be noted that the largest of the eight numbers, 12,489,781, is separated from the lowest, 12,388,121, _i.e._, the black number from the red one of the first serpent, by only 101,660, _i.e._, by not a full one per cent of the entire magnitude. 101,660 = 5 × 18,980 + 26 × 260 or 391 × 260 or 7820 × 13. It is to be noted also that the differences between the black and red numbers in the second and third serpents (60,021 and 28,132) are divisible by 13 (4617 × 13 and 2164 × 13). They _must_ be, since all six numbers refer to the day III. Finally the question naturally arises, how did the computer obtain these values, _i.e._, how was the whole structure built up? On page 63 we found a 136,864 (not 136,884) set down in strikingly small characters and crowded between the other numbers, which would remain a mystery unless one assumed that it was reserved there for this structure; it is 91 × 1504. At first I thought it possible that this 136,864 had been again multiplied by 91, the real basal number of this section; for we had found a second power once before (on pages 46-50) by computation, viz:--2 × 260 × 260. The result of multiplication in this case would be 12,454,624, and the differences between the eight numbers in the serpents would be as follows:--1a + 35,157, 1b - 66,503, 2a + 137, 2b and 4b - 60,884, 3a - 17,814, 3b + 12,318, 4a - 165. But these differences are doubtful, inasmuch as they bear no relation to the dates beginning and ending the serpent numbers. On the other hand, another number contains the desired properties. I refer to the 12,412,920, _i.e._, it is 109 times the so-called Ahau-Katun of 113,880 days, and I believe I have found that the Ahau-Katun and its multiples were mostly used in the formation of the large numbers. In the following table I have placed this number beside each of the serpent numbers, have then found the difference between the two and have added to it the interval between the first and last day of each serpent number:-- 1a) 12,489,781 1b) 12,388,121 12,412,920 12,412,920 ---------- ---------- 76,861 = 295 × 260 + 161 -24,799 = 95 × 260 + 99 XI Kan - III Chicchan = 161. III Chicchan - XI Kan = 99. 2a) 12,454,761 2b) 12,394,740 12,412,920 12,412,920 ---------- ---------- 41,841 = 160 × 260 + 241 -18,180 = 69 × 260 + 240 IX Kan - III Chicchan = 241. III Kan - IX Kan = 240. 3a) 12,438,810 3b) 12,466,942 12,412,920 12,412,920 ---------- ---------- 25,890 = 99 × 260 + 150 54,022 = 207 × 260 + 202 IX Kan - III Ix = 150. IX Kan - III Cimi = 202. 4a) 12,454,459 4b) = 2b 12,412,920 ---------- 41,539 = 159 × 260 + 199 IX Kan - XIII Akbal = 199. Where the serpent number is less than 12,412,920, I have had to place the last day before the initial day. The work of the Indian computer was, therefore, as follows:-- He took the days for granted. First he determined the differences between them; then he added to each difference a multiple of 260; and the choice of the multiple seems to have been quite arbitrary. The number thus obtained he added to 12,412,920, unless it was the smaller, in which case he subtracted it from 12,412,920, and the result he wrote down in the serpents. We shall find the same process, only somewhat amplified, with the serpent on page 69. Are the seven numbers intended to denote the destruction of the seven planets? I hope this question will be answered in the near future. There now remains of the contents of these pages only the two columns on the left of page 61, which we will now examine and at the same time compare them with the corresponding column of page 69, the upper part of which is exactly the same, and the lower very nearly so. Each column consists of 18 hieroglyphs, which I count from the top downward, designating those of the first column by _a_ and those of the second by b. At the first glance these double columns remind one of the inscriptions in the temples and on the stelae, especially of their beginnings, the so-called initial series. Here, in the second column, we find the statement of the usual periods:--144,000, 7200, 360, 20, 1, but in the first column we find faces belonging to them. In his work "The Archaic Maya Inscriptions," 1897, which, on the whole, contains more of imagination than of science, J. T. Goodman unqualifiedly declares these faces to be numbers by which the periods indicated beside them are to be multiplied, and this theory has already found considerable recognition; we will therefore try to follow where he leads. 1a and 1b are effaced on page 61; they probably contained a sort of superscription as on the inscriptions. 2a is effaced on page 61, but the sign may be recognized from page 69 as that with which on page 46 the series of the twenty deities begins after 236 (4 × 59) days. On pages 61 and 69 it takes the place of a face, to which I am inclined to assign the numerical value 4. In 2b, which is C's head, I am inclined to look for the value 2,880,000 = 20 × 20 × 20 × 360 days, which is not at all inappropriate for C, as the sign of the north pole around which everything revolves. I therefore propose to read 2ab as 4 × 2,880,000 = 11,520,000. 3b, it seems to me, resembles the sign for 144,000, which I found in the inscriptions and which is repeated in 12a. It must, however, be left undecided by what this same number in 3a is to be multiplied; 3a is repeated besides in 8a and 13b. 4a contains the head of E, and 4b that of the Moan. 4a seems to refer to 5a, and 4b to 5b. But 5a and 5b are the same sign, which, inserted between the 144,000 and the 7200, can scarcely mean anything else than the so-called Ahau-Katun of 6 × 18,980 = 113,880 days. Have we two such periods here? Were they designated by consecutive numbers? Now comes the 7200 in 6a, and the number 8 with E's head and the inserted sign for 360 days in 6b (on page 69 without E's head), therefore 8 × 360 = 2880. Seler also thinks 7a has the numerical value 16 (Einiges mehr über die Monumente von Copan, etc., page 217); 7b belongs to 7a. 7b, a Kin with a I and a suffix and a leaf-shaped prefix, is inserted between the 360 and 20. What can it mean? Hardly the 260, for this is represented elsewhere (_e.g._, page 24) by the thirteenth month Mac. Or can it possibly refer to the month Yaxkin (days 120-140)? 8b is a Chuen sign, which, with its prefix (superfix on page 69) always denotes twenty days in the inscriptions. It is multiplied with the same unknown head in 8a, which we have already met with in 3a. 9a contains H's head, and 9b is an unknown head with inserted Kin; the two signs must of necessity indicate the single days still to be added to the period, though as yet we do not know how. The normal date IV Ahau 8 Cumhu then follows in 10ab. If it refers to the signs just now discussed, then they must denote a number of about the same magnitude as the serpent numbers. 653 or 654 times 18,980 seems to suggest itself, but we shall have more to say later on this subject. My efforts to reach a definite result here have failed. Nor does the lower part of the two columns lead me to the desired goal. As it seems to consist of several groups, I will first combine 11ab and 12ab. I look upon 11a as denoting 20, and with regard to 11b I have already expressed the surmise in the Zeitschrift für Ethnologie XXIII, page 153, that it may mean 8760 = 24 × 365, _i.e._, three Venus-solar periods. That would be 20 × 8760 = 480 × 365 = 175,200. The Moan in 12a may have the value 13, for this number is so often combined with the Moan. As we saw under page 51, 12b is = 18,980; 13 × 18,980 = 246,740. Accordingly the four signs taken together may mean 421,940 = 1156 × 365. The second group, from 13a to 15b, refers, on the other hand, to the year of 360 days. First 13a = 144,000, having in 13b the unknown multiplier, which we have already seen in 3a and 8a. Then follows in 14a, 15 × 7200 = 108,000; in 14b, 9 × 360 = 3240; in 15a, a 20 with a prefixed 1 (21?); and in 15b, three days. It would be more correct to place the 1 beside the following 3. The whole sum would then end with the number 4, which would agree with the day Kan, the date specified below. In the third group the 16a = 19 × 18,980 = 360,620, remains a mystery; an empty outline of a sign is added in 16b. 17ab also forms a group by itself. 17a contains a sign, which rather suggests the Bacab, upon whose period of 91 days the series belonging here is based. The Imix in 17b with a superfix is still unintelligible. The columns end in 18 with the date IX Kan XII Kayab, the starting-point of the serpent numbers. Pages 65--69. I think it very likely that this section bears the same relation to pages 61-64 as pages 46-50 do to 24 and as 53-58 to 51-52. For here, too, a period of time forming the basis of the earlier section seems to be divided into smaller parts. On page 64 we recognize as the basis of the series the number 91, the quarter of the ritual year of 364 days; here we have to do with the fourfold division of 91 into 13 unequal parts. And the real starting-points on these pages, as on the previous ones, are the days III Chicchan and XIII Akbal. The four series of numbers, the top one of which I have probably correctly restored from what still remains, are as follows:-- 9 XII, 5 IV, 1 V, 10 II, 6 VIII, 2 X, 11 VIII, 7 II, 3 V, 12 IV, 8 XII, 4 III, 13 III. 11 I, 13 I, 11 XII, 1 XIII, 8 VIII, 6 I, 4 V, 2 VII, 13 VII, 6 XIII, 6 VI, 8 I, 2 III. 11 XI, 13 XI, 11 IX, 1 X, 8 V, 6 XI, 4 II, 2 IV, 13 IV, 6 X, 6 III, 8 XI, 2 XIII. 9 IX, 5 I, 1 II, 10 XII, 6 V, 2 VII, 11 V, 7 XII, 3 II, 12 I, 8 IX, 4 XIII, 13 XIII. The first two lines, forming together a single period of 182 days, refer to a day III, as we see by the ending, and the last two to XIII, which undoubtedly refers to the III Chicchan and XIII Akbal, the days so significant in the preceding section. Hence an interval of 218 days (III Chicchan to XIII Akbal) is to be assumed between the second and third lines, with the addition of which interval each of the two periods extends over 400 days. The first and fourth series have the same difference; and the second and third correspond with one another in this respect. In the first and fourth the differences follow a rule, viz:--as if one were walking in a ring having on its edge the numbers 1 to 13, and kept stepping backward four numbers. The differences of the second and third series apparently do not follow any rule. Hence I think that the fourth series follows the third by mistake and ought rightfully to precede it. Only the fifth member in the first and second series has the same day VIII and the day V in the third and fourth series, otherwise the week-days of each series differ from those of the others. As I regard III Chicchan and XIII Akbal as unquestionably the starting-points, I will here give a table of the days on which each of the twenty-six members of each series must fall and at the same time I will indicate for each day its number from the beginning of the series. Accordingly the first 182 days present the following appearance:-- III 2. 1. 9. XII Ix 2. 14. IV Cauac 3. 15. V Ahau 4. 25. II Oc 5. 31. VIII Cib 6. 33. X Eznab 7. 44. VIII Muluc 8. 51. II Cib 9. 54. V Cauac 10. 66. IV Chuen 11. 74. XII Cauac 12. 78. III Akbal 13. 91. III Cib 14. 102. I Manik 15. 115. I Ahau 16. 126. XII Chuen 17. 127. XIII Eb. 18. 135. VIII Ahau 19. 141. I Cimi 20. 145. V Oc 21. 147. VII Eb 22. 160. VII Chicchan 23. 166. XIII Chuen 24. 172. V Caban 25. 180. I Chicchan 26. 182. III Manik In the same way I will tabulate the second group of 182 days, but in this case I shall place the fourth line before the third, which is probably correct, and which shows for the first time parallelism of the two rows:-- XIII 20. 1. 9. IX Eb 2. 14. I Caban 3. 15. II Ezanab 4. 25. XII Lamat 5. 31. V Ix 6. 33. VII Cib 7. 44. V Manik 8. 51. XII Ix 9. 54. II Caban 10. 66. I Muluc 11. 74. IX Caban 12. 78. XIII Imix 13. 91. XIII Ix 14. 102. XI Chicchan 15. 115. XI Ezanab 16. 126. IX Muluc 17. 127. X Oc 18. 135. V Ezanab 19. 141. XI Kan 20. 145. II Lamat 21. 147. IV Oc 22. 160. IV Akbal 23. 166. X Muluc 24. 172. III Men 25. 180. XI Akbal 26. 182. XIII Chicchan It would be very essential now to know what place these days occupy in the year, and what year is meant; the answer to one of these questions would at the same time solve the other. Now I think I come nearer to the solution of this problem by assuming that the pictures and hieroglyphs refer here only to the more important of the two days, XIII Akbal, and that III Chicchan is represented only by the numbers of the series. Thus both the pictures and the hieroglyphs of the two sections connect without the interval of 218 days, which must be assumed in the case of the numbers. Here, as is usually the case of series, we have to begin at the bottom. Now the first group of the lower half of page 65 contains the sign 9 Kan. If, as it seems, this actually denotes the year, then the day XIII Akbal must be the first of the eleventh month, _i.e._, the 201st day of the year. Hence I will again set down the twenty-six dates, but add to them the position in the year. 0. XIII Akbal I Zac (9 Kan) 1. 9. IX Eb 10 Zac 2. 14. I Caban 15 Zac 3. 15. II Ezanab 16 Zac 4. 25. XII Lamat 6 Ceh 5. 31. V Ix 12 Ceh 6. 33. VII Cib 14 Ceh 7. 44. V Manik 5 Mac 8. 51. XII Ix 12 Mac 9. 54. II Caban 15 Mac 10. 66. I Muluc 7 Kankin 11. 74. IX Caban 15 Kankin 12. 78. XIII Imix 19 Kankin 13. 91. XIII Ix 12 Muan 14. 102. XI Chicchan 3 Pax 15. 115. XI Ezanab 16 Pax 16. 126. IX Muluc 7 Kayab 17. 127. X Oc 8 Kayab 18. 135. V Ezanab 16 Kayab 19. 141. XI Kan 2 Cumhu 20. 145. II Lamat 6 Cumhu 21. 147. IV Oc 8 Cumhu 22. 160. IV Akbal 21 Cumhu 23. 166. X Muluc 2 Pop (10 Muluc) 24. 172. III Men 8 Pop 25. 180. XI Akbal 16 Pop 26. 182. XIII Chicchan 18 Pop Let us now prove the correctness of my theory by an examination of groups 22 and 23. In 22 the 160th day of this period, the 361st day of the year is reached, _i.e._, the first of the five Uayeyab days. The year 9 Kan is ended and the year 10 Muluc is not yet reached. In the corresponding picture we see B occupied in conveying in a bag the image of God K to whom belongs the next year. B is armed with the official staff and the bag also contains water (rain). In the 23d group the 166th day has passed and the second of the year 10 Muluc is reached, which gives the name to this year. The first hieroglyph shows two personages sitting back to back. This representation is repeated on a larger scale below in the Janus picture of B who is sitting on signs of planets. The second hieroglyph, with equal fitness, represents a clamp, which is intended for fastening two objects together, and which is repeated twice over the Janus picture, black in one case and white in the other. Rain is pouring over the second half of the picture, for it has long been known that Muluc and rain belong together, and in our examination of page 7a we saw that K is the ruler of the day Muluc (6). Now, before I begin the examination of the separate pictures and the groups of six hieroglyphs belonging to each picture, I wish to mention three things which are often repeated here. First, B's picture, which appears in all the twenty-six pictures with the exception of 20, 24 and 25, and represents the god in the most varied positions and activities. These pictures are very similar to those on pages 29-46 and we shall therefore make frequent reference to the section there represented. Second, the first hieroglyph in groups 1 to 13, strange to say, is not found in the second half. It is hieroglyph _f_, which appears in exactly the same way in close combination with B in two sections, which differ from each other but are placed side by side on pages 30c-39c. In the present passage it has a distinct prefix resembling the beak of a bird or tortoise, but in the former passage it has rather a stunted appearance. It seems to refer to the eagle in B's hands in group 13. Third, the head with no underjaw, which is the sixth hieroglyph in groups 1 to 13, but does not occur in groups 14 to 26. It is repeated in a very similar fashion in the last hieroglyph but one on page 23b. I propose to attribute to it the meaning of fasting. Now for the single groups:-- 1. B is seated rowing in a boat, as he is represented also on pages 29c, 36b, 40c and 43c. A creature is swimming beneath him, which may be a crocodile. The fifth hieroglyph is the important 9 Kan already discussed, the fourth is _a_ and the second the cross _b_ combined with Caban. The day is the 210th of the year. 2. B is walking with the atlatl in his hand, and armed with javelins. Hieroglyph 5, Manik, denotes the chase, but has a prefix, which often seems to have the meaning of 20. 2 is the elongated head _q_ with the prefix of the east belonging to the Kan years. 4 is a Moan sign (c) with the leaf-shaped prefix. Does this perhaps denote the slaying of game in the forest? It is remarkable that B's feet are hidden, as if he were walking in sand or in a bog. 3. B is walking, carrying a large stick like that for tilling the field, as on pages 38b and 39b, and he bears a carrying-frame; there are footprints below him. Hieroglyph 2 is the compound of the signs for south and east, 4 (_r_) may denote rain, and 5 is two elongated heads with an unknown prefix. 4. B, is seated on astronomical signs as on page 37c. The copal pouch is hanging from his neck and he is brandishing his hatchet. Sign 2 is _b_, 4 is _a_ and 5 is _r_, but all three signs have unusual prefixes; the first of these prefixes appears again in the tenth group, 41 days later. 5. B is seated on a head, probably that of D, which, however, is peculiar owing to the ornaments resembling bunches of grapes in place of both the eye and the ear (compare pages 39c and 41a). I do not venture to decide what he holds in his hand nor what are the other objects which he carries. Sign 2 is _r_ with a prefix, 4 is Imix perhaps with a knife as a prefix, 5 is the skeleton which sometimes belongs to the lightning beast, but also to the 14th month; its prefix is unknown. 6. B is seated on a support, which contains two cross-bones, down to which he points with his right hand, while his left hand holds the hatchet on his knee. Sign 2 is the crouching naked personage, with the cross _b_ prefixed, 4 is the elongated head with a prefixed Yax, and 5 is Kan with a vessel as a prefix (instead of Imix) from which steam or froth is rising. The day is the 234th of the year, _i.e._, the end of a week of 18 × 13 days. 7. B is sitting on a tree at the root of which his own head appears (compare with this the representations on pages 31c, 33c, and especially 40a, and also 41b and 42b). The second sign is Yax with a prefix; 4 is Kin within which there is a 1, as is several times the case, for example, on pages 61 and 69. The fifth sign is still a mystery to me. The day here is V Manik. Do the hieroglyphs suggest that the interval from the day IX Kan, which gives the name to the year, to V Manik is exactly the same as that from the normal date IV Ahau to the true starting-point of our passage, the day XIII Akbal? Both intervals are 243. 8. B is seated in a house, on the roof, wall and floor of which are several Caban signs, just as on page 30a; he seems to be pointing forward. Sign 2 is Caban with a prefix, the 4th and also the 5th is Kan with two unusual prefixes. 9. Water is pictured at the bottom of this picture, and in it are a fish, a mussel and a snail (possibly page 37b may be compared with this). There seems to be a suggestion of footprints on the margin of the water, back of which B is walking, his legs hidden as far as the knees. He holds the hatchet uplifted in his left hand and his right holds what may be a long-stemmed aquatic plant (compare page 42b). Sign 2 is composed of _b_, Imix, the mouth and nose of C and the object which apparently is a beak, previously met with in sign 1. 4 is Kan-Imix, and 5 is Kan with prefix and suffix. 10. B is seated in an expectant attitude, his hands resting on his knees. We see a very similar representation of him on page 38a, where he faces himself, and in general the remaining pictures of that passage furnish a striking parallel to the present one. Sign 2 is a head (E's?) with a call seemingly issuing from its mouth. 4 is the elongated head _q_ with the Ben-Ik superfix and an unusual prefix, which we found on page 66c prefixed to the cross _b_; 5 is Kan with the same prefix, which I regarded as denoting a call in sign 2, and which is probably answered here by an affirmative cry. 11. The expectation has been fulfilled. B is seated on a mat holding a woman in the same position as on page 38a. Sign 2 is the cross _b_ with the prefixed beak as in 1, and also with another prefix, which seems sometimes to denote the number 20. 4 is exactly the same Kin with 1 and the leaf-shaped prefix, which occurred in the same place with the seventh picture. 5 contains the sign for 73 days; a new period of this length begins here on the 74th day. 12. As in the parallel passage on page 38 B seems to be offering a Kan, so here his gift consists of a kind of wreath, like the one in the fifth picture; he is seated on astronomical signs, which contain the cross _b_ twice as does also hieroglyph 2. 4 is Kin-Akbal, and 5 is a Kan with the prefix which generally belongs to the south as a superfix. 13. B is seated on the elongated head _q_ with a superfix and a prefix, exactly as on pages 37c and 40a, and this sign is repeated in the hieroglyphs (in 2) just as it is in the two former places. He holds the eagle on his lap and we see him connected with the same bird in a different way on page 43c. Is B represented here as the preventer of evil? Hieroglyph 4 is _a_, while 5 is Kan, apparently with the sign of the south as a prefix. A Bacab period of 91 days ends here. We come now to the upper series of pictures. 14. B is walking in the rain, with the copal pouch around his neck and the hatchet uplifted in his left hand. An unknown object, possibly held in his right hand, is hanging in front of his legs. Hieroglyphs 1 and 3 are effaced, 2 is indistinct, 5 seems to be a Xul (end, close) and 6 is E's head. 15. B is walking, brandishing the hatchet in his left hand, and holding in his right an object resembling a cornucopia filled with fruit; below this hangs what appears to be a flower. The god wears the copal pouch. Hieroglyph 1 is a hand holding K's head; it is curious that this sign should also occur in the next group as an indication of the approaching Muluc year. 3 is a sign still undetermined; but the prefix is the crouching naked personage with dots suggesting stars around its head. I have often thought that similar figures represented Mercury; it is remarkable that exactly the 115th day of this section is reached here, corresponding with the apparent revolution of Mercury = 115 days. Similarly sign 2 invites computation; it is a face resembling an Ahau sign, with a 3 as a superfix and a 9 as a prefix; compare the other places containing the same face, with 33c. After the fashion of the inscriptions this would denote 9 + 3 × 20 = 69, which by the way is three fifths of the Mercury revolution. 5 is a compound of Akbal and Imix and 6 a compound of a Moan sign (_c_) with a. 16. B is in a half sitting position and holds a strange object before himself. On top of his own head is K's, which is repeated in sign 2. I do not know how to explain 1, unless it is the bat-god; 3 is a Xul = end (but of what?) combined with Imix, and 5 is the usual Kan-Imix. 6 is a Kin with an 8 back of it (as 36b, 37b, 67a, 68a) and over it is a hand pointing to the right, just like those in groups 20 and 25. This looks as if we ought to count forward 8 days, but what can be the purpose of doing so? 17. B is walking armed with spear and shield. Sign 1 is _b_, 2 the face resembling an Ahau, which occupied the second place in group 15, 3 is probably Xul again, but with an effaced prefix; of 5 also only an Imix remains; while 6 is the usual compound of Muluc-Caban. 18. We have now reached the day 16 Kayab, a day very close to the day 18 Kayab, which on page 24 we recognized as an especially important day, while in my article "Zur Entzifferung III" I regarded it as the day of the summer solstice. Computed from the normal date IV Ahau 8 Cumhu it may also have denoted the end of a lunar year, as on pages 51-58 where it is the basis of the series. The picture here agrees with this. B is sitting in the pouring rain of the rainy season and gazing upward at the planets, as on page 36c and particularly on 39c; the sun and moon are also represented, but below the planets. The hieroglyphs likewise contain the sun and moon in 1 and 2, in 3, Ahau and Xul with a prefix, as if this were the end of the increase of the sun's power; 5 is Kin-Akbal, day and night, and 6 is Caban with the cross b. 19. B is walking armed with hatchet and shield. He holds a serpent in his hand as on page 40c, but here with the head downward. Hieroglyphs 1 and 2 are destroyed, 3 is the cross _b_ with a suffix and the horse-shoe prefix _e_, known to us from pages 5 and 6. 5 is Imix combined with Chuen and probably with Yax, and 6 is E's head. 20. This is the old red woman with the tiger claws, whom we saw on pages 39b and 43b and shall see again on page 74; she reinforces the water falling from the planets by pouring a stream from her jug. The first three hieroglyphs are effaced, 4 is the elongated head _q_, 5 is Kin-Akbal, 6, as in group 16, is again the enigmatical 8 with a hand pointing to the right. 21. B is walking and bears pouch, spear and shield. Hieroglyph 1 is a hand holding the sign of the rising Moan, just as in 15 a hand holds the head of K; 2 is again K, whose sign is probably effaced several times in the last groups of this series. 3 is E with the sign of the east; 5 is compounded of Imix, Chuen and _b_, and 6 is Kin with the sign of the north. Here the day of the normal date is reached, but this may be significant only for the year 9 Ix. 22. We come now to the representation of the change of the year, which we have already mentioned. Hieroglyph 1 is curious, consisting of the moon with a stripe running around it like a strap; 3 and 5 are not clear to me and are doubtless closely connected with one another; 3 also contains a trace of K and is perhaps a determinative of the same. 6 is again E, and suggests the tilling of the fields. 23. This picture as well as the first two hieroglyphs have already been discussed above. The crouching personage, repeated again in 3 as a prefix to the cross _b_, is curious. 5 is again E and 6 is Imix, referring to grain and honey. 24. The picture and three of the hieroglyphs plainly correspond. The grain deity E holds food and drink in his hand. Rain is pouring from the planets, and the wind-beast plunges down, as on pages 44 and 45. Sign 3 is E's hieroglyph, 6 is Kan-Imix and 2 is the wind-beast. B is superfluously added in 4 and the same is true of the cross _b_ in 1, while Kin-Akbal in 5 seems to fit almost everywhere. Pages 29a, 30a and 45c show the lightning-beast in a different form. 25. As is usually the case, rain is pouring from the stars and below them are the sun and moon as before. This time C is sitting in the rain, clad in the gala mantle and holding Kan. Hieroglyphs 1, 2 and 4, the latter apparently representing C, are effaced. The other three are enigmatical, 3 is again Xul with a prefixed 9, 5 a Caban, but with an unintelligible prefix, and 6 is again the mysterious 8. 26. B is sitting on a tree or sacrificial stone, which is colored half blue and half red, and may denote the ceasing of the rainy season; he is brandishing his hatchet. Hieroglyphs 1, 2 and 3 are effaced; 4 is B's sign, 5 might be Xul and 6 is _a_ with _c_ added and thus referring to the Moan. And here the half of the ritual year ends with the 182nd day, which is XIII Chicchan 18 Pop (10 Muluc); and it is left to the reader to imagine or to find hieroglyphs and pictures for the other two series of numeral signs. I am troubled about the five naked crouching figures of this section, which I am inclined to regard as the sign for Mercury with its apparent revolution of 115 days, which, however, seems sometimes (as on pages 54, 56 and 58 in the upper sections) to be raised to the value of half a Tonalamatl = 130 days. This may be explained by the fact that it is difficult to determine exactly the length of the revolution of Mercury. In group 15 this figure appears exactly on the 115th day of this section, but in group 6 on the 234th day of the year, _i.e._, approximately at the expiration of two Mercury periods after the beginning of the year. But now for group 23. Here there are three of these crouching figures. The two upper ones leaning back to back must serve the purpose of indicating the change in the year. But they would hardly do so, if the third personage were not added, which may indicate that the solar year consists approximately of three Mercury periods. I look upon this view of the matter merely as the first attempt at an explanation. Pages 69--73. The chief subject of the last great section of this Manuscript is two of the usual series, from which large numbers are developed in the usual way and the largest of all is finally recorded in a serpent. This section thus forms a parallel to the contents of pages 61-64, but is somewhat more composite. Before I begin the discussion of these series, I wish to examine two passages, which I think are not connected with these series, but are independent, like the instance on pages 51-58, where the hieroglyphs were found to be quite independent of the numerals. The Mayas took advantage of space wherever it presented itself, which is admissible in ideographic writing. The first of these two passages is at the top of pages 71-73. Here there are four horizontal rows of twelve hieroglyphs each. Since, however, the top row is entirely effaced and none of the other three are perfectly preserved, it is quite impossible at present to judge of the interconnection of the whole. But I must point out a certain resemblance to the passage on pages 44b-45b, where a period of 78 days is considered with reference to the wind-deities. The first and sixth columns of pages 71-72 likewise contain the signs for wind and the pierced ears. The fact that the Bacab sign occurs in the eighth column, and in no other, must attract 'attention; if we knew it to be effaced in the first column, then each column might refer to 13 days, though 12 × 13, it is true, does not form a natural whole. C's sign is the only hieroglyph of a god to be found in both passages. E also occurs on pages 44b-45b and may be one of the effaced signs on pages 71-72. There is no trace left of the others. The fact that some hieroglyphs occur in both the passages referred to proves nothing with regard to signs in frequent use and I can find no cases of correspondence among those occurring more rarely. Hence this passage must be left for the present as an almost complete mystery. I have discussed the second passage in detail in my article "Zur Entzifferung der Mayahandschriften V," of the year 1895, and from it I will borrow the following. This second passage fills the middle and lower thirds of pages 71-73, occupying the same space as the first passage in the upper third, and offering far more reliable material than the latter. That these hieroglyphs are not connected with the numerals above and below, can be deduced from the fact that the numbers follow one another from right to left and the hieroglyphs in the reversed order. This is proved by the hand pointing to the right, which occurs here at least eight times like the one occurring twenty times on pages 46-50. But the scribe, misled by the direction of the numeral series, began on page 71 to write the _first_ of these hieroglyphs from the right instead of from the left, but after the first four groups he corrected his mistake. Hence I read the groups of three hieroglyphs each, in the following order:-- Page 71. Page 72. Page 73. 2 1 | 5 6 7 8 9 10 11 | 19 20 21 22 23 4 3 | 12 13 14 15 16 17 18 | 24 25 26 27 28 The number 28 shows that we have to do here with 28 weeks of 13 days each, _i.e._, with a ritual year of 364 days, as was the case on pages 31-32, 63-64 and 65-69. This year, however, is divided into four parts of 7 x 13 = 91 days, _i.e._, into four so-called Bacab periods. This is very plainly indicated here, for groups 4, 11, 18 and 25, _i.e._, those separated by seven groups each, are exactly alike, but in group 4b (I will designate the three hieroglyphs of each group from top to bottom by _a_, _b_ and _c_) there is a prefixed 4 which refers to the four Bacabs as does the same 4 prefixed to the Bacab sign at the top of page 72. Now the question arises as to when this ritual year began. Undoubtedly its beginning day was very different from that of the civil year (360 days) and from that of the astronomical year (365 days). In this matter I follow Mrs. Zelia Nuttall, who has rendered such estimable service to Aztec science. At the Congress of Americanists at Stockholm in 1894, she submitted an article entitled "Note on the Ancient Mexican Calendar System," in which with keen discernment she pointed out a year beginning with the spring equinox and including in its centre the sacred Tonalamatl, _i.e._, 260 days, which were preceded and followed by 52 days. I recognize this ritual year also in the present passage of the "Dresdensis," as the one current in the Maya country. It probably began about the 10th of March, at that period about the time of the vernal equinox, according to the Julian Calendar. Beginning with this date, I will now attempt to tabulate the chronology of this passage. In the first column I will place the number of the group of hieroglyphs in question, in the second I will set down to what day of the Maya year each group refers; in the third, the corresponding day of our year, and finally in the fourth, the 20-day periods which agree in general with the dates. 1. 1-13 March 10-22 Ceh. 2. 14-26 March 23-April 5 Mac. 3. 27-39 April 6-18 } Kankin. 4. 40-52 April 19-May 1 } 5. 53-65 May 2-14 Moan. 6. 66-78 May 15-27, Pax. 7. 79-91 May 28-June 9 } Kayab. 8. 92-104 June 10-22 } 9. 105-117 June 23-July 5 } Cumhu. 10. 118-130 July 6-18 } 11. 131-143 July 19-31 Pop. 12. 144-156 August 1-13 } Uo. 13. 157-169 August 14-26 } 14. 170-182 August 27-September 8 Zip. 15. 183-195 September 9-21 } Zotz. 16. 196-208 September 22-October 4 } 17. 209-221 October 5-17 Zec. 18. 222-234 October 18-30 } Xul. 19. 235-247 October 31-November 12 } 20. 248-260 November 13-25 Yaxkin. 21. 261-273 November 26-December 8 } Mol. 22. 274-286 December 9-21 } 23. 287-299 December 22-January 3 } Chen. 24. 300-312 January 4-16 } 25. 313-325 January 17-29 Yax. 26. 326-338 January 30-February 11 } Zac. 27. 339-351 February 12-24 } 28. 352-364 February 25-March 8 Ceh. In the following I will call attention to a few points by which this arrangement is justified. Hieroglyph 1a admits of explanation. It consists of four parts:--the left top is Kin, meaning sun or day, the right top is the sign of the year, the right bottom is the knife as symbol of separation or division, and the left bottom, which is especially decisive, is the month Ceh. Hence I read 1a thus:--the day of the change of year in the month Ceh. The sign 1b is the familiar Kin-Akbal signifying either the beginning day or the day Akbal. If the year should be named from this sign, then this would mean a Kan year, as in the preceding section the beginning lay in the year 9 Kan. If the year in the latter section had been as equally divided as the one in question here, it would have furnished us with some very remarkable parallels. Again the four groups:--4, 11, 18 and 25, which are alike, are important. The cross in sign _a_, combined with the three dotted lines passing from top to bottom, may refer to the wind and this meaning is further confirmed by the Ik sign (wind) in c. Further the sign _b_ between them is that for the Bacab, the wind deity itself. The most important events of the year are obviously the sowing and harvesting of the maize together with the beginning and end of the rainy season. Now we find the first two in connection with the god E, the maize-god, who is represented in 6c and 13c, 91 days apart, corresponding to the end of May and the beginning of August. Generally speaking, sixty days only were reckoned as the time between sowing and reaping, but here a quarter of a year may have been taken as a round number and it may also have reference to a more elevated region. I am inclined to think that the beginning and end of the rainy season are referred to in signs 8c and 16c, where, as it seems to me, three lines of drops are falling from a rectangle denoting the sky (as is usual) like the representation of rain dropping from a cloud at the bottom of page 36 (second picture). The serpent 8b as symbol of water may also refer to the same thing, especially as it is combined with an Akbal (often denoting beginning). The sign, which I think denotes the rainy season, is very similar, but not the same as another one, which is common to the Dresdensis and Tro-Cortesianus, the significance of which is certainly very close to the idea of the week of 13 days. I have some other ideas on this subject, which, however, are mere conjectures, advanced with some hesitation. If the Chuen sign in 7a is actually a serpent's jaw, then it might refer to the beginning of the astronomical year in May, since the serpent so often designates that time. In 9b we find a crouching figure with the sign which is usually considered that of the death-bird. In another place (Zur Entzifferung IV, 12) I have regarded the naked human figure placed upside down on page 58 as the sign for Mercury, and on page 60 at the bottom, left, I also regarded the crouching figure as representing Mercury vanquished by Venus. But in 9b, which belongs to the 105th-117th days of the year, a 115 day revolution of Mercury is computed. A crouching figure, like that in 9b, likewise appears on page 65a in the second series of 91 days after 11 + 13 = 24 days of this series have elapsed, _i.e._, directly after the 115 days of the apparent revolution of Mercury. In 10b, and it is the only place in this passage, we find the hieroglyph of B, the leading god of this Manuscript. This corresponds with the time of the greatest power of the sun and of the change in the civil year (July 16th). In Group 12, do _a_ and _c_ mean the year and is _b_ the head with the Akbal eye, thus denoting the beginning of the civil year? It ought really to have formed group 11, but there was no room for it, since it was necessary that the signs for the period of 91 days should be set down there. Signs 14a and the combined signs 15bc are almost alike and suggest 1a. Is it intended to designate here the ritual year, the time of the autumnal equinox (September 10th?). In 15a two hooks, turned in opposite directions proceed from one side of the sun-glyph. Do they signify two halves of the year and does the 3 in front of them signify the third quarter of the year? 20b is the sign of the death-god A, probably not placed accidentally here at the end of the month Xul, which denotes the end; but the end of what? The hieroglyph in 23a is a black bird, with two hooks, one pointing up and the other down, projecting from its head. Usually these hooks belong to K, and by means of them this bird becomes the storm-bird; the year symbol is below. Does this hieroglyph signify the time of the shortest day, when darkness predominates? A peculiarity of this passage is the striking frequency of the sign looked upon as that of the death-bird as well as of the cognate sign, which is commonly considered as that of the rising Moan. The first bird is in the 14th group, in the 9th it is combined with the apparent Mercury sign, and in the 17th with the year sign. The second bird with the prefixed Yax is in the 2nd group. But it is especially striking that several times both signs, and this is the case nowhere else, are combined into a single sign in groups 9, 13 and 26 and also probably in 19 where, however, the Moan sign seems to be effaced. This is all I have to say at the present time in reference to this calendar. Some of my statements are positive and some are only conjectures. Compare my treatise "Zwei Hieroglyphenreihen in der Dresdener Mayahandschrift" (Zeitschrift für Ethnologie, 1905, 2 and 3). Having disposed in this way of the two supplementary subjects of this section, I will now proceed to consider the principal theme, viz:--the two series and whatever is connected with them. 1. The 54-Series of the Day IX Ix. As with the other series, we begin here at the right, _i.e._, with page 73. There in the last column we find the superscription as it were. It is true that nothing positive can be gathered from the top part consisting of five hieroglyphs, which are mostly destroyed. The third hieroglyph seems to be the sign in group 2a discussed above. The fourth is an Akbal with a prefixed arm as on pages 8a, 36a, and the fifth is an Ik with a prefix. Below these are three numbers:--14,040, 702 and 54, which are in the proportion of 260, 13 and 1, so that the 14,040 is a Tonalamatl, as it were, of 260 periods of 54 days each. The fact that 54 is chosen here as the difference of the following series is curious, because usually only parts of 260 or of 364 are selected. But 54 is probably only a secondary matter, while 14,040, with its marvellous property of divisibility into the most varied and important periods, is the chief subject. There is a 9 in a red circle under the three numbers. It is meant to denote the starting-point of the series, the day IX Ix. Perhaps these two as well as the 54 are connected with the 9 "señores de las noches." In passing on to the left, I shall not consider the hieroglyphs and numbers in the next two columns in the upper third, since they are only set down here in order to secure space for them. They will be discussed later. The series itself begins in the upper third of page 71, in the next to the last column; it is continued on page 72 and on page 73 as far as the third column. The first twelve numbers are written from left to right contrary to the usual practice, doubtless occasioned by the passage above the series, which has already been discussed. And below, again contrary to rule, we find not the week and month days, but only the week days and they are in red circles. If written in the usual way, the series would have the following form (with the usual omission of the initial day IX Ix):-- 54 108 162 216 270 324 378 XI Lamat XIII Ik II Cib IV Oc VI Kan VIII Ezanab X Eb 432 486 540 594 648 XII Cimi I Ahau III Ix V Lamat VII Ik. The series must now continue with the 702 already specified on page 73, which it proceeds to do from right to left in the middle of page 71, and continues from there on with regularly added dates and with the 702 itself as the difference. At the same time, since 702 = 54 × 13, the week-days are forced to come to a standstill on the IX, while each of the month days ascends by two (702 = 35 × 20 + 2). The 4914 = 7 × 702 is obtained in the next to the last column of page 70. On page 71 the 702 is incorrectly set down as 1. 15. 2. instead of 1. 17. 2. The series continues on page 71 in the same way beyond the 702, until in 7020 a number is obtained which is also divisible by 260, so that now the accompanying day must be IX Ix. Now we ought to expect to see here the double of 7020, the very 14,040 abovementioned, but it is omitted just because it was set down on page 73. Nevertheless this very number forms the new difference with which the series returns from page 70 to the top line of page 71, where the numbers are mostly effaced, but enough remains to enable us to assume that the last number on page 71 is the 10th multiple of 14,040, and this may be followed by the 11th and 12th multiples, the last number being 168,480. 2. The 65-Series of the Day IV Eb. This series begins in the middle of page 73 with the day IV Caban, the zero-point therefore being IV Eb. It then advances to the left across 28 members, until on page 71 it reaches the number 1820 = 5 years of 364 days = 7 Tonalamatls. From there on, 1820 itself is the difference, and the accompanying day therefore remains IV Eb. Then, in the two lowest sections of pages 71 and 70, the fourth multiple of 1820, _i.e._, 7280, is the third difference and thus the series advances to 15 × 7280 = 109,200 on page 71, after which on page 70 the omitted 8 × 7280 = 58,240 is written out. Close beside this number are the figures 1. 0. 12. 3. and a 0 below the latter, which was not successfully erased; this would be the number 7443 of which I can make nothing at all. The initial dates of the two series, IX Ix and IV Eb, are 138 days apart and reversely 122 days. 3. The Groups of Hieroglyphs. The transition, as it were, from the series to the large numbers is formed by a few groups of hieroglyphs. The first of these groups is at the top of pages 69-70; its first top line is completely effaced. The remainder I will designate by the following numbers:-- 1 2 5 6 9 13 3 4 7 8 10 14 11 15 12 16. The date IX Kan 12 Kayab, set down under 3 and 4 does not belong there but to the serpent below and will be discussed later. I take sign 1 to be that of a Bacab, 2 I do not understand and it is half obliterated; it seems to occur again on page 73 in the column to the extreme right. 3 and 7 are the elongated head _q_ with an unusual superfix, 4 and 8 correspond with one another, but I cannot explain them. 5, 10 and 14 denote the beginning, 6, 11 and 15, the end. 9 and 13 both designate the 8th day of the month Kayab and over them IV Ahau must have been set down twice. 12 and 16 are two heads of gods, 12 is probably D's with the sign for west and 16, B's with that of the east. On page 70, in the middle of the third and fourth columns, the day IX Ix occurs twice. In one case it ought to have been IV Eb and the scribe has really changed the IX to IV, but he omitted changing the Ix to Eb. Directly below these dates we find the second group, consisting of two rows of four hieroglyphs. I think these eight hieroglyphs can be interpreted as follows:-- 1) 13 Pax 2) 20 Pop or 25 Cumhu 3) VIII Ahau 4) 13 Yaxkin 5) 10 Muan 6) 37,960 7) 20 8) 1 Zec. The following is to be noted in this connection:-- 3 is really set down X Ahau, but an VIII is written above the Ahau by way of correction. The day VIII Ahau will presently prove to be important. 6, a compound of Imix and the superfix denoting multiplication, is the sign for 18,980, and its prefix seems to me to denote duplication. We have long known how important the 37,960 = 146 × 260 = 104 × 365 is, and, if my theory is correct, we shall see directly that it occurs again here. 8 seems really to be 1 Zec, but the composite prefixes demand further examination. Impenetrable darkness still shrouds the meaning of the whole group. Though it is clear that in several cases certain days are specified according to their position in the year, their distance apart does not agree with the interval between days IV Eb, IX Ix and IV Ahau under discussion here. If signs 3 and 4 ought to be read together as VIII Ahau 13 Yaxkin, then this date would come in the year 7 Muluc. In the Zeitschrift für Ethnologie I explained the five hieroglyphs in the third column at the bottom of page 70 (the third group) as civil years of 360 and astronomical years of 365 days:-- 1) 8,760 = 24 × 365 = 15 × 584 2) 2,920 = 8 × 365 = 5 × 584 3) 7,200 = 20 × 360 4) 18,720 = 52 × 360 = 72 × 260 5) 360 ------ 37,960. This, it is true, is a striking explanation and certainly a surprising one! Now the date IX Ix 12 Kayab is at the very bottom of the fourth column. This, without apparent reason, would refer to the year 4 Kan. Should it not be read IX Kan 12 Kayab (4 Ix), thus indicating that the entire passage is only the preparation for the date from which the serpent numbers proceed? The scribe may have had in mind the IX Ix of the series. The fourth and last group on page 73, above the two numbers 83,474 and 34,732, consists of four hieroglyphs. The two upper hieroglyphs on the left are effaced, and the top one on the right. I think it probable that the day VIII Ahau, which will be discussed later, may have stood in the top line, and possibly with a month date. Of the two remaining signs of the fourth group, the upper is the moon and the lower Imix, probably with the hieroglyph of the east as a prefix; but there is nothing to be done with it owing to the obliteration of the sign above it. In the Zeitschrift für Ethnologie, 1891, page 153, I have endeavored to explain these three signs on the right above 34,732, by suggesting for them the values 18,980 = 52 × 365 8,760 = 24 × 365 7,200 = 20 × 360 ------ 34,940 and calling special attention to the fact that between IV Eb and IV Ahau there are 208 days, and that the 34,732 placed below them in the Manuscript, increased by 208, is equal to 34,940. This group then seems really to belong to the day IV Eb and to the 65-series, while manifold problems are still to be encountered in interpreting the other groups. 4. The Large Numbers. The Manuscript offers material with which to work, beginning on page 70:-- 1,394,120 1,437,020 1,567,332 1,520,654 (606) (1646) IV Eb IX Ix IV Ahau IV Ahau VIII Ahau; 13 Yaxkin (7 Muluc). 8 Cumhu 8 Cumhu IX Ix IV Eb 1,201,200 1,202,240 111,554 101,812 (86) (208) IV Ahau IV Ahau 8 Cumhu 8 Cumhu This is followed at the right top of page 73 by 83,474 34,732 IX Ix IV Eb. Two of the numbers and two of the dates are conjectural:-- I read the 1,202,240 as 8. 6. 19. 10. 0. while the Manuscript has 16 instead of 6. I read the 101,812 as 14. 2. 14. 12. the Manuscript has 16 instead of the second 14. And in two places in the third column of page 70, I have restored the day IV Eb, where the Manuscript incorrectly repeats the IX Ix, and does the same thing on page 73. Let us now first consider the construction of those large numbers, which are connected with the day IX Ix and thus with the 54-series. These numbers are the two upper ones of columns 1 and 2 and the lower one of column 1 on page 70. 174 is the starting-point, the number of the day is IX Ix, which seems to have been chosen because it divides the Tonalamatl approximately in the proportion of 2 to 1. (IV Ahau - IX Ix = 174.) The 5359th, 5520th and 4619th multiples of 260 have been added to 174; why precisely these multiples were chosen remains a mystery. In this way were obtained the following numbers, which the Manuscript suppresses. I will give them with their corresponding dates:-- 1,393,514 = IX Ix 12 Muan (5 Kan). 1,435,374 = IX Ix 17 Chen (3 Cauac). 1,201,114 = IX Ix 7 Mac (11 Muluc). When we add to the above the three encircled numbers 606, 1,646 and 86, the resulting sums are the three numbers found in the Manuscript:-- 1,394,120 = IV Ahau 8 Chen (7 Ix). 1,437,020 = IV Ahau 23 Cumhu (7 Cauac). 1,201,200 = IV Ahau 13 Kayab (11 Muluc). I am placing the first two not far from the present and the third in the past. As multiples of 260 these three numbers have the following form:-- 1,394,120 = 5362 × 260. 1,437,020 = 5527 × 260. 1,201,200 = 4620 × 260. Some curious facts come to light with regard to their magnitude and their mutual relation. The two largest numbers are 165 × 260 = 660 × 65 apart; this recalls the 65-series. The third lowest number is 165 × 7280 and thus contains not only the 65 but = 165 × 65 × 112. The ritual year (364) and its excess over the Tonalamatl (104) is likewise contained in these numbers, at least in the first and third:-- 1,394,120 = 3830 × 364 = 13,405 × 104. 1,201,200 = 3300 × 364 = 11,550 × 104. The three encircled numbers are connected with one another because the first = 2 × 260 + 86, the second = 6 × 260 + 86 and the third is 86 itself. The larger encircled numbers are, therefore, 1040 = 4 × 260 apart, and this is also the interval between the two numbers near the bottom. 1040, however, also = 5 × 208, and 208 is the interval from IV Eb to IV Ahau. Now it is curious that the two numbers below are 5775 × 208 and 5780 × 208, though the third belongs to day IX Ix and the fourth to IV Eb. One result of this is that 1,201,200 = 1155 × 1040 and 1,202,240 = 1156 × 1040. As these three numbers relate to day IX Ix and the 54-series, so the fourth relates to IV Eb and the 65-series. Here the starting-point is the number 52, which belongs to day IV Eb and this is separated from IV Ahau by 208 days _i.e._, it divides the Tonalamatl in the proportion of 1 to 4. To the number 52 then, for unknown reasons was added 4623 × 260 = 1,201,980, and thus the number 1,202,032, suppressed in the Manuscript, was obtained for the day IV Eb. To this sum the encircled number 208 was then added and the result was 1,202,240, the number in the Manuscript. The number = 23,120 × 52 = 4624 × 260, which is self-evident, but it also = 5780 × 208, _i.e._, it is a multiple of the encircled number. It consequently also = 11,560 × 104, and thus it is related to the first and third numbers just now discussed. The position of this number is IV Ahau 18 Kankin (1 Kan) and the position of the suppressed number is IV Eb 10 Zotz (also 1 Kan). We ought now to discuss the last two numbers of this section amounting to millions:--1,567,332 and 1,520,654, which are in the third and fourth columns at the top of page 70. But before going further, we must examine four other numbers, two of which, 111,554 and (with my correction) 101,812, are in column 4 on the lower part of page 70, and the other two, 83,474 and 34,732, are on the top of page 73. Although these four numbers are not ornamented with circles, they all have the significance of the numbers enclosed in circles and are designations of differences between suppressed and specified numbers. Let us first of all examine their curious relation to one another:-- The Manuscript should have set down under these numbers the day IX Ix twice and IV Eb twice, from which days the numbers in question must be computed; but here the two errors already mentioned were made. 111,554 - 101,812 is 9742, the very same number which we shall afterward find as the difference of the serpent numbers on page 69. 83,474 - 34,732 = 48,742. If 9472 be subtracted from this, the remainder is exactly 39,000 = 150 Tonalamatls = 50 revolutions of Mars. I have already found this number on page 31a, and also the double of it, 78,000, on page 24, and this I found by using 68,900 + 9100 for my computation. 111,554 - 83,474 = 28,080, _i.e._, exactly the double of the important 14,040, which is recorded on page 73. 101,812 - 34,732 = 67,080, _i.e._, = 258 Tonalamatls or 86 revolutions of Mars. 111,554 - 34,732 = 76,822; if 122, the interval from IV Eb to IX Ix be subtracted from this, the remainder is 76,700 = 295 Tonalamatls. 101,812 - 83,474 = 18,338; if 138, the interval from IX Ix to IV Eb, be subtracted from 18,338, the remainder is 18,200 = 70 Tonalamatls = 50 ritual years of 364 days each, _i.e._, exactly the double of the 9100 specified on page 24. Now we also have the following equations for the four numbers:-- 111,554 = 429 × 260 + 14. 83,474 = 321 × 260 + 14. 101,812 = 391 × 260 + 152. 34,732 = 133 × 260 + 152. A day VIII Ahau is 14 days back of the day IX Ix, and another VIII Ahau is 152 days back of IV Eb. Thus a day VIII Ahau hitherto unmentioned is introduced into the computations. This day has no doubt been chosen, because it divides the Tonalamatl beginning with IV Ahau into two parts of 160 and 100 days, which are in the proportion of 8 to 5, _i.e._, the same proportion as the Venus year to the solar year. This day VIII Ahau may also figure in the large numbers of the first two columns on page 70, for 1,394,120 and 1,201,200 are both divisible by 14, the interval between VIII Ahau and IX Ix. Now I believe that the large numbers were constructed in the following twofold manner (I add the corresponding dates):-- 160 1,408,940 = 5419 × 260 --------- 1,409,100 = VIII Ahau 3 Yax (9 Cauac). 111,554 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc). 160 1,437,020 = 5527 × 260 --------- 1,437,180 = VIII Ahau 18 Mol (8 Kan). 83,474 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc). 160 1,465,360 = 5636 × 260 --------- 1,465,520 = VIII Ahau 8 Uo (8 Ix). 101,812 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc). 160 1,532,440 = 5894 × 260 --------- 1,532,600 = VIII Ahau 13 Pax (9 Muluc). 34,732 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc). The last record of the date of VIII Ahau seems to throw light on the date 13 Pax (page 70, column 3), which is directly above the date VIII Ahau, and which I have already mentioned in the discussion of the groups of hieroglyphs. Indeed, it seems as if a day VIII Ahau occurred a fifth time in that passage, for in consequence of the correction made by the scribe we read here VIII Ahau 13 Yaxkin. This would point to a year 7 Muluc, the position of which between the other four is, of course, undetermined. If the two large numbers in the Manuscript were treated in the same way as the other large numbers, they would not be recorded at all, but instead of them there would have been two numbers belonging to the day IV Ahau and under them would have been the encircled numbers 208 and 86, or these numbers increased by a multiple of 260. This passage would then read about as follows:-- 1,567,540 (IV Ahau) 1,520,740 (IV Ahau) 208 (IV Eb) 86 (IX Ix). These two numbers for IV Ahau are equal to 6029 and 5849 Tonalamatls. If 5549 × 260 be subtracted from these, the remainders are 480 and 300 Tonalamatls respectively, _i.e._, 124,800 and 78,000, and these are in the proportion of 8 to 5. Now the two large numbers have the difference 46,678 = 179 × 260 + 138; the latter is the interval from IX Ix to IV Eb. The four numbers of the days VIII Ahau seem to stand in very irregular relation to one another and yet they show the following striking results, if the first and third and also the second and fourth numbers be combined (as I combined them under page 24):-- In the first case we see the following:-- 1,465,520 - 1,409,100 = 56,420 = 3 × 18,980 - 520. 3 Yax (9 Cauac) to 8 Uo (8 Ix) = 18,460 = 18,980 - 520. 56,420 - 18,460 = 37,960 = 2 × 18,980. While in the second case:-- 1,532,600 - 1,437,180 = 95,420 = 5 × 18,980 - 520. 18 Mol (8 Kan) to 13 Pax (9 Muluc) = 520. 95,420 - 520 = 94,900 = 5 × 18,980. 5. The Serpent. As in the section occupying pages 61-64, the single series is crowned by four serpents with eight large numbers, so in this section the two series end in a single serpent with two numbers, one for each series, but both bear some obscure relation to the day VIII Ahau, which has made its appearance here. The two sections also correspond, inasmuch as the numbers in both are computed not from the normal date, but from the date IX Kan 12 Kayab (4 Ix). The serpent pictured here is different from the previous ones, inasmuch as it is partly black. The god B is sitting on its opened jaws, and this time he, too, is painted black (as on page 31c); there is an animal's head upon the god's head, in which we again recognize that of the animal with the fourth serpent in the preceding section. The god is armed with spear and shield and recalls his picture at the bottom of page 74. There are eight hieroglyphs above this picture, just as there are over each of the first four serpents. The two top hieroglyphs are obliterated. Of the legible hieroglyphs, the one at the left top is the Bacab sign, which also occurs over the first of the four serpents. In the third line are the same two hieroglyphs, which are in the third line of the first and second columns on page 70. The first of the two also occupies the same place on page 62 above the fourth serpent. But here at the bottom we find the date IX Kan 12 Kayab (4 Ix), the same date which we found over the fourth serpent, which is thus again brought into closer connection with the single serpent. There can be no doubt here regarding the two numbers in the serpents, but notice should be taken of the fact that the figure 1 is barely visible in the red number. The black number here has the figures 4. 5. 19. 13. 12. 8. and the red 4. 6. 1. 0. 13. 10. The black is therefore 12,381,728, and the red 12,391,470. The black number is somewhat less than the eight numbers in the four serpents, and the red is somewhat larger than the least of them. The difference of the two is 9742 = 37 × 260 + 122; but 122 is the interval between days IV Eb and IX Ix. Now this is the same 9742 which we found on page 70, as the difference between 111,554 and 101,812. In order not merely to examine these numbers, but also to understand them, we will again make use of 109 Ahau-Katuns = 12,412,920, as we did in the first four serpents, and we shall have the following:-- Black Red 12,381,728 12,391,470 12,412,920 12,412,920 ---------- ---------- -31,192 = 119 × 260 + 252 -21,450 = 82 × 260 + 130 IV Eb - IX Kan = 252 IX Ix - IX Kan = 130 The date given for both numbers was the day IX Kan, which was likewise the starting-point for six of the eight numbers in the previous serpents. Besides this the day IV Eb, the starting-point of the 65-series, is given for the black number, and therefore also the interval between IV Eb and IX Kan = 252. To this 252 was added a multiple of 260, not an arbitrary choice, but one which combined with 252 resulted in a number divisible by 8, the interval from IX Kan to IV Eb. 31,192 = 3899 × 8 = 119 × 260 + 252 was thus obtained. The subtraction of this number from 12,412,920 resulted in the serpent number 12,381,728. In addition to all this the day IX Ix, the starting-point of the 54-series, is given for the red number; consequently also the interval between IX Ix and IX Kan = 130, which, at the same time, is reversely the interval from IX Kan to IX Ix. To this 130 was added a multiple of 260, which _must_ in every case be a multiple also of 130. Thus we obtain the 21,450 = 82 × 260 + 130. The subtraction of this number from 12,412,920 results in the serpent number 12,391,470. Reckoned from the starting-point IX Kan 12 Kayab (4 Ix) the black number corresponds to the date IV Eb 5 Chen (10 Muluc) and the red to IX Ix 12 Zip (11 Kan), and these two dates must certainly have been under the serpent; the months unfortunately are effaced. It is self evident that the black number is exactly divisible by 8 and the red by 130. The two events indicated by the two numbers must be to some extent coincident with the beginning of the seven events recorded in the previous four serpents. These large numbers pertaining to the destruction of the world are a reminder of the numbers, which on page 24 we believed were connected with the creation of the world. Thus here, too, we have the genesis and the apocalypse of all the mythologies. 6. The Columns of Hieroglyphs. The last portion of this section is formed by the two middle columns of hieroglyphs on page 69. They bear an extraordinary resemblance to those discussed under page 61 even in regard to the fact that each column contains 18 signs. Besides, the upper 10 lines, _i.e._, the upper 20 signs, are exactly alike on the two pages, aside from slight variations, and differ only in so far as the passage on page 69 is written on blue ground and the one on page 61 on white. But also the lower part, with eight signs in each column, shows many points in common with page 61. Here as there the whole is divided into several groups. With the four signs 11ab and 12ab, which formed the first group there, I can compose only the two signs 11ab here. In the cross 11a, as on pages 24 and 58 of the Manuscript, I see the sign for 20 with the prefixed 5 making 25. In 11b we find the sign for 18,980 days, which we have already met with several times. Hence 11ab would have the value of 25 × 18,980 = 474,500 days, as on page 61 the corresponding four signs seemed to form 421,940. And as the number there was 1156 × 365, so on page 69 we have 1300 × 365. I believe there is a disarrangement in what follows, inasmuch as I assume that the two signs 12b and 13a ought to be placed _before_ and not _after_ 12a. Assuming that the two little crosses on either side of the 1 are meaningless, we should assign the value of 61 to the 3 Chuen, 1 Kin. Here, in the first place, the intention seems to be to establish some connection with the two days VII Kan and IV Ik specified with their numbers on page 63, column 3, as well as with the days most important there, III Chicchan and XIII Akbal, _i.e._, a connection with the previous section of the four serpents in general; for the interval from VII Kan to III Chicchan, as well as that between IV Ik and XIII Akbal is 61 and on pages 70-73 the two most important days, IV Eb and IX Ix, are 122 days apart, and 122 is the second multiple of 61. I can now put the 144,000 of 12a in the place of the 13a. Then, secondly, the four signs from 13a to 14b in the one section are exactly like those in the other section, and therefore need not be discussed here. Only 15ab differs from the signs in the other passages inasmuch as on page 69 we find 4 × 20 + 4 × 1. The last 4 agrees even better than it does there with the distance from IV Ahau to the day Kan with which the serpent numeral begins. Nothing on page 69 corresponds to the signs in 16ab and 17ab of page 61. On the contrary, the initial date of the serpent IX Kan 12 Kayab, which on page 61 does not appear until 18ab is set down in 16ab. On the other hand on page 69 the four signs 17ab and 18ab are added, 17a being a sign as yet unknown with 13 as a superfix. I feel inclined, though with many misgivings, to treat 17ab like 5a and b of page 61 and to assign to them the value of an Ahau-Katun of 113,880 days. For then they would denote the 13th Ahau-Katun, which extends from the day 1,366,560 (page 24) to 1,480,440 and which contains the two large numbers on page 70, left, top, while the two lower numbers in the first and second columns of that page belong to the 12th Ahau-Katun, and the two in the third and fourth belong to the 14th Ahau-Katun. The 13th would be the present and the 12th and 14th the past and future; but all this could only be confirmed by further research. At all events, the signs for beginning in 17b and for end in 18a refer to past and future. Unfortunately, 18b is entirely effaced. Page 74.[5] Besides the picture, this page contains only 15 hieroglyphs in three horizontal rows. Only about six of these signs are decipherable. The second, third and fourth of the lower line are three different heads; the middle is the familiar head of god B, the one on the left has the Akbal eye and the abbreviated sign for the south, which is repeated in the affix; the head on the right has the sign for the west as a prefix. Very little more is to be said of the other hieroglyphs than that the second and third of the second line have the sign for the east; the first of the second line, however, was the one which we found on pages 71-73 as the constant companion of the Bacabs and which suggested the wind. The last sign of the second line must have contained that for north, so that the four cardinal points all came together here. The picture begins below these signs. Astronomical figures, apparently Venus, Mars, Mercury and Jupiter, end in the fore part of a crocodile. Below the astronomical signs are the signs for the sun and moon. Streams of water are falling from the jaws of the crocodile and also from the sun and moon. And a fourth stream is being poured from a jug by the old woman with the tiger claws, and with the serpent on her head, whom we saw on pages 39, 43 and 67 engaged in the same occupation. Cross-bones are represented on her skirt as the symbol of death. The sign of the ninth day, Eb, appears on the jug; this is the day which was avoided in the Tonalamatls, for not a single Tonalamatl begins with Eb in the Dresdensis, nor does one begin with the week-day IX; does Bolon meaning nine suggest Balam, the jaguar? Still further down on the page sits a black god, who may be the same as the god on pages 7a and 16b, with a bird of prey on his head. There are two arrows in his right hand and his left hand holds what may be an atlatl, but it is very much longer than is usually the case; at the same time it can be regarded as a spear. This page can denote nothing but the end of the world, for which the serpent numbers have prepared the way. Perhaps what looks like a zero above the sign Eb in the stream of water may likewise point to this calamity. * * * * * INDEX. ------ The numbers in the first column refer to the pages of the Manuscript, and those in the second column to the pages of the Commentary. FIRST PART. 1 | 55 | 16a | 90 | 42a-44a | 146 2 | 55 | 16a-17a | 90 | 45a | 148 3 | 59 | 18a-19a | 92 | 29b-30b | 150 4a-10a | 61 | 19a-21a | 93 | 30b-31b | 151 4b-5b | 67 | 21a-22a | 93 | 31b-35b | 152 10a-12a | 69 | 22a-23a | 95 | 35b-37b | 156 12a | 69 | 16b-17b | 96 | 38b-41b | 159 5b-6b | 70 | 17b-18b | 97 | 41b-43b | 162 6b-7b | 71 | 16c-17c | 98 | 43b-44b | 164 8b | 72 | 17c-18c | 99 | 44b-45b | 165 9b | 73 | 18c-19c | 100 | 29c-30c | 167 10b | 74 | 19c-20c | 100 | 30c-33c | 168 10b-11b | 75 | 19b | 101 | 33c-39c | 170 12b | 76 | 19b-20b | 101 | 40c-41c | 176 4c-5c | 77 | 20b | 102 | 42c-45c | 178 5c-6c | 78 | 21b | 103 | 6c-7c | 79 | 21c-22c | 104 | SECOND PART. 8c | 80 | 22c-23c | 105 | 9c | 81 | 22b | 107 | 46-50 | 182 10c-11c | 82 | 23b | 108 | 51a-52a | 197 12c | 83 | 24 | 110 | 51-58 | 200 13a | 84 | 25-28 | 120 | 58-59 | 215 13b-14b | 85 | 29a-30a | 132 | 60 | 219 13c-14c | 86 | 30a-31a | 133 | 61-64 | 222 14a-15a | 85 | 31a-32a | 133 | 65-69 | 235 15a | 88 | 32a-39a | 138 | 69-73 | 245 15b-16b | 88 | 40a-41a | 144 | 74 | 265 15c | 89 | | | | * * * * * [Illustration: GLYPHS REFERRED TO IN THE TEXT.] [Illustration: CARDINAL POINTS.] * * * * * Notes [1] The Manuscript has incorrectly 8 and 18. [2] = 20 Chen. [3] The sign denotes the end of the 360-day year. [4] = 20 Zotz. [5] Compare the Peresianus, page 20. 
43491	----	SMITHSONIAN INSTITUTION BUREAU OF AMERICAN ETHNOLOGY BULLETIN 57 AN INTRODUCTION TO THE STUDY OF THE MAYA HIEROGLYPHS BY SYLVANUS GRISWOLD MORLEY [Illustration] WASHINGTON GOVERNMENT PRINTING OFFICE 1915 * * * * * {iii} LETTER OF TRANSMITTAL SMITHSONIAN INSTITUTION, BUREAU OF AMERICAN ETHNOLOGY, _Washington, D. C., January 7, 1914._ 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 recommend its publication as a bulletin of the Bureau of American Ethnology. The hieroglyphic writing developed by the Maya of Central America and southern Mexico was probably the foremost intellectual achievement of pre-Columbian times in the New World, and as such it deserves 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 Förstemann, of the Royal Library at Dresden. About 1880 Professor Förstemann 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 manuscript. 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 enough, about the same time, or a little later (in 1891), another student of the same subject, Mr. J. T. Goodman, of Alameda, California, working independently and without knowledge of Professor Förstemann'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 {iv} tables, "The Archaic Chronological Calendar" and "The Archaic Annual Calendar," which 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 those relating to the calendar and chronology; that is, the signs for the 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-fifths probably tell the 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 deciphering of this textual residuum is enormously complicated by the character of the Maya glyphs, which for the greater part are ideographic 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 from 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 wherever they occur, and thus words are formed. While the Maya glyphs largely represent ideas, indubitable traces of phoneticism and phonetic composition appear. There are perhaps half a dozen glyphs in all which are known 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 inscriptions may be summarized as follows: The Maya calendar, chronology, and astronomy as recorded in the hieroglyphic texts have been carefully worked out, and it is unlikely that future discoveries will 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 of the events which took place on the dates recorded. An analogy would be the following: Supposing, in scanning a history of the United States, only the dates could be read. We would find, for example, July 4, 1776, followed by unknown characters; April 12, 1861, by others; and March 4, 1912, by others. This, then, is the case with the Maya glyphs--we find dates followed by glyphs of unknown meaning, which presumably set forth the nature of the corresponding events. In a word, we know now the {v} 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 widely scattered and inaccessible, that it is difficult for students of Central American archeology to become familiar with what has been accomplished in this important field of investigation. In the present memoir Mr. Morley, who has devoted a number of years to the study of Maya archeology, and especially to the hieroglyphs, summarizes the results of these researches to the present time, and it is believed 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. Very respectfully, F. W. HODGE, _Ethnologist-in-Charge._ Dr. CHARLES D. WALCOTT, _Secretary of the Smithsonian Institution,_ _Washington, D. C._ * * * * * {vii} PREFACE With the great expansion of interest in American archeology during the last few years there has grown to be a corresponding need and demand for primary textbooks, archeological 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 specialist rather than those of the beginner, are for the greater part too advanced and technical for general comprehension; and (2) these writings are scattered through many publications, periodicals as well as books, some in foreign languages, and almost all difficult 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 publication 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. {viii} Acknowledgment should be made here to Mr. Bowditch for his courtesy in permitting the reproduction of a number of drawings from his book, the examples of the period, day and month glyphs figured being derived almost entirely from this source; and in a larger sense for his share in the establishment of instruction in this field of research 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 this 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, government, and religion of the ancient Maya, so that the reader may gather a general idea of the remarkable people whose writing and calendar he is about to study. * * * * * {ix} CONTENTS Page CHAPTER I. The Maya 1 Habitat 1 History 2 Manners and customs 7 II. The Maya hieroglyphic writing 22 III. How the Maya reckoned time 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. The codices 251 Texts recording tonalamatls 251 Texts recording Initial Series 266 Texts recording Serpent Numbers 273 Texts recording Ascending Series 276 * * * * * {x} List of Tables Page TABLE I. The twenty Maya day names 37 II. Sequence of Maya days 42 III. The divisions of the Maya year 45 IV. Positions of days at the end of a year 48 V. Relative positions of days beginning Maya years 53 VI. Positions of days in divisions of Maya year 55 VII. Positions of days in divisions of Maya year according to Maya notation 55 VIII. The Maya time-periods 62 IX. Sequence of katuns in u kahlay katunob 80 X. Characteristics of head-variant numerals 0-19, inclusive 103 XI. Sequence of twenty consecutive dates in the month Pop 111 XII. Comparison of the two methods of numeration 133 XIII. Values of higher periods in terms of lowest, in inscriptions 135 XIV. Values of higher periods in terms of lowest, in codices 135 XV. The 365 positions in the Maya year 141 XVI. 80 Calendar Rounds expressed in Arabic and Maya notation 143 XVII. Interrelationship of dates on Stelæ E, F, and J and Zoömorph G, Quirigua 239 {xi} 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 (according to Förstemann) 32 4. Diagram showing occurrence of dates recorded in Cycle 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 167 8. Glyphs 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 use 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 Copan--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 Secondary Series on Stela 1, Piedras Negras 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 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 {xii} 31. Page 24 of the Dresden Codex, showing Initial Series 266 32. Page 62 of the Dresden Codex, showing the Serpent Numbers 273 FIGURE 1. Itzamna, chief deity of the Maya Pantheon 16 2. Kukulcan, God of Learning 17 3. Ahpuch, God of Death 17 4. The God of War 17 5. Ek Ahau, the Black Captain, war deity 18 6. Yum Kaax, Lord of the Harvest 18 7. Xaman Ek, the North Star God 19 8. Conflict between the Gods of Life and Death (Kukulcan and Ahpuch) 19 9. Outlines of the glyphs 22 10. Examples of glyph elision, showing elimination of all parts except essential element 23 11. Normal-form and head-variant glyphs, showing retention of essential element in each 24 12. Normal-form and head-variant glyphs, showing absence of common 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 Zoömorph B, Quirigua 71 33. Full-figure variant of uinal 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 {xiii} 42. Examples showing the way in which numerals 1, 2, 6, 7, 11, 12, 16, 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 with period, day, or month signs 90 44. Normal forms of numerals 1 to 13, inclusive, in the Books of Chilan Balam 91 45. Sign for 20 in the codices 92 46. Sign for 0 in the codices 92 47. Sign for 0 in the inscriptions 93 48. Figure showing possible derivation of the sign for 0 in the inscriptions 93 49. Special sign for 0 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 0 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 month signs 104 56. Examples of the first method of numeration, used almost exclusively 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 composed 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 showing 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 Statuette 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} 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; _b_, 9. 15. 6. 14. 6 6 Cimi 4 Tzec 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. Calendar-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 * * * * * {xv} BIBLIOGRAPHY AGUILAR, SANCHEZ DE. 1639. Informe contra idolorum cultores del Obispado de Yucatan. Madrid. (Reprint in _Anales Mus. Nac. de Mexico_, VI, pp. 17-122, Mexico, 1900.) BOWDITCH, CHARLES P. 1901 a. Memoranda on the Maya calendars used in the Books of Chilan Balam. _Amer. Anthr._, n. s., III, No. 1, pp. 129-138, New York. ---- 1906. The Temples of the Cross, of the Foliated Cross, and of the Sun at Palenque. Cambridge, Mass. ---- 1909. Dates and numbers in the Dresden Codex. _Putnam Anniversary Volume_, pp. 268-298, New York. ---- 1910. The numeration, calendar systems, and astronomical knowledge of the Mayas. Cambridge, Mass. BRASSEUR DE BOURBOURG, C. E. 1869-70. Manuscrit Troano. Études sur le système graphique et la langue des Mayas. 2 vols. Paris. BRINTON, DANIEL G. 1882 b. The Maya chronicles. Philadelphia. (No. 1 of _Brinton's Library of Aboriginal American Literature_.) ---- 1894 b. A primer of Mayan hieroglyphics. _Pubs. Univ. of Pa._, Ser. in Philol., Lit., and Archeol., III, No. 2. BULLETIN 28 of the Bureau of American Ethnology, 1904: Mexican and Central American antiquities, calendar systems, and history. Twenty-four papers by Eduard Seler, E. Förstemann, Paul Schellhas, Carl Sapper, and E. P. Dieseldorff. Translated from the German under the supervision of Charles P. Bowditch. COGOLLUDO, D. L. 1688. Historia de Yucathan. Madrid. CRESSON, H. T. 1892. The antennæ and sting of Yikilcab as components in the Maya day-signs. _Science_, XX, pp. 77-79, New York. DIESELDORFF, E. P. See BULLETIN 28. FÖRSTEMANN, E. 1906. Commentary on the Maya manuscript in the Royal Public Library of Dresden. _Papers Peabody Mus._, IV, No. 2, pp. 48-266, Cambridge. _See also_ BULLETIN 28. GATES, W. E. 1910. Commentary upon the Maya-Tzental Perez Codex, with a concluding note upon the linguistic problem of the Maya glyphs. _Papers Peabody Mus._, VI, No. 1, pp. 5-64, Cambridge. GOODMAN, J. T. 1897. The archaic Maya inscriptions. (Biologia Centrali-Americana, Archæology, Part XVIII. London.) [_See_ Maudslay, 1889-1902.] ---- 1905. Maya dates. _Amer. Anthr._, n. s., VII, pp. 642-647, Lancaster, Pa. HEWETT, EDGAR L. 1911. Two seasons' work in Guatemala. _Bull. Archæol. Inst. of America_, II, pp. 117-134, Norwood, Mass. HOLMES, W. H. 1907. On a nephrite statuette from San Andrés Tuxtla, Vera Cruz, Mexico. _Amer. Anthr._, n. s., IX, No. 4, pp. 691-701, Lancaster, Pa. LANDA, DIEGO DE. 1864. Relacion de las cosas de Yucatan. Paris. LE PLONGEON, A. 1885. The Maya alphabet. Supplement to _Scientific American_, vol. XIX, Jan. 31, pp. 7572-73, New York. MALER, TEOBERT. 1901. Researches in the central portion of the Usumatsintla valley. _Memoirs Peabody Mus._, II, No. 1, pp. 9-75, Cambridge. ---- 1903. Researches in the central portion of the Usumatsintla valley. [Continued.] Ibid., No. 2, pp. 83-208. ---- 1908 a. Explorations of the upper Usumatsintla and adjacent region. Ibid., IV, No. 1, pp. 1-51. {xvi} MALER, TEOBERT. 1908 b. Explorations in the Department of Peten, Guatemala, and adjacent region. Ibid., No. 2, pp. 55-127. ---- 1910. Explorations in the Department of Peten, Guatemala, and adjacent region. [Continued.] Ibid., No. 3, pp. 131-170. ---- 1911. Explorations in the Department of Peten, Guatemala. Tikal. Ibid., V, No. 1, pp. 3-91, pls. 1-26. MAUDSLAY, A. P. 1889-1902. Biologia Centrali-Americana, or contributions to the knowledge of the flora and fauna of Mexico and Central America. Archæology. 4 vols. of text and plates. London. MORLEY, S. G. 1910 b. Correlation of Maya and Christian chronology. _Amer. Journ. Archeol._, 2d ser., XIV, pp. 193-204, Norwood, Mass. ---- 1911. The historical value of the Books of Chilan Balam. Ibid., XV, pp. 195-214. PONCE, FRAY ALONZO. 1872. Relacion breve y verdadera de algunas cosas de las muchas que sucedieron al Padre Fray Alonzo Ponce, Comisario General en las provincias de Nueva España. _Colección de documentos ineditos para la historia de España_, LVII, LVIII. Madrid. ROSNY, LEON DE. 1876. Essai sur le déchiffrement de l'écriture hiératique de l'Amérique Centrale. Paris. SAPPER, CARL. _See_ BULLETIN 28. SCHELLHAS, PAUL. _See_ BULLETIN 28. SELER, EDUARD. 1901 c. Die alten Ansiedelungen von Chaculá im Distrikte Nenton des Departements Huehuetenango der Republik Guatemala. Berlin. ---- 1902-1908. Gesammelte Abhandlungen zur amerikanischen Sprach- und Alterthumskunde. 3 vols. Berlin. _See also_ BULLETIN 28. SPINDEN, H. J. 1913. A study of Maya art, its subject-matter and historical development. _Memoirs Peabody Mus._, VI, pp. 1-285, Cambridge. STEPHENS, J. L. 1841. Incidents of travel in Central America, Chiapas, and Yucatan. 2 vols. New York. ---- 1843. Incidents of travel in Yucatan. 2 vols. New York. THOMAS, CYRUS. 1893. Are the Maya hieroglyphs phonetic? _Amer. Anthr._, VI, No. 3, pp. 241-270, Washington. VILLAGUTIERRE, SOTOMAYOR J. 1701. Historia de la conquista de la provinzia de el Itza, reduccion, y progressos de la de el Lacandon y otras naciones de el reyno de Guatimala, a las provincias de Yucatan, en la America septentrional. Madrid. * * * * * [Illustration: THE MAYA TERRITORY, SHOWING LOCATIONS OF PRINCIPAL CITIES] * * * * * {1} 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 America. (See pl. 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 peninsula, 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 climate 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 million people in all. These live in the same general region their ancestors occupied, but under greatly changed conditions. Formerly the Maya were the van of civilization in the New World,[1] but to-day they are a dwindling {2} 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 barbarism 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.[2] How long a time had been required for the development of their complex calendar and hieroglyphic system 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 intensively developed minds. That this period was measured by centuries rather than by decades seems probable; the achievement was far too great to have been performed 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 line. City after city sprang into prominence throughout the southern part of the Maya territory,[3] each contributing its share to the general progress and art of the time. With accomplishment came confidence and a quickening of pace. All activities doubtless shared in the general uplift which followed, though little more than the material evidences 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 until about the close of the sixth century, may be called {3} perhaps 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, architecture 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. All 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 decline 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 course, 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 century, there is a sudden and final cessation of dates in all the southern cities, apparently indicating that they were abandoned about this time. Still another condition doubtless hastened the general decline if indeed it did no more. There is strong documentary evidence[4] 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 establish the absolute accuracy of any theory relating to times so {4} 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 civilization doubtless underwent important modification.[5] The period of colonization, with the strenuous 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 localities, all of which retarded the development of architecture, sculpture, and other arts. Bakhalal (see pl. 1), the first settlement in the north, was occupied for only 60 years. Chichen Itza, the next location, although occupied for more than a century, was finally abandoned and the search for a new home resumed. Moving westward from Chichen Itza, Chakanputun was seized and occupied at the beginning of the eighth century. Here the Maya are said to have lived for 260 years, until the destruction of Chakanputun 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 fully 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 under way. The opening of the eleventh century witnessed important and far-reaching political changes in Yucatan. After the destruction of Chakanputun the horizon of Maya activity expanded. Some of the fugitives from Chakanputun reoccupied Chichen Itza while others established 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,[6] in which each was to share equally in the government of the country. Under the peaceful conditions which {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 embellishment to architecture, it lived again. The one had become handmaiden to the other. Façades were treated with a sculptural decoration, which for intricacy and elaboration has rarely been equaled by any people at any time; and yet this result was accomplished without sacrifice of beauty or dignity. During this period probably there arose the many cities which to-day are crumbling 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 politic to its foundations and disrupted the Triple Alliance 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,[7] 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 plunged the country into civil war; and this struggle in turn paved the way for the final eclipse of Maya supremacy in the fifteenth century. After the dissolution of the Triple Alliance 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[8] shows in its architecture and bas-reliefs that it was undoubtedly inspired by Nahua rather than by Maya ideals. According to Spanish historians, the fourteenth century was characterized by increasing arrogance and oppression on the part of the rulers of Mayapan, who found it necessary to surround themselves with Nahua allies in order to keep the rising discontent of their {6} subjects in check.[9] 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. All authorities, native as well as Spanish, agree that the destruction 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 split 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 restraining 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 peninsula 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[10] on the shores of Yucatan. The natives were so hostile, however, that he returned to Cuba, having accomplished little more than the discovery of the country. In the following year Juan de Grijalva descended on the peninsula, but he, too, met with so determined a resistance that he sailed away, having gained little more than hard knocks for his pains. In the following year (1519) Hernando 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 {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,[11] 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-ornaments, of which the people were very fond. Squint-eye was considered 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 application 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 religious beliefs, 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 all 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 {8} corresponding 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 ornaments 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, constituted 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 young. When boys arrived at a marriageable age their fathers consulted the professional 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 young 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 husband. 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 considered sufficient for a widower to call on his prospective wife and eat in her house. Marriage between people of the same name was considered an evil practice, possibly in deference to some former exogamic law. It was thought improper to marry a mother-in-law or an aunt {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 unsuccessful both parties were at liberty to remarry. If there were young 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. Communal 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 peculiar kind were the media of exchange. These were accepted in return for all the products of the country, even including 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} 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 punishment 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, corn 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 all 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 obligation 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 skill 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 military 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 (_holcanes_) 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, continuing the tumult of war after war had ceased. In times of great stress when it became necessary to call on all 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 {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 brilliant 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 mutilated 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 filled with ground corn 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[12] 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 elaborate. 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 temples erected over them.[13] When the deceased {12} 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 skull. 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 still 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 being 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 skill 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 settlements, 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 tributary to each _halach 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 uinic of Mayapan probably attempted to establish a more autocratic form of government, arrogating to himself still 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 {13} doubtless his will prevailed just so far as he had sufficient strength to enforce it. The _batabs_, 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 all 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 all 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 visited his underchiefs, holding court in their houses, and meeting at night in council to discuss matters touching the common good. The batabs frequently entertained one another with dancing, hunting, and feasting. The people as a community tilled the batab's fields, reaped his corn, and supplied his wants in general. The underchiefs were similarly provided for, each according to his rank and needs. The _ahkulel_, 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 business 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 _ahholpop_, 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} [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 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 bring up, because according to their usage the mother has no power of her own. When the guardian was 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 lives, and, if there were no brothers the priests and principal people selected a man suitable for the position.[14] 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 though 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 improbable that Bishop Landa's statement to the contrary 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 kaba_, "he who has a name." The elaborate attention given to the subject of lineage, and the exclusive right of the _ah kaba_ to the benefits of education, show that in the northern part of the Maya territory at least government 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 feudalism prevailed. [Illustration: DIAGRAM SHOWING PERIODS OF OCCUPANCY OF PRINCIPAL SOUTHERN CITIES] {15} In attempting to gain an approximate understanding of the form of government which existed in the southern part of the Maya territory 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 light of the known conditions in the north. The chronology of the several southern cities (see pl. 2) indicates that many of them were contemporaneous, and that a few, namely, Tikal, Naranjo, Palenque, and Copan were occupied approximately 200 years, a much longer period than any of the others.[15] 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 culture, together with the location and contemporaneity of its largest centers, suggests that originally the southern territory was divided into several extensive political divisions, all in close intercourse 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 religious 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 official 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, particularly as the northern civilization was but an outgrowth of the {16} southern. There is some ground for believing that the highest office in the south may have been elective, the term being a _hotun_[16] (1,800 days), and the choice restricted to the members of a certain family. The existence of this restriction, which closely parallels the Aztec procedure in selecting rulers,[17] rests on very slender evidence, however, so far as the Maya are concerned and is mentioned here simply by way of suggestion. [Illustration: FIG. 1. Itzamna, chief deity of the Maya Pantheon (note his name glyphs, below).] The religion 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 civilization, the first priest of the Maya religion, 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, Roman nose, and sunken toothless mouth. [Illustration: FIG. 2. Kukulcan, God of Learning (note his name glyph, below).] Scarcely less important was the great god Kukulcan, or Feathered Serpent, the personification of the West. It is related of him that he came into Yucatan from the west and 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 dissension to peace and prosperity, he left by the same way he had entered, tarrying only at Chakanputun 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 {17} and life history are so human that it is not improbable he may have been an actual historical character, some great lawgiver and organizer, the memory of whose benefactions lingered long after death, and whose personality was eventually deified. 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. [Illustration: FIG. 3. Ahpuch, God of Death (note his name glyphs, below).] 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 unmistakable. His head is the fleshless skull, showing the truncated nose, the grinning teeth, and fleshless lower jaw, sometimes even the cranial sutures are portrayed. 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 attached. 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. [Illustration: FIG. 4. The God of War (note his name glyph, below).] 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 curving, sometimes straight, supposed to be symbolical of war paint, or, according to others, of his gaping wounds. He appears in the picture-writings as the Death God's companion. He presides with him over the body of a sacrificial victim, and again follows him applying torch and knife to the habitations of man. His hieroglyph shows as its characteristic the line of black paint (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 {18} with a spear or an ax. It was said of him that he was a very great and very cruel warrior, who commanded a band of seven blackamoors 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). [Illustration: FIG. 5. Ek Ahau, the Black Captain, war deity (note his name glyph, below).] Contrasted with these gods of death, violence, and destruction 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 picture-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 leaves, symbolic 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 conventionalized ear of corn surrounded by leaves. [Illustration: FIG. 6. Yum Kaax, Lord of the Harvest (note his name glyph, below).] Another important deity about whom little or nothing is known 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 curious 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 applied 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 flowers of which were the immortal principle of man, the soul. Above hung heavy clouds, the fructifying waters upon which all growth and life depend. The religion was dualistic in spirit, a constant struggle between the powers of {19} 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. [Illustration: FIG. 7. Xaman Ek, the North Star God (note his name glyph, below).] The Maya believed in the immortality of the soul and in a spiritual life hereafter. As a man lived 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 sorrow 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 materialism of the Maya heaven and hell need not surprise, nor lower our estimate of their civilization. Similar realistic conceptions of the hereafter have been entertained by peoples much higher in the cultural scale than the Maya. [Illustration: FIG. 8. Conflict between the Gods of Life and Death (Kukulcan and Ahpuch).] 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 propitiate 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 religious rites was the expulsion of the evil spirits from the midst of the worshipers. This was accomplished sometimes by prayers and benedictions, set formulæ 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 religion. Their number was literally legion, and they answered almost every contingency within the range of human experience. First of all were the ceremonies dedicated 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 ritualistic year brought around by the ever-recurring {20} 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 all articles, which took place at this tine; the feasts of the various trades and occupations--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 fall the ceremonies held on extraordinary 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 functionary 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 concerning 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 well 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 all, gave the responses of the gods to petitioners. The _ahuai chac_ was a priest who brought the rains on which the prosperity of the country was wholly dependent. The _ah macik_ conjured the winds; the _ahpul_ 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 {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 unlike 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 civilization, 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, alike the invention and the exclusive property of the priesthood. To its need for sanctuary may be attributed the origin of Maya architecture; to its desire for expression, the rise of Maya sculpture. All 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. {22} CHAPTER II. THE MAYA HIEROGLYPHIC WRITING The inscriptions herein described are found throughout the region formerly occupied by the Maya people (pl. 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 role 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. [Illustration: FIG. 9. Outlines of the glyphs: _a_, _b_, In the codices; _c_, in the inscriptions.] The materials upon which the Maya glyphs are presented are stone, wood, stucco, bone, shell, metal, plaster, pottery, and fiber-paper; the first-mentioned, however, occurs more frequently than all of the others combined. Texts have been 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 Honduras, engraved on metal from Chichen Itza, drawn on the plaster-covered walls of Kabah, Chichen Itza, and Uxmal, and painted in fiber-paper books. All of these, however, with the exception of the first and the last (the inscriptions on stone and the fiber-paper books or codices) just mentioned, occur so rarely that they may be dismissed from present consideration. The stones bearing inscriptions are found in a variety of shapes, the commonest being the monolithic shafts or slabs known as _stelæ_. Some of the shaft-stelæ 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-stelæ, on the other hand, are shorter and most of them bear inscriptions only on the reverse. Frequently associated with these stelæ are smaller monoliths known as "altars," which vary greatly in size, shape, and decoration, some bearing 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, approximate more nearly in form rhomboids or even ovals (fig. 9, _a_, _b_). This difference in outline, however, is only superficial in significance and involves no corresponding difference in meaning between {23} otherwise 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 uppermost 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 knows 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 multiplicity of these combinations leads at first to the conclusion that a great number of signs were employed in Maya writing, but closer study will 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 connection: "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 little 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." [Illustration: FIG. 10. Examples of glyph elision, showing elimination of all parts except essential element (here, the crossed bands).] 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 phonetic elements or signs are unchanging under all conditions of composition. 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 {24} design, but also may exactly fill its allotted space. All such modifications probably in no way affect the meaning of the element thus mutilated. [Illustration: FIG. 11. Normal-form and head-variant glyphs, showing retention of essential element in each.] The element shown in figure 10, _a-e_ is a case in point. In _a_ and _b_ 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 conclude, therefore, is the essential characteristic of this glyph, particularly since there is no regularity in 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 "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_, _b_, in which the entire glyph _a_ is used as a headdress in glyph _b_, the meaning of the two forms remaining 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 () of _e_ to the head in _f_, giving rise to a head variant, the meaning of which suffered no corresponding change. The element (+) in figure 11, _g_, has been reduced in size in _h_, though the other two essential elements remain unchanged. A final step appears in _i_ and _j_, where in _j_ the position of one of the two essential elements of _i_ () and the form of the other (++) have been changed. These variants {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 _l_ of figure 11 is a "head" variant of _k_; 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 differ more in appearance than _a_ and _b_, 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 _f_. The occurrence of forms so absolutely unlike in appearance, yet identical in meaning, greatly complicates the problem of glyph identification. Indeed, identity in both meaning and use must be clearly established 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 _h_, figure 12, as synonyms, notwithstanding the fact that their use seems to be identical, _h_ occurring in two or three texts under exactly the same conditions as does _g_ in all the others. [Illustration: FIG. 12. Normal-form and head-variant glyphs, showing absence of common essential element.] 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 well as those arising from careless drawing and actual mistakes. The foregoing difficulties, as well as others which await the student who would classify the Maya glyphs according to form and appearance, 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} 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) Astronomical, 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 fall 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.[18] 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 believes 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 corresponding chronological parts. It is here, if anywhere, that fragments of Maya history will be found recorded, and precisely here is the richest field for future research, since the successful interpretation of this "textual residue" will 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 sound, and entirely dissociated from the representation of any thought or idea. 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 {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_, frequently 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 _b's_, _c_, _t_, _e_, _h_, _i_, _ca_, _k_, two _l's_, _m_, _n_, two _o's_, _pp_, _p_, _cu_, _ku_, two _x's_, two _v's_, _z_. This alphabet, which was first published in 1864 by Abbé Brasseur de Bourbourg (see Landa, 1864), was at once heralded by Americanists as the long-awaited key which would unlock 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[19] which have appeared since, have completely broken down. This failure to establish the exclusive phonetic character of the Maya glyphs has resulted in the general acceptance of the second theory, that the signs are ideographic. Doctor Brinton (1894b: p. 14), however, has pointed out two facts deducible from the Landa alphabet 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 sound, 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 unknown, and, indeed, both the inscriptions and the codices establish the truth of this contention. For example, the sign in _a_, figure 13, has the phonetic value _kin_, and the sign in _b_ the phonetic value _yax_. In the latter glyph, however, only the upper part (reproduced in _c_) is to be regarded as the essential element. It is strongly indicative of phoneticism therefore to find the sound _yaxkin_, a combination of these two, expressed by the sign found in d. Similarly, the character representing the phonetic value _kin_ is found also as an element in the glyphs for the words _likin_ {28} and _chikin_ (see _e_ and _f_, respectively, fig. 13), each of which has _kin_ 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 _katun_ is represented 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 _k_ replacing the comblike element _h_. Far from destroying the phonetic character of this composite glyph, however, this variant _k_ in reality strengthens it, since in Maya the word for fish is _cay_ (_c_ hard) and consequently the variant reads _caytun_, a close phonetic approximation of _katun_. The remaining element of this glyph (_l_) has the value _cauac_, the first syllable of which is also expressed by either _h_ or _k_, figure 13. Its use in _i_ and _j_ 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 their function was to convey ideas, and that only secondarily were they used in their phonetic senses. [Illustration: FIG. 13. Glyphs built up on a phonetic basis.] 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 writing Doctor Brinton has called _ikonomatic_, 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 sounds 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 {29} personal pronoun 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."[20] It has long been known that the Aztec employed ikonomatic characters 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 many 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 _tollin_ 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_ means "near something" and its second syllable _tlan_ is found also in the word _tlantli_, 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, _b_, 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 _l_ of _acatl_ being lost in composition. [Illustration: FIG. 14. A rebus. Aztec, and probably Maya, personal and place names were written in a corresponding manner.] 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. {30} 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 united 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 Förstemann 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 expression 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 abstract 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 direction. [Illustration: FIG. 15. Aztec place names: _a_, The sign for the town Toltitlan; _b_, the sign for the town Acatzinco.] Doctor Brinton (1894 b: p. 13) held an opinion 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 subject 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 in 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. {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 primarily, if indeed not exclusively, with the counting of time in some form or other. Doctor Förstemann, the first successful interpreter of the codices, has shown that these writings have for their principal theme the passage of time in its varying relations to the Maya calendar, 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 _tonalamatl_, in connection with which various ceremonies, offerings, sacrifices, and domestic occupations are set forth. Doctor Förstemann 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 _Relacion_ (p. 286). In describing a festival held in the month Uo, 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 contains five Venus years of 584[21] 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 {32} first 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 invisibility 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 _tonalamatls_, or sacred years of 260 days each. Finally, the last number (37,960) with all 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[22]--certainly a remarkable achievement for the aboriginal mind. It is probable that the revolutions of the planets Jupiter, Mars, Mercury, and Saturn are similarly recorded in the same manuscript. Toward the end of the Dresden Codex the numbers become greater and greater until, in the so-called "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 pl. 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 malevolent 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, prophetic, and ritualistic material above described, the codices contained records of historical events. It is doubtful whether this is 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. [Illustration: PAGE 74 OF THE DRESDEN CODEX, SHOWING THE END OF THE WORLD (ACCORDING TO FÖRSTEMANN)] {33} 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 Förstemann] 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 sky 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.[23] While admitting that the inscriptions may, and probably do, contain such astronomical matter as Doctor Brinton and Mr. Bowditch have suggested, the writer believes nevertheless that fundamentally 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 fall 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 arbitrary 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 {34} length of the one used for the same purpose in the older cities. The following 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.[24] The other is even more explicit: Their lustras having reached five in number, 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 signifies "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 Simancas.[25] It seems almost necessary to conclude from such a parallel that the inscriptions of the southern cities will also be found to treat of historical matters. _Second._ When the monuments 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 establish the sequence of these periods and that of the monuments in them. Finally, it has demonstrated beyond all doubt that the great majority of the dates on Maya monuments refer to the time of their erection, so that the inscriptions which they present are historical in that they are the contemporaneous records of different epochs. _Third._ The dates on the monuments are such as to constitute a strong antecedent probability 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 prosperity they were, comparatively speaking, common. Finally, as decline set in, fewer and fewer monuments were erected, and eventually effort in this field ceased altogether. The increasing number of 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: [Illustration: DIAGRAM SHOWING OCCURRENCE OF DATES RECORDED IN CYCLE 9] {35} 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 establish 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 corresponding intervals between the dates of such monuments[26] the length of which would indicate the identity of the determining phenomenon; and they would hardly have presented the same logical increase due to the natural growth of a nation, which the accompanying diagram clearly sets forth. _Fourth._ Although no historical codices[27] are known to have survived, history was undoubtedly recorded in these ancient Maya books. The statements of the early Spanish writers are very explicit on this point, as the following quotations from their works will show. Bishop Landa (here, as always, one of the most reliable authorities) 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 books_." And again, [p. 316], "This people also used certain characters or letters with which _they wrote in their books 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 understood by many and explained by some old Indians, sons of the priests {36} 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 LVIII, 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, pestilences, 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: lib. VI, cap. IV) in 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 in 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, in 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 indicate the extreme importance of the element of time in Maya writing. The very great preponderance of astronomical, calendary, and numerical 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 familiarize ourselves with their arithmetic and its signs and symbols. Third, and last, after this has been accomplished, 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. {37} CHAPTER III. HOW THE MAYA RECKONED TIME Among all peoples and in all ages the most obvious unit for the measurement of time has been the day; and the never-failing reappearance of light after each interval of darkness 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 operation 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 all combined to render that luminary of little account in measuring the passage of time. The round of the seasons was even more unsatisfactory. 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 determined, 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 in 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 Ik Akbal Kan Chicchan Cimi Manik Lamat Muluc Oc Chuen Eb Ben Ix Men Cib Caban Eznab Cauac Ahau In conformity with the universal practice just mentioned the Maya made the day, which they called _kin_, the primary unit of their calendar. 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 {38} Maya conception of the rotation of days firmly in his mind at the outset, since all that is to follow depends upon the absolute continuity of this twenty-day sequence in endless repetition. [Illustration: FIG. 16. The day signs in the inscriptions.] [Illustration: FIG. 17. The day signs in the codices.] The glyphs for these twenty days are shown in 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 glyphs in these two figures shows on the whole a fairly close similarity between the forms for the same {39} day in each. The sign for the first day, Imix, is practically identical in both. Compare figure 16, _a_ and _b_, with figure 17, _a_ and b. The usual form for the day Ik in the inscriptions (see fig. 16, _c_), however, is unlike the glyph for the same day in the codices (fig. 17, _c_, _d_). The forms for Akbal and Kan are practically the same in each (see fig. 16, _d_, _e_, and _f_, and fig. 17, _e_ and _f_, respectively). The day Chicchan, figure 16, _g_, occurs rarely in the inscriptions; when present, it takes the {40} 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 inscriptions. 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 common form in the codices, the variant in _j_ more closely resembles the form in figure 16, _h_, _i_. The day Manik is practically the same in both (see figs. 16, _j_, and 17, _k_), as is also Lamat (figs. 16, _k_, _l_, and 17, _l_, _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, _n_). The glyph for the day Oc (fig. 16, _o_, _p_, _q_) is not often found 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 inscriptions where the form is clear enough to distinguish its characteristic (see fig. 16, _r_). This form bears a general resemblance to the glyph for this day in the codices (fig. 17, _p_, _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 prominent dots or circles. The day Men occurs very rarely on the monuments. 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 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'_, _b'_, and 17, _x_, _y_, show a satisfactory resemblance to each other. The forms for the day Eznab are also practically identical (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 {41} far the most important, since it is found 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 found 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'-k_', appear on some of the monuments, and because of the great importance 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 occur, 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 portrayed, as the stone of the monuments and the fiber paper of the codices; consequently, such differences may be regarded as unessential. 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 difficult to understand, as this number has no parallel period in nature. Some have conjectured that this number was chosen because it represents the number of man's digits, the twenty fingers and toes. Mr. Bowditch has pointed out in this connection that the Maya word for the period composed of these twenty named days is _uinal_, while the word for 'man' is _uinik_. The parallel is interesting and may possibly explain why the number twenty was selected as the basis of the Maya system of numeration, which, as we shall see later, was vigesimal, that is, increasing by twenties or multiples thereof. THE TONALAMATL, OR 260-DAY 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 number ranging from 1 to 13, inclusive, as 6 Imix or 13 Akbal. Then and only then did a Maya day receive its complete 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} any one of the twenty names[28] as a starting point, Kan for example, the number 1 was prefixed to it. See Table II, in which the names of Table I have been repeated with the numbers 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 Chicchan. The next name, Cimi, was given the next number (3), namely, 3 Cimi, and so on as follows: 4 Manik, 5 Lamat, 6 Muluc, 7 Oc, 8 Chuen, 9 Eb, 10 Ben, 11 Ix, 12 Men, 13 Cib. TABLE II. SEQUENCE OF MAYA DAYS 5 Imix 6 Ik 7 Akbal *1 Kan 2 Chicchan 3 Cimi 4 Manik 5 Lamat 6 Muluc 7 Oc 8 Chuen 9 Eb 10 Ben 11 Ix 12 Men 13 Cib 1 Caban 2 Eznab 3 Cauac 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 number 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 count continued 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. [Illustration: TONALAMATL WHEEL, SHOWING SEQUENCE OF THE 260 DIFFERENTLY NAMED DAYS] {43} _Rule 2._ The sequence of the numerical coefficients 1 to 13, inclusive, repeats itself again and again without interruption, 1 following immediately 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 indefinitely in this manner. It is a simple question of arithmetic to determine the number 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 numbers 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 common multiple of 13 and 20. As these two numbers, contain no common factor, their least common multiple is their product (260), which is the number sought. Therefore, any given day can not reappear in the sequence until after the 259 days immediately following it shall have elapsed. Or, in other words, the 261st day will 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-clockwise, the days will 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. [Illustration: FIG. 18. Sign for the tonalamatl (according to Goodman).] This round of the 260 differently named days was called by the Aztec the _tonalamatl_, or "book of days." The Maya name for this period is unknown[29] 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, {44} namely, 4×65, 5×52, 10×26, 13×20, and 2×130. Tonalamatls divided into 4, 5, and 10 equal parts of 65, 52, and 26 days, respectively, occur repeatedly throughout the codices. It is all the more curious, therefore, that this period is rarely represented in the inscriptions. The writer recalls but one city (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 ritualistic 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. Mr. Goodman has identified the glyph shown in figure 18 as the sign for the 260-day period, but on wholly insufficient 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 efforts 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 _haab_ 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, like 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 hours." 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 examination of the tonalamatl, or round of days (see pl. 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, {45} each returning into itself and beginning anew after completion, he will have grasped the most fundamental principle of Maya chronology--its absolute continuity throughout. It may be taken for granted, therefore, in the discussion to follow that no interpolation of intercalary days was actually made. It is equally probable, however, that the priests, in 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 in 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, designated in Maya _uinal_, and a closing period of 5 days known as the _xma kaba kin_, or "days without name." The sum of these (18×20+5) exactly made up the calendar year. TABLE III. THE DIVISIONS OP THE MAYA YEAR Pop Uo Zip Zotz Tzec Xul Yaxkin Mol Chen Yax Zac Ceh Mac Kankin Muan Pax Kayab Cumhu Uayeb 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 first 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 July.[30] Uayeb, the last division of the year, contained only 5 days, the last day of Uayeb 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 ill-omened. Says Pio Perez (see Landa, 1864: p. 384) in speaking of these closing days of the year: "Some call them _u yail kin_ or _u yail haab_, which may be translated, the sorrowful and laborious days or part of the year; for they [the Maya] {46} 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 closing days of the year in the same superstitious dread. Persons born in this unlucky period were held to be destined by this fact to wretchedness and poverty for life. These days were, moreover, prophetic in character; what occurred during them continued 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 count and number our 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 counting 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 reality 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: 0^{hr.} 30^{min.} 0^{sec.}, and quarter of 1, 0^{hr.} 45^{min.} 0^{sec.}. Indeed one hour can not be written until the first hour after midnight is completed, or until it is 1 o'clock, namely, 1^{hr.} 0^{min.} 0^{sec.}. 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 immediately 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. {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, using 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 cardinal "twelve." We may then summarize our methods of counting time as follows: (1) All periods less than the day, as hours, minutes, and seconds, are referred to in terms of past time; and (2) the day and all 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 until, like the hour of astronomical 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 counting 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 19 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 Uayeb, contained only 5 days, whereas all the other periods (the 18 uinals) had 20 days each. Curiously enough no glyph for the _haab_, or year, has been identified as yet, in spite of the apparent importance of this period.[31] The {48} glyphs which 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 19 Cumhu last day of the month Cumhu. 361st day of the year 0 Uayeb first day of Uayeb. 362d day of the year 1 Uayeb 363d day of the year 2 Uayeb 364th day of the year 3 Uayeb 365th day of the year 4 Uayeb last day of Uayeb and of the year. 1st day of next year 0 Pop first day of the month Pop, and of the next year. 2d day of next year 1 Pop 3d day of next year 2 Pop 4th day of next year 3 Pop 5th day of next year 4 Pop 6th day of next year 5 Pop 7th day of next year 6 Pop 8th day of next year 7 Pop 9th day of next year 8 Pop 10th day of next year 9 Pop 11th day of next year 10 Pop 12th day of next year 11 Pop 13th day of next year 12 Pop 14th day of next year 13 Pop 15th day of next year 14 Pop 16th day of next year 15 Pop 17th day of next year 16 Pop 18th day of next year 17 Pop 19th day of next year 18 Pop 20th day of next year 19 Pop last day of the month Pop. 21st day of next year 0 Uo first day of the month Uo. 22d day of next year 1 Uo etc. etc. 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 _kin_ sign. The latter is found in both the forms figured, though only a part of the former appears in figure 20, a. Uo has two forms in the inscriptions (see fig. 19, _b_, _c_),[32] which are, however, very similar to each other as well as to the corresponding forms in the codices (fig. 20, _b_, _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_,[33] and 20, _e_, are also similar to each other. The essential {49} characteristic seems to be the prominent upturned and flaring nose. The forms for Tzec (figs. 19, _g_, _h_, and 20, _f_) show only a very general similarity, and those for Xul, the next month, are even more unlike. The 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 essential 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 surrounded with dots. [Illustration: FIG. 19. The month signs in the inscriptions.] {50} [Illustration: FIG. 20. The month signs in the codices.] The sign for the month Yaxkin is identical in both figures 19, _k_, _l_, and 20, _i_, _j_. The sign for the month Mol in figures 19, _m_, _n_, and 20, _k_ exhibits the same close similarity. The forms for the month Chen in figures 19, _o_, _p_, and 20, _l_, _m_, on the other hand, bear only a slight resemblance to each other. The forms for the months Yax (figs. 19, _q_, _r_, and 20, _n_), Zac (figs. 19, _s_, _t_, and 20, _o_), and Ceh (figs. 19, _u_, _v_, and {51} 20, _p_) are again identical in each case. The signs for the next month, Mac, however, are entirely dissimilar, the form commonly found in the inscriptions (fig. 19, _w_) bearing absolutely no resemblance to that shown in figure 20, _q_, _r_, the only form for this month in the codices. The very unusual variant (fig. 19, _x_), from Stela 25 at Piedras Negras is perhaps a trifle nearer the form found in the codices. The flattened oval in the main part of the variant is somewhat like the upper part of the glyph in figure 20, _q_. The essential element of the glyph for the month Mac, so far as the inscriptions are concerned, is the element () found as the superfix in both _w_ and _x_, 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'_, _b'_, and 20, _u_, _v_) show only a general 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 Cumhu (figs. 19, _g'_, _h'_, and 20, _z_, _a'_, _b'_) 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 essentially 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 corresponding 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 figures 16, 17, 19, and 20, since his progress will depend largely on his ability to recognize these glyphs when he encounters them in the texts. THE CALENDAR ROUND, OR 18980-DAY PERIOD Before taking up the study of the Calendar Round 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 (pl. 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} 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 principles which governed its composition is therefore absolutely essential to the understanding of the Maya system of counting time. It has been explained (see p. 41) that the complete designation or name of any day in the tonalamatl consisted of two equally essential parts: (1) The name glyph, and (2) the numerical coefficient. Disregarding 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 units 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 units 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 multiple of the other, it is clear that only the last of the three contingencies 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 × 18. Therefore the 362d will be the same as the 2d, the 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 as 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 11th name in the sequence. Similarly it could be shown {53} that the _third year_, beginning with the 11th 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 = 4×365+1 = 73×20+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 important 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 Akbal Kan Chicchan Cimi MANIK Lamat Muluc Oc Chuen EB Ben Ix Men Cib CABAN Eznab Cauac Ahau 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 necessarily true because these 19 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 division 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} 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, it 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, throughout the 20 days of the month. For example, if a year began with the day-name Ik, all of the divisions in that year also began with the same name, and the second days of all 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 11th, and Manik the 16th, and in the years when Caban is the 1st, Ik will 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 Cauac will 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 will 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 well as the positions in the divisions of the years which the names of each group may occupy. A comparison with Table V will demonstrate that this arrangement is inevitable. {55} TABLE VI. POSITIONS OF DAYS IN DIVISIONS OF MAYA YEAR --------------------------------------------------------------------+ | | { 1st, | 2d, | 3d, | 4th, | 5th, | | Positions held | { 6th, | 7th, | 8th, | 9th, | 10th, | | by days | { 11th, | 12th, | 13th, | 14th, | 15th, | | | { 16th | 17th | 18th | 19th | 20th | |----------------+----------+---------+---------+---------+---------+ | | { Ik | Akbal | Kan | Chicchan| Cimi | | Names of | { Manik | Lamat | Mulac | Oc | Chuen | | days in | { Eb | Ben | Ix | Men | Cib | | each group | { Caban | Eznab | Cauac | Ahau | Imix | --------------------------------------------------------------------+ 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 according to our system. It was shown there that the first day of Pop was not written 1 Pop, but 0 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 0 Pop, 5 Pop, 10 Pop, or 15 Pop) would be written in our notation 1st Pop, 6th Pop, 11th Pop, and 16th 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 will 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 ascertained 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 OF DAYS IN DIVISIONS OF MAYA YEAR ACCORDING TO MAYA NOTATION ------------------------------------------------------------------------+ | Positions held by | | | | | | | days expressed in |{ 0, 5, | 1, 6, | 2, 7, | 3, 8, | 4, 9, | | Mayan notation |{ 10, 15 | 11, 16 | 12, 17 | 13, 18 | 14, 19 | |--------------------+----------+---------+---------+---------+---------+ | | { Ik | Akbal | Kan | Chicchan| Cimi | | Names of days in | { Manik | Lamat | Mulac | Oc | Chuen | | each group | { Eb | Ben | Ix | Men | Cib | | | { Caban | Eznab | Cauac | Ahau | Imix | ------------------------------------------------------------------------+ 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} _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 preceding 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 dealing with the complete designations of the Maya days, but only their _name parts_ or name glyphs, the positions of which in the several divisions of the year we have ascertained. It now remains to join the tonalamatl, 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, 0 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 0 Pop. Perhaps the easiest way to visualize the combination of the tonalamatl 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 days of the tonalamatl and follows the sequence shown in plate 5. The second wheel, B (fig. 21), is somewhat 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 0 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 {57} 0 Pop in B, after which both wheels start to revolve in the directions indicated by the arrows. [Illustration: FIG. 21. Diagram showing engagement of tonalamatl wheel of 260 days (A), and haab wheel of 365 positions (B); the combination of the two giving the Calendar Round, or 52-year period.] 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 0 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 successively fall into their appropriate positions in the divisions 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 revolution), before the latter will have made one complete revolution; and, further, that when the latter (B) has returned to its starting point, 0 Pop, the corresponding 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 0 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 problem falls under the third contingency there presented. Consequently, only certain of the 260 days can occupy the position 0 Pop, or, in other words, cog 2 Ik in A will return to the position 0 Pop in B in fewer than 260 revolutions of A. The actual solution of the problem {58} 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 0 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 0 Pop can not recur until after a number of days shall have passed equal to the least common multiple of these numbers, which is (260/5)×(365/5)×5, or 52×73×5 = 18,980 days. But 18,980 days = 52×365 = 73×260; in other words the day 2 Ik 0 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 Round 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 the year. The Aztec name for this period was _xiuhmolpilli_ or _toxiuhmolpia_.[34] 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 probably never progressed beyond the Calendar Round. At least no greater period of time than the round 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 corresponding event is to be referred; consequently, the true sequence of events in Aztec history still remains uncertain. Professor Seler says in this connection:[35] 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 chronology ... but in regard to all that precedes this date, even to events tolerably near the time of the Spanish conquest, the statements differ widely. {59} Such confusion indeed is only to be expected from a system of counting time and recording events which was so loose as to permit the occurrence 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. [Illustration: FIG. 22. Signs for the Calendar Round: _a_, According to Goodman; _b_, according to Förstemann.] The glyph which stood for the Calendar Round has not been determined with any degree of certainty. Mr. Goodman believes the form shown in figure 22, _a_, to be the sign for this period, while Professor Förstemann is equally sure that the form represented by _b_ of this figure expressed the same idea. This difference of opinion between two authorities so eminent well illustrates the prevailing doubt as to just what glyph actually represented the 52-year period among the Maya. The sign in figure 22, _a_, as the writer will 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 likened to a large cogwheel having 18,980 teeth, each one of which represented one of the dates of this period, and that this wheel revolved forever, each cog passing a fixed point once every 52 years. {60} 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 distinguished 1 day from the other 18,979 of the Calendar Round. 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 Babylonians 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 in 311 B. C. by Seleucus Nicator began the so-called Era of Seleucidæ. The conquest of Spain by Augustus Cæsar 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 chronology has for its starting point some actual historic event, the occurrence, if not the date of which, is indubitable. Some chronologies, however, commence with an event of an altogether different character, 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, {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 Round. This was a certain date, 4 Ahau 8 Cumhu,[36] that is, a day named 4 Ahau, which occupied the 9th position 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[37] is unknown, 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[38] refer to a time fully 3,000 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 chronological system, during which time no events were recorded. This interesting 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 designates. 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 contemporaneous record, and {62} 2. That after this long period had elapsed all the dated monuments[39] had their origin in the comparatively short period of four centuries. Consequently, it is safe to conclude that no matter what the Maya 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 distinctive 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 numbers 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 mathematicians 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 numbers 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 system of numeration, with but a single exception. (See Table VIII.) TABLE VIII. THE MAYA TIME-PERIODS 1 kin = 1 day 20 kins = 1 uinal = 20 days 18 uinals = 1 tun = 360 days 20 tuns = 1 katun = 7,200 days 20 katuns = 1 cycle = 144,000 days 20[40] cycles = 1 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), {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 vigesimal 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 system, 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 0 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 composed 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[41] 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 {64} 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. [Illustration: FIG. 23. Diagram showing section of Calendar-round wheel.] 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. Indeed, it is only a question of the number of revolutions 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 initial date, 4 Ahau 8 Cumhu. This is actually what happened according to the Maya conception of time. For example, let us imagine that a certain Initial Series expresses in terms of cycles, katuns, tuns, uinals, and kins, the number 1,461,463, and that the date recorded by this number of days is 7 Akbal 11 Cumhu. Referring to figure 23, it is evident that 77 revolutions of the cogwheel A, that is, 77 Calendar Rounds, will use up 1,461,460 of the 1,461,463 days, since 77×18,980 = 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 1,461,462d 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 subject will be considered in greater detail. 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. {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_, _b_). 4. The trinal subfix. [Illustration: FIG. 24. Initial-series "introducing glyph."] In addition to these four constant elements there is one variable element which is always found between the pair of comblike lateral appendages. In figure 24, _a_, _b_, _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.[42] A variant of the comblike appendages is shown in figure 24, _c_, _e_, in which these elements are 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, therefore, that the comblike 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 conventionalized fin () seems to be indicated by several facts: (1) On Stela D at Copan, where only full-figure glyphs are presented,[43] the two comblike appendages of the "introducing glyph" appear unmistakably as two fishes. (2) In some of the earliest stelæ at Copan, as Stelæ 15 and P, while these elements are not fish forms, a head (fish?) appears with the conventionalized comb element in each case. The writer believes the interpretation of this phenomenon to be, that at the early epoch in which {66} Stelæ 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 comblike element in the "introducing glyph," it was also the original form of the same element in the katun glyph. (Compare the comb elements () in figures 27, _a_, _b_, _e_, and 24, _a_, _b_, _d_ with each other.) If this is true, a natural explanation for the use of the fish in the katun sign lies near at hand. As previously explained on page 28, the comblike element stands for the sound _ca_ (_c_ hard); while _kal_ in Maya means 20. Also the element () stands for the sound _tun_. Therefore _catun_ or _katun_ means 20 tuns. But the Maya word for "fish," _cay_ (_c_ hard) is also a close phonetic approximation of the sound _ca_ or _kal_. Consequently, the fish sign may have been the original element in the katun glyph, which expressed the concept 20, and which the conventionalization of glyphic forms gradually reduced to the element () without destroying, however, its phonetic value. Without pressing this point further, it seems not unlikely that the comblike 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, _f_, may be a form of the "introducing glyph"; at least it precedes an Initial Series in four places in the Dresden Codex (see pl. 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 identification on the fact that in the codices units of the 6th place stand immediately above[44] 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[45] 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, {67} moreover, the glyph in the 6th position is unlike the forms in figure 24. (4) Five periods, not six, in every Initial Series express the distance 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 glyph" 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 monuments at Copan, notably Stelæ 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 monuments 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_, will 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.[46] 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 occur 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 found, they do not occur as units in Initial Series. As head variants also should be classified the so-called "full-figure glyphs," in which the periods given in Table VIII are represented by full figures instead of by heads. In these forms, however, only the heads of the figures are essential, since they alone present the determining 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 {68} corresponding 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 full-figure glyphs are exceedingly rare, having been found only in five Initial Series throughout the Maya area: (1) On Stela D at Copan; (2) on Zoömorph 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 [Illustration: FIG. 25. Signs for the cycle: _a-c_, Normal forms; _d-f_, head variants.] [Illustration: FIG. 26. Full-figure variant of cycle sign.] The Maya name for the period of the 5th order in Table VIII is unknown. It has been called "the cycle," however, by Maya students, 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_, _b_, 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, _b'_), 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 characteristic of this grotesque head with its long beak is the hand element (), which forms the lower jaw, though in a _very few instances_ even this is absent. In the full-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 [Illustration: FIG. 27. Signs for the katun: _a-d_, Normal forms; _e-h_, head variants.] [Illustration: FIG. 28. Full-figure variant of katun sign.] The period of the 4th place or order was called by the Maya the _katun_; that is to say, 20 tuns, since it contained 20 units of the 3d {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_, _b_) surmounted by the pair of comblike appendages, which we have elsewhere seen meant 20, and which were probably derived from the representation of a fish. The whole glyph thus graphically 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_, _b_). Several head variants are found. The most easily recognized, though not the most common, is shown in figure 27, _e_, in which the superfix is the same as in the normal form; that is, the element (), which probably signifies 20 in this connection. To 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 it is difficult to fix on any essential characteristic. The general shape of the head is like the head variant of the cycle glyph. Perhaps the oval () in the top of the head in figure 27, _f_-_h_, and the small curling fang (++) represented as protruding from the back part of the mouth are as constant as any of the other elements. The head of the full-figure 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} THE TUN GLYPH [Illustration: FIG. 29. Signs for the tun: _a-d_, Normal forms; _e-h_, head variants.] [Illustration: FIG. 30. Full-figure variant of tun sign.] 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. Compare so-called hotun or katun stones described on page 34. The normal sign for the tun in the inscriptions (see fig. 29, _a_, _b_) 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 the cycle and katun, has several forms. The one most readily recognized, because it has the normal sign for its superfix, is shown in figure 29, _d_, e. The determining characteristic of the head variant of the tun glyph, however, is the fleshless lower jaw (), as shown in figure 29 _f_, _g_, though even this is lacking in some few cases. The form shown in figure 29, _h_, is found at Palenque, where it 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 figure 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 [Illustration: FIG. 31. Signs for the uinal: _a-c_, Normal forms; _d-f_, head variants.] [Illustration: FIG. 32. Full-figure variant of uinal sign on Zoömorph B, Quirigua.] [Illustration: FIG. 33. Full-figure variant of uinal sign on Stela D, Copan.] The period occupying the 2d place was called by the Maya _uinal_ or _u_. This latter word means also "the moon" in Maya, and the fact that the moon is visible for just 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_, _b_) is practically identical with the form in the codices (see fig. 31, _c_). {71} Sometimes the subfixial element () is omitted in the inscriptions, as in figure 31, a. The head variant of the uinal 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 animal represented in the full-figure variants of the uinal is that of a frog (fig. 32,) the head of which presents precisely the same characteristics as the head variants of the uinal, just described. That the head variant of the uinal-period glyph was originally derived from the representation of a frog can hardly be denied in the face of such striking confirmatory evidence as that afforded by the full-figure form of the uinal in figure 33. Here the spotted body, flattened head, prominent mouth, and bulging eyes of the frog are so realistically portrayed that there is no doubt as to the identity of the figure intended. Mr. Bowditch (1910: p. 257) has pointed out in this connection an interesting phonetic coincidence, which can hardly be other than intentional. The Maya word for frog is _uo_, which is a fairly close phonetic approximation 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 figure of a frog in the uinal-period glyph would not recall the object which it pictures, but the sound of that object's name, _uo_, approximating the sound of _u_, which in turn expressed the intended idea, namely, the 20-day period. Mr. Bowditch has suggested also that the grotesque birds which stand for the cycle, katun, and tun periods in these full-figure forms may also have been chosen because of the phonetic similarity of their names to the names of these periods. {72} THE KIN GLYPH [Illustration: FIG. 34. Signs for the kin: _a_, _b_, Normal forms; _c_, _d_, miscellaneous; _e-k_, head variants.] The period of the 1st, or lowest, order was called by the Maya _kin_, which meant the "sun" and by association the "day." The kin, as has been explained, was the primary unit used by the Maya in counting 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, _b_). 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 variants, as in figure 34, _c_, for example, which bears no resemblance whatever to the normal form of the kin sign. It is difficult to understand 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_, _d_) 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 given. The form shown in figure 34, _e_, may be readily recognized by its subfixial element () and the element (+), {73} both of which appear in the normal form, figure 34, a. In some cases, as in figure 34, _f-h_, this variant 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 headdress. A very unusual head variant is that shown in figure 34, _k_, the essential characteristic of which seems to be the crossbones in the eye. Mr. Bowditch has included also in his list of kin signs the form shown in figure 34, _l_, from an inscription at Tikal. While this glyph in fact does stand between two dates which are separated by one day from each other, that is, 6 Eb 0 Pop and 7 Ben 1 Pop, the writer believes, nevertheless, that only the element ()--an essential part of the normal form for the kin--here represents the period one day, and that the larger characters above and below have other meanings. In the full-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 figure 34, _i_, _j_, having the same banded headdress.[47] [Illustration: FIG. 35. Full-figure variant of kin sign.] 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 preponderance of the former over the latter in all Initial Series known is in the proportion of about 80 per cent of the total[48] 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 {74} nearly 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 _b_ 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 variation occurred from first to last. Similarly, it may be said, the head variants for any given period, while differing greatly in appearance at different epochs, retained, nevertheless, the same essential characteristic throughout. For example, although the uinal sign in figure 36, _e_, precedes the one in figure 36, _f_, 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 _h_, figure 36, the essential characteristic of the early form (fig. 36, _g_), the hand, is still retained as the essential part of the late form (_h_). [Illustration: FIG. 36. Period glyphs, from widely separated sites and of different epochs, showing persistence of essential elements.] 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 full-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,[49] 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; {75} (3) the Katun glyph; (4) the Tun glyph; (5) the Uinal glyph; (6) the Kin 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 separated 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;[50] 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,[51] 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, will 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 Cumhu, or whether we count 1,461,466 days forward from the starting point of Maya chronology, 4 Ahau 8 Cumhu since in each case the date reached will 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 {76} 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 corresponding Initial Series were expressed in full. If, on the other hand, a Secondary 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 unknown. CALENDAR-ROUND DATES Dates of the character just described may be called Calendar-round dates, since they are accurate only within the Calendar Round, or range of 52 years. While accurate enough for the purpose of distinguishing 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 Yaxchilan 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. {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 dating. In this method a date was described as being at the end of some particular period in the Long Count; that is, closing a certain cycle, katun, or tun.[52] 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 uinal, 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 kin 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 in 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 appearing 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 {78} superfix (see fig. 37, _a_, whereby the end of Cycle 10 is indicated[53]), 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_. [Illustration: FIG. 37. Ending signs and elements.] The hand-ending sign rarely appears as modifying period glyphs, although a few examples of such use have been found (see fig. 37, _j_, _k_). This ending sign usually appears as the main element in a separate 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 suffix in _l_, _m_, _n_, _q_, and the element (+) as a postfix therein, also in _o_ and _p_. In a few cases the hand is combined with the other ending signs, sometimes with one and sometimes with the other. {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 implies 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 certain 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 purposes, 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 (1910: pp. 176 et seq.) has reviewed fully the use of ending signs, and students are referred to his work for further information on this subject. U KAHLAY KATUNOB In addition to the foregoing methods of measuring time and recording dates, the Maya of Yucatan used still another, which, however, was probably derived directly from the application of Period-ending dating to the Long Count, and consequently introduces no new elements. This has been designated the Sequence of the Katuns, 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 katun_, "the series of the katuns"; or _u kahlay uxocen katunob_, "the record of the count of the katuns"; or even more simply, _u kahlay katunob_, "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 designation 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, always 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} which they occupied in the cycle, as Katun 14, for example, but by the different days Ahau with which they ended, as Katun 2 Ahau, Katun 13 Ahau, etc. See Table IX. TABLE IX.--SEQUENCE OF KATUNS IN U KAHLAY KATUNOB Katun 2 Ahau Katun 8 Ahau Katun 13 Ahau Katun 6 Ahau Katun 11 Ahau Katun 4 Ahau Katun 9 Ahau Katun 2 Ahau Katun 7 Ahau Katun 13 Ahau Katun 5 Ahau Katun 11 Ahau Katun 3 Ahau Katun 9 Ahau Katun 1 Ahau Katun 7 Ahau Katun 12 Ahau Katun 5 Ahau Katun 10 Ahau Katun 3 Ahau, etc. The peculiar retrograding sequence of the numerical coefficients 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 katun 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 demonstration 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 numerical coefficients, and (2) these follow each other without interruption, 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 counted 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 numerical coefficients in Table IX, we shall find that it accounts for the retrograding sequence there observed. The first katun in Table IX, Katun 2 Ahau, is named after its ending day, 2 Ahau. Now let us see whether the application of this rule will 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 katun; therefore we must first deduct from 7,200 all the 13s possible. 7,200 ÷ 13 = 553-11/13. In other words, after we have deducted all the 13's possible, that is, {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; therefore 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 13 (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 must deduct 13 from it in order to find out the resulting coefficient. 24 - 13 = 11, and 11 is the coefficient of the ending day of the third katun 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 katun. Since 7,200 is always the number of days in any katun, after deducting all the 13s possible the remainder will always be 11, which has to be added to the known coefficient to find the unknown. But since 13 has to be deducted from the resulting number when it is above 13, subtracting 2 will always give us exactly the same coefficient as adding 11; consequently we may formulate for determining the numerical 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 Katun 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 fixed in a _long_ stretch of time, there was always the possibility of a maximum error of about 20 years in {82} 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 Tun 13 of Katun 2 Ahau. This fixed a date as falling somewhere within a certain 360 days, which was accurately 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 could not recur until after the lapse of at least 7,000 years. The great majority 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 particular division (tun) of this period. Such accuracy doubtless was sufficient 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 accuracy of this method of dating 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 katuns 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, accuracy in dating could be secured for as long a period as the sequence remained unbroken. Indeed, the u kahlay katunob[54] 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 uncertain. 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 statement, namely, that the u kahlay katunob has not been found in the inscriptions. Mr. Bowditch (1910: pp. 192 et seq.) has pointed out {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-h_, respectively). In such cases the month part is sometimes 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 Ahau 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 elements shown in figure 38 may indicate that such days were the katun ending days nearest to the time when the inscriptions presenting them were engraved. The snake variants shown in figure 38, _a-d_, are all from Palenque; the knot variants (_e-h_ of the same figure) are found at both Copan and Quirigua. [Illustration: FIG. 38. "Snake" or "knot" element as used with day sign Ahau, possibly indicating presence of the u kahlay katunob in the inscriptions.] 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 katun ending day by itself can not be construed as an u kahlay katunob, or sequence of katuns. The difference here, however, is apparent rather than real, and results from the different character of the monuments and the native chronicles. The u kahlay katunob in Table IX is but a part of a much longer sequence of katuns, 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 chronological synopses of Maya history, and from their very nature they have to do with long periods. This is not true of the monuments,[55] 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. Consequently, each monument would have inscribed upon it only one or two {84} 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[56] 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 periodicals of current events, the latter histories of the past. The former in 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 foregoing 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 accompanying 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 count 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 katunob 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 made 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 count 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 katunes." Cogolludo (1688: lib. 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 katunob had entirely replaced the Initial Series in recording the Long Count centuries before the Spanish Conquest; and if the latter method of dating were known {85} at all, the knowledge of it came only from half-forgotten records the understanding of which was gradually passing 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 dating 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, since monuments presenting this method of dating have been found at a few of the northern cities, namely, at Chichen Itza, Holactun, and Tuluum. On the other hand, it is equally certain that Initial Series could not have been used very extensively in the north, since they have been discovered in only these three cities in Yucatan up to the present time. Moreover, 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 consideration, 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 accuracy, since the u kahlay katunob was far less exact than Initial-series dating; not only could 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 monument, 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 glyphs, 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 with the invention of Secondary Series. Somewhat later, dating by period-endings was introduced, obviating the {86} necessity for the use of even one Initial Series on every monument, in order that one date might be fixed in the Long Count to which the others (Secondary Series) could be referred. For all practical purposes, as we have seen, Period-ending dating was as accurate as Initial-series dating for fixing dates in the Long Count, and its substitution for Initial-series dating resulted in a further saving of glyphs and a corresponding economy of space. Still 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 corresponding Initial Series would have been far too cumbersome a practice. 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 combination 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 Calendar 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 do with the counting of time: The 13 numerical coefficients of the day names, the 20 day names, 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 numeration. When the conclusion of any one of these sequences had been reached, the sequence began anew without the interruption or omission 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. {87} 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,[57] 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 Roman 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 number 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 numerals extends to the formation of the higher numbers. Thus, the Maya formed the head-variant numerals for 14, 15, 16, 17, 18, and 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[58] 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 numerical value, 1, and the bar, or line (--) which represented the numeral, or numerical value, 5. By various combinations of these two {88} elements alone the Maya expressed all the numerals from 1 to 19, inclusive. The normal 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 elaborate, the dots and bars both taking on various decorations. Some of the former contain a concentric circle () or cross-hatching (); some appear as crescents (+) or curls (++), more rarely as (++) or (++++). The bars show even a greater variety of treatment (see fig. 41). All these decorations, 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 the inscriptions, and their use was probably due to the desire to make the bar and dot serve a decorative as well as a numerical function. [Illustration: FIG. 39. Normal forms of numerals 1 to 19, inclusive, in the codices.] [Illustration: FIG. 40. Normal forms of numerals 1 to 19, inclusive, in the inscriptions.] [Illustration: FIG. 41. Examples of bar and dot numeral 5, showing the ornamentation which the bar underwent without affecting its numerical value.] 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.[59] 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 outlines 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[60] side of the bar, or bars, as the case may be, and consequently {89} the left-hand edge of the glyph block in each case is ragged. Similarly in _b_, _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 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 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 {90} crescents 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 _h_ of the same figure a single crescent stands between the two numerical dots, and this again harmoniously fills in the glyph block. While the crescent () is the usual form taken by this purely decorative element, crossed lines (**) are found in places, as in (); or, again, a pair of dotted elements (++), as in (++). These variants, however, are of rare occurrence, the common form being the crescent shown in figure 43. [Illustration: FIG. 42. Examples showing the way in which the numerals 1, 2, 6, 7, 11, 12, 16, and 17 are _not_ used with period, day, or month signs.] [Illustration: FIG. 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.] [Illustration: FIG. 44. Normal forms of numerals 1 to 13, inclusive, in the Books of Chilan Balam.] 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 ornamental 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 all times in identifying these {91} numerals in the inscriptions, or otherwise he will quickly find himself involved in a tangle from which there seems to be no egress. Probably 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, accompanied 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 addition to these they used a line; one line meant five years, two lines meant ten years; if one line and above it one dot, six years; if 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 dots, twelve; if three dots, thirteen. This description is so clear, and the values therein assigned to the several combinations of bars and dots have been verified so extensively throughout both the inscriptions and the codices, that we are justified in identifying 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,[61] because {92} (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 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 positions were numbered not from 1 to 20, but on the contrary from 0 to 19, a system which eliminated the need for a character expressing 20. [Illustration: FIG. 45. Sign for 20 in the codices.] In spite of the foregoing fact, however, the number 20 has been found in the codices (see fig. 45). A peculiar condition there, however, accounts satisfactorily for its presence. In the codices the sign for 20 occurs only in connection with tonalamatls, 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 bottom to top in the usual way, but had to be written horizontally from left to right. This destroyed the possibility of numeration by position,[62] 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 purpose. 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. [Illustration: FIG. 46. Sign for 0 in the codices.] If the Maya numerical system had no vital need for a character to express the number 20, a sign to represent zero was absolutely {93} indispensable. 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 units 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 lenticular; it presents an interior decoration which does not follow any fixed scheme.[63] Only a very few variants occur. The last one in figure 46 has clearly as one of its elements the normal form (lenticular). The remaining two are different. It is noteworthy, however, that these last three forms all stand in the 2d, or uinal, place in the texts in which they occur, though whether this fact has influenced their variation is unknown. [Illustration: FIG. 47. Sign for 0 in the inscriptions.] [Illustration: FIG. 48. Figure showing possible derivation of the sign for 0 in the inscriptions: _a_, Outline of the days of the tonalamatl as represented graphically in the Codex Tro-Cortesiano; _b_, half of same outline, which is also sign for 0 shown in fig. 47.] 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 Codex Tro-Cortesiano[64] the 260 days of a tonalamatl are graphically represented as forming the outline shown in figure 48, a. Half of this (see fig. 48, _b_) is the sign which stands for zero (compare with fig. 47). The train of association by which half of the graphic representation 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 {94} applicable 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 between 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,[65] is chiefly interesting because of its highly specialized function. Indeed, it was used 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 0 Pop, 0 Uo, 0 Zip, etc., which, as we have seen (pp. 47, 48), corresponded with our first days of the months. The forms shown in figure 49, _a_-_e_, are from the inscriptions and those in _f_-_h_ from the Dresden Codex. They are all similar. The general outline 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 roughly circular infix in each. 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_, _b_, 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 _f_ and _g_. Although comparatively rare, this glyph is so unusual in form that it can be readily recognized. Moreover, if the student will bear in 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. [Illustration: FIG. 49. Special sign for 0 used exclusively as a month coefficient.] (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_, _k_, _r_, _x_, _y_, respectively), since these four alone, as appears in Table VII, can occupy the 0 (zero) positions in the several divisions of the haab. {95} [Illustration: FIG. 50. Examples of the use of bar and dot numerals with period, day, or month signs. The translation of each glyph appears below it.] 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.[66] The student is advised to familiarize himself with these forms, since on his ability 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 until Chapter VI is reached, which treats of the codices exclusively. {96} HEAD-VARIANT NUMERALS Let us next turn to the consideration of the Maya "Arabic notation," that is, the head-variant numerals, which, like all other known head variants, are practically restricted to the inscriptions.[67] It should be noted here before proceeding further that the full-figure numerals found in connection with full-figure period, day, and month glyphs in a few inscriptions, have been classified with the head-variant numerals. As explained on page 67, the body-parts of such glyphs have no function in determining their meanings, and it is only the head-parts which present in each case the determining characteristics 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[68] 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 application of the essential characteristic of the head for 10 to the heads for 3 to 9, inclusive. No head forms for the numeral 20 have yet been discovered. 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 identification of head-variant numerals is the apparent 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. {97} [Illustration: FIG. 51. Head-variant numerals 1 to 7, inclusive.] The head-variant numerals are shown in figures 51-53. Taking these up in their numerical order, let us commence with the head signifying 1; see figure 51, _a-e_. The essential element of this head is its forehead ornament, which, to signify the number 1, must be composed of more than one part (), in order to distinguish it from the forehead ornament (), which, as we shall see presently, 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. {98} The head for 2 (fig. 51, _f_, _g_) has been found only twice in the inscriptions--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 characteristic of the head for 2, admitting at the same time that the evidence is insufficient. [Illustration: FIG. 52. Head-variant numerals 8 to 13, inclusive.] The head for 3 is shown in figure 51, _h_, _i_. Its determining characteristic is the fillet, or headdress. The head for 4 is shown in figure 51, _j-m_. It is to be distinguished by its large prominent eye and square irid (). (probably eroded in _l_), the snaglike front tooth, and the curling fang protruding from the back part of the mouth () (wanting in _l_ and _m_). {99} The head for 5 (fig. 51, _n-s_) is always to be identified by its peculiar headdress (), which is the normal form of the tun sign. Compare figure 29, _a_, b. The same element appears also in the head for 15 (see fig. 53, _b-e_). The head for 5 is one of the most constant of all the head numerals. [Illustration: FIG. 53. Head-variant numerals 14 to 19, inclusive, and 0.] The head for 6 (fig. 51, _t-v_) is similarly unmistakable. It is always characterized by the so-called hatchet eye (), which appears also in the head for 16 (fig. 53, _f-i_). 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} the large ornamental scroll passing under the eye and curling up in front of the forehead (), is better seen in the head for 17 (fig. 53, _j-m_). The head for 8 is shown in figure 52, _a-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 forehead ornament, which is composed of but a single element (). 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 _f_ the tongue or tooth of a grotesque animal head forms the forehead ornament. The heads for 18 (fig. 53, _n-q_) follow the first variants (fig. 51, _a_, _b_), having the large curl, except _q_, which is similar to _d_ in 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 all Initial Series record dates which fell after the completion of Cycle 9, but before the completion of Cycle 10. Consequently, 9 is the coefficient attached to the cycle glyph in almost all Initial Series.[69] The head for 9 is shown in figure 52, _g-l_. It has for its essential characteristic the dots on the lower cheek or around the mouth (). Sometimes these occur in a circle or again irregularly. Occasionally, as in _j-l_, the 9 head has a beard, though this is not a constant element as are the dots, which appear also in the head for 19. Compare figure 53, _r_. The head for 10 (fig. 52, _m-r_) is extremely important since its essential element, the fleshless lower jaw (), stands for the 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 skull, 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--Zoömorph 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 (fig. 52, _s_) has been found only once in the inscriptions, 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, therefore, 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. {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 characteristic 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-b'_) is grotesque. It seems to be characterized by its long pendulous nose surmounted by a curl (), its large bulging eye (**), and a curl () or fang (++) protruding from the back part 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 Stairway 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 fleshless 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, _b-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, _f-i_) is characterized by the fleshless 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 fleshless 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 0 (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 in the ending signs used with {102} 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 this sign are[70] (1) the clasped hand, identical with the hand in the head-variant forms for zero, and (2) the large element above it, containing a curling infix. This latter element also occurs though below the clasped hand, in the "ending signs" shown in figure 37, _l_, _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 throughout the inscriptions. [Illustration: 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_, for forms used interchangeably in the inscriptions to express the idea of 0 or of completion.)] In order to familiarize 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 glyphs 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 earliest 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 {103} have head-variant numerals; but that the earliest of these latter antedate the earnest bar and dot Initial Series may well be doubted. TABLE X. CHARACTERISTICS OF HEAD-VARIANT NUMERALS 0 TO 19, INCLUSIVE +-------------+---------------------------------------------------------+ | Forms | Characteristics | +-------------+---------------------------------------------------------+ | Head for 0 | Clasped hand across lower part of face. | | Head for 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 irid, snaglike front tooth, | | | curling fang from back of mouth. | | 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 in some | | | cases beard. | | Head for 10 | Fleshless lower jaw and in some cases other | | | death's-head characteristics, truncated nose, etc. | | Head for 11 | Undetermined. | | Head for 12 | Undetermined; type of head known, however. | | Head for 13 | (_a_) Long pendulous nose, bulging eye, and curling | | | fang from back of mouth. | | | (_b_) Head for 3 with fleshless 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 5 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 for 8 with fleshless lower jaw of head for 10. | | Head for 19 | Head for 9 with fleshless lower jaw of head for 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 0 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 inscriptions, 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 0 to 19, inclusive, as multipliers 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[71] in certain relative positions, each of which had a fixed numerical value of its own, like the positions to the right and left of the decimal point in our own numerical notation. {104} The first of these 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 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: [Illustration: FIG. 55. Examples of the use of head-variant numerals with period, day, or month signs. The translation of each glyph appears below it.] 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 supplied mentally with the bar and dot numeral. {105} FIRST METHOD OF NUMERATION [Illustration: FIG. 56. Examples of the first method of numeration, used almost exclusively in the inscriptions.] In the first of the above methods the numbers 0 to 19, inclusive, were expressed by multiplying the kin sign by the numerals[72] 0 to 19 in turn. Thus, for example, 6 days was written as shown in figure 56, _a_, 12 days as shown in _b_, and 17 days as shown in _c_ of the same {106} figure. In other words, up to and including 19 the numbers were expressed by prefixing the sign for the number desired to the kin sign, that is, the sign for 1 day.[73] The numbers 20 to 359, inclusive, were expressed by multiplying both the kin and uinal signs by the numerical forms 0 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 12 uinals. The sum of these two products = 257. Again, the number 300 is written as in figure 56, e. The 15 uinals (three bars attached to the uinal sign) = 15 × 20 = 300 kins, exactly the number expressed. However, since no kins are required to complete the number, it is necessary to show that none were involved, and consequently 0 kins, or "no kins" is written immediately below the 15 uinals, and 300 + 0 = 300. One more example will suffice to show how the numbers 20 to 359 were expressed. In figure 56, _f_, the number 198 is shown. The 9 uinals = 9 × 20 = 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 numerals 0 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 tun = 18 uinals; but 18 uinals = 360 kins (18 × 20 = 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 writing 0 uinals immediately below the 1 tun, and 0 kins immediately below the 0 uinals. The sum of these three products equals 360 (360 + 0 + 0 = 360). Again, the number 3,602 is shown in figure 56, _h_. The 10 tuns = 10 × 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 0 uinals between the 10 tuns and 2 kins. The sum of these three products = 3,602 (3,600 + 0 + 2). Again, in figure 56, _i_, the number 7,100 is recorded. The 19 tuns = 19 × 360 = 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 {107} 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, uinal, tun, and katun signs by the numerals 0 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 × 360); therefore 1 katun = 7,200 kins. This number falls short of the number recorded by exactly 4 kins, or in other words, no tuns or uinals are involved in its composition, a fact shown by the 0 tuns and 0 uinals between the 1 katun and the 4 kins. The sum of these four products = 7,204 (7,200 + 0 + 0 + 4). The number 75,550 is shown in figure 56, _k_. The 10 katuns = 72,000; the 9 tuns, 3,240; the 15 uinals, 300; and the 10 kins, 10. The sum of these four products = 75,550 (72,000 + 3,240 + 300 + 10). Again, the number 143,567 is shown in figure 56, _l_. The 19 katuns = 136,800; the 18 tuns, 6,480; the 14 uinals, 280; and the 7 kins, 7. The sum of these four products = 143,567 (136,800 + 6,480 + 280 + 7). The numbers 144,000 to 1,872,000 (the highest number, according to some authorities, which has been found[74] in the inscriptions) were expressed by multiplying the kin, uinal, tun, katun, and cycle signs by the numerals 0 to 19, inclusive, and adding together the resulting 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 katuns = 144,000 kins; therefore 6 cycles = 864,000 kins; and 17 katuns = 122,400 kins; and 2 tuns, 720 kins; and 10 uinals, 200 kins; 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 number in the inscriptions upon which all are agreed is 1,872,000, as shown in figure 56, _n_. It equals 13 cycles (13 × 144,000), and consequently all the periods below--the katun, tun, uinal, and kin--are indicated as being used 0 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 opinions; and although its presentation will entail a somewhat lengthy digression from the subject under consideration it is so pertinent to the general question of the higher numbers and their formation, that the writer has thought best to discuss it at this point. In a vigesimal system of numeration the unit of increase is 20, and so far as the codices are concerned, as we shall presently see, this {108} number was in fact the only unit of progression used, except in the 2d order, in which 18 instead of 20 units were required to make 1 unit 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) incline 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 inscriptions are numbered from 1 to 13, inclusive, and not from 0 to 19, inclusive, as in the case of all the other periods except the uinal, which is numbered from 0 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[75] 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 0 to 19, inclusive, like all the other periods.[76] 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 numbered from 0 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 0 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 0 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. {109} But because 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 _not_ proceeding from the date 4 Ahau 8 Cumhu, 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 Palenque and on the east side of Stela C at Quirigua. In these two cases, if the long numbers 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.[77] However, by counting _backward_ each of these long numbers from their respective terminal days, 8 Ahau 18 Tzec, in the case of the Palenque 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 uniformity 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 inscriptions was formed in the same way. 2. The numerical 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 irregularity in the 5th place in the inscriptions (for such the use of 13 in a vigesimal system must be called), it would have been found also in the codices. {110} 3. Moreover, in the inscriptions themselves the cycle glyph occurs at least twice (see fig. 57, _a_, _b_) 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 tuns, or 20 katuns are recorded, each of these being expressed as 1 uinal, 1 tun, 1 katun, and 1 cycle, respectively.[78] Therefore, if 13 cycles had made 1 great cycle, 14 cycles would 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 _b_ 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 a great cycle, or unit of the 6th place, in the inscriptions as well as in the codices. [Illustration: FIG. 57. Signs for the cycle showing coefficients above 13: _a_, From the Temple of the Inscriptions, Palenque; _b_, from Stela N, Copan.] The above points are simply positive evidence in support of this hypothesis, however, and in no way attempt to explain or otherwise account for the undoubtedly contradictory points given in the discussion of (1) 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 is 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 fell on the same day. In other words, if there had been 13 cycles in a great cycle, the cycles would have been numbered from 0 to 12, inclusive, and the last, Cycle 13, would have been recorded instead as completing some great cycle. It is necessary to {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 found in the inscriptions it occurs with a Cycle 13, and an "ending sign" which is practically identical with other undoubted "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 Zoömorph 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 signify 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 Katun 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 Katun 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 concerning the length of the great cycle in the inscriptions. TABLE XI. SEQUENCE OF TWENTY CONSECUTIVE DATES IN THE MONTH POP 1 Ik 0 Pop 2 Akbal 1 Pop 3 Kan 2 Pop 4 Chicchan 3 Pop 5 Cimi 4 Pop 6 Manik 5 Pop 7 Lamat 6 Pop 8 Muluc 7 Pop 9 Oc 8 Pop 10 Chuen 9 Pop 11 Eb 10 Pop 12 Ben 11 Pop 13 Ix 12 Pop 1 Men 13 Pop 2 Cib 14 Pop 3 Caban 15 Pop 4 Eznab 16 Pop 5 Cauac 17 Pop 6 Ahau 18 Pop 7 Imix 19 Pop The numerical coefficients of the days, as we have seen, were numbered from 1 to 13, inclusive, and then began again with 1. See {112} 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 different 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 0 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 coefficients 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 katun there given, the name of this katun is Katun 2 Ahau, although it occupied the _first_ 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 coefficient 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 explanation not only accounts for the use of the 14 cycles or 17 cycles, as {113} shown in figure 57, _a_, _b_, but also satisfactorily provides for the enumeration 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 cycle 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 until numerical series containing more than 5 terms shall have been considered. (See pp. 114-127 for this discussion.) 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 counting 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 counting 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 believe that the Maya commenced 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 starting 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 believe, 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,[79] it was the 8th division of the grand cycle which ended on the day 4 Ahau 8 Cumhu, {114} 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 would 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 Cumhu) in a much grander chronological scheme, as will appear presently. [Illustration: FIG. 58. Part of the inscription on Stela N, Copan, showing a number composed of six periods.] [Illustration: FIG. 59. Part of the inscription in the Temple of the Inscriptions, Palenque, showing a number composed of seven periods.] [Illustration: FIG. 60. Part of the inscription on Stela 10, Tikal (probably an Initial Series), showing a number composed of eight periods.] 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 number recorded. Commencing at the bottom of figure 58 with the highest period involved and reading up, A6,[80] the 14 great cycles = 40,320,000 kins (see Table VIII, in which 1 great cycle = 2,880,000, and consequently 14 = 14 × 2,880,000 = {115} 40,320,000); A5, the 17 cycles = 2,448,000 kins (17 × 144,000); A4, the 19 katuns = 136,800 kins (19 × 7,200); A3, the 10 tuns = 3,600 kins (10 × 360); A2, the 0 uinals, 0 kins; and the 0 kins, 0 kins. The sum of these products = 40,320,000 + 2,448,000 + 136,800 + 3,600 + 0 + 0 = 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 coefficient 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} great cycle = 2,880,000; therefore the great-great cycle = twenty times 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; B1, 12 uinals = 240; B1, 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 follows the great-great cycle, which we found above consisted of 57,600,000, we may assume that it is the great-great-great cycle, and that it consisted 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 = 54,720,000; A5, 9 cycles = 1,296,000; A6, 3 katuns = 21,600; A7, 6 tuns = 2,160; A8, 2 uinals = 40; A9, 0 kins = 0.[81] The sum of these (1,152,000,000 + 633,600,000 + 54,720,000 + 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 inscriptions 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 certainty 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 important 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 (fig. 58) that only the lowest four periods--the 19 katuns, the 10 tuns, the 0 uinals, and the 0 kins--A2, A3, and A4,[82] 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 {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 offers 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 afforded by the very glyph upon which his reading depends for its verification, namely, the glyph which he interprets Katun 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 the determining characteristic of the cycle head. Indeed, this element is so clearly portrayed in the glyph in question that its identification as a head 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, tun, katun, and cycle, respectively, it is probable that the sixth and last, which follows immediately the fifth, without a break or interruption of any 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 applied to these three numbers to test their accuracy, the writer knows of no better check than to study the characteristics 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, B1 (see fig. 31, _a_, _b_), and the head variant in figure 60, A8. (See fig. 31, _d-f_.) Below the uinal sign in A3, figure 58, and A2, figure 59, and above A7, in figure 60 the tuns are recorded 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 curling 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} figs. 59, B2, 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_, b. 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, _a-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 (fig. 61, _a_) is a head variant, while in the Palenque and Tikal texts (_a_ and _b_ of the same figure, respectively) it is a normal form. Inasmuch as these three inscriptions are the only ones in which numerical series composed of 6 or more consecutive terms are recorded, it is unfortunate 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, however, the writer believes it will be possible to show clearly that the head variant in figure 61, _a_, and the normal forms in _b_ and _c_ are only variants of one and the same sign, and that all three stand for one and the same thing, namely, the great cycle, or unit of the sixth order. [Illustration: 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.] 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 elsewhere, is the determining characteristic of the head variant for the cycle. In figure 61, _b_, _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, _b_, _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 characteristics of these three glyphs must be their superfixial elements. In the normal form in figure 61, _b_, the superfix is very clear. Just inside the outline and parallel to it there is a line of smaller circles, {119} and in the middle there are two infixes like shepherds' crooks facing away from the center (). In _c_ of the last-mentioned figure the 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 _b_ 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 proportions this element is so similar to the corresponding elements in figure 61, _b_, _c_, that, taken together with the similarity of the other details pointed out above, it seems more than likely that all 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 characteristic 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 position 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-like 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 slight difference that the hand in _e_ holds a rod. Indeed, the similarity of the two forms is so close that in default of {120} any evidence to the contrary the writer believes 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 summarized as follows: 1. Both glyphs are made up of the same elements--(_a_) The normal form of the cycle sign; (_b_) a superfix composed of a hand with a tassel-like 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 is, the sixth terms of the series in which they occur. By this same line 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 established 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 like 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 line of investigation and turn to another for further light 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 all--the sign for the cycle, or period of 144,000 days. Indeed, A5 is composed of this sign alone with its usual coefficient of 9. Moreover, the next glyphs (A6, A7, A8, and A9[83]) are the signs for the katun, tun, uinal, and kin, respectively, and, together with A5, form a regular descending series of 5 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 containing 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 {121} 20 cycles, or 1 great cycle (that is, 20 × 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 figure 60 (A4, A5, A6, A7, A8, 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 fig. 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 all probability 20, not 13, great cycles made 1 great-great cycle. Therefore, since the great-great cycle signs in figure 61, _d_, _e_, are composed of the cycle sign plus a superfix (), this superfix must have the value of 400 (20 × 20) in order to make the whole glyph have the value of 20 great cycles, or 1 great-great cycle (20 × 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 number 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 (_b_) a semicircular element in which dots appear. {122} But this same hand in the super-fix of the great-great cycle increased the cycle sign 400 times (20 × 20; see A3, fig. 60). Therefore we must assume the same condition obtains here. And finally, since the eighth term = 20 × 20 × 20 × 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 important 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 elements have the same outline, roughly semicircular; (2) both elements have the same chain of dots around 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' difference in time between the carving of A2, figure 60, and _a_, figure 61, and more than 200 years between the former and figure 61, b. The writer believes both are variants of the same element, and consequently A2, figure 60, is probably composed of elements which signify 20 × 400 (20 × 20) × 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 numeration. The several points supporting this conclusion may be summarized as follows: 1. The eight periods[84] 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 composed 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 inscriptions and a generally[85] 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 {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. Goodman 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 all the terms present probably belong to one and the same number. 8. Finally, the two occurrences of the cycle sign with a coefficient 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 progression in the higher numbers in the inscriptions just as it was in the codices. Before closing the discussion 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 A1 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, A1, figure 60, is very clearly another Initial-series introducing glyph, having all of the five elements common to that sign. Compare A1 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 A1, 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 date in A1, A5-A9? The writer believes that the only possible effect they could have would be to fix Cycle 9 of Maya chronology in a far more comprehensive and elaborate chronological conception, a conception which {124} indeed staggers the imagination, dealing as it does with more than five million years. If these eight terms all belong to one and the same numerical series, a fact the writer believes he has established in the foregoing pages, it means that Cycle 9, the first historic period of the Maya civilization, was Cycle 9 of Great Cycle 19 of Great-great Cycle 11 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 Cumhu, 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 chronological 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 Cumhu. This is true because on the above date (1. 11. 19. 0. 0. 0. 0. 0. 4 Ahau 8 Cumhu) all the five periods lower than the great cycle are at 0. It proves, furthermore, 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 11: 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 {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: 1 great-great-great cycle = 1 × 20 × 20 × 20 cycles = 8,000 cycles 11 great-great cycles = 11 × 20 × 20 cycles = 4,400 cycles 19 great cycles = 19 × 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 find the name of the first cycle of Great-great-great Cycle 1, the highest Maya time period of which we have any knowledge: 983 × 13 = 12,779. And deducting this from the number of cycles involved (12,780), we have-- 12,780 12,779 ------ 1 This counted 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 A1, 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-like 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 superfix in A1 (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} The writer believes that whatever it may be, it is at least _not_ a member of this series, and in support of his belief he suggests that if it were, why should it alone be retained in recording _all_ 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 suggestion as a possible solution of the meaning of the Initial-series introducing glyph. It is suggested that in A1 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 civilization 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 admitting the correctness of this interpretation of A1, 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 uncertain, 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 omitted as well as the two higher periods in a date without giving rise to confusion 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 believes 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 could never be any doubt concerning them. {127} It is not necessary to press this point further, though it is believed 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 earlier 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 introducing glyph may still have retained its numerical value, 1, but in later times this middle dot lost its numerical characteristics and frequently appears as a scroll itself. The early date of Stela 10 makes it not unlikely 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 A1, 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 following 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 vigesimal 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 numerical value of the series wherein the omission occurs. In such cases the coefficient of the kin sign is usually prefixed to the uinal sign, the coefficient of the uinal itself standing above the uinal sign. In figure 58, for example, the uinal and the kin coefficients are both 0. In this case, however, the 0 on the left of the uinal sign is to be understood as belonging to the kin sign, which is omitted, while the 0 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 coefficient 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 _o_ of the same figure, that is, with the kin sign omitted and its coefficient 17 prefixed to the uinal sign, while the uinal's own coefficient 12 appears above. Or again, the 9 uinals and 18 kins recorded in _f_ 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 all 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} and the uinal coefficient stands _on the left_ of the uinal sign, while the kin coefficient stands _above_. This interchange in certain cases probably resulted from the needs of glyphic balance and symmetry. 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 block 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, seems to have prevailed extensively in connection with both Initial Series and Secondary Series; indeed, in the latter it is the rule to which there are but few exceptions. [Illustration: FIG. 62. Glyphs showing misplacement of the kin coefficient (_a_) or elimination of a period glyph (_b_, _c_): _a_, Stela E, Quirigua; _b_, Altar U, Copan; _c_, Stela J, Copan.] 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, b. 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 0 kins and 10 tuns. Such cases are exceedingly 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 {129} lowest period, so long as its several periods always stand in the same relation to each other. For example, in figure 56, _q_, 6 cycles, 17 katuns, 2 tuns, 10 uinals, and 0 kins represent exactly the same number as 0 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 all 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 decimal 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 to 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 position 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 {130} 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 0 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 calculations 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 0 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 should 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 0 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, b. The 17 in the kin place has a value of 17 (17 × 1) and the 1 in the uinal, or second, place a value of 20 (1 (the numeral) × 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 0 in the kin place has the value 0 (0 × 1), and the 15 in the second place has the value of 300 (15 × 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 0 in the lowest place indicates that 0 kins are involved, the 0 in the second place indicates that 0 uinals or 20's are involved, while the 1 in the third place shows that there is 1 tun, or 360, kins recorded (1 (the numeral) × 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. {131} The 13 in the lowest place equals 13 (13 × 1); the 13 in the second place, 260 (13 × 20); and the 19 in the third place, 6,840 (19 × 360). The sum of these three products equals 7,113 (13 + 260 + 6,840), [Illustration: 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, _f_. {132} The 2 in the first place equals 2 (2×1); the 0 in the second place, 0 (0×20); the 0 in the third place, 0 (0×360); and the 1 in the fourth place, 7,200 (1×7,200). The sum of these four products equals 7,202 (2+0+0+7,200). Again, the number 100,932 is recorded in figure 63, _g_. Here the 12 in the first place equals 12 (12×1); the 6 in the second place, 120 (6×20); the 0 in the third place, 0 (0×360); and the 14 in the fourth place, 100,800 (14×7,200). The sum of these four products equals 100,932 (12+120+0+100,800). The numbers 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 numerical value of 144,000. (See Table VIII.) For example, the number 169,200 is recorded in figure 63, _h_. The 0 in the first place equals 0 (0×1); the 0 in the second place, 0 (0×20); the 10 in the third place, 3,600 (10×360); the 3 in the fourth place, 21,600 (3×7,200); and the 1 in the fifth place, 144,000 (1×144,000). The sum of these five products equals 169,200 (0+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 (1×1); the 3 in the second place, 60 (3×20); the 19 in the third place, 6,840 (19×360); the 17 in the fourth place, 122,400 (17×7,200); 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 0 in the first place equals 0 (0×1); the 3 in the second place, 60 (3×20); the 0 in the third place, 0 (0×360); the 10 in the fourth place, 72,000 (10×7,200); the 0 in the fifth place, 0 (0×144,000); and the 2 in the sixth place, 5,760,000 (2×2,880,000). The sum of these six terms equals 5,832,060 (0+60+0+72,000+0+5,760,000). The highest number in the codices, as explained above, is 12,489,781, which is recorded on page 61 of the Dresden Codex. This number is expressed as in figure 63, _k_. The 1 in the first place equals 1 (1×1); the 15 in the second place, 300 (15×20); the 13 in the third place, 4,680 (13×360); the 14 in the fourth place, 100,800 (14×7,200); the 6 in the fifth place, 864,000 (6×144,000); and the 4 in the sixth place, 11,520,000 (4×2,880,000). The sum of these six products equals 12,489,781 (1+300+4,680+100,800+864,000+11,520,000). {133} It is clear that in numeration by position the order of the units could not be reversed as in the first 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 multiplicands--the period glyphs, each of which had a fixed numerical value--are always expressed[86] with their corresponding multipliers--the numerals 0 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 second method the Maya were obliged not only to fix arbitrarily the direction of reading, as from bottom to top, but also to confine themselves 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[87] the several methods of counting time and recording events found in each are all derived from the same source, and all are expressions 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 | SECOND METHOD | 1. Use confined almost exclusively | 1. Use confined exclusively to to the inscriptions. | the codices. | 2. Numerals represented by both | 2. Numerals represented by normal forms and head variants. | normal forms exclusively. | 3. Numbers expressed by using | 3. Numbers expressed by using the numerals 0 to 19, inclusive, | the numerals 0 to 19, as multipliers with the period | inclusive, as multipliers in glyphs as multiplicands. | certain positions the | fixed numerical values of | which served as | multiplicands. | 4. Numbers presented as | 4. Numbers presented as ascending or descending series. | ascending series | exclusively. | 5. Direction of reading either | 5. Direction of reading from from bottom to top, or vice | bottom to top exclusively. versa. We have seen in the foregoing pages (1) how the Maya wrote their 20 {134} 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 applied 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 have had but one use throughout the Maya texts, namely, to express the time elapsing between dates_.[88] In the codices and the inscriptions alike 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.[89] Hence, we may accept the following as the _first step_ in ascertaining the meaning of any number: FIRST 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 application of this rule to any Maya number, no matter of how many terms, will always give the actual number of primary units which it contains, and in this form it can be more conveniently utilized 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 inscriptions, and Table XIV for the same purpose in the codices. {135} TABLE XIII. VALUES OF HIGHER PERIODS IN TERMS OF LOWEST, IN INSCRIPTIONS 1 great cycle = [90]2,880,000 1 cycle 144,000 1 katun 7,200 1 tun 360 1 uinal 20 1 kin 1 TABLE XIV. VALUES OF HIGHER PERIODS IN TERMS OF LOWEST, IN CODICES 1 unit of the 6th place = 2,880,000 1 unit of the 5th place 144,000 1 unit of the 4th place 7,200 1 unit of the 3d place 360 1 unit of the 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 multiplicand which is to be multiplied 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 first order (3×7,200). Again, 5 attached to the uinal sign reduces to 100 units of the first order (5×20). 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 (5×360=1,800). Again, a 10 in the fourth place indicates that the 10'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; consequently, it is clear that no single rule can be formulated which will cover all 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[91] 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 {136} between.[92] 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 unattached 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 Initial Series the date from which it should be counted will be found to be 4 Ahau 8 Cumhu.[93] 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,[94] 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 numerous. No rule can be given covering 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 _backward_ 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 overwhelming majority of Maya numbers are counted _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. {137} [Illustration: FIG. 64. Figure showing the use of the "minus" or "backward" sign in the codices.] In the codices, moreover, when the count is backward, or contrary to the general practice, the fact is clearly indicated[95] by a special character. This character, although attached only to the lowest term[96] of the number which is to be counted backward, is to be interpreted as applying to all 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 0 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 follows from the fact that in numeration by position the order is from bottom to top. Therefore the starting point from which the 2,200 recorded in figure 64 is counted will be found to be below it, that is, the date 4 Ahau 8 Cumhu[97] (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[98] 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 exception 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 chiefly to Secondary Series, and it is in {138} 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 statement of general rules. Hence, we will formulate our rules after the processes which they govern have been fully explained. In counting any number, as 31,741, or 4.8.3.1 as it would be expressed in Maya notation,[99] from any date, as 4 Ahau 8 Cumhu, there are four unknown 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 0 to 19, inclusive. 4. The name of the division of the year, which must be one of the nineteen given in Table III. 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 understand the calculations which follow. It was explained in the text (see pp. 41-44) and also shown graphically in the tonalamatl wheel (pl. 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. {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 ÷ 13 = 2,441-8/13. 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 coefficient: 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.[100] Hence the following rule for determining the first unknown on page 138 (the day coefficient): _Rule 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 from 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 8/13. Assuming that the count is forward from the starting point, 4 Ahau 8 Cumhu, 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 Cumhu), 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 no 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 multiple 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 because, 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. {140} Returning to the number 31,741, let us deduct from it the highest multiple of 20 which it contains, found by dividing the number by 20 and multiplying the whole number part of the resulting quotient by 20; 31,741 ÷ 20 = 1,587-1/20. Multiplying 1,587 by 20, we have 31,740, which is the highest multiple of 20 that 31,741 contains, and which may be 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 resulting 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 seen above that its division by 20 gives us as the fractional part of the quotient, 1/20. 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, Ahau (4 Ahau 8 Cumhu), the day sign reached will be the day sign of the resulting date. Counting forward 1 from Ahau 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 kaba kin_ 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 {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 ÷ 365 = 86-351/365. 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 of 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 resulting date): _Rule 3._ To find the position in 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 +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ |Month|P |U |Z |Z |T |X |Y |M |C |Y |Z |C |M |K |M |P |K |C |U | | |o |o |i |o |z |u |a |o |h |a |a |e |a |a |u |a |a |u |a | | |p | |p |t |e |l |x |l |e |x |c |h |c |n |a |x |y |m |y | | | | | |z |c | |k | |n | | | | |k |n | |a |h |e | | | | | | | | |i | | | | | | |i | | |b |u |b | | | | | | | | |n | | | | | | |n | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ |Posi-| | | | | | | | | | | | | | | | | | | | |tion |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 |0 | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 |1 | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 |2 | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 |3 | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 |4 | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |5 |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |6 |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |7 |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |8 |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |9 |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|10|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |11|11|11|11|11|11|11|11|11|11|11|11|11|11|11|11|11|11|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |12|12|12|12|12|12|12|12|12|12|12|12|12|12|12|12|12|12|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |13|13|13|13|13|13|13|13|13|13|13|13|13|13|13|13|13|13|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |14|14|14|14|14|14|14|14|14|14|14|14|14|14|14|14|14|14|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |15|15|15|15|15|15|15|15|15|15|15|15|15|15|15|15|15|15|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |16|16|16|16|16|16|16|16|16|16|16|16|16|16|16|16|16|16|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|17|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|18|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | Do |19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|19|--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ {142} 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 Cumhu, the position of the day of the starting point, 4 Ahau 8 Cumhu. A glance at the month of Cumhu in Table XV shows that after the position 8 Cumhu there are 11 positions in that month; adding to these the 5 in Uayeb, 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 will fall the 335th position from the beginning of the year. In other words, 320 positions of our 335 will exactly use up all the positions of the first 16 months, namely, Pop, Uo, Zip, Zotz, Tzec, Xul, Yaxkin, Mol, Chen, Yax, Zac, Ceh, Mac, Kankin, 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 will see that 15 positions counted forward in this month will reach the position 14 Kayab, which is also the position reached by counting forward 31,741 positions 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 "terminal 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 _backward_, 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. {143} Since the foregoing is true, it follows, that this number 18,980 or any multiple thereof, may be deducted from the number which 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 in 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. _Rule_. 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 number to be handled, and consequently involves fewer calculations. In Table XVI are given 80 Calendar Rounds, that is, 80 multiples of 18,980, in 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 Round, 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 backward had the count been backward in our 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 in the first case. Mathematical proof of this point follows: 12,761 ÷ 13 = 981-8/13 12,761 ÷ 20 = 638-1/20 12,761 ÷ 365 = 34-351/365 The numerators of the fractions in 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 in 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 resulting terms together will form the corresponding 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 point would both reach this same terminal date, since subtracting 2 Calendar Rounds, 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} TABLE XVI. 80 CALENDAR ROUNDS EXPRESSED IN ARABIC AND MAYA NOTATION +--------+---------+-----------------+ |Calendar| Days| Cycles, Etc.| | Rounds| | | +--------+---------+-----------------+ | 1| 18,980| 2. 12. 13. 0| +--------+---------+-----------------+ | 2| 37,960| 5. 5. 8. 0| +--------+---------+-----------------+ | 3| 56,940| 7. 18. 3. 0| +--------+---------+-----------------+ | 4| 75,920| 10. 10. 16. 0| +--------+---------+-----------------+ | 5| 94,900| 13. 3. 11. 0| +--------+---------+-----------------+ | 6| 113,880| 15. 16. 6. 0| +--------+---------+-----------------+ | 7| 132,860| 18. 9. 1. 0| +--------+---------+-----------------+ | 8| 151,840| 1. 1. 1. 14. 0| +--------+---------+-----------------+ | 9| 170,820| 1. 3. 14. 9. 0| +--------+---------+-----------------+ | 10| 189,800| 1. 6. 7. 4. 0| +--------+---------+-----------------+ | 11| 208,780| 1. 8. 19. 17. 0| +--------+---------+-----------------+ | 12| 227,760| 1. 11. 12. 12. 0| +--------+---------+-----------------+ | 13| 246,740| 1. 14. 5. 7. 0| +--------+---------+-----------------+ | 14| 265,720| 1. 16. 18. 2. 0| +--------+---------+-----------------+ | 15| 284,700| 1. 19. 10. 15. 0| +--------+---------+-----------------+ | 16| 303,680| 2. 2. 3. 10. 0| +--------+---------+-----------------+ | 17| 322,660| 2. 4. 16. 5. 0| +--------+---------+-----------------+ | 18| 341,640| 2. 7. 9. 0. 0| +--------+---------+-----------------+ | 19| 360,620| 2. 10. 1. 13. 0| +--------+---------+-----------------+ | 20| 379,600| 2. 12. 14. 8. 0| +--------+---------+-----------------+ | 21| 398,580| 2. 15. 7. 3. 0| +--------+---------+-----------------+ | 22| 417,560| 2. 17. 19. 16. 0| +--------+---------+-----------------+ | 23| 436,540| 3. 0. 12. 11. 0| +--------+---------+-----------------+ | 24| 455,520| 3. 3. 5. 6. 0| +--------+---------+-----------------+ | 25| 474,500| 3. 5. 18. 1. 0| +--------+---------+-----------------+ | 26| 493,480| 3. 8. 10. 14. 0| +--------+---------+-----------------+ | 27| 512,460| 3. 11. 3. 9. 0| +--------+---------+-----------------+ | 28| 531,440| 3. 13. 16. 4. 0| +--------+---------+-----------------+ | 29| 550,420| 3. 16. 8. 17. 0| +--------+---------+-----------------+ | 30| 569,400| 3. 19. 1. 12. 0| +--------+---------+-----------------+ | 31| 588,380| 4. 1. 14. 7. 0| +--------+---------+-----------------+ | 32| 607,360| 4. 4. 7. 2. 0| +--------+---------+-----------------+ | 33| 626,340| 4. 6. 19. 15. 0| +--------+---------+-----------------+ | 34| 645,320| 4. 9. 12. 10. 0| +--------+---------+-----------------+ | 35| 664,300| 4. 12. 5. 5. 0| +--------+---------+-----------------+ | 36| 683,280| 4. 14. 18. 0. 0| +--------+---------+-----------------+ | 37| 702,260| 4. 17. 10. 13. 0| +--------+---------+-----------------+ | 38| 721,240| 5. 0. 3. 8. 0| +--------+---------+-----------------+ | 39| 740,220| 5. 2. 16. 3. 0| +--------+---------+-----------------+ | 40| 759,200| 5. 5. 8. 16. 0| +--------+---------+-----------------+ | 41| 778,180| 5. 8. 1. 11. 0| +--------+---------+-----------------+ | 42| 797,160| 5. 10. 14. 6. 0| +--------+---------+-----------------+ | 43| 816,140| 5. 13. 7. 1. 0| +--------+---------+-----------------+ | 44| 835,120| 5. 15. 19. 14. 0| +--------+---------+-----------------+ | 45| 854,100| 5. 18. 12. 9. 0| +--------+---------+-----------------+ | 46| 873,080| 6. 1. 5. 4. 0| +--------+---------+-----------------+ | 47| 892,060| 6. 3. 17. 17. 0| +--------+---------+-----------------+ | 48| 911,040| 6. 6. 10. 12. 0| +--------+---------+-----------------+ | 49| 930,020| 6. 9. 3. 7. 0| +--------+---------+-----------------+ | 50| 949,000| 6. 11. 16. 2. 0| +--------+---------+-----------------+ | 51| 967,980| 6. 14. 8. 15. 0| +--------+---------+-----------------+ | 52| 986,960| 6. 17. 1. 10. 0| +--------+---------+-----------------+ | 53|1,005,940| 6. 19. 14. 5. 0| +--------+---------+-----------------+ | 54|1,024,920| 7. 2. 7. 0. 0| +--------+---------+-----------------+ | 55|1,043,900| 7. 4. 19. 13. 0| +--------+---------+-----------------+ | 56|1,062,880| 7. 7. 12. 8. 0| +--------+---------+-----------------+ | 57|1,081,860| 7. 10. 5. 3. 0| +--------+---------+-----------------+ | 58|1,100,840| 7. 12. 17. 16. 0| +--------+---------+-----------------+ | 59|1,119,820| 7. 15. 10. 11. 0| +--------+---------+-----------------+ | 60|1,138,800| 7. 18. 3. 6. 0| +--------+---------+-----------------+ | 61|1,157,780| 8. 0. 16. 1. 0| +--------+---------+-----------------+ | 62|1,176,760| 8. 3. 8. 14. 0| +--------+---------+-----------------+ | 63|1,195,740| 8. 6. 1. 9. 0| +--------+---------+-----------------+ | 64|1,214,720| 8. 8. 14. 4. 0| +--------+---------+-----------------+ | 65|1,233,700| 8. 11. 6. 17. 0| +--------+---------+-----------------+ | 66|1,252,680| 8. 13. 19. 12. 0| +--------+---------+-----------------+ | 67|1,271,660| 8. 16. 12. 7. 0| +--------+---------+-----------------+ | 68|1,290,640| 8. 19. 5. 2. 0| +--------+---------+-----------------+ | 69|1,309,620| 9. 1. 17. 15. 0| +--------+---------+-----------------+ | 70|1,328,600| 9. 4. 10. 10. 0| +--------+---------+-----------------+ | 71|1,347,580| 9. 7. 3. 5. 0| +--------+---------+-----------------+ | 72|1,366,560| 9. 9. 16. 0. 0| +--------+---------+-----------------+ | 73|1,385,540| 9. 12. 8. 13. 0| +--------+---------+-----------------+ | 74|1,404,520| 9. 15. 1. 8. 0| +--------+---------+-----------------+ | 75|1,423,500| 9. 17. 14. 3. 0| +--------+---------+-----------------+ | 76|1,442,480|10. 0. 6. 16. 0| +--------+---------+-----------------+ | 77|1,461,460|10. 2. 19. 11. 0| +--------+---------+-----------------+ | 78|1,480,440|10. 5. 12. 6. 0| +--------+---------+-----------------+ | 79|1,499,420|10. 8. 5. 1. 0| +--------+---------+-----------------+ | 80|1,518,400|10. 10. 17. 14. 0| +--------+---------+-----------------+ {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 ÷ 13 = 446-1/13. 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 = 289-19/20. Counting forward the numerator of the fractional 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 ÷ 365 = 15-324/365. 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; 13 × 20 + 5 = 265, and 265 + 12 = 277. This latter number subtracted from 324, the total number of positions 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 use 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 number, say 322,920, which we will assume is to be counted forward from the starting point 13 Ik 0 Zip. Since this number is above 18,980, we may apply our preliminary rule (p. 143) and deduct all the Calendar {146} Rounds possible. By turning to Table XVI we see that 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 260 ÷ 13 = 20. Since there is no fraction in the quotient, the numerator of the fraction will be 0, and counting 0 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 ÷ 20 = 13. Since there is no fraction in the quotient, the numerator of the fraction will be 0, and counting forward 0 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 will 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.[101] Dividing by 365 we have: 260 ÷ 365 = 260/365. Counting forward the numerator of the fraction, 260, from the year position of the starting point, 0 Zip, in Table XV, the position in the year of the day of the terminal date will be found to be 0 Pax. Since 260 days equal just 13 uinals, we have only to count forward from 0 Zip 13 uinals in order to reach the year position; that is, 0 Zotz is 1 uinal; to 0 Tzec 2 uinals, to 0 Xul 3 uinals, and so on in Table XV to 0 Pax, which will complete the last of the 13 uinals (rule 3, p. 141). Combining the above values, we find that in counting forward 322,920 (or 260) from the starting point 13 Ik 0 Zip, the terminal date reached is 13 Ik 0 Pax. In order to illustrate the method of procedure when the count is _backward_, 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 number by 13, we have: 9,663 ÷ 13 =743-4/13. Counting the numerator of the fractional part of this quotient, 4, _backward_ 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 = 483-3/20. Counting the numerator of the fractional part of this quotient, 3, _backward_ 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 count will be 12 Eznab. Dividing the given number by 365, we have {147} 9,663 ÷ 365 = 26-173/365. Counting _backward_ the numerator of the fractional 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 _backward_ to the end of the month Cumhu (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 Cumhu, we may count _backward_ 8 whole uinals, namely: Cumhu, 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 0 Zac, that is, beginning with position 19 Yax: 19, 18, 17, 16, 15, 14, 13, 12, 11; so 11 Yax is the position in 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 backward, the method is the same, the only difference being in the direction of the counting. This concludes the discussion of the actual arithmetical processes involved in counting forward or backward any given number 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 applied to the Long Count. The numbers 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 distinct 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, tuns, 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 distinguished 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, 0 katuns, 0 tuns, 0 uinals, and 0 kins {148} from 4 Ahau 8 Cumhu, the starting point of Maya chronology (always unexpressed in Initial Series), the terminal date reached will be 8 Ahau 13 Ceh."[102] Or again: 9.14.13.4.17. 12 Caban 5 Kayab This Inital Series reads thus: "Counting forward 9 cycles, 14 katuns, 13 tuns, 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 recurred upward of 70 times since the beginning of their chronology, the Maya were able to distinguish any particular 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. Similarly, any particular 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, in 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 particular 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[103] 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 katuns, 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. {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 Ceh 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 calculation 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 counted 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 accompanying text-- 9.12. 2. 0.16 5 Cib 14 Yaxkin 12. 9.15 [9.12.14.10.11][104] 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 the only parts actually recorded are the Initial Series 9.12.2.0.16 {150} 5 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, belonging 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 like 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 terminal 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 Ahau 8 Uo. Reducing 3 uinals and 2 kins to kins, we have 62 units of the first order. Counting forward 62 from 5 Ahau 8 Uo, as indicated by the rules on pages 138-143, it is found that the terminal date will be 2 Ik 10 Tzec. Since the Initial-series value of the starting point 5 Ahau 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) 5 Ahau 8 Uo 3.2 (distance from 5 Ahau 8 Uo 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, unexpressed 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 Uo. One more example presenting a "backward count" 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 5 Kayab. Reducing 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 5 Kayab is known, namely, 9.14.13.4.17, the Initial-series value of {151} the terminal date may be calculated by _subtracting_ the distance number 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 calculations 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 under the fourth step (pp. 138-143), the terminal date may be found by calculation. 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 closing 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} This applies equally to all terminal dates, whether in Initial Series, Secondary Series, Calendar-round dating or Period-ending dating, though in the case of Initial Series a peculiar division or partition of the terminal date is to be noted. Throughout the inscriptions, excepting in the case of Initial Series, the month parts of the dates almost invariably follow immediately the days whose positions in the year they designate, without any other glyphs standing between; as, for example, 8 Ahau 13 Ceh, 12 Caban 5 Kayab, etc. In Initial Series, on the other hand, the day parts of the dates, as 8 Ahau and 12 Caban, in the above examples, are almost invariably separated from their corresponding month parts, 13 Ceh or 5 Kayab, by several intervening glyphs. The positions of the day parts in Initial-series terminal dates are quite regular according to the terms of the above rule; that is, they follow immediately the lowest period of the number which in each 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 intervening glyphs have been called the Supplementary Series, though the count which they record has not as yet been deciphered.[105] The month glyph in the great majority of cases follows immediately the closing[106] glyph of the Supplementary Series. The form of this latter sign is always unmistakable (see fig. 65), and it is further characterized by its numerical coefficient, which can never be anything but 9 or 10.[107] See examples of this sign in the figure just mentioned, where both normal forms _a, c, e, g,_ and _h_ and head variants _b, d,_ and _f_ are included. The student will find this glyph exceedingly helpful in locating the month parts of Initial-series terminal dates in the inscriptions. For example, let us suppose in deciphering the Initial Series 9.16.5.0.0 8 Ahau 8 Zotz that the number 9.16.5.0.0 has been counted forward {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 0 kins of the number 9.16.5.0.0. Now, if the student will follow 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 will be in all probability 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. [Illustration: FIG. 65. Sign for the "month indicator": _a, c, e, g, h_, Normal forms; _b, d, f_, head variants.] In all other cases in the inscriptions, including also the exceptions to the above rule, that is, where the month parts of Initial-series terminal 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[108] usually follow immediately the days signs to which they belong. The most notable exception[109] 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 {154} different date--2 Ahau 3 Cumhu, 2 Ahau 3 Zotz, and 2 Ahau 13 Yax. In these pages the month signs, with a few exceptions, do not follow immediately the days to which they belong, but on the contrary they are separated from them by several intervening glyphs. This abbreviation in the record of these dates was doubtless prompted by the desire or necessity for economizing space. In the above example, instead of repeating the 2 Ahau with each of the two lower month signs, 3 Zotz and 13 Yax, by writing it once above the upper month sign, 3 Cumhu, the scribe intended that it should be used in turn with each one of the three month signs standing below it, to form three different dates, saving by this abbreviation the space of two glyphs, that is, double the space occupied by 2 Ahau. With the exception of the Initial-series dates in the inscriptions and the Venus-Solar dates on pages 46-50 of the Dresden Codex, we may say that the regular position of the month glyphs in Maya writing was immediately following the day glyphs whose positions in the year they severally designated. In closing the presentation of this last step in the process of deciphering numbers in the texts, the great value of the terminal date as a final check for all the calculations involved under steps 1-4 (pp. 134-151) should be pointed out. If after having worked out the terminal date of a given number according to these rules the terminal date thus found should differ from that actually recorded under step 5, we must accept one of the following alternatives: 1. There is an error in our own calculations; or 2. There is an error in the original text; or 3. The case in point lies without the operation of our rules. It is always safe for the beginner to proceed on the assumption that the first of the above alternatives is the cause of the error; in other words, that his own calculations are at fault. If the terminal date as calculated does not agree with the terminal-date as recorded, the student should repeat his calculations several times, checking up each operation in order to eliminate the possibility of a purely arithmetical error, as a mistake in multiplication. After all attempts to reach the recorded terminal date by counting the given number from the starting point have failed, the process should be reversed and the attempt made to reach the starting point by counting backward the given number from its recorded terminal date. Sometimes this reverse process will work out correctly, showing that there must be some arithmetical error in our original calculations which we have failed to detect. However, when both processes have failed several times to connect the starting point with the recorded terminal date by use of the given number, there remains the possibility that either the starting point or the terminal date, or perhaps both, do not belong to the given number. The rules for determining this fact {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 belong 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 V and 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 obliged 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 are unknown may govern such cases. At all events, the failure 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 concern. 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. {156} 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 application to the inscriptions[110] of the material presented in Chapters III and IV. [Illustration: FIG. 66. Diagram showing the method of designating particular glyphs in a text.] Before proceeding with this discussion it will first be necessary to explain the method followed in designating particular glyphs in a 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[111] in each pair of columns being from left to right and from top to bottom. For convenience in referring 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 glyph-blocks in columns A and B are read together from left to right and top to bottom, thus, A1 B1, A2 B2, A3 B3, etc. When glyph-block B10 is reached the next in order is C1, which is followed by D1, C2 D2, C3 D3, etc. Again, when D10 is reached the next in order is E1, which is followed by F1, E2 F2, E3 F3, etc. In this way the order of reading proceeds from left to right and from top to bottom, in pairs of columns, that is, G H, I J, K L, and M N throughout the inscription, and usually closes with the glyph-block in the lower right-hand corner, as N10 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 [alpha] is referred to as D3; glyph [beta] as F6; glyph [gamma] as K4; glyph [delta] as N10. In a few texts the glyph-blocks are so irregularly placed that it is impracticable to designate them by the above coordinates. In such cases the order of the glyph-blocks will be indicated by numerals, 1, 2, 3, etc. In two Copan texts, Altar S (fig. 81) and Stela J (pl. 15), made from the drawings of Mr. Maudslay, his numeration of the glyphs has been followed. This numeration appears in these two figures. [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND NORMAL-FORM PERIOD GLYPHS] {157} TEXTS RECORDING INITIAL SERIES Because of the fundamental importance of Initial Series in the Maya system of chronology, the first class of texts represented will illustrate this method of dating. Moreover, since the normal forms for the numerals and the period glyphs will be more easily recognised 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.[112] In plate 6 is figured the drawing of the Initial Series[113] from Zoömorph P at Quirigua, a monument 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, A1-B2.[114] Analysis of this form shows that it possesses all the elements mentioned on page 65 as belonging to the so-called Initial-series introducing glyph, without which Initial Series never seem to have been recorded in the inscriptions. These elements are: (1) the trinal {158} superfix, (2) the pair 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 A1-B2. Moreover, a comparison of A1-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 follow.[115] Exceptions to this rule are so very rare (see p. 67) that the beginner will do well to disregard them altogether. The next glyph after the introducing glyph in an Initial Series is the cycle sign, the highest period ever found in this kind of count[116]. 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 figure 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[117]. The glyph following the cycle sign in an Initial Series is always the katun 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 numeral 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, b_, shows this to be the case. The numeral 5 (1 bar prefixed to the tun sign) shows that this period is to be used 5 times; that is, multiplied 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 0 uinals recorded in B4. A comparison 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 like the coefficient of B4, which, we have seen, meant zero, hence glyph A5 stands for 0 kins. Summarizing the above, we may say that glyphs A3-A5 record an Initial-series number consisting of 6 cycles, 18 katuns, 5 tuns, 0 uinals, and 0 kins, which we may write thus: 9.18.5.0.0 (see p. 138, footnote 1). {159} Now let us turn to Chapter IV and apply the several steps there given, by means of which Maya numbers may be solved. The first 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 multiplication by the coefficients recorded in the Initial Series in plate 6, A are given below: A3 = 9 × 144,000 = 1,296,000 B3 = 18 × 7,200 = 129,600 A4 = 5 × 360 = 1,800 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 ---------- 1,427,400 Therefore 1,427,400 will be the number used in the following calculations. 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 Cumhu. Exceptions to this rule 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 Cumhu. The third step (see step 3, p. £136) is to determine the direction of the count, whether forward or backward. In this connection it was stated that the general practice is to count forward, and that the student should always proceed upon this assumption. However, in the present case there is no room for uncertainty, since the direction 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 fourth step (see step 4, p. 138) is to count the given number from its starting point; and the rules governing this process will be found on pages 139-143. Since our given number (1,427,400) is greater than 18,980, or 1 Calendar Round, the preliminary rule on page 143 applies in the present case, and we may therefore subtract from 1,427,400 all the Calendar Rounds possible before proceeding to count 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} 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.[118] 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; counting forward 0 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 resulting quotient, the numerator of an assumed fractional part will be 0; counting forward 0 in Table I, from Ahau, the day sign of the starting 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, occupied. In order to find the position in the year which the day of the terminal date occupied, it is necessary, under rule 3, page 141, to divide the given number or its equivalent by 365; 3,900 ÷ 365 = 10-250/365. Since the numerator of the fractional part of the resulting 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 count 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 11 uinals in the year will use up exactly 220 of our 234 positions (11 × 20 = 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); counting forward 14 positions in Ceh, we reach 13 Ceh, which is, therefore, the month glyph of our terminal date. In other words, counting 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. {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, position 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 Ceh in counting forward 250 from 8 Cumhu, counting 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_ 250 from 13 Ceh; if our calculations have been correct, the starting point 8 Cumhu will 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;[119] 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 terminal 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 calculation. 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 Supplementary Series, usually a matter of six or seven glyphs. Returning to our text (pl. 6, _A_), we find that the kins are recorded in A5, therefore the day part of the terminal date should appear in B5. The glyph in B5 quite 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-C1a, which record the Supplementary Series,[120] we reach in C1a 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 C1a it has the coefficient 9 (4 dots and 1 bar) and is followed in C1b by the month part {162} 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 Ceh 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, C1b agrees with the terminal date determined by calculation, we may conclude 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 Zoömorph P at Quirigua was formally consecrated or dedicated as a time-marker, or in other words, that Zoömorph P was the monument set up to mark the hotun, or 5-tun period, which came to a close on the date 9.18.5.0.0 4 Ahau 13 Ceh of Maya chronology.[121] In plate 6, _B_, is figured a drawing of the Initial Series on Stela 22 at Naranjo.[122] The text opens in A1 with the Initial-series introducing glyph, 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 corresponding normal forms, and the student will have no difficulty in identifying them and reading the number, as above recorded. By means of Table XIII this number may be reduced to units of the 1st order, in which form it may be more conveniently used. This reduction, which forms the first step in the process of solving Maya numbers (see step 1, p. 134), follows: B1 = 9 × 144,000 = 1,296,000 A2 = 12 × 7,200 = 86,400 B2 = 15 × 360 = 5,400 A3 = 13 × 20 = 260 B3 = 7 × 1 = 7 --------- 1,388,067 And 1,388,067 will be the number used in the following calculations. The next step is to find the starting point from which 1,388,067 is counted (see step 2, p. 135). Since this number is an Initial Series, in all 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 count (see step 3, p. 136); since our number is an Initial Series, the count can only be forward (see rule 2, p. 137).[123] {163} Having determined 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 Round), 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 deducting 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 = 194-5/13, and counting forward 5, the numerator 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 = 126-7/20; 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 = 6-337/365; 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 0 Kayab as the year position of the terminal date. The calculations by means of which 0 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 = (16 × 20) + 1; hence it will reach through the first 16 uinals in Table XV and to the first position in the 17th uinal, 0 Kayab. Combining this with the day obtained above, we have for our terminal date determined by calculation, 9 Manik 0 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 terminal 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 figure 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; consequently 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} 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 0 Kayab, and by referring to figure 49 we find the only form which can be used to express the 0 position with the month signs--the so-called "spectacles" glyph--which must be recorded somewhere in this text to express the idea 0 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 figure 19, _d'-f'_; that is, 0 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 in A4, A6 the same terminal date, 9 Manik 0 Kayab, as determined by calculation, and may conclude, therefore, that our text records without error the date 9.12.15.13.7 9 Manik 0 Kayab[124] of Maya chronology. The next text presented (pl. 6, C) shows the Initial Series from Stela I at Quirigua.[125] Again, as in plate 6, A, the introducing glyph occupies the space of four glyph-blocks, namely, A1-B2. Immediately after this, in 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 0 used with the uinal and kin signs in A4a and A4b, respectively, which differs from the form for 0 recorded with the uinal and kin signs in plate 6, A, B4, and A5, respectively. In the latter text the 0 uinals and 0 kins were expressed by the hand and curl form for zero shown in figure 54; in the present text, however, the 0 uinals and 0 kins are expressed by the form for 0 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 = 9 × 144,000 = 1,296,000 B3a = 18 × 7,200 = 129,600 B3b = 10 × 360 = 3,600 A4a = 0 × 20 = 0 A4b = 0 × 1 = 0 --------- 1,429,200 Deducting from this number all the Calendar Rounds possible, 75 {165} (see Table XVI), it may be reduced to 5,700 without affecting its value in the present connection. Applying rules 1 and 2 (pp. 139 and 140, respectively) to this number, 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 found to be 8 Zac. Therefore, by calculation we have determined that the terminal 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 coefficient being unusually clear, and practically unmistakable. Compare B4a with figure 16, _e'-g'_, the sign for the day name Ahau. Consequently the day recorded agrees with the day determined by calculation. 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 will be found in the regular position for the month glyphs in all other kinds of dates in the inscriptions, namely, immediately following the day glyph to which it belongs. In the present text we found 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 following 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. [Illustration: FIG. 67. Signs representing the hotun, or 5-tun, period.] 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 Zoömorph P at Quirigua (see pl. 6, _A_). As explained in Chapter II (pp. 33-34), the interval between succeeding monuments at Quirigua is in every case 1,800 days, or 5 tuns. Therefore, it would seem probable that at Quirigua at least this period was the unit used for marking the lapse of time. As each 5-tun period was completed, its close was marked by the erection of a monument, on which was recorded its ending date. Thus the writer believes Zoömorph P marked the close of the 5-tun period ending 9.18.5.0.0 4 Ahau 13 Ceh, and Stela I, the 5-tun period next following, that ending 9.18.10.0.0 {166} 10 Ahau 8 Zac. In other words, Zoömorph 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 _hotun_, _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-tun period, _katun_, which we have seen may have been named directly from its numerical value, _kal_ being the word for 20 in Maya and _kaltun_ contracted to katun, thus meaning 20 tuns. Although no glyph for the _hotun_ has as yet been identified,[126] the writer is inclined to believe that the sign in figure 67, _a, b_, which is frequently encountered in the texts, will be found to represent this time period. The bar at the top in both _a_ and _b_, figure 67, surely signifies 5; therefore the glyph itself must mean "1 tun." This form recalls the very unusual variant of the tun from Palenque (see fig. 29, _h_). Both have the wing and the () element. The next Initial Series presented (see pl. 6, _D_) is from Stela 24 at Naranjo.[127] The text opens with the introducing glyph, which is in the same relative position as the introducing glyph in the other Naranjo text (pl. 6, _B_) at A1. Then follows regularly in B1-B3 the number 9.12.10.5.12, the numbers 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 determining the number as given above. Reducing this according to rule 1, page 134, the following result should be obtained: B1 = 9 × 144,000 = 1,296,000 A2 = 12 × 7,200 = 86,400 B2 = 10 × 360 = 3,600 A3 = 5 × 20 = 100 B3 = 12 × 1 = 12 --------- 1,386,112 Deducting[128] 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 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 Yax;[129] hence, the terminal date as determined by calculation will be 4 Eb 10 Yax. [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS] {167} Turning again to the text (pl. 6, _D_), 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 usually 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-u_) 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 glyph in B6. Compare the left half of B6 with the forms given in figure 65. The coefficient 9 or 10 is expressed by a considerably effaced head numeral. Immediately following the month-sign "indicator" is the month sign itself in A7. The student will have little difficulty 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 in _q_ and _r_, just cited. This difference, however, is immaterial. The month coefficient is quite clearly 10,[130] 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 in 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 will have its period glyphs expressed by head variants. In A, plate 7, is figured the Initial Series from Stela B at Copan.[131] The introducing glyph appears at the head of the inscription in A1 {168} 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 assuming 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 certainty. Both heads have the same clasped hand in the same position, across the lower part of the face, which, as explained 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 comparison of this form with the head variant for katun 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 fleshless lower jaw (see p. 70). The coefficient is 0 (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, 0 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 kin 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 0 kins. The number 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 = 9 × 144,000 = 1,296,000 A3 = 15 × 7,200 = 108,000 A4 = 0 × 360 = 0 A5 = 0 × 20 = 0 A6 = 0 × 1 = 0 --------- 1,404,000 Deducting from this number 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 found to be 4 Ahau. Applying rule 3 (p. 141), the position of 4 Ahau in the year will be found to be 13 Yax. Therefore the terminal date determined by calculation will be 4 Ahau 13 Yax. {169} According to step 5 (p. 151), the day reached should follow immediately the last period glyph, which in this case was in A6; hence the day should be recorded in A7. This glyph has a coefficient 4, but the glyph 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 comparing 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 following in A8 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 hotun in the Long Count, but of a katun as well. In _B_, plate 7, is figured the Initial Series from Stela A at Copan.[132] The introducing glyph appears in A1 B1, and is followed by the Initial-series number in A2-A4. The student will 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 in A4, which are the essential elements of the head variants for the cycle, katun, tun, uinal, and kin, respectively. Compare these glyphs with figures 25, _d-f_, 27, _e-h_, 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 number as 9.14.19.8.0.[133] Reducing this by means of Table XIII to units of the 1st order, we have: A2 = 9 × 144,000 = 1,296,000 B2 = 14 × 7,200 = 100,800 A3 = 19 × 360 = 6,840 B3 = 8 × 20 = 160 A4 = 0 × 1 = 0 --------- 1,403,800 Deducting from this all the Calendar Rounds possible, 73 (see Table XVI), and applying 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 encountered in plate 6, _A_, B5 and _C_, B4b, and in plate 7, _A_, A7. Turning {170} now to the forms for the day sign Ahau in figure 16, it is seen that the form in A4 resembles the third variant _j_' or _k'_, 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 Series. Following along the glyphs next in order, we reach in A9 a glyph with a coefficient 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 Cumhu (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 probable that it is a variant of the month-glyph "indicator";[134] and consequently that the month glyph itself follows, as we have seen, in B9. In other words, the terminal date recorded, 12 Ahau 18 Cumhu, 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.[135] The introducing glyph occupies the space of four glyph-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 still be distinguished. The katun head in B3 is also unmistakable, 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 coefficient 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,[136] respectively, are effaced, their coefficients may be distinguished as 10 and 0, respectively. In such a case the student is perfectly justified in assuming that the tun and uinal signs originally stood here. In B4a the kin period glyph is expressed by its normal form and the kin coefficient by a head-variant numeral, the clasped hand of which indicates that it stands for 0 (see fig. 53, _s-w_).[137] The number here recorded is 9.12.10.0.0. [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS] {171} Reducing this to units of the 1st order by means of Table XIII, we have: A3 = 9 × 144,000 = 1,296,000 B3 = 12 × 7,200 = 86,400 A4a = 10 × 360 = 3,600 A4b = 0 × 20 = 0 B4a = 0 × 1 = 0 --------- 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 calculations 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 _k'_ 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 numeral, 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 _f_ 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[138] 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.[139] The introducing glyph stands in A1-B2 and is followed by the five period glyphs in A3-A5. The cycle is very clearly recorded in A3, the clasped hand being of a particularly realistic form. Although {172} 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 in assuming that this was the period originally recorded here. The coefficient 10 appears clearly. The uinal head in B4 is totally unfamiliar and seems to have the fleshless lower jaw properly belonging to the tun head; from its position, however, the 4th in the number, we are justified in calling this glyph the uinal sign. Its coefficient denotes that 0 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 number, we are justified once more in assuming that 0 kins were originally recorded, here. It seems at first glance that the above reading of the number 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 in B4 is a uinal head. 4. That the effaced glyph in A5 was a kin sign. The last three are really certainties, since the Maya practice in recording Initial Series demanded that the five period glyphs requisite--the cycle, katun, tun, uinal, and kin--should follow each other in this order, and in no other. Hence, although the 3d, 4th, and 5th glyphs are either irregular or effaced, they must have been the tun, uinal, and kin signs, respectively. Indeed, the only important assumption consisted in arbitrarily designating 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 choosing 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 obtain: A3 = 9 × 144,000 = 1,296,000 B3 = 6 × 7,200 = 43,200 A4 = 10 × 360 = 3,600 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,342,800 {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 remainder, the date determined by the resulting calculations will be 8 Ahau 13 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 _h'_ 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. Following along through A6, B6, A7, B7, the closing glyph of the Supplementary Series is reached in A8. The glyph itself is on the left and the coefficient, here expressed by a head variant, is on the right. The student will 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 jaw in the head numeral in both places. The following glyph, B8, is one of the clearest in the entire text. The numeral 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 follows, 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 monument presenting this inscription, Stela 9, records the next to earliest Initial Series[140] yet deciphered at Copan.[141] 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 glyph 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. {174} [Illustration: FIG. 68. Initial Series showing bar and dot numerals and head-variant period glyphs: _A_, Stela C (west side), Quirigua; _B_, Stela M, Copan.] In figure 68, _A_, is figured the Initial Series on the west side of Stela C at Quirigua.[142] The introducing glyph in A1-B2 is followed by the number in A3-A5, which the student will have no difficulty in reading except for the head-variant numeral attached to the kin sign in A5. The clasped hand in this glyph, however, suggests that 0 kins are recorded here, and a comparison of this form with figure 53, _s-w_, confirms the suggestion. The number therefore reads 9.1.0.0.0. Reducing this number by means of Table XIII to units of the 1st order, we obtain: A3 = 9 × 144,000 = 1,296,000 B3 = 1 × 7,200 = 7,200 A4 = 0 × 360 = 0 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,303,200 Deducting from this number all the Calendar Rounds 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 {175} no bar and dot coefficient. These several points indicate that the day sign is not the glyph in B5, also that the day sign is, therefore, out of its regular position. The next glyph 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 _k_ or _l_ is the form here recorded; therefore the terminal date recorded agrees with the terminal date reached by calculation, and the text reads 9.1.0.0.0 6 Ahau 13 Yaxkin.[143] In figure 68, _B_, is shown the Initial Series on Stela M at Copan.[144] The introducing glyph appears in A1 and the Initial-series number in B1a-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 B1a, A2a, and A2b, respectively, being expressed by the latter, and the katun and kin in B1b 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): B1a = 9 × 144,000 = 1,296,000 B1b = 16 × 7,200 = 115,200 A2a = 5 × 360 = 1,800 A2b = 0 × 20 = 0 B2a = 0 × 1 = 0 --------- 1,413,000 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 terminal date reached by the resulting calculations will be 8 Ahau 8 Zotz. Turning to our text, the student will have no difficulty in recognizing in B2b the day 8 Ahau. The month glyph in this inscription irregularly follows immediately {176} the day glyph. Compare the form in A3a with the month signs in 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 illustrating the use of bar and dot numerals with both normal-form and head-variant period glyphs, with which the student should be perfectly familiar by this time. In plate 9, _A_, is figured a photograph of the Initial Series on the front of Stela 11 at Yaxchilan.[145] The introducing glyph appears in A1 B1; 9 cycles in A2; 16 katuns in B2, 1 tun in A3, 0 uinals in B3, and 0 kins in B4. The student will note the clasped hand in the cycle head, the oval in the top of the katun 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 units of the first order by means of Table XIII, we have: A2 = 9 × 144,000 = 1,296,000 B2 = 16 × 7,200 = 115,200 A3 = 1 × 360 = 360 B3 = 0 × 20 = 0 A4 = 0 × 1 = 0 --------- 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 terminal 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 C1 D1, 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. Compare D3 with figure 19, _g-h_. The month coefficient is 8. The terminal 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 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 unknown. [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS] {177} In plate 9, _B_, is figured the Initial Series on an altar in front of Structure 44 at Yaxchilan.[146] The introducing glyph appears in A1 B1 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 numerals. 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 resulting terminal days is the one actually recorded in A4. Reducing the number 9.12.8.14.0 to units of the first order by means of Table XIII, we have: A2 = 9 × 144,000 = 1,296,000 B2 = 12 × 7,200 = 86,400 A3= 8 × 360 = 2,880 B3 = 14 × 20 = 280 A4= 0 × 1 = 0 --------- 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 following 9.12.8.14.0 11 Ahau 3 Pop. Therefore our four possible terminal 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 immediately 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 0 or 1. Comparing the glyph in B4 with the day signs in figure 16, the form here recorded will be found to be identical 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 {178} we have just seen appears in B4. This further proves that the kin coefficient in A4 is 1. The final confirmation of this identification will come from the month glyph, 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, C1 D1, and C2, we, reach in D2a the closing glyph of the Supplementary Series, here showing the coefficient 9. Compare 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.[147] The introducing glyph, though somewhat effaced, may still be recognized in A1. 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 presented 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 assumed 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 identification based on position. The student will have no difficulty 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: B1 = 9 × 144,000 = 1,296,000 A2 = 2 × 7,200 = 14,400 B2 = 13 × 360 = 4,680 A3 = 0 × 20 = 0 B3 = 0 × 1 = 0 --------- 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. Compare figure 16, _h', i'_. The coefficient of A4 is very clearly 4 dots, that is, 4, and consequently this glyph agrees with the day as determined by calculation, 4 Ahau. Passing over B4, A5, B5, and A6, we reach in B6 the closing glyph 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 figure 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. [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS--STELA 3, TIKAL] [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS--STELA A (EAST SIDE), QUIRIGUA] {179} This Initial Series is extremely important, because it records the earliest contemporaneous[148] date yet found on a monument[149] in the Maya territory. In plate 11 is figured the Initial Series from the east side of Stela A at Quirigua.[150] The introducing glyph appears in A1-B2 and the Initial-series number in A3-A5. The student will have little difficulty 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 curl 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 = 9 × 144,000 = 1,296,000 B3 = 17 × 7,200 = 122,400 A4 = 5 × 360 = 1,800 B4 = 0 × 20 = 0 A5 = 0 × 0 = 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, {180} 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. Comparing this with the head-variant numerals in figures 51-53, the student will have little difficulty in identifying it as the head for 6 (see fig. 51, _t-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 closing glyph of the Supplementary Series, here showing the head-variant coefficient 10 (see fig. 52, _m-r_). In B9, the next glyph, 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 numerals with the exception of an incidental head-variant number here and there. By this time the student should have become thoroughly familiar with the use of bar and dot numerals in the inscriptions and should be ready for the presentation of texts showing head-variant numerals, a more difficult 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.[151] The introducing glyph appears in A1 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, katun, 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 part_ (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.[152] The katun coefficient in A4 resembles closely the cycle coefficient except that its forehead ornament is composed of but a single part, a large curl. 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 A4 B4, 18 (8 + 10) katuns. The tun coefficient in A5 has for its determining characteristic the tun headdress, which, as explained on page 99, is the essential element of the head for 5 (see fig. 51, _n-s_). Therefore A5 represents 5, and A5 B5, 5 tuns. The uinal coefficient in A6 has for its essential elements the large bulging eye, square irid, and snaglike front tooth. As stated on page 98, these characterize the head for 4, examples of which are given in figure 51, _j-m_. Consequently, A6 B6 records 4 uinals. The kin coefficient in A7 is quite clearly 0. The student will readily recognize the clasped hand, which is the determining characteristic of the 0 head (see p. 101 and fig. 53, _s-w_). The number recorded in A3-B7 is, therefore, 1.18.5.4.0. Reducing this number to units of the 1st order by means of Table XIII, we obtain: [Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF HEAD-VARIANT NUMERALS AND PERIOD GLYPHS] {181} A3B3 = 1 × 144,000 = 144,000 A4B4 = 18 × 7,200 = 129,600 A5B5 = 5 × 360 = 1,800 A6B6 = 4 × 20 = 80 A7B7 = 0 × 1 = 0 ------- 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 B8. Compare the head in A8 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, _h', 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 therefore reads 1.18.5.4.0 1 Ahau 13 Mac. In plate 12, _B_, is figured the Initial Series on the tablet from the Temple of the Sun at Palenque.[153] The introducing glyph appears in A1-B2 and is followed by the Initial-series 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 (pl. 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 headdress, or fillet, which distinguishes the head for 3, as explained on page 98 (see fig. 51 _h, i_). We have then in A6 B6 record of 3 {182} uinals. The kin coefficient 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-v_. The number recorded in 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 × 144,000 = 144,000 A4B4 = 18 × 7,200 = 129,600 A5B5 = 5 × 360 = 1,800 A6B6 = 3 × 20 = 60 A7B7 = 6 × 1 = 6 ------- 275,466 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, to the remainder, the terminal date reached will be 13 Cimi 19 Ceh. If this inscription is regular, the day part of the above date should follow in A8 B8, the former expressing the coefficient 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 occurs 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 glyph in A9 should 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 (pl. 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 reasonable, and, the writer believes, will be generally accepted by Maya students. {183} [Illustration: 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.] In figure 69, _A_, is shown the Initial Series inscribed on the rises and treads of the stairway leading to House C in the Palace at Palenque.[154] The introducing glyph is recorded in A1, and the Initial-series number follows in B1-B3. The student will readily recognize the period glyphs in B1b, A2b, B2b, A3b, and B3b. The head expressing the cycle coefficient in B1a has for its essential element the dots centering around the corner of the mouth. As explained on page 100, this characterizes the head for 9 (see fig. 52, _g-l_, where variants for the 9 head are figured). In B1, therefore, we have recorded 9 cycles, the number almost always found 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 18 in the two preceding examples, pl. 12, _A_, A4, and pl. 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 B1a; that is, 9, having the same dotting of the face near the corner of the mouth. The uinal coefficient in A3a is 13. Compare this head numeral with A8, plate 12, _B_, which also denotes 13, and also with figure 52, _x-b'_. The essential elements (see p. 101) {184} 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 effaced, let us call it 0 for the present[155] and proceed to reduce our number 9.8.9.13.0 to units of the first order by means of Table XIII: B1 = 9 × 144,000 = 1,296,000 A2 = 8 × 7,200 = 57,600 B2 = 9 × 360 = 3,240 A3 = 13 × 20 = 260 B3 = 0 × 1 = 0 --------- 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 kin coefficients, 0 to 19, has a corresponding day to which it will always lead, that is, Ahau 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 Chicchan 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 characteristic, namely, the forehead ornament composed of one part. A comparison of this ornament with the ornament on the head for 8 in A2a will show that the two forms are identical. The bifurcate ornament surmounting the head in A4a is a part of the headdress, and as such should not be confused with the forehead ornament. The failure to recognize this point might cause the student to identify {185} A4a as the head for 1, that is, having a forehead ornament composed of more than one part, instead of the head for 8. The month glyph, which follows in B4b, is unfortunately effaced, though its coefficient in B4a is clearly the head for 13. Compare B4a with the uinal coefficient 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 calculation, 8 Ahau 13 Pop. In all probability the effaced sign in B4b originally 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.[156] The introducing glyph appears in A1-B2 and is followed by the Initial-series number in A3-B4. The student will 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 units of the first order by means of Table XIII, we obtain: A3 = 9 × 144,000 = 1,296,000 B3 = 9 × 7,200 = 64,800 A4 = 10 × 360 = 3,600 B4a = 0 × 20 = 0 B4b = 0 × 1 = 0 --------- 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).[157] Passing over A5b, B5, and A6 we reach in B6a the closing glyph of the Supplementary Series, and in the following glyph, B6b, the month part of this terminal date. The coefficient is 13, and comparing 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. {186} [Illustration: FIG. 70. Initial Series, showing head-variant numerals and period glyphs, from Zoömorph G at Quirigua.] In figure 70 is illustrated the Initial Series from Zoömorph G at Quirigua.[158] The introducing glyph appears in A1-B2 and is followed in C1-H1 by the Initial-series number. Glyphs C1 D1 record 9 cycles. The dots on the head for 9 in C1 are partially effaced. In C2 is the katun coefficient and in D2 the katun sign. The determining characteristic of the head for 7 appears in C2, namely, the scroll passing under the eye and projecting upward and in front of the forehead. See page 100 and figure 51, _w_. It would seem, then, at first sight that 7 katuns were recorded in C2 D2. That this was not the case, however, a closer examination 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 E1 F1, 15 tuns are recorded. The tun headdress in E1 gives the value 5 to the head there depicted (see fig. 51, _n-s_) and the fleshless lower jaw adds 10, making the value of E1 15. Compare figure 53, _b-e_, where examples of the head for 15 are given. Glyphs E2 and F2 represent 0 uinals and G1 H1 0 kins; note the clasped hand in E2 and G1, which denotes the 0 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: C1 D1 = 9 × 144,000 = 1,296,000 C2 D2 = 17 × 7,200 = 122,400 E1 F1 = 15 × 360 = 5,400 E2 F2 = 0 × 20 = 0 G1 H1 = 0 × 1 = 0 --------- 1,423,800 Deducting from this number all the Calendar Rounds possible, 75 (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 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'-k'_. The presence of the tun headdress in G2 indicates that the coefficient here recorded must have been either 5 or 15, depending on whether or not the lower part of the head originally had a fleshless 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 coefficients as stated in Chapter III, can never rise above 13. Consequently the number 15 can not be recorded in G2, and this form must stand for the number 5. [Illustration: OLDEST INITIAL SERIES AT COPAN--STELA 15] {187} Passing over I1 J1, I2 J2, K1 Ll, K2 L2, we reach in M1 the closing glyph of the Supplementary Series, here shown with a coefficient of 10, the head having a fleshless lower jaw. The month sign follows in N1. The coefficient is 3 and by comparing the sign itself with the month glyphs in figure 19, it will be apparent that the sign for Muan in _a'_ or _b'_ is recorded here. The Initial Series of this monument 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[159] (see pl. 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 all 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 tun sign. The glyphs A6, B6 clearly record 0 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[160] (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.?. Calling 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 × 144,000 = 1,296,000 A4 B4 = 4 × 7,200 = 28,800 A5 B5 = 10 × 360 = 3,600 A6 B6 = 0 × 20 = 0 0 × 1 = 0 --------- 1,328,400 Deducting from this number all the Calendar Rounds possible, 69 {188} (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 missing kin coefficient was zero. This is a fairly safe assumption, since when the tun coefficient is either 0, 5, 10, or 15 (as here) and the uinal coefficient is 0 (as here), the kin coefficient is almost invariably 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 inclined 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 earliest 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.[161] 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 will 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.[162] The introducing glyph is recorded in A1. 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.[163] [Illustration: INITIAL SERIES ON STELA D, COPAN, SHOWING FULL-FIGURE NUMERAL GLYPHS AND PERIOD GLYPHS] {189} The Initial-series number itself appears in B1-B3. The cycle sign is a grotesque bird, designated by Mr. Bowditch a parrot, an identification 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 full-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 bound to the back of an anthropomorphic figure, which we have every reason to suppose records the cycle coefficient. 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 B1 as recording 9 cycles. The katun and its coefficient 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 coefficient, shows the essential element of the head for 5, the tun headdress. It has also the fleshless lower jaw of the head for 10. The combination of these two elements in one head, as we have seen, indicates the numeral 15, and A2 therefore records 15 katuns. Compare the head of this anthropomorphic figure with figure 53, _b-e_. The tun and its coefficient are represented in B2. The former again appears as a grotesque bird, though in this case of undetermined nature. Its head, however, very clearly shows the essential element of the head-variant tun sign, the fleshless lower jaw. Compare this form with figure 29, _e-g_, and the other head-variant tun signs already illustrated. The head of the anthropomorphic figure, which denotes the tun coefficient, is just like the head of the anthropomorphic figure in the preceding glyph (A2), except that in B2 the head has no fleshless lower jaw. Since the head in A2 with the fleshless 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 {190} elsewhere, 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 0 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 number, is better established from its position in the number 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 0 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: B1 = 9 × 144,000 = 1,296,000 A2 = 15 × 7,200 = 108,000 B2 = 5 × 360 = 1,800 A3 = 0 × 20 = 0 B3 = 0 × 1 = 0 --------- 1,405,800 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 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, crouching 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 anthropomorphic figure, the day coefficient, the head of which is the skull, denoting the numeral 10. Note the fleshless lower jaw of this head and compare it with the same element in 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 in 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, p_. [Illustration: INITIAL SERIES ON STELA J, COPAN] {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 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 (pl. 7, _A_). According to the writer's opinion, therefore, Stelæ B and D marked two successive hotuns at this city. We come now to the consideration of Initial Series which are either unusual 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_,[164] is figured because of the very unusual order followed by its glyphs. The sequence in which these succeed each other is given in _B_ of that plate. The scheme followed seems to have been that of a mat pattern. The introducing glyph appears in position 0 (pl. 15, _B_), and the student will readily recognize it in the same position in _A_ of the same plate. The Initial Series number follows in 1, 2, 3, 4, and 5 (pl. 15, _B_). Referring 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 0 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 0 kins. This number 9.13.10.0.0 reduces by means of Table XIII to units of the first order, as follows: 1 = 9 × 144,000 = 1,296,000 2 = 13 × 7,200 = 93,600 3 = 10 × 360 = 3,600 4 = 0 × 20 = 0 5 = 0 × 1 = 0 --------- 1,393,200 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, respectively) to the remainder, the terminal date reached will be 7 Ahau 3 Cumhu. Referring 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 {192} glyph 6 is effaced, and consequently the day is missing. Passing over 7, 8, 9, 10, and 11, in _A_ 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.[165] This glyph is very clearly the form for the month Cumhu (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 Cumhu, 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, having been inserted solely to balance this glyph. If it had been omitted, the month sign would have had to be greatly elongated and its proportions 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 Cumhu. 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.[166] The drawing of this inscription appears in a of this figure and the key to the sequence of the glyphs in b. The introducing glyph occupies position 1 and is followed by the Initial Series in 2-6. The student will have little difficulty in identifying 2, 3, and 4 as 9 cycles, 16 katuns, and 0 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 extent on other inscriptions here at Quirigua. For example, every monument at Quirigua which presents an Initial Series marks the close of some particular hotun in the Long Count; consequently, all the Initial Series at Quirigua which record these Katun endings have 0 for their uinal and kin coefficients.[167] This {193} absolute 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 0 uinals and 0 kins were originally recorded in glyphs 5 and 6, respectively. Furthermore, an inspection of the coefficients of these two glyphs in figure 71, _a_, shows that both of them are of the same general size and shape as the tun coefficient in 4, which, as we have seen, is very clearly 0. It is more than probable that the uinal and kin coefficients in this text were originally 0, like the tun coefficient, and that through weathering they have been eroded down to their present shape. In figure 72, _a_, is shown the tun coefficient and beside it in _b_, the uinal or kin coefficient. The dotted parts in _b_ are the lines which have disappeared through erosion, if this coefficient was originally 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. [Illustration: FIG. 71. Initial Series on Stela H, Quirigua: _a_, Mat pattern of glyph sequence; _b_, key to sequence of glyphs in a.] Reducing this to units of the first order by means of Table XIII, we have: 5 = 9 × 144,000 = 1,296,000 6 = 16 × 7,200 = 115,200 7 = 0 × 360 = 0 8 = 0 × 20 = 0 9 = 0 × 1 = 0 --------- 1,411,200 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 terminal date 2 Ahau 13 Tzec will be reached. [Illustration: FIG. 72. The tun, uinal, and kin coefficients on Stela H, Quirigua: _a_, Tun coefficient; _b_, suggested restoration of the uinal and kin coefficients like the tun coefficient.] In spite of some weathering, the day part of the terminal date appears in glyph 7 immediately after the kin glyph in 6. The coefficient, 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 figure 16, _h', i'_. The agreement of {194} the day recorded with the day determined by calculations based on the assumption that the kin and uinal coefficients are both 0, of itself tends to establish the accuracy of these assumptions. 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 representing 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 main element the remaining two-thirds. Compare this form with the sign for Tzec in figure 19, _g, h_. Although this text is too much weathered to permit absolute certainty with reference to the reading of this Initial Series, the writer nevertheless believes 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 earliest hotun-marker at Quirigua.[168] The student will have noticed from the foregoing texts, and it has also been stated several times, that the cycle coefficient is almost invariably 9. Indeed, the only two exceptions to this rule in the inscriptions already figured are the Initial Series from the Temples of the Foliated Cross and the Sun at Palenque (pl. 12, _A_ and _B_, respectively), in which the cycle coefficient 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 fall 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 mythological events, even though the dates which they record fall in a cycle earlier than Cycle 9. It was stated, further, in the same place that these two Initial Series were not found inscribed on large monuments but on smaller antiquities, one of them being a small nephrite figure 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 contemporaneous events in the historic period of the Maya civilization. {195} [Illustration: FIG. 73. The Initial Series on the Tuxtla Statuette, the oldest Initial Series known (in the early part of Cycle 8).] [Illustration: FIG. 74. The introducing glyph (?) of the Initial Series on the Tuxtla Statuette.] 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; in other words, both record dates which fell in the cycle immediately preceding that of the historic period, or Cycle 9. Finally, at least one of these two Initial 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 round numbers, that it may be considered as belonging to the historic period, and hence constitutes the earliest historical inscription from the Maya territory. {196} The Initial Series on the first of these minor antiquities, the Tuxtla Statuette, is shown in figure 73.[169] The student will note at the outset one very important difference between this Initial Series--if indeed 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), and plates 31 and 32. This at once distinguishes the Initial Series on the Tuxtla Statuette from every other Initial Series in the inscriptions now known. The number is preceded by a character which bears some general resemblance to the usual Initial-series introducing glyph. See figure 74. The most striking point of similarity is the trinal superfix, which is present in both signs. The student will have little difficulty in 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 × 144,000 = 1,152,000 6 × 7,200 = 43,200 2 × 360 = 720 4 × 20 = 80 17 × 1 = 17 --------- 1,196,017 Solving this Initial-series number for its terminal date, it will be found to be 8 Caban 0 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, unfortunately, effaced. The month coefficient 0 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 0 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.[170] [Illustration: FIG. 75. Drawings of the Initial Series: _A_, On the Leyden Plate. This records a Cycle-8 date and next to the Tuxtla Statuette Initial Series, 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 of the latest Initial Series known.] The other Initial Series showing a cycle coefficient 8 is on the Leyden Plate, a drawing of which is reproduced in figure 75, _A._ This Initial Series is far more satisfactory than the one just described, and {197} its authenticity, generally speaking, is unquestioned. The student will easily identify A1-B2 as an Initial-series introducing glyph, even though the pair of comblike appendages flanking the central element and the tun tripod are both wanting. Compare this form with figure 24. The Initial-series number, expressed by normal-form numerals and head-variant period glyphs, follows in A3-A7. The former are all very clear, and the number may be read from them in spite of certain irregularities in the corresponding period glyphs. For example, the katun head in A4 has the clasped hand, which is the distinguishing characteristic of the cycle head, and as such should have appeared in the head in A3. Neither the tun head in A5 nor the kin head in A7 shows an essential element heretofore found distinguishing these particular period glyphs. Indeed, the only period glyph of the five showing the usual essential element is the uinal head in A6, where the large mouth curl appears very clearly. However, the number recorded here may be read as 8.14.3.1.12 from the sequence of the coefficients--that is, their position 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 position after the introducing glyph. {198} Reducing this number to units of the first order by means of Table XIII, we have: A3 = 8 × 144,000 = 1,152,000 A4 = 14 × 7,200 = 100,800 A5 = 3 × 360 = 1,080 A6 = 1 × 20 = 20 A7 = 12 × 1 = 12 --------- 1,253,912 Deducting from this number all the Calendar Rounds possible, 66 (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 1 Eb 0 Yaxkin. The day part of this date is very clearly recorded in A8, the coefficient 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 unmistakably records the month Yaxkin. (See fig. 19, _k, l_.) Note the _yax_ and _kin_ 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 coefficient 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 0 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 reflect the crudities and uncertainties of its time. Indeed, it is quite possible that at the very early period from which it probably dates (8.14.3.1.12 1 Eb 0 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 earliest contemporaneous date from the monuments, 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. {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 unusual. 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 will have little difficulty in deciphering all of the coefficients except that belonging to the kin in A5, which is a head-variant numeral, and the whole number 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 still indeterminate. First substituting 0 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. Consequently, 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 will 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_. {200} [Illustration: FIG. 76. The Cycle-10 Initial Series from Quen Santo (from drawings): _A_, Stela 1; _B_, Stela 2. There is less than a year's difference in time between the Chichen Itza Initial Series and the Initial Series in _B_.] Two other Initial Series whose cycle coefficient is 10 yet remain to be considered, namely, Stelæ 1 and 2 at Quen Santo.[171] The first of these is shown in figure 76, A, but unfortunately 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 number 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 unmistakable katun sign in B3 we are perfectly justified in assuming that 5 tuns are recorded here. Both the coefficient and the glyph in B4 are unfamiliar. However, as the former must be one of the numerals 0 to 19, inclusive, since it is 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 uinal or the head variant; but since it occupies the 4th position after the introducing glyph, B4, we are justified in assuming that 0 uinals are recorded here. Beyond this we can not proceed with certainty, though the values for the missing parts 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 hotun 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 believes this monument marks. For {201} this reason it seems probable that the glyph which stood in A5 recorded 0 kins. Reducing this number to units of the first order by means of Table XIII, we obtain: A3 = 10 × 144,000 = 1,440,000 B3 = 2 × 7,200 = 14,400 A4 = 5 × 360 = 1,800 B4 = 0 × 20 = 0 A5[172] = 0 × 1 = 0 --------- 1,456,200 Deducting from this number all the Calendar Rounds 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 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 workmanship on this monument is somewhat better than on Stela 1 and, moreover, 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 uneffaced 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 corner of the glyph-block as the uneffaced dot does to the lower left-hand corner. Moreover, if 3 had been recorded here the uneffaced 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 assuming 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 0 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 0 kins are recorded here. The whole number expressed in A3-A5 is {202} therefore 10.2.10.0.0. Reducing this to units of the first order by means of Table XIII, we have: A3 = 10 × 144,000 = 1,440,000 B3 = 2 × 7,200 = 14,400 A4 = 10 × 360 = 3,600 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,458,000 Deducting from this number all the Calendar Rounds 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 coefficient 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 _p_, _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 Ahau (see Table VII); since the kin coefficient in A5 is 0, the effaced day sign must have been Ahau. 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 hotun 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.[173] 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 {203} were colonizing Yucatan the southern branch was laying the foundation 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 approximately 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 all later than those recorded on the Chichen Itza lintel and the Quen Santo stelæ. 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,[174] 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.[175] The introducing glyph appears in A1-B2, and is followed by the Initial-series number in A3-A5. The student will easily read this as 13.0.0.0.0. Reducing this number to units of the first order by means of Table XIII, we have: A3 = 13 × 144,000 = 1,872,000 B3 = 0 × 7,200 = 0 A4 = 0 × 360 = 0 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,872,000 Deducting from this number all the Calendar Rounds possible, 98[176] (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, under 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 Ahau 8 Cumhu, and not 4 Ahau 3 Kankin. The month part in A6 is unusually clear, and there can be no doubt {204} that it is 8 Cumhu. Compare A6 with figure 19, _g', h'_. If we have made no mistake in 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. Further, since the count in Initial Series has never been known to be backward,[177] we are forced to accept one of two conclusions: Either the starting point is not 4 Ahau 8 Cumhu, or there is some error in the original text. However, there is one way by means of which we can ascertain 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 operation and count the given number, 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. [Illustration: FIG. 77. Initial Series which proceed from a date prior to 4 Ahau 8 Cumhu, the starting point of Maya chronology: _A_, Stela C (east side) at Quirigua; _B_, Temple of the Cross at Palenque.] Deducting from this number, as before, all the Calendar Rounds possible, 98 (see p. 203, footnote 3), and applying rules 1, 2, and 3 (pp. 139, 140, 141, respectively) to the remainder, remembering that in each operation the direction of the count is _backward_, 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 reservation. The most we can say at present is that if the number recorded 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. {205} Let us next examine the Initial Series on the tablet from the Temple of the Cross at Palenque, which is shown in figure 77, _B_.[178] The introducing glyph appears in A1-B2, and is followed by the Initial-series number in 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 fleshless 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 value 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 fleshless lower jaw of the 10 head, the combination of the two giving the head for 13 (fig. 52, _w_).[179] The head for 4 and the hand zero sign appear as the coefficient of the uinal and kin signs in A6 and A7, respectively. The number will read, therefore, ?.19.13.4.0. Let us examine the cycle coefficient in A3 again. The natural assumption, of course, 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 fleshless 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,[180] 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 units 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 will 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 {206} between the day coefficient and the month coefficient is that the latter has a fleshless lower jaw, increasing its value by 10. Moreover, comparison of the month sign in B9 with _g_ and _h_, figure 19, shows unmistakably that the month here recorded is Tzec. But the terminal 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 Cumhu, or there is some error in the original text.[181] Assuming that the ancient scribes made no mistakes in this inscription, let us count backward from the recorded terminal date, 8 Ahau 18 Tzec, each of the three numbers 2.19.13.4.0, 11.19.13.4.0, and 12.19.13.4.0, one of which, we have seen, is recorded in 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 number 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 almost identical with the other two head-variant numerals, whose values are known to be 12. These three head numerals are shown side by side in figure 52, _t-v, 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 numeral 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 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. [Illustration: INITIAL SERIES AND SECONDARY SERIES ON LINTEL 21, YAXCHILAN] {207} 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 discussion 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 Count, may be worked out even though they are not recorded in the text. The first example presented will be the inscription on Lintel 21 at Yaxchilan, which is figured in plate 16.[182] As usual, when an Initial Series is recorded, the introducing glyph opens the text and this sign appears in A1, being followed by the Initial-series number itself in B1-B3. This the student will readily decipher as 9.0.19.2.4, recording 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[183] and deducting all the Calendar Rounds possible, 68 (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 Kan 2 Yax. This date the student will find recorded in A4 and A7a, glyph B6b being the month-sign "indicator," or the closing glyph of the {208} Supplementary Series, here shown with the coefficient 9. Compare the day sign in A4a with the sign for Kan in figure 16, _f_, and the month sign in A7a with the sign for Yax in figure 19, _q, r_. We have then recorded in A1-A4[184], 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 lintel was inscribed, but a closer examination reveals a different condition. Following along through the glyphs of this text, there is reached in C3-C4 still another number in which the normal forms of the katun, tun, and uinal signs clearly appear in connection with bar and dot coefficients. The question at once arises, Has the number recorded here anything to do with the Initial Series, which precedes it at the beginning of this text? Let us first examine this number 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 possibility that it might be an Initial Series. 2. There is no kin period glyph, the uinal sign 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 heretofore. It has been explained (see p. 129) that in 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 uinals, 1 tun, 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 by C3-C4, 15.1.16.5. Reducing this number to units of the first order by means of Table XIII, we have: C4 = 15 × 7,200 = 108,000 D3 = 1 × 360 = 360 C3 = 16 × 20 = 320 C3 = 5 × 1 = 5 ------- 108,685 Since all the Calendar Rounds which this number contains, 5 (see {209} Table XVI) may be deducted from it without 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 preceding 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 units 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 count is forward, by applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), to 13,785, the new terminal date reached will 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 adding 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 Secondary 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 7 Muluc 17 Tzec 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 will 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?[185] 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 unknown meaning in the text, is totally unknown. It is possible to gather from other sources, however, some little data concerning their significance. In the first place, 9.16.1.0.9 7 Muluc 17 Tzec is almost surely the "contemporaneous date" of this lintel, the date indicating the time at or near which it was formally dedicated or put into use. This point is established almost to a certainty by the fact that all the other dates known at Yaxchilan are very much nearer to 9.16.1.0.9 7 Muluc 17 Tzec in point {210} of time than to 9.0.19.2.4 2 Kan 2 Yax, the Initial-series date recorded on this lintel. Indeed, while they range from 9 days[186] 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 Muluc 17 Tzec indicates the "contemporaneous time" of this lintel and that 9.0.19.2.4 2 Kan 2 Yax referred to some earlier event which took place perhaps even before the founding of the city. And finally, since this inscription is on a lintel, we may perhaps go a step further and hazard the conclusion that 9.16.1.0.9 7 Muluc 17 Tzec records the date of the erection of the structure of which this lintel is a part. We may draw from this inscription a conclusion which will be found to hold good in almost all 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 Muluc 17 Tzec, the Initial-series value of which was found to be 9.16.1.0.9, is in all probability its contemporaneous 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.[187] The order of the glyphs in this text is somewhat irregular. It will be noted that there is an uneven 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 A1 and is followed by the Initial-series number 9.12.2.0.16 in A2-A6. The student should be perfectly familiar by this time with the processes involved in counting this number from its starting point, and should have no difficulty in determing by calculation the terminal date recorded in A7, C2, namely, 5 Cib 14 Yaxkin.[188] Compare A7 with the sign for Cib in figure 16, _z_, and C2 with the sign for Yaxkin in figure 19, _k, l_. The Initial Series recorded in A1-A7, C2 is 9.12.2.0.16 5 Cib 14 Yaxkin. [Illustration: INITIAL SERIES AND SECONDARY SERIES ON STELA 1, PIEDRAS NEGRAS] {211} 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 preceding text, these points are both characteristic of Secondary-series numbers, and we may conclude therefore that D2 E2 records a number of this kind. Finally, since the kin coefficient 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 = 12 × 360 = 4,320 D2 = 9 × 20 = 180 D2 = 15 × 1 = 15 ----- 4,515 Remembering 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 Chuen 9 Kankin, which is recorded in F1 G1, though unfortunately 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 F1 G1. Passing over F2 G2, the meanings of which are unknown, we reach in F3 an inverted Ahau with the coefficient 5 above it. As explained on page 72, this probably signifies 5 kins, the inversion of the glyph changing its meaning from that of a particular 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 number consisting of 5 kins, which is to be counted 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} 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 difficulty 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 0 units of some period are involved is to record the period with a coefficient 0. However, 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 = 1 × 7,200 = 7,200 ([189]) 0 × 360 = 0 G6 = 2 × 20 = 40 G6 = 5 × 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 terminal 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, b_, 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 preceding it, the Initial Series of 5 Imix 19 Zac may be determined in the same way. 9.12. 14. 10.16 1 Cib 14 Kankin 1. 0.[189] 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 A1-A7, C2 5 Cib 14 Yaxkin 12. 9.15 D2 E2 9.12. 14. 10.11 F1 G1 9 Chuen 9 Kankin 5 F3 9.12. 14. 10.16 G3 G4 1 Cib 14 Kankin 1. 0.[189] 2. 5 G6 G7 9.13. 14. 13. 1 G8 G9 5 Imix 19 Zac [Illustration: INITIAL SERIES (_A_) AND SECONDARY SERIES (_B_) ON STELA K, QUIRIGUA] {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.[190] 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 number counted. This regularity, however, is far from universal in Secondary-series texts, and the following examples comprise some of the more common departures from the usual practice. In plate 18 is figured the Initial Series from Stela K at Quirigua.[191] The text opens on the north side of this monument (see pl. 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 = 10 × 20 = 200 A6 = 10 × 1 = 10 --- 210 The first assumption 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, respectively) the terminal date reached will 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 unmistakably 18 Kayab (see fig. 19, _d'-f'_). Here then instead of finding the date determined by calculation, 5 Oc 8 Uo, the date recorded is 1 Oc 18 Kayab, and consequently there is some departure from the practices 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 number. If the count is forward, we have just proved that this can not be the case; so let us next count the {214} number backward and see whether we can reach the date recorded in B6b-A7a (1 Oc 18 Kayab) in this way. Counting 210 _backward_ from 3 Ahau 3 Yax, according to rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), 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 Series, 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. 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 monument in a very unusual manner (see pl. 18, _B_). In B3a appears the month-sign indicator, here recorded as a head variant with a coefficient 10, and following immediately in B3b a Secondary-series number composed of 0 uinals and 0 kins, or, in other words, nothing. It is obvious that in counting this number 0.0, or nothing, either backward or forward from the date next preceding 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 count 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,[192] and this whole text so far as deciphered will read: 9.18.15. 0. 0 3 Ahau 3 Yax 10.10 backward 9.18.14. 7.10 1 Oc 18 Kayab 0. 0 forward from Initial Series 9.18.15. 0. 0 3 Ahau 3 Yax The reason for recording a Secondary-series number equal to zero, the writer believes, 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 monument 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 hotun-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 pl. 6, _C_). Mr. Bowditch (1910: p. 208) has advanced a very plausible explanation to account for the presence of the date 9.18.14.7.10 1 Oc 18 Kayab {215} on this monument. He shows that at the time when Stela K was erected, namely, 9.18.15.0.0 3 Ahau 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,[193] in 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 calendar 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 Katun 18 of Cycle 9 had been completed. Mr. Bowditch suggests the following free interpretation of this passage: "The sun has just set at its northern point[194] and we are counting the day 3 Yax--210 days from 18 Kayab--which is the true date in the calendar according to our traditions 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. [Illustration: FIG. 78. The Initial Series on Stela J, Quirigua.] In figures 78 and 79 are illustrated the Initial Series and Secondary Series from Stela J at Quirigua.[195] 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 number 9.16.5.0.0 follows in A4-B8. This leads to the terminal date 8 Ahau 8 Zotz, which is recorded in A9, B9, B13, the glyph in A13 being the month-sign indicator here shown with the coefficient 9. Compare B9 with the second variant for Ahau in figure 16 _h', i'_, and B13 with the sign for Zotz in figure 19, _e, f_. The {216} Initial-series part of this text therefore in A1-B9, B13, 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. [Illustration: FIG. 79. The Secondary Series on Stela J, Quirigua.] The first 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 0 katuns, which we may write 0.11.13.3. This number presents one feature, which, so far as the writer knows, is unique in the whole range of Maya texts. The highest order of units actually involved in this number is the tun, but for some unknown reason the ancient scribe saw fit to add the katun sign also, B2, which, however, he proceeded to nullify at once by attaching to it the coefficient 0. For in so far as the numerical value is concerned, 11.13.3 and 0.11.13.3 are equal. The next peculiarity is that the date which follows this number in B3-A4 is not its terminal date, as we have every reason to expect, but, on the contrary, its starting point. In other words, in this Secondary Series the starting point follows instead of precedes the number counted from it. This date is very clearly 12 Caban 5 Kayab; compare B3 with the sign for Caban in figure 16, _a', b'_, 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 recorded 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 our calculations as such. Reducing 0.11.13.3 to units of the first order, we have: B2 = 0 × 7,200 = 0 A2 = 11 × 360 = 3,960 B1 = 13 × 20 = 260 B1 = 3 × 1 = 3 ----- 4,223 {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. 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, h_--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 corresponding 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 = 18 × 360 = 6,480 B2 = 3 × 20 = 60 B2 = 14 × 1 = 14 ----- 6,554 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. 0 8 Ahau 8 Zotz But this was the Initial Series recorded on the reverse of this monument, consequently the Secondary-series dates, both of which have {218} preceded the Initial-series date in point of time, bring this count up to the contemporaneous time of this monument, 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][196] [1.14. 6][197] 9.15. 6.14. 6 6 Cimi 4 Tzec Figure 79, _B_, B2-A3 18. 3.14 B1-A2 9.16. 5. 0. 0 8 Ahau 8 Zotz Figure 78, A1-B9, B13 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 Secondary Series which the student will do well to bear in mind: (1) The starting points of Secondary-series numbers do not always precede the numbers counted 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, _A_, is figured the Initial Series from the west side of Stela F at Quirigua.[198] The introducing glyph appears in A1-B2 and is followed by the Initial-series number 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', b'_, and 19, _d'-f'_, respectively. The Initial Series therefore reads 9.14.13.4.17 12 Caban 5 Kayab.[199] [Illustration: INITIAL SERIES (_A_) AND SECONDARY SERIES (_B_) ON STELA F (WEST SIDE), QUIRIGUA] {219} Passing over B6-A10, the meanings of which are unknown, we reach in B10 the Secondary-series number 13.9.9. Reducing this to units of the first order, we have: B10b = 13 × 360 = 4,680 B10a = 9 × 20 = 180 B10a = 9 × 1 = 9 ----- 4,869 Assuming that our 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_, B11b-A12a. Compare B11b with the sign for Cimi in figure 16, _h, i_, and A12a 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[200] In A15 is recorded the date 3 Ahau 3 Mol (compare A15a with fig. 16, _k', i'_, and A15b with fig. 19, _m, n_) and in A17 the date 4 Ahau 13 Yax (compare A17a with fig. 16, _e'-g'_ and A17b 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 full 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 B17-A18a is recorded another Secondary-series number composed of 3 kins, 13 uinals, 16 tuns, and 1 katun, which we may write thus: 1.16.13.3. The student will note that the katun coefficient in A18a is expressed by an unusual form, the thumb. As explained on page 103, this has a numerical value of 1. Again, our text presents another irregular feature. Instead of being counted either forward or backward from the date next preceding it in the text; that is, 4 Ahau 13 Yax in A17, this number is counted from the date following it in the text, like the two Secondary-series numbers in Stela J, just discussed. This starting date recorded in A18b B18a 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 {220} assuming, therefore, that the 12 Caban 5 Kayab in A18b-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 in B17-A18a, namely, 1.16.13.3, to units of the first order, we have: A18a = 1 × 7,200 = 7,200 B17b = 16 × 360 = 5,760 B17a = 13 × 20 = 260 B17a = 3 × 1 = 3 ------ 13,223 Remembering that this number 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 coefficient of the day sign in A19a with the coefficient of the katun sign in A18a, and the day sign itself with the profile variant for Ahau in figure 16, _h', i'_. For the month sign, compare A19b with figure 19, d. But since 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. 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 pl. 20).[201] 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 little difficulty in reading it as 9.16.10.0.0. The terminal date which this number reaches is recorded in B5-B8; that is, 1[202] 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 monument, 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 hotun-marker. Here again, as in the case of Stela J at Quirigua, the importance of the "contemporaneous 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. [Illustration: INITIAL SERIES ON STELA F (EAST SIDE), QUIRIGUA] {221} [Illustration: FIG. 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; _b_, 9. 15. 6. 14. 6 6 Cimi 4 Tzec.] 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. While it is impossible to prove that this particular Initial Series was the one which the ancient scribes had in mind when they recorded this date 3 Ahau 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 5 Kayab Plate 19, _A_, A1-A6 13. 9. 9 Plate 19, _A_, A10 9.15. 6.14. 6 6 Cimi 4 Tzec Plate 19, _B_, B11b-A12a [9.15.10. 0. 0] 3 Ahau 3 Mol Plate 19, _B_, A15 [9.15. 0. 0. 0] 4 Ahau 13 Yax Plate 19, _B_, A17 9.14.13. 4.17 12 Caban 5 Kayab Plate 19, _B_, A18b B18a 1.16.13. 3 Plate 19, _B_, B17 A18a 9.16.10. 0. 0 1 Ahau 3 Zip Plate 19, _B_, A19 (repeated as Initial Series on east side of monument) 9.16.10. 0. 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 hotuns which they mark; and finally, both are hotun-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, Stelæ J, F, and E, and Zoömorph 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} it is possible to regard as being contemporaneous. Hence, it is not improbable that it might refer to the founding of the city or some similar event, though this is of course a matter of speculation. The fact, however, that 9.14.13.4.17 12 Caban 5 Kayab is the earliest date on four different hotun-markers shows that it was of supreme importance in the history of Quirigua. This concludes the discussion of texts showing the use of Secondary Series with Initial Series. TEXTS RECORDING 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 purposes, 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 will 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, flourished, 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 "current cycle" was spoken of. After the date 9.0.0.0.0 8 Ahau 13 Ceh 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 +) years. Consequently, after Cycle 9 had commenced many succeeding generations 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, probably 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 +) years; that is, three or four times in the lifetime of many individuals; hence, there was 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. [Illustration: EXAMPLES OF PERIOD-ENDING DATES IN CYCLE 9] {223} 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, _A_, is figured a Period-ending date from Stela 2 at Copan.[203] The date 12 Ahau 8 Ceh appears 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, _o_, will be evident. Indeed, figure 37, _o_, has precisely the same lower element as glyph 3. In glyph 4 follows the particular katun, 11, whose end fell on the date recorded in glyphs 1 and 2. The student 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 katun 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 all brought to their respective 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 units of the first order, then deducting from it all the Calendar Rounds 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 (pl. 21, _B_) is taken from the tablet in the Temple of the Foliated Cross at Palenque.[204] In glyph 1 appears the date 8 Ahau 8 Uo (compare the month form with fig. 19, _b, 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 coefficient 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 accuracy of the record by changing this Period-ending date to its {224} 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 Ahau 8 Uo. In plate 21, _C_, is figured a Period-ending date taken from Stela 23 at Naranjo.[205] The date 6 Ahau 13 Muan appears very clearly in glyphs 1 and 2 (compare the month form with fig. 19, _a', b'_). 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-like 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 in 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 illustrating its use are shown in figure 37, _a-h_, with which the ending element in glyph 4 should be compared. The glyphs 1 to 4 in plate 21, _C_, therefore record that Katun 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 pl. 21, _D_).[206] The date itself appears in glyphs 1 and 2 and is followed in 3 by a sign which is almost exactly like the ending sign in glyph 3 just discussed (see pl. 21, _C_). The subfixes are identical in both cases, and it is possible to distinguish 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 suffice to illustrate the use of katun Period-ending dates. In plate 21, _E_, is figured a Period-ending date from Stela 4 at Copan.[207] 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 common "ending" element (see fig. 37, _j, k_) with a grotesque head superfix, also another "ending sign" (see _i, r, u, v_ of the plate just named). In glyph 4 follows the particular katun (Katun 15) whose {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 tun, as Tun 10, for example, had come to its end left much to be desired in the way of accuracy, since there was a Tun 10 in every katun, and consequently any given tun recurred after an interval of 20 years; in other words, there were three or four different Tun 10'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 in mind the 60 or 70 various tun endings which the average lifetime included. For these reasons tun-ending dates occur but rarely, only when there was little or no doubt concerning the particular katun 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.[208] In glyph 1 appears an ending sign showing the hand element and the grotesque flattened 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, _h_). 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 tun occurred somewhere 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 Katun 8 of Cycle 9. Moreover, shortly after the tun-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, {226} and this tun ending corresponded, therefore, to the Initial Series 9.8.13.0.0 5 Ahau 18 Tzec. Another tun-ending date from Stela 5 at Tikal is figured in plate 21, _G_.[209] In glyphs 1 and 2 the date 4 Ahau 8 Yaxkin appears, the month sign being represented as a head variant, which has the essential elements of the sign for Yaxkin (see fig. 19, _k, l_). Following this in glyph 3 is Tun 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 fell. 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 assume, 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[210] (see pl. 21, _H_). In glyphs 1 and 2 appears the number 0 kins, 0 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, all 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 unsuccessful, and we must seek another explanation for the four glyphs here under discussion. If this were a Period-ending date it would mean that Tun 5 of Katun 17 came to an end on the date 6 Ahau 13 Kayab. Let us see whether this is true. Assuming that our cycle coefficient 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 number: 9.17.5.0.0. Reducing this number to units of the 1st order, and applying the rules previously given for solving Initial Series, the terminal date reached will be 6 Ahau 13 Kayab, identical with the date recorded in 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," this being identical with the Initial Series 9.17.5.0.0 6 Ahau 13 Kayab. [Illustration: EXAMPLES OF PERIOD-ENDING DATES IN CYCLES OTHER THAN CYCLE 9] {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.[211] In glyphs 1 and 2 appears the date 4 Ahau 8 Cumhu (compare the month form in glyph 2 with fig. 19, _g', h'_), and in glyph 3 an ending sign (compare glyph 3 with the ending signs in fig. 37, _l-q_, 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 starting point of Maya chronology. This same date is again recorded on a round altar at Piedras Negras (see pl. 22, _B_).[212] In glyphs 1 and 2 appears the date 4 Ahau 8 Cumhu, and in glyph 3a the ending 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, _l-q_, and figure 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, _C_, is figured a Period-ending date from the tablet in the Temple of the Foliated Cross at Palenque.[213] In glyph 1 appears an ending sign in which the hand element and tassel-like postfix show clearly. This is followed in glyph 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'_).[214] The glyphs in plate 22, _C_, record, therefore, 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. Reducing this to units 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 (pl. 22, _A-C_) are not to be considered as referring to times contemporaneous with the erection of the monuments upon which they are severally inscribed, since they {228} precede the opening of Cycle 9, the first historic epoch of the Maya civilization, 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 adjoining Period-ending date that may have been historical. This case is figured in plate 22, _G_.[215] In glyphs 4 and 5 appears the date 8 Ahau 13 Ceh (compare the month form in glyph 5 with fig. 16, _u, v_). This is followed in glyph 6 by a sign which shows the same ending element as the forms 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 (compare 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 uinals, or 6.3. This looks so much like a Secondary Series that we are justified in treating it as such until 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 will 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 3 = 6 × 20 = 120 Glyph 3 = 3 × 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 in 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 subtracting 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. 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 {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, while 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.[216] Glyphs 1 and 2 declare the date 7 Ahau 18 ?, the month sign in glyph 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 ending sign as that shown in figure 37, _a-h_, and it would seem probable, 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, tun, uinal, and kin coefficients must be 0 and the Initial-series number 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 believe that it was "contemporaneous" rather than "prophetic." The same can not be said, however, for the Cycle-10 ending date on Zoömorph G at Quirigua (see pl. 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-h_. Hence we have recorded here the fact that "Cycle 10 ended on the date 7 Ahau 18 Zip," a fact proved also by calculation in connection with the preceding example. Does this date represent, therefore, the contemporaneous time of Zoömorph 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 Zoömorph 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 grounds of antecedent probability, we are justified in assuming at the outset that this date {230} therefore indicates the epoch or position of Zoömorph G in the Long Count, because it alone appears as an Initial Series. In the case of all the other monuments at Quirigua,[217] where there is but one Initial Series in the inscription, that Initial Series marks the position of the monument in the Long Count. 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 Zoömorph 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 pl. 22, _F_).[218] Other features of this text point to the same conclusion. In addition 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 points to the conclusion that it was the contemporaneous date of this monument. There is still another, perhaps the strongest reason of all, for believing that Zoömorph 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 hotun ending 9.17.15.0.0 5 Ahau 3 Muan is left without its corresponding monument 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 Zoömorph 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 mentioned leaves no room for doubt. If this is true, as the writer believes, the date "Cycle 10 ending on 7 Ahau 18 Zip" on Zoömorph G is "prophetic" in character, since it did not occur until nearly 45 years after the erection of the monument 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 contemporaneous, is that on Stela 11 at Seibal, {231} the latest of the great southern sites.[219] 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."[220] Compare the ending-sign superfix in glyph 3 with figure 37, _a-h_. 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." Counting 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 Stelæ 8, 9, and 10, at the same city. Another Cycle-10 ending date which was probably "prophetic", like the one on Zoömorph 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.[221] Reducing the number in glyph 6a to units of the first order, we have: 6a = 5 × 7,200 = 36,000 {0 × 360 = 0 Not recorded {0 × 20 = 0 {0 × 1 = 0 ------ 36,000 {232} [Illustration: FIG. 81. The Initial Series, Secondary Series, and Period-ending date on Altar S, Copan.] Counting this number forward from the date 4 Ahau 13 Yax, the terminal date reached will 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-h_. Therefore the Secondary-series date 7 Ahau 18 Zip, there recorded, closed Cycle 10. The same fact could have been determined by adding the Secondary-series number in 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 [Illustration: INITIAL SERIES, SECONDARY SERIES, AND PERIOD-ENDING DATES ON STELA 3, PIEDRAS NEGRAS] {233} 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 Zoömorph G at Quirigua. One reason which renders this probable is that the sculpture on Altar S very closely resembles the sculpture on Stelæ 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 glyphs 7 and 8a, a Period-ending date. This practice is not at all unusual in the inscriptions and several texts illustrating it are figured below. TEXTS RECORDING 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 A1 and is followed by the Initial-series number 9.12.2.0.16 in B1-B3. 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 Cib 14 Yaxkin, which the student will readily recognize in A4-B7; the "month-sign indicator" appearing 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, _k, l_. The Initial Series recorded in A1-A4, B7 reads, therefore, 9.12.2.0.16 5 Cib 14 Yaxkin. In C1 D1 is recorded the number 0 kins, 10 uinals, and 12 tuns; that is, 12.10.0, the first of several Secondary Series in this text. Reducing this to units of the first order and counting it forward from the terminal date of the Initial Series, 5 Cib 14 Yaxkin, the terminal date of the Secondary Series will be found to be 1 Cib 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 Cib 14 Yaxkin 12.10. 0 9.12.14.10.16 1 Cib 14 Kankin Following along the text, the next Secondary-series number appears in D4-C5a and consists of 10 kins,[222] 11 uinals, 1 tun, and 1 katun; that {234} 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 Kankin in C2b D2a, the new terminal date reached will be 4 Cimi 14 Uo, which the student will find recorded in D5-C6. Compare the day sign in D5 with figure 16, _h, i_, and the month sign in C6 with figure 19, _b, 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 E1 and consists of 15 kins,[223] 8 uinals, 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 Uo, 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, b_, 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 Uo 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 units 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' b'_. But the glyph following this date in F9 is very clearly an ending sign; note the hand, tassel-like postfix, and subfixial element showing the curl infix, all of which are characteristic ending elements (see figs. 37, _l-q_, and 54). Moreover, in F10 is recorded "the end of Katun 14." Compare the ending prefix in this glyph with figure 37, _a-h_. 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. 0 6 Ahau 13 Muan [Illustration: INITIAL SERIES, SECONDARY SERIES, AND PERIOD-ENDING DATES ON STELA E (WEST SIDE), QUIRIGUA] {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 5 Cib 14 Yaxkin A1-A4, B7 12.10. 0 C1 D1 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 E1 9.13.19.13. 1 11 Imix 14 Yax E2 F2 4.19 F6 9.14. 0. 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 unusually regular, the numbers 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-ending dating, all 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, Stelæ 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 found 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.[224] 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[225].4.17 in A4-A6. Reducing this number to units of the first order, remembering the correction in the tun coefficient in A5 noted below, and applying the rules previously given for solving Initial Series, the terminal date {236} 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," here shown with a head-variant coefficient 10. Compare B6 with figure 16, _a', b'_, 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 B10b-A11a, a Secondary-series number consisting of 3 kins, 13 uinals, and 6 tuns, that is, 6.13.3. Counting this number forward from the date next preceding it in the text, 12 Caban 5 Kayab, the date reached will be 4 Ahau 13 Yax, which the student will find recorded in B11. Compare the month form in B11b with figure 19, _q, r_. But since the Initial-series value of 12 Caban 5 Kayab is known, the Initial-series value of 4 Ahau 13 Yax may be calculated from it as follows: 9.14.13. 4.17 12 Caban 5 Kayab 6.13. 3 9.15. 0. 0. 0 4 Ahau 13 Yax [Illustration: FIG. 82. The Initial Series on Stela E (east side), Quirigua.] The next Secondary-series number appears in B12, plate 24, _B_, and consists of 6 kins, 14 uinals, and 1 tun, that is, 1.14.6.[226] The student will find that all efforts to reach the next date recorded in the text, 6 Cimi 4 Tzec in A13b B13a, by counting forward 1.14.6 from 4 Ahau 13 Yax in B11, the date next preceding this number, will prove unsuccessful. However, by counting _backward_ 1.14.6 from 6 Cimi 4 Tzec, he will find the date from which the count proceeds is 10 Ahau 8 Chen, though this latter date is nowhere recorded in this text. We have seen elsewhere, on Stela F for example (pl. 19, _A, B_), that the date 6 Cimi 4 Tzec corresponded to the Initial-series number 9.15.6.14.6; consequently, we may calculate the position of the unrecorded {237} date 10 Ahau 8 Chen in the Long Count from this known Initial Series, by subtracting[227] 1.14.6 from it: 9.15.6.14.6 6 Cimi 4 Tzec 1.14.6 9.15.5. 0.0 10 Ahau 8 Chen We now see that there are 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 counted from the unexpressed date 10 Ahau 8 Chen to reach the terminal date 6 Cimi 4 Tzec recorded in A13b B13a. The next Secondary-series number appears in A14b B14 and consists of 15 kins, 16 uinals, 1 tun, and 1 katun, that is, 1.1.16.15. As in the preceding case, however, all efforts to reach the date following this number, 11 Imix 19 Muan in A15b B15a, 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 _backward_ from 11 Imix 19 Muan to determine the starting point. Performing 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 elsewhere at Quirigua, we must leave their corresponding Initial-series values indeterminate for the present. The last Secondary Series in this text is recorded in A17b B17a and consists of 19 kins,[228] 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 A15b B15a, the terminal date reached will be 13 Ahau 18 Cumhu, which the student will find recorded in A18. Compare the month sign with figure 19, _g', h'_. But immediately following this date in B18a is Katun 17 and in the upper part of B18b the hand-denoting ending. These glyphs A18 and B18 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 this period ending into its corresponding Initial-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, had 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 {238} by counting forward 8.4.19 from 11 Imix 19 Muan, the Initial-series value of the latter may be calculated by subtracting 8.4.19 from the Initial-series value of the former: 9.17. 0. 0. 0 13 Ahau 18 Cumhu 8. 4.19 9.16.11.13. 1 11 Imix 19 Muan And since the date 11 Imix 19 Muan was reached by counting forward 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 A18 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,[229] and A10. 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.[230]4.17 12 Caban 5 Kayab Plate 24, _A_, A1-B5, B8b 6. 13. 3 Plate 24, _A_, B10b-A11a 9.15. 0. 0. 0 4 Ahau 13 Yax Plate 25, _A_, B11 [5. 0. 0] Undeclared 9.15. 5. 0. 0 10 Ahau 8 Chen " 1. 14. 6 Plate 24, _B_, B12 9.15. 6. 14. 6 6 Cimi 4 Tzec Plate 24, _B_, A13b, B13a [3. 0. 0] Undeclared {239} 9.15. 9. 14. 6 7 Cimi 9 Zotz " 1. 1. 16.15 Plate 24, _B_, A14b B14 9.16.11. 13. 1 11 Imix 19 Muan Plate 24, _B_, A15b B15a 8. 4.19 Plate 24, _B_, A17b B17a 9.17. 0. 0. 0 13 Ahau 18 Cumhu Plate 24, _B_, A18 End of Katun 17 Plate 24, _B_, B18 East side: 9.17. 0. 0. 0 13 Ahau 18 Cumhu Figure 82, A1-A6, A7, A10 Comparing the summary of the inscription on Stela E at Quirigua, just given, with the summaries of the inscriptions on Stelæ J and F, and Zoömorph G, at the same city, all four of which are shown side by side in Table XVII,[231] the interrelationship of these four monuments appears very clearly. TABLE XVII. INTERRELATIONSHIP OF DATES ON STELÆ E, F, AND J AND ZOÖMORPH G, QUIRIGUA Date Stela J Stela F Stela E Zoömorph G 9.14.13. 4.17 12 Caban 5 Kayab X X X X 9.15. 0. 0. 0 4 Ahau 13 Yax - X X - 9.15. 5. 0. 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. 0 3 Ahau 3 Mol - X - - 9.16. 5. 0. 0 8 AHAU 8 ZOTZ X - - - 9.16.10. 0. 0 1 AHAU 8 ZIP - X - - 9.16.11.13. 1 11 Imix 19 Muan - - X - 9.17. 0. 0. 0 13 AHAU 18 CUMHU - - X - 9.17.15. 0. 0 5 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.[232] It is necessary, however, to {240} caution 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 in the present state of our knowledge entirely a matter of conjecture. Passing on, it will be seen from Table XVII that two of the monuments, namely, Stelæ E and F, bear the date 9.15.0.0.0 4 Ahau 3 Yax, and two others, Stelæ E and J, the date 9.15.5.0.0 10 Ahau 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 Zoömorph G, which records a half 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-series, and Period-ending, dating, with which the student should be sufficiently 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 83, A, is shown a part of the inscription on Altar M at Quirigua.[233] In A1 B1 appears a number consisting of 0 kins, 2 uinals, and 3 tuns, that is, 3.2.0, and following this in 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 have: B1 = 3 × 360 = 1,080 A1 = 2 × 20 = 40 A1 = 0 × 1 = 0 ----- 1,120 [Illustration: CALENDAR-ROUND DATES ON ALTAR 5, TIKAL] {241} Counting this number forward from 4 Ahau 13 Yax, the nearest date to it in the text, the terminal date reached will be found to be 6 Ahau 18 Zac, the date which, we have seen, was recorded in A3b B3. It 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 found recurring 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 obvious. [Illustration: FIG. 83. Calendar-round dates: _A_, Altar M, Quirigua; _B_, Altar Z, Copan.] The overwhelming majority of Maya dates fall in Cycle 9, and nearly all inscriptions have at least one date which closed some hotun or tun of that cycle. Referring to Goodman's Tables, in which the tun endings of Cycle 9 are given, the student will find that the date 4 Ahau 13 Yax occurred as a tun ending in Cycle 9, at 9.15.0.0.0 4 Ahau 13 Yax, in which position it closed not only a hotun but also a katun. 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 {242} 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, Stelæ E and F, with this same date. In figure 83, _B_, is shown a part of the inscription from Altar Z at Copan.[234] In A1 B1 appears a number consisting of 1 kin, 8 uinals, and 1 tun, that is, 1.8.1, and following this in B2-A3 is the date 13 Ahau 18 Cumhu, 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 counting this number backward, giving 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 be 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 since 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 _q_ of the same figure), it seems probable that 13 Ahau 18 Cumhu is the terminal date and also a Period-ending date. Referring 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 hotun but a katun as well.[235] If this is true, the unrecorded starting point 12 Cauac 2 Zac can be shown to have the following Initial-series value: 9.17. 0.0. 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 probability amounting 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). {243} Compare glyph 1 with figure 16, _m_, _n_, and glyph 2 with figure 19, _a', b'_. In glyphs 8 and 9 appears a Secondary-series number consisting of 18 kins, 11 uinals, 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 0 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 units of the first order and counting forward from the date next preceding it in the text, 13 Manik 0 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, _h, 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 Kankin, which the student will find is just three days later than 11 Cimi 19 Mac, that is, one day 12 Manik 0 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 Count. 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 Count, 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-round dates may sometimes be referred to their proper positions in the Long Count. A monument which shows only Calendar-round 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} 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 discoverer of this monument:[236] "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 monument has already been deciphered as "6 Ahau 13 Muan ending Katun 14" (see pl. 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 Kankin 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) earlier 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 0 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 Sometimes, however, monuments showing Calendar-round dates stand {245} alone, and in such 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. ERRORS IN THE ORIGINALS Before closing the presentation of the subject of the Maya inscriptions the writer has thought it best to insert a few texts which show actual errors in the originals, mistakes due to the carelessness or oversight of the ancient scribes. [Illustration: FIG. 84. Texts showing actual errors in the originals: _A_, Lintel, Yaxchilan; _B_, Altar Q, Copan; _C_, Stela 23, Naranjo.] 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 Yaxchilan--will show that the uinal coefficient in C1 represents an impossible condition from the Maya point of view. This glyph as it stands {246} unmistakably records 19 uinals, a number which had no existence in the Maya system of numeration, since 19 uinals are always recorded as 1 tun and 1 uinal.[237] Therefore the coefficient in C1 is incorrect on 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.?.1 appearing in B1-D1, 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 0 to 17, inclusive. Trying 0 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. Consequently, our first trial number 9.15.6.0.1 falls short of the number necessary 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 in C1 should have been 13, instead of 19 as recorded. Another error 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, _f_, and the lower half with figure 19, _b, 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 starting 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 Uo. 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 {247} 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 inscription was intrusted engraved here 3 dots instead of 2 dots, and 1 ornamental 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 found 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 terminal 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 will 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 5 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 difference 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} 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-ending 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, _b, 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, _k, l_). This has every appearance of being a Secondary Series, of which 8 Eznab 16 Uo is the starting point, 4.17, the number to be counted, and 2 Men 13 Yaxkin the terminal date. Reducing 4.17 to units of the first order and counting it forward from the starting 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 slight change in the original text, we are probably justified in assuming; 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 A1 and is followed by the Initial-series number 9.16.10.0.0 in 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. Assuming 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 [Illustration: INITIAL SERIES ON STELA N, COPAN, SHOWING ERROR IN MONTH COEFFICIENT] {249} The number in the above list 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 tuns, that is, changing 2 bars to 4 dots, and (2) replacing 0 uinals in A5 by 17 uinals, that is, changing the 0 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 number recorded in order to reach 1 Ahau 8 Zip, we are forced to the conclusion that the error must be in the terminal date, not in one of the coefficients of the period glyphs. Let us therefore assume 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 Count 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 A15 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 altogether, and to assume when he finds 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 exceedingly 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[238] 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, {250} that many, if indeed not most, of the monuments, were "time markers" or "period stones," in every way similar to the "period stones" which the northern Maya are known to[239] have erected at regularly recurring periods. That the period which was used as this chronological unit may have varied in different localities 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. Whatever 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 commemorate 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 background. 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. {251} CHAPTER VI THE CODICES The present chapter will treat of the application 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 tonalamatls 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,[240] 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 _once_ 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 begin 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. {252} Most of the numbers, that is (2) and (3), in the tonalamatl are presented in a horizontal row across the page or pages[241] of the manuscript, the red alternating with the black. In some instances, however, the numbers appear in a vertical column or pair of columns, though in this case also the same alternation in color is to be observed. More rarely the numbers are scattered over the page indiscriminately, 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 in 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 belonging 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 column of the day signs, to the uppermost[242] 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 will 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 {253} coefficient of the beginning day of the second _subdivision_ of the first division, the _second black number_ is to be counted forward in order to reach the third red number, which is the coefficient of the day beginning 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 will 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 until the last red number in the last division of the tonalamatl has been reached--that is, the 260th day--the count will be found to have reentered itself, or in other words, the day reached by counting forward 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 all 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 immediately preceding them in each case, and, after subtracting all the multiples of 13 possible, the resulting number will be the coefficient of the beginning day desired. _Rule 3._ To find the day signs of the beginning days of the succeeding 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 _main divisions_ of the tonalamatl, the day sign reached will be found to be recorded in the column of day signs, but if at the beginning 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 will equal exactly 260 if the tonalamatl is perfectly regular and correct. {254} In plate 27 is figured page 12 of the Dresden Codex. It will 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, _b_ 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 pl. 27). The student will readily recognize the three essential parts mentioned on page 251: (1) The column of day signs, (2) the red numbers, and (3) the black numbers. 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 subdivisions 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 number immediately preceding it--in this case 1--in order to give the coefficient of the day beginning the next subdivision, all 13s possible being first deducted from the resulting number. Furthermore, this coefficient will be the red number next following the black number. Applying this rule to the present case, we have: 1 (first red number) + 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 will 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 will be Manik. But since this day begins only a _subdivision_ in this tonalamatl, not one of the _main divisions_, its day sign will not be recorded, and we have, therefore, the day 1 Manik, of which the 1 is expressed by the second red number and the name part Manik only indicated by the calculations. [Illustration: PAGE 12 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN ALL THREE DIVISIONS] {255} 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 first to examine the next black number in our tonalamatl. This will be found 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: (), 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 (): 1 unit of the second order (20 units of the first order) + 6 units of the first order = 26. As explained on page 92, however, numeration by position--that is, columns of units--was impossible in the tonalamatls, in which many of the numbers 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 preceding 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 number 1, which is the coefficient of the beginning day of the next _subdivision_, will be found recorded just to the right of the black 26. The day sign corresponding to this coefficient 1 will be found 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 number in our text is 13, and proceeding as before, this is to be added to the red number next preceding it, 1, the abbreviation 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).[243] 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 _second main division_ of {256} the tonalamatl (see p. 253), and this is found to be the case, since the day sign Cimi is _the second_ in the column of day signs to the left. Compare this form with figure 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 with 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 beginning 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 first, 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, commencing 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 continuous, therefore, reentering itself immediately on its conclusion and commencing anew. {257} There follows below an outline[244] of this particular tonalamatl: ---------------------+---------+-----------+---------+---------+--------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+---------+-----------+---------+---------+--------- 1st part, 13 days, | | | | | beginning with day |1 Ix |1 Cimi |1 Eznab |1 Oc |1 Ik | | | | | 2d part, 26 days, | | | | | beginning with day |1 Manik |1 Cauac |1 Chuen |1 Akbal |1 Men | | | | | 3d part, 13 days, | | | | | beginning with day |1 Ben |1 Chicchan |1 Caban |1 Muluc |1 Imix | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+---------+-----------+---------+---------+--------- Next tonalamatl: 1st Division, 1st part, 13 days, beginning with the day 1 Ix, etc. We may now apply rule 4 (p. 253) as a test to this tonalamatl. Multiplying the sum of all the black numbers, 13 + 26 + 13 = 52, by the number of day signs in the column of day signs, 5, we obtain 260 (52 × 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 subdivisions 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 jaw, the truncated nose, and the vertebræ. 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[245] 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 explained, that the four or six glyphs which stand above each of the pictures in a tonalamatl tell the meaning of the picture to which they are appended, and any advances made, looking toward their deciphering, will lead to far-reaching results in the meaning of the {258} nonnumerical and noncalendric signs. In part at least they show the name glyphs of the gods above which they occur, and it seems not unlikely that the remaining glyphs 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 number, 13, to the first day sign, Chuen (see fig. 17, _p, q_), according to rule 1 (p. 252), the beginning day of the tonalamatl will be found to be 13 Chuen. Adding to this the first black number, 26, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will 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. Commencing 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 beginning day of the next or _second 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 will have no difficulty in working out the beginning days of the remaining divisions and subdivisions of this tonalamatl. These are given below, though the student is urged to work them out independently, using the following outline simply as a check on his work. Adding the last black number, 13, to the beginning day of the last subdivision of the last division, 13 Eznab, will bring the count back to the day 13 Chuen with which the tonalamatl began: {259} ---------------------+----------+---------+----------+---------- |1st |2d |3d |4th |Division |Division |Division |Division ---------------------+----------+---------+----------+---------- 1st part, 26 days, | | | | beginning with day |13 Chuen |13 Cib |13 Imix |13 Cimi | | | | 2d part, 26 days, | | | | beginning with day |13 Caban |13 Ik |13 Manik |13 Eb | | | | 3d part, 13 days, | | | | beginning with day |13 Akbal |13 Lamat |13 Ben |13 Eznab | | | | Total number of days |65 |65 |65 |65 ---------------------+----------+---------+----------+---------- Next tonalamatl: 1st 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,[246] 65 × 4 = 260, the exact number of days in a tonalamatl. The next tonalamatl (see the upper part of pl. 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, respectively, 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 glyph remains. Its position, however, above the column of day signs, seems to indicate its color and use, and we are 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 calculation 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. {260} In this manner all of the beginning days could be worked out as below: ---------------------+----------+---------+----------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 27 days, | | | | | beginning with day |8 Ahau |8 Eb |8 Kan |8 Cib |8 Lamat | | | | | 2d part, 25 days, | | | | | beginning with day |9 Manik |9 Cauac |9 Chuen |9 Akbal |9 Men | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+----------+----------+-------- The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. As previously explained, the second column of day signs belongs to another tonalamatl, 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 |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+---------+---------+---------- 1st part, 27 days, | | | | | beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab | | | | | 2d part, 25 days, | | | | | beginning with day |9 Caban |9 Muluc |9 Imix |9 Ben |9 Chicchan | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+---------+---------+---------- The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. It is interesting 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 was 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 illustrates 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 number, 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 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 be found to be 5 Eb, which appears as the second day sign in the column of day signs. [Illustration: PAGE 15 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN ALL THREE DIVISIONS] {261} The last red number is 5, thus establishing as correct our restoration of a red 5 above the column of day signs. From here this tonalamatl presents no unusual features and it may be worked as follows: ---------------------+----------+---------+----------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 34 days, | | | | | beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat | | | | | 2d part, 18 days, | | | | | beginning with day |13 Ix |13 Cimi |13 Eznab |13 Oc |13 Ik | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+----------+----------+-------- Applying rule 4 (p. 253), we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The next tonalamatl (see lower part of pl. 28, that is, Dresden 15c) has 10 day signs arranged in two parallel columns of 5 each. This, at its face value, would seem to be divided into 10 divisions, and the calculations confirm the results of the preliminary inspection. The tonalamatl opens with the day 3 Lamat. Adding to this the first black number, 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 number, 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 column.[247] Commencing with 3 Ix and adding to it the first black number 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 |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 12 days, | | | | | beginning with day |3 Lamat |3 Ix |3 Ahau |3 Cimi |3 Eb | | | | | 2d part, 14 days, | | | | | beginning with day |2 Ahau |2 Cimi |2 Eb |2 Eznab |2 Kan | | | | | Total number of days |26 |26 |26 |26 |26 ---------------------+----------+---------+----------+----------+-------- {262} (Concluded) ---------------------+----------+---------+----------+----------+-------- |6th |7th |8th |9th |10th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 12 days, | | | | | beginning with day |3 Eznab |3 Kan |3 Oc |3 Cib |3 Ik | | | | | 2d part, 14 days, | | | | | beginning with day |2 Oc |2 Cib |2 Ik |2 Lamat |2 Ix | | | | | Total number of days |26 |26 |26 |26 |26 ---------------------+----------+---------+----------+----------+-------- Applying rule 4 (p. 253) to this tonalamatl, we have: 10 × 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 will have little difficulty in 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 |2d |3d |4th |Division |Division |Division |Division ---------------------+----------+---------+----------+---------- 1st part, 13 days, | | | | beginning with day |1 Ik |1 Manik |1 Eb |1 Caban | | | | 2d part, 31 days, | | | | beginning with day |1 Men |1 Ahau |1 Chicchan|1 Oc | | | | 3d part, 8 days, | | | | beginning with day |6 Cimi |6 Chuen |6 Cib |6 Imix | | | | 4th part, 13 days, | | | | beginning with day |1 Ix |1 Cauac |1 Kan |1 Muluc | | | | Total number of days |65 |65 |65 |65 ---------------------+----------+---------+----------+---------- Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the exact number of days in a tonalamatl. The tonalamatls heretofore 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 workmanship 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 pl. 29) extends across the middle part of two pages (Tro-Cor. 10b, 11b). 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.[248] Adding to this the first black number 9, the day 9 Chuen is reached, and proceeding in this manner the tonalamatl may be outlined as follows: [Illustration: MIDDLE DIVISIONS OF PAGES 10 AND 11 OF THE CODEX TRO-CORTESIANO, SHOWING ONE TONALAMATL EXTENDING ACROSS THE TWO PAGES] [Illustration: PAGE 102 OF THE CODEX TRO-CORTESIANO, SHOWING TONALAMATLS IN THE LOWER THREE SECTIONS] {263} ---------------------+----------+----------+----------+---------- |1st |2d |3d |4th |Division |Division |Division |Division ---------------------+----------+------- --+----------+---------- 1st part, 9 days, | | | | beginning with day |13 Ik |13 Manik |13 Eb |13 Caban | | | | 2d part, 9 days, | | | | beginning with day |9 Chuen |9 Cib |9 Imix |9 Cimi | | | | 3d part, 10 days, | | | | beginning with day |5 Ahau |5 Chicchan|5 Oc |5 Men | | | | 4th part, 6 days, | | | | beginning with day |2 Oc |2 Men |2 Ahau |2 Chicchan | | | | 5th part, 2 days, | | | | beginning with day |8 Cib |8 Imix |8 Cimi |8 Chuen | | | | 6th part, 10 days, | | | | beginning with day |10 Eznab |10 Akbal |10 Lamat |10 Ben | | | | 7th part, 5 days, | | | | beginning with day |7 Lamat |7 Ben |7 Eznab |7 Akbal | | | | 8th part, 7 days, | | | | beginning with day |12 Ben |12 Eznab |12 Akbal |12 Lamat | | | | 9th part, 7 days, |6 Ahau |6 Chicchan|6 Oc |6 Men beginning with day |[249] |[249] |[249] |[249] | | | | Total number of days |65 |65 |65 |65 ---------------------+----------+----------+----------+---------- Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the exact number of days in a tonalamatl. Another set of interesting tonalamatls is figured in plate 30, Tro-Cor., 102.[250] 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 tonalamatl: ---------------------+---------+---------+---------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+---------+---------+---------+----------+-------- 1st part, 2 days, | | | | | beginning with day |4 Manik |4 Cauac |4 Chuen |4 Akbal |4 Men | | | | | 2d part, 7 days, | | | | | beginning with day |6 Muluc |6 Imix |6 Ben |6 Chicchan|6 Caban | | | | | 3d part, 2 days, | | | | | beginning with day |13 Cib |13 Lamat |13 Ahau |13 Eb |13 Kan | | | | | 4th part, 10 days, | | | | | beginning with day |2 Eznab |2 Oc |2 Ik |2 Ix |2 Cimi | | | | | 5th part, 9 days, | | | | | beginning with day |12 Lamat |12 Ahau |12 Eb |12 Kan |12 Cib | | | | | 6th part, 22 days, | | | | | beginning with day |8 Caban |8 Muluc |8 Imix |8 Ben |8 Chicchan | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+---------+---------+---------+----------+-------- Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, {264} the exact number of days in a tonalamatl. The next tonalamatl on this page (see third division in pl. 29, that is, Tro-Cor., 102c) is interesting 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 |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+---------+---------+-------- 1st part, 17 days, | | | | | beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat | | | | | 2d part, 13 days, | | | | | beginning with day |8 Caban |8 Muluc |8 Imix |8 Ben |8 Chicchan | | | | | 3d part, 10 days, | | | | | beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab | | | | | 4th part, 12 days, | | | | | beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat | | | | | Total number of | | | | | days |52 |52 |52 |52 |52 ---------------------+----------+---------+---------+---------+-------- Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 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 tonalamatl just given, 4 Ahau, 4 Eb, 4 Kan, 4 Cib, 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 + 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 + 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: {265} ----------------------+----------+---------+---------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ----------------------+----------+---------+---------+----------+-------- 1st part, 29 days, | | | | | beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat | | | | | 2d part, 23[251] days,| | | | | beginning with day |7 Muluc |7 Imix |7 Ben |7 Chicchan|7 Caban | | | | | Total number of days |52 |52 |52 |52 |52 ----------------------+----------+---------+---------+----------+-------- Applying rule 4 (p. 253) to this tonalamatl, we have: 52 × 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; (_b_) 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 practically determined. The first is the calendric background, the chronological 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 prognostications 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 Förstemann 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} line of research in the codices is the groups of glyphs above the pictures, and from their decipherment will probably come the determination of the meaning of this interesting and unusual period. TEXTS RECORDING 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 confined to unessentials, and the system of counting and measuring time in the Initial Series from the inscriptions 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 introducing 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 Supplementary 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 starting point, the date 4 Ahau 8 Cumhu, 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 will 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 (uinals) and the zero in the 1st place (kins) 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_. [Illustration: PAGE 24 OF THE DRESDEN CODEX, SHOWING INITIAL SERIES] {267} 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 XIV the values of the several positions in the second method of writing the numbers will be found, and using these with their corresponding coefficients in each case the Initial-series number here recorded may be reduced to units of the 1st order, as follows: 9 × 144,000 = 1,296,000 9 × 7,200 = 64,800 16 × 360 = 5,760 0 × 20 = 0 0 × 1 = 0 ---------- 1,366,560 Deducting from this number all the Calendar Rounds possible, 72 (see Table XVI), it may be 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 Cumhu, exactly the same as the starting point of Maya chronology. This must be true, since counting forward 0 from the date 4 Ahau 8 Cumhu, the date 4 Ahau 8 Cumhu will be reached. Instead of recording this date immediately below the last period of its Initial-series number, that is, the 0 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, _z-b'_. 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: 9 × 144,000 = 1,296,000 9 × 7,200 = 64,800 9 × 360 = 3,240 16 × 20 = 320 0 × 1 = 0 ---------- 1,364,360 Deducting from this number all the Calendar Rounds possible, 71 (see Table XVI), it may be 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} 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 Kayab. 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 0 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 direction 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 0 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 Cumhu, the date reached will be 1 Ahau 18 Kayab. But since the date 4 Ahau 8 Cumhu is stated in the text to have corresponded 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 difficult 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 _below_ 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 displacement 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 displacement in its terminal date likewise. {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 consisting 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, _f_). 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: 8 × 144,000 = 1,152,000 16 × 7,200 = 115,200 15 × 360 = 5,400 16 × 20 = 320 1 × 1 = 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 under the Initial-series number 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 number connected in some way with our Initial Series. The red circle surmounted by a knot which surrounds the 16 kins of this Secondary-series number (1.4.16) indicates that the whole number is to be counted _backward_ from some date. Ordinarily, the first Secondary Series in a text is to be counted from the terminal date of the Initial Series, which we have found by calculation (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 _backward_ from the date 4 Imix 9 Mol. Performing all the operations indicated in such cases, the terminal date reached will be found to be 3 Chicchan 18 Zip; this is very close to the date which is actually recorded just above the Secondary-series number and just below the Initial-series number. The date here recorded is 3 Chicchan 13 Zip, and it is not improbable that the {270} ancient scribe intended to write instead 3 Chicchan 18 Zip, the date indicated by the calculations. We probably have here: 8.16.15.16. 1 (4 Imix 9 Mol) 1. 4.16 Backward 8.16.14.11. 5 3 Chicchan 18[252] Zip In these calculations the terminal date of the Initial Series, 4 Imix 9 Mol, is suppressed, and the only date given is 3 Chicchan 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 right 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: 8 × 144,000 = 1,152,000 16 × 7,200 = 115,200 14 × 360 = 5,040 15 × 20 = 300 4 × 1 = 4 ---------- 1,272,544 Deducting from this number all the Calendar Rounds 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 Yaxkin. This date is not recorded. There follows below, however, a Secondary-series number consisting 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 _backward_ from some date, probably, as in the preceding case, from the terminal date of the Initial Series above it. Assuming that this is the case, and counting 6.1 backward from 8.16.14.15.4 4 Kan 17 Yaxkin, 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 Akbal 15 Pop, represents an impossible condition from the Maya point of view, since the day name Akbal could occupy only the first, sixth, eleventh, and sixteenth positions of a month. See Table VII. Consequently, through 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 making 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 {271} in making the correction here suggested. We have recorded here therefore: 8.16.14.15.4 (4 Kan 17 Yaxkin) 6.1 Backward 8.16.14. 9.3 13 Akbal 16[253] 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 terminal date of the Secondary Series. The above will suffice to show the use of Initial Series in 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 Förstemann[254] there are 27 of these altogether, distributed as follows: Page 24: 9. 9.16. 0. 0[255]| Page 58: 9.12.11.11. 0 Page 24: 9. 9. 9.16. 0 | Page 62: 8.16.15.16. 1 Page 31: 8.16.14.15. 4 | Page 62: 8.16.14.15. 4 Page 31: 8.16. 3.13. 0 | Page 63: 8.11. 8. 7. 0 Page 31: 10.13.13. 3. 2[256]| Page 63: 8.16. 3.13. 0 Page 43: 9.19. 8.15. 0 | Page 63: 10.13. 3.16. 4[257] Page 45: 8.17.11. 3. 0 | Page 63: 10.13.13. 3. 2 Page 51: 8.16. 4. 8. 0[258]| Page 70: 9.13.12.10. 0 Page 51: 10.19. 6. 1. 8[259]| Page 70: 9.19.11.13. 0 Page 52: 9.16. 4.11.18[260]| Page 70: 10.17.13.12.12 Page 52: 9.19. 5. 7. 8[261]| Page 70: 10.11. 3.18.14 Page 52: 9.16. 4.10. 8 | Page 70: 8. 6.16.12. 0 Page 52: 9.16. 4.11. 3 | Page 70: 8.16.19.10. 0 Page 58: 9.18. 2. 2. 0 | 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 difference 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 {272} 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 following dates are prophetic. It is a difficult 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 about the middle of Cycle 9. Says Professor Förstemann (_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 writer 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 Förstemann 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 Förstemann 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, _b, c_. The date 1 Ahau 18 Uo occurs at 9.8.16.16.0, but the writer sees no reason for believing that this date or the reading suggested by Professor Förstemann 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 is the date from which the whole calculation starts."[262] The reasons which have led Mr. Bowditch to this conclusion 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 colonization of Yucatan. There can be no doubt that very early dates appear in the Dresden Codex, but rather than accept one so early as 9.9.9.16.0 or 9.9.16.0.0 as the contemporaneous date of the manuscript 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. [Illustration: PAGE 62 OF THE DRESDEN CODEX, SHOWING THE SERPENT NUMBERS] {273} 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: 4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 7 × 7,200 = 50,400 12 × 360 = 4,320 4 × 20 = 80 10 × 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 _backward_ 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-- 4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 11 × 7,200 = 79,200 10 × 360 = 3,600 7 × 20 = 140 2 × 1 = 2 ---------- 12,466,942 {274} Assuming that the date below this number, 3 Cimi 14 Kayab, was its terminal date, the starting point can be reached by counting backward. This will be found to be 9 Kan 12 Kayab, a date actually found on this page (see pl. 32), just above the animal figure emerging from the second serpent's mouth. The black number in the second serpent reads 4.6.9.15.12.19, which reduces as follows: 4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 9 × 7,200 = 64,800 15 × 360 = 5,400 12 × 20 = 240 19 × 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. The last Serpent number in plate 32, the red number in the second serpent, reads, 4.6.1.9.15.0 and reduces as follows: 4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 1 × 7,200 = 7,200 9 × 360 = 3,240 15 × 20 = 300 0 × 1 = 0 ---------- 12,394,740 Assuming that the date below this number, 3 Kan 17 Uo,[263] 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. [Illustration: FIG. 85. Example of first method of numeration in the codices (part of page 69 of the Dresden Codex).] It will be seen from the foregoing that three 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 all-important question of course is, What position did the date 9 Kan 12 Kayab occupy in the Long Count? The page (62) of the Dresden Codex we {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 kins (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 forward 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 be 9 Kan 7 Cumhu, not 9 Kan 12 Kayab, as recorded. The most plausible explanation for this number and date the writer can offer is that the whole constitutes a Period-ending date. On the west side of Stela C at Quirigua, as explained on page 226, is a Period-ending date almost exactly like this (see pl. 21, _H_). On this monument 17.5.0.0 6 Ahau 13 Kayab is recorded, and it was proved by calculation that 9.17.5.0.0 would lead to this date if counted forward from the starting point of Maya chronology. In effect, then, 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, unexpressed) 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 earlier than 9 Kan 12 Kayab, and if we add one bar to the four dots of the uinal coefficient, 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} 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, every 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.[264] Of this series the number 8.2.0 just above the 9 Ahau 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[265] in this particular case. Counting forward then 8.2.0 from 1 Ahau, the unexpressed starting point, the first terminal date, 9 Ahau, will be reached. See the lower right-hand corner in the following outline, in which the Maya numbers have all been reduced to units of the first order: 151,840[266] 113,880[266] 75,920[266] 37,960[266] 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[267] 8,760 5,840 2,920 7 Ahau 12 Ahau 4 Ahau 9 Ahau (Unexpressed starting point, 1 Ahau.) In the above outline 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 counted forward from 4 Ahau in order to reach 12 Ahau, but from 1 Ahau instead, and so on throughout the series. {277} Beginning with the number 2,920 and the starting point 1 Ahau, the first twelve terms, that is, the numbers in the three lowest rows, are the first 12 multiples of 2,920. 2,920 = 1 × 2,920 20,440 = 7 × 2,920 5,840 = 2 × 2,920 23,360 = 8 × 2,920 8,760 = 3 × 2,920 26,280 = 9 × 2,920 11,680 = 4 × 2,920 29,200 = 10 × 2,920 14,600 = 5 × 2,920 32,120 = 11 × 2,920 17,520 = 6 × 2,920 35,040 = 12 × 2,920 The days recorded under each of these numbers, as mentioned above, are the terminal dates of these distances from the starting point, 1 Ahau. Passing over the fourth row from the bottom, which, as will appear presently, is probably an interpolation of some kind, the thirteenth number--that is, the right-hand one in the top row--is 37,960. But 37,960 is 13 × 2,920, 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 thirteenth term itself (37,960) is used as a difference to reach the remaining three terms on this top line, all of which are multiples of 37,960. 37,960 = 1 × 37,960 or 13 × 2,920 75,920 = 2 × 37,960 or 26 × 2,920 113,880 = 3 × 37,960 or 39 × 2,920 151,840 = 4 × 37,960 or 52 × 2,920 Counting forward each one of these from the starting point of this entire series, 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 difficult to understand, and the explanation offered by Professor Förstemann, that the first and third terms and the second and fourth are to be combined by addition or subtraction, leaves much to be desired. Omitting this row, however, the remaining numbers, those which are multiples of 2,920, admit of an easy explanation. In the first place, the opening term 2,920, which 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 8 Solar years of 365 days each and 5 Venus years of 584 days each. This important period is the subject of extended treatment elsewhere in the Dresden Codex (pp. 46-50), 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, 13 × 2,920, the exact number of {278} 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 three divisions of these pages. This 13th term (37,960) is the first in which 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 Maya. At the same time it represents two Calendar 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 remarkable 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 Rounds of 18,980 days each It will be noted in plate 31 that the concealed starting point of this series is the day 1 Ahau, and that just to the left on the same plate are two dates, 1 Ahau 18 Kayab and 1 Ahau 18 Uo, both of which show this same day, and one of which, 1 Ahau 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 Ahau 18 Kayab, which in turn was 9.9.9.16.0 1 Ahau 18 Kayab 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 Ahau 18 Kayab, as its terminal date. Hence, it is not improbable (more it would be unwise to say) that the series of numbers which we have been discussing was counted from the date 9.9.9.16.0. 1 Ahau 18 Kayab. 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 specialize in this field of the glyphic writing the writer recommends the treatises of Prof. Ernst Förstemann as the most valuable contribution to this subject. * * * * * {279} INDEX ABBREVIATION IN DATING, use, 222, 252 ADDITION, method, 149 ADULTERY, punishment, 9-10 AGUILAR, S. DE, on Maya records, 36 AHHOLPOP (official), 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 rulership succession, 16 BACKWARD SIGN-- glyph, 137 use, 137, 268 BAKHALAL (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, 45, 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, _Dr._ 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 _See also_ CALENDAR ROUND; CHRONOLOGY; DATING; LONG COUNT. CALENDAR ROUND-- explanation, 51-59 glyph, 59 CALENDAR-ROUND DATING-- examples, 240-245 limitations, 76 CHAKANPUTAN (city), founding and destruction 4 CHICHEN ITZA (city)-- history, 3, 4, 5, 202-203 Temple of the Initial Series, lintel, interpretation, 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, diagram showing, 15 rise and fall of, 2-5 CIVILIZATION, rise and fall, 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 errors in, 154-155 CONFEDERATION, formation and disruption, 4-5 {280} COPAN (city)-- Altar Q, error on 246, 248 Altar S, interpretation 231-233 Altar Z, interpretation 242 history 15 Stela A, interpretation 169-170 Stela B, interpretation 167-169 Stela D, interpretation 188-191 Stela J, interpretation 191-192 Stela M, interpretation 175-176 Stela N, error on 248-249 interpretation 114-118, 248-249 Stela P, interpretation 185 Stela 2, interpretation 223 Stela 4, interpretation 224-225 Stela 6, interpretation 170-171 Stela 8, interpretation 229 Stela 9, antiquity 173 interpretation 171-173 Stela 15, interpretation 187-188 CRESSON, H. T., cited 27 CUSTOMS. _See_ MANNERS AND CUSTOMS. CYCLE-- glyphs 68 length 62, 135 number of, in great cycle 107-114 numbering of, in inscriptions 108, 227-233 CYCLE 8, dates 194-198, 228-229 CYCLE 9-- dates 172, 183, 185, 187, 194, 222 prevalence in Maya dating 194 CYCLE 10, dates 199-203, 229-233 CYCLE, GREAT-- length 135, 162 number of cycles in 107-114 CYCLES, GREAT, GREAT, AND HIGHER-- discussion 114-129 glyphs 118 omitted in dating 126 DATES-- abbreviation 222, 252 errors in computing 154-155 errors in originals 245-250, 270-271, 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 shown by red glyphs in codices 251 DATES, INITIAL. _See_ INITIAL-SERIES DATING. DATES, INITIAL AND SECONDARY, interpretation 207-222 DATES, INITIAL, SECONDARY, AND PERIOD-ENDING, interpretation 233-245 DATES, PERIOD-ENDING. _See_ PERIOD-ENDING DATES. DATES, PROPHETIC-- examples 229-233 use 271-272 DATES, SECONDARY. _See_ SECONDARY-SERIES DATING. DATES, TERMINAL-- absence 218 finding 138-154 importance 154-155 position 151-154 DATING-- methods 46-47, 63-86 change 4 _See also_ CALENDAR-ROUND DATING; INITIAL-SERIES; PERIOD-ENDING; SECONDARY-SERIES. starting point 60-62, 113-114, 124-125 determination 135-136 DAY-- 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 in solar year 52-58 round of 42-44 DAYS, INTERCALARY, lack of 45 DAYS, UNLUCKY, dates 45-46 DEATH, fear of 11, 17 DEATH GOD-- glyph 17, 257 nature 17 DECIMAL SYSTEM, parallel 129 _See also_ VIGESIMAL SYSTEM. DESTRUCTION OF THE WORLD, description 32 DIVINATION, codices used for 31 DIVORCE, practice 9 DOT, numerical value 87-88 DOT AND BAR NUMBERS. _See_ BAR AND DOT NUMBERS. DRESDEN CODEX-- date 271-273 publication iii texts 254-262, 266-278 plates showing 32, 254, 260, 266, 273 DRUNKENNESS, prevalence 10 EK AHAU (god), nature 17-18 ENDING SIGNS-- in Period-ending dates 102 in "zero" 101-102 ENUMERATION-- systems 87-134 comparison 133 _See also_ NUMERALS. ERRORS IN TEXTS-- examples 245-250, 270-271, 274 plate showing 248 FEATHERED SERPENT (god), nature 16-17 FIBER-PAPER BOOKS. _See_ CODICES. FISH, used in introducing glyph 65-66, 188 FIVE-TUN PERIOD. See HOTUN. FÖRSTEMANN, _Prof._ ERNST-- cited 26, 137 investigations iii, 265, 276 methods of solving numerals 134 on hieroglyphics 30 on prophetic dates 272 FULL-FIGURE GLYPHS-- nature 67-68, 188-191 plate showing 188 _See also_ TIME PERIODS. FUNERAL CUSTOMS, description 11-12 FUTURE LIFE, belief as to 19 {281} GLYPH BLOCK, definition, 156 GLYPHS. _See_ HIEROGLYPHS. 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 GREAT CYCLE-- length, 135 number of cycles in, 107-114 HAAB (solar year)-- first day, 52-56 glyph, 47 nature, 44-51 position of days in, 48, 52-58 subdivisions, 45 HABITAT OF THE MAYA, 1-2 map, 1 HAIR, method of dressing, 7 HALACH UINIC (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, 24-25, 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_ FULL-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, 154-155 errors in original text, 245-250 methods, 134-155 inversion of significance, 211 mat pattern, 191-194 materials inscribed upon, 22 modifications, 23-25 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 HISTORY-- codices containing, 32-33 dates, 179, 221-222, 228-229, 249-250 decipherment, iv-v, 26, 250 dates only, 249-250 outline, 2-7 recording, methods, 33-36 HODGE, F. 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 IKONOMATIC 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, 84-85, 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, 157-191 replacement by u kahlay katunob 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, 245-250 historical dates, 179 interpretation, 33-35 examples, 156-250 method, 134-155 length of great cycle used in, 107-114 numeration glyphs. _See_ NUMERALS. _See also_ MONUMENTS; STELÆ. INTRODUCING GLYPH-- lack, 208 nature, 64-68, 125-127, 136, 157-158 INVERTED GLYPH, meaning, 211 ITZAMNA (god), nature, 16 JUSTICE, rules of, 9 KATUN (time period)-- glyph, 68-69 identification in u kahlay katunob, 79-82 length, 62, 135 monument erected to mark end, 250 naming, 80-82 series of, 79-86 use of, in Period-ending dates, 222-225 {282} KIN. _See_ DAY. KUKULCAN (god), nature, 16-17 LABOR, 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 LANDRY, M. D., investigations, 194 LEYDEN PLATE, interpretation, 179, 194-198 LITERATURE, list, xv-xvi See also BIBLIOGRAPHY. LONG COUNT-- date fixing in, 147-151, 240-245 nature, 60-63 See also CHRONOLOGY. MAIZE GOD, nature, 18 MALER, TEOBERT-- 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 MARS-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 UINAL. 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_ STELÆ. MOON, computation of revolutions, 32 MORLEY, S. G., on Books of Chilan Balam, 3 MYTHOLOGY, dates, 179, 180, 194, 228 NACON (official), duties, 13 NAHUA, influence on Maya, 5-6 NARANJO (city)-- antiquity, 15 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-PERIOD GLYPHS. _See_ TIME PERIODS. NORTH STAR, deification, 18 NUMBERS, 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, for 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_ HIEROGLYPHS; THIRTEEN; TWENTY; ZERO. NUMERICAL COEFFICIENTS 127-128 PALENQUE (city)-- history, 15 palace stairway inscription, interpretation, 183-185 Temple of the Cross, tablet, interpretation, 205-207, 227 Temple of the Foliated Cross, tablet, interpretation, 180-181, 223-224, 227 Temple of the Inscriptions, tablet, interpretation, 84, 225-226 Temple of the Sun, tablet, interpretation, 181-182 PERIOD-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 PIEDRAS 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 {283} QUEN SANTO (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 founding 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, 235-240 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 Zoömorph G, interpretation, 186-187, 229-230, 239-240 Zoömorph P, interpretation 157-162 READING, order of, 23, 129, 133, 135, 138, 156, 170, 268 RELIGION, nature, 16-21 RENAISSANCE, commencement, 4 ROCHEFOUCAULD, F. A. DE LA, alphabet devised by, 27 ROMAN SYSTEM OF NUMBERS, parallel, 87 ROSNY, LEON DE, cited, 27 RULERSHIP-- 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 SELER, _Dr._ EDUARD-- 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 STELÆ-- character, 22 dates, 33, 83-84 inscriptions on, 22, 33-35 See also MONUMENTS, and names of cities. STONES, inscriptions on 22 SUPERFIX, effect 120-122 SUPPLEMENTARY SERIES-- closing-sign, 152-153, 170 explanation, 152, 161 lack of, examples, 163-164, 175 position, 152, 238 SYMMETRY IN 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, 226 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, 134-155 expression, 63-64, 105-107 indicated by black glyphs, 251 marked by monuments, 33-35, 249-250 method of describing, 46-48 recording, 33-36 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, 67-68, 188-191 plate showing, 188 head-variant glyphs, 67-74 plates showing, 167, 170, 176, 178, 179, 180 length, 62 normal glyphs, 67-74 plate showing, 157 omission of, 128 reduction to days, 134-135 _See also_ CYCLE; GREAT CYCLE; HAAB; KATUN; TONALAMATL; TUN; UINAL. TONALAMATL (time period)-- graphic representation, 93 interpretation, 254-266 {284} nature, 41-44, 265 relation to zero sign, 93-94 starting point, 252-253 subdivisions, 44 texts recording, 251-266 essential parts of, 265 use of glyph for "20" with, 92, 130, 254, 260, 263 used in codices, 251-266 plates showing, 254, 260, 262, 263 used in divination, 251 wheel of days, 43 _See also_ YEAR, SACRED. TRANSLATION OF GLYPHS-- errors, 154-155 methods, 134-155 progress, 250 TUN (time period)-- glyph, 70 length, 62, 135 use of, in Period-ending dates, 225-226 TUXTLA STATUETTE, interpretation, 179, 194-196 TWENTY-- glyphs, 91-92, 130 need for, in codices, 92, 130 needlessness of, in inscriptions, 92 use of in, 254, 260, 263 UINAL-- days, 42 first day, 53 glyph, 94 glyph, 70-71 length, 45, 62, 135 list, 45 names and glyphs for, 48-51 U KAHLAY KATUNOB DATING-- accuracy, 82 antiquity, 82-85 explanation, 79-86 katun sequence, 80-82 order of reading, 137 replacement of Initial-series dating by, 84-86 UXMAL (city), founding, 4 VENUS-SOLAR PERIOD-- divisions, 31-32 relation to tonalamatl, 32, 277-278 VIGESIMAL NUMERATION-- discovery, iii explanation, 62-63, 105-134 possible origin, 41 used in codices, 266-273 VILLAGUTIERE, S. J., on Maya records, 36 WAR GOD, nature, 17 WEAPONS, character, 10-11 WORLD, destruction, prophecy, 32 WORLD EPOCH, glyph, 125-127 WORSHIP, practices, 19-20 WRITING. _See_ HIEROGLYPHICS; NUMERALS; READING. XAMAN EK (god), nature 18 YAXCHILAN (city)-- lintel, error in, 245-246 Lintel 21, interpretation, 207-210 Stela 11, interpretation, 176-177 Structure 44, interpretation, 177-178 YEAR, SACRED, use in divination, 251 _See also_ TONALAMATL. YEAR, SOLAR. _See_ HAAB. YUCATAN-- colonization, 3-4 Spanish conquest, 6-7 water supply, 1 YUM KAAX (god), nature. 18 ZERO-- glyphs, 92-95, 101-102 origin, 93-94 variants, 93 * * * * * NOTES [1] 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. [2] The correlation of 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 Archæology_, No. 11). See Morley, 1910 b, cited in BIBLIOGRAPHY, pp. XV, XVI. There are at least six other systems of correlation, however, on which the student must pass judgment. Although no two of these agree, all are based on data derived from the same source, namely, the Books 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 Calendars used in The Books of Chilan Balam." 2. That of Prof. Eduard Seler (1902-1908: I, pp. 588-599). See also _Bulletin 28_, 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. 434-459; II, 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 urged to examine with care The Books of Chilan Balam. [3] It is probable that at this early date Yucatan had not been discovered, or at least not colonized. [4] This evidence is presented by The Books of Chilan Balam, "which were copied or compiled in Yucatan 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 Tizimia, and so on. Although much of the material 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 accounts 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."--MORLEY, 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 documents from which they were copied were probably aboriginal, and contemporaneous, or approximately so, with the later periods of the history which they record. [5] As will appear later, on the calendric 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 well 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. [6] The confederation of these three Maya cities may have served as a model for the three Nahua cities, Tenochtitlan, Tezcuco, and Tlacopan, when they entered into a similar alliance some four centuries later. [7] By Nahua is here meant the peoples who inhabited the valley of Mexico and adjacent territory at this time. [8] The Ball Court, a characteristically Nahua development. [9] One authority (Landa, 1864: p. 48) says in this connection: "The governor, Cocom--the ruler of Mayapan--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 Xicalango, 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." [10] 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 survivors 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 sacrificed. 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 expedition, however. [11] Diego de Landa, second bishop of Merida, whose remarkable 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 born in Cifuentes de l'Alcarria, Spain, in 1524. At the age of 17 he joined the Franciscan order. He came to Yucatan during the decade following 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 Abbé 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. [12] 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. [13] 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. [14] Landa, 1864: p. 137. [15] 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 Sacrificios, Quirigua, and Seibal. The occupancy 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 9.19.10.0.0; and of Altar de Sacrificios to 9.14.0.0.0. (This new material is not embodied in pl. 2.) [16] As will be explained in chapter V, the writer has suggested the name _hotun_ for the 5 tun, or 1,800 day, period. [17] Succession in the Aztec royal house was not determined by primogeniture, though the supreme office, the _tlahtouani_, as well as the other high offices of state, was hereditary in one family. On the death of 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 for that exalted office. The situation may be summarized by the statement that while the supreme ruler among the Aztec had to be of the "blood royal," his selection was determined by personal merit rather than by primogeniture. [18] There can be no doubt that Förstemann has identified the sign for the planet Venus and possibly a few others. (See Förstemann, 1906: p. 116.) [19] Brasseur de Bourbourg, the "discoverer" of Landa's manuscript, added several signs of his own invention to the original Landa alphabet. See his introduction 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. Hilborne 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 he was perhaps the best of them all, much of his work in this particular respect will not stand. [20] Thus the whole rebus in figure 14 reads: "Eye bee leaf ant rose can well bear awl four ewe." These words may be replaced by their homophones as follows: "I believe Aunt Rose can well bear all for you." Rebus writing depends on the principle of homophones; that is, words or characters which sound alike but have different meanings. [21] The period of the synodical revolution of Venus as computed to-day is 583.920 days. [22] According to modern calculations, the period of the lunar revolution is 29.530588, or approximately 29½ days. For 405 revolutions the accumulated error would be .03×405=12.15 days. This error the Maya 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 total of 177 days; and the second 6 revolutions also being computed at 29.5 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 modern calculations, 502.02. [23] This is the tropical year or the time from one equinox to its return. [24] Landa, 1864: p. 52. [25] Cogolludo, 1688: I, lib. IV, V, p. 186. [26] 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. [27] It is possible that the Codex Peresianus may treat of historical matter, as already explained. [28] Since the sequence of the twenty day names was continuous, it is obvious that it had no beginning or ending, like the rim of a wheel; consequently any day name may be chosen arbitrarily as the starting point. In the accompanying 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 days or calendar is called Hun-ymix [i. e. 1 Imix]". Again, "Here commences the count of the calendar of the Indians, saying in their language Hun Imix (*) [i. e. 1 Imix]." (Ibid., p. 246.) [29] Professor Seler says the Maya of Guatemala called this period the _kin katun_, or "order of the days." He fails to give his authority for this statement, however, and, as will appear later, these terms have entirely different meanings. (See _Bulletin 28_, p. 14.) [30] As Bishop Landa wrote not later than 1579, this is Old Style. The corresponding day in the Gregorian Calendar would be July 27. [31] This is probably to be accounted for by the fact that 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 follow, and the writer believes the sign for the haab will yet be discovered. [32] Later researches of the writer (1914) have convinced him that figure 19, _c_, is not a sign for Uo, but a very unusual variant of the sign for Zip, found only at Copan, and there only on monuments belonging to the final period. [33] The writer was able to prove during his last trip to the Maya field that figure 19, _f_, is not a sign for the month Zotz, as suggested by Mr. Bowditch, but a very unusual form representing Kankin. This identification is supported by a number of examples at Piedras Negras. [34] 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. [35] _Bulletin 28_, p. 330. [36] All Initial Series now known, with the exception of two, have the date 4 Ahau 8 Cumhu as their common point of departure. The two exceptions, the Initial Series on the east side of Stela C 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 born 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. [37] Some writers have called the date 4 Ahau 8 Cumhu, the normal date, probably because it is the standard date from which practically all Maya calculations proceed. The writer has not followed this practice, however. [38] That is, dates which signified present time when they were recorded. [39] This statement does not take account of the Tuxtla Statuette and the Holactun Initial Series, which extend the range of the dated monuments to ten centuries. [40] 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. [41] 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 Quirigua, already noted. [42] Mr. Bowditch (1910: App. VIII, 310-18) discusses the possible meanings of this element. [43] For explanation of the term "full-figure glyphs," see p. 67. [44] See the discussion of Serpent numbers in Chapter VI. [45] These three inscriptions are found on Stela N, west side, at Copan, the tablet of the Temple of the Inscriptions at Palenque, and Stela 10 at Tikal. For the discussion of these inscriptions, see pp. 114-127. [46] The discussion of glyphs which may represent the great cycle or period of the 6th order will be presented on pp. 114-127 in connection with the discussion of numbers having six or more orders of units. [47] The figure on Zoömorph B at Quirigua, however, has a normal human head without grotesque characteristics. [48] The full-figure glyphs are included with the head variants in this proportion. [49] Any system of counting time which describes a date in such a manner that it can not recur, satisfying all the necessary conditions, for 374,400 years, must be regarded as absolutely accurate in so far as the range of human life on this planet is concerned. [50] There are a very few monuments which 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, Stelæ F, D, E, and A at Quirigua, Stela 17 at Tikal, and Stela 11 at Yaxchilan. [51] Refer to p. 64 and figure 23. It will be noted that the third tooth (i. e. day) after the one named 7 Akbal 11 Cumhu is 10 Cimi 14 Cumhu. [52] This method of dating does not seem to have been used with either uinal 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. [53] 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. [54] The u kahlay katunob on which the historical summary given in Chapter I is based shows an absolutely uninterrupted sequence of katuns for more than 1,100 years. See Brinton (1882 b: pp. 152-164). It is necessary to note here a correction on p. 153 of that work. Doctor Brinton has omitted a Katun 8 Ahau from this u kahlay katunob, which is present in the Berendt copy, and he has incorrectly assigned the abandonment of Chichen Itza to the preceding katun, Katun 10 Ahau, whereas the Berendt copy shows this event took place during the katun omitted, Katun 8 Ahau. [55] 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. [56] 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 katuns. [57] The word "numeral," as used here, has been restricted to the first twenty numbers, 0 to 19, inclusive. [58] See p. 96, footnote 1. [59] In one case, on the west side of Stela E at Quirigua, the number 14 is also shown with an ornamental element (). 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. [60] In the examples given the numerical coefficients are attached as prefixes to the katun sign. Frequently, however, they occur as superfixes. In such cases, however, the above observations apply equally well. [61] Care should be taken to distinguish the number or 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. [62] The Maya numbered by relative position from bottom to top, as will be presently explained. [63] This form of zero is always red and is used with black bar and dot numerals as well as with red in the codices. [64] 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 Féjerváry-Mayer an outline formed by the 260 days of the tonalamatl exactly like the one in fig. 48, _a_, is shown. [65] 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 three times in the Codex Peresianus. [66] 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. [67] The following possible exceptions, however, should be noted: In the Codex Peresianus the normal form of the tun sign sometimes occurs attached to varying heads, as (). Whether these heads denote numerals is unknown, 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 head () is almost surely that for the number 16, the hatchet eye denoting 6 and the fleshless lower jaw 10. Compare (+) with fig. 53, _f-i_, where the head for 16 is shown. The glyph () here shown is the normal form for the kin sign. Compare fig. 34, b. The meaning of these two forms would thus seem to be 16 kins. In the passage in which these glyphs occur the glyph next preceding the head for 16 is "8 tuns," the numerical coefficient 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 the general consideration of head-variant numerals presented above. [68] 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 for 3 (i. e., 10 + 3 = 13). [69] For the discussion of Initial Series in cycles other than Cycle 9, see pp. 194-207. [70] The subfixial element in the first three forms of fig. 54 does not seem to be essential, since it is wanting in the last. [71] As previously explained, the number 20 is used only in the codices and there only in connection with tonalamatls. [72] 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. [73] The numerals and periods given in fig. 56 are 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 in fig. 56 could be expressed equally well by its corresponding head form without affecting in the least the values of the resulting numbers. [74] There may be three other numbers in the inscriptions which are considerably higher (see pp. 114-127). [75] 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. [76] This case occurs on the tablet from the Temple of the Foliated Cross at Palenque. [77] 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. [78] 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. [79] 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. [80] See p. 156 and fig. 66 for method of designating the individual glyphs in a text. [81] The kins are missing from this number (see A9, fig. 60). At the maximum, however, they could increase this large number only by 19. They have been used here as at 0. [82] As will be explained presently, the kin sign is frequently omitted and its coefficient attached to the uinal glyph. See p. 127. [83] Glyph A9 is missing but undoubtedly was the kin sign and coefficient. [84] The lowest period, the kin, is missing. See A9, fig. 60. [85] The use of the word "generally" seems reasonable here; these three texts come from widely separated centers--Copan in the extreme southeast, Palenque in the extreme west, and Tikal in the central part of the area. [86] A few exceptions to this have been noted on pp. 127, 128. [87] The Books of Chilan Balam have been included here as they are also expressions of the native Maya mind. [88] This excludes, of course, the use of the numerals 1 to 13, inclusive, in the day names, and in the numeration of the cycles; also the numerals 0 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. [89] 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. Bowditch (1910: pp. 302-309) is probably the most serviceable. Of the tables Mr. Goodman's Archæic Annual Calendar and Archæic 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 calendar. This method was first devised by Prof. Ernst Förstemann, and has the advantage of being the most readily understood by the beginner, sufficient reason for its use in this book. [90] This number is formed on the basis of 20 cycles to a great cycle (20×144,000=2,880,000). The writer assumes that he has established the fact that 20 cycles were required to make 1 great cycle, in the inscriptions as well as in the codices. [91] 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. [92] These intervening glyphs the writer believes, as stated in Chapter II, are those which tell the real story of the inscriptions. [93] Only two exceptions to this rule have been noted throughout the Maya territory: (1) The Initial Series on 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. [94] In the inscriptions an Initial Series may always be identified by the so-called introducing glyph (see fig. 24) which invariably precedes it. [95] Professor Förstemann 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.) [96] There are a few cases in which the "backward sign" includes also the numeral in the second position. [97] In the text wherein this number is found the date 4 Ahau 8 Camhu stands below the lowest term. [98] It should be noted here that in the _u kahlay katunob_ also, from the Books of Chilan Balam, the count is always forward. [99] For transcribing the Maya numerical notation into the characters of 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 kin are written 4.8.3.1; and 9 cycles, 16 katuns, 1 tun, 0 uinal, and 0 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. [100] The reason 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. [101] The student can prove this point for himself by turning to the tonalamatl wheel in pl. 5; after selecting any 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. [102] The student may prove this for himself 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. [103] 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 be used as bases of reference for dates whose positions in the Long Count are not recorded. [104] In adding two Maya numbers, for example 9.12.2.0.16 and 12.9.5, care should be taken first to arrange like units 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 18s possible have been deducted from this sum (here 0) place the remainder (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. 5 ------------ 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; 0 katuns from 11 katuns (1 katun having been borrowed) = 11 katuns; and 0 cycles from 9 cycles = 9 cycles. [105] The Supplementary Series present perhaps the most promising field for future study and investigation in the Maya texts. They clearly have to do with a numerical count of some kind, which of itself should greatly facilitate progress in their interpretation. Mr. Goodman (1897: p. 118) has suggested that in some way the Supplementary Series record the dates of the Initial Series they accompany according to some other and unknown method, though he offers no proof in support of this hypothesis. Mr. Bowditch (1910: p. 244) believes they probably relate to time, because the glyphs of which they are composed have numbers attached to them. He has suggested the name Supplementary Series by which they are known, implying in the designation that these Series in some way supplement or complete the meaning of the Initial Series with which they are so closely connected. The writer believes that they treat of some lunar count. It seems almost certain that the moon glyph occurs repeatedly in the Supplementary Series (see fig. 65). [106] The word "closing" as used here means only that in reading from left to right and from top to bottom--that is, in the normal order--the sign shown in fig. 65 is always the last one in the Supplementary Series, usually standing immediately before the month glyph of the Initial-series terminal date. It does not signify, however, that the Supplementary Series were to be read in this direction, and, indeed, there are strong indications that they followed the reverse order, from right to left and bottom to top. [107] In a few cases the sign shown in fig. 65 occurs elsewhere in the Supplementary Series than as its "closing" glyph. In such cases its coefficient is not restricted to the number 9 or 10. [108] 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 Imix, 7 Kan, etc. This is nearly always the case in tonalamatls and in certain series of numbers in the Dresden Codex. [109] Only a very few month signs seem to be recorded in the Codex Tro-Cortesiano and the Codex Peresianus. The Tro-Cortesiano has only one (p. 73b), in which the date 13 Ahau 13 Cumhu is recorded thus (). Compare the month form in this date with fig. 20, _z-b'_. Mr. Gates (1910: p. 21) finds three month signs in the Codex Peresianus, on pp. 4, 7, and 18 at 4c7, 7c2, and 18b4, respectively. The first of these is 16 Zac (). Compare this form with fig. 20, _o_. The second is 1 Yaxkin (+). Compare this form with fig. 20, _i-j_. The third is 12 Cumhu (++); see fig. 20, _z-b'_. [110] As used throughout this work, the word "inscriptions" is applied only to texts from the monuments. [111] 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 columns, that is, from left to right and top to bottom. [112] Initial Series which have all their period glyphs expressed by normal forms are comparatively rare; consequently the four examples presented in pl. 6, although they are the best of their kind, leave something to be desired in other ways. In pl. 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 Supplementary 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 reproduction), 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 differentiation than the corresponding head variants. [113] 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 Zoömorph P at Quirigua will be found in Maudslay, 1889-1902: II, pls. 53, 54, 55, 56, 57, 59, 63, 64. [114] All glyphs expressed in this way are to be understood as inclusive. Thus A1-B2 signifies 4 glyphs, namely, A1, B1, A2, B2, [115] The introducing 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. [116] The Initial Series on Stela 10 at Tikal is the only exception known. See pp. 123-127. [117] As will appear in the following examples, nearly all Initial Series have 9 as their cycle coefficient. [118] In the present case therefore so far as these calculations are concerned, 3,900 is the equivalent of 1,427,400. [119] It should be remembered in this connection, as explained on pp. 47, 55, that the positions in the divisions 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. [120] As stated in footnote 1, p. 152, the meaning of the Supplementary Series has not yet been worked out. [121] The reasons which have led the writer to this conclusion are given at some length on pp. 33-36. [122] For the full text of this inscription see Maler, 1908 b: pl. 36. [123] Since nothing but Initial-series texts will be presented in the plates and figures immediately following, a fact which the student will readily detect by the presence of the introducing glyph at the head of each text, it is unnecessary to repeat for 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 Series hereinafter figured will always be the date 4 Ahau 8 Cumhu and that the direction of the count will always be forward. [124] As will appear later, in connection with the discussion of the Secondary Series, the Initial-series date 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. [125] For the full text of this inscription see Hewett, 1911: pl. XXXV _C_. [126] So far as the writer knows, the existence of a period containing 5 tuns has not been suggested heretofore. The very general practice of closing inscriptions with the end of some particular 5-tun period in the Long Count, as 9.18.5.0.0, or 9.18.10.0.0, or 9.18.15.0.0, 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. Consequently, it seems likely that there was a special glyph to express this unit. [127] For the full text of this inscription see Maler, 1908 b: pl. 39. [128] The student should note that from this point steps 2 (p. 139) and 3 (p. 140) have been omitted in discussing each text (see p. 162, footnote 3). [129] In each of the above cases--and, indeed, in all the examples following--the student should perform the various calculations by which the results are reached, in order to familiarize himself with the workings of the Maya chronological system. [130] 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, _s-u_, above. [131] The full text of this inscription will be found in Maudslay, 1889-1901: I, pls. 35-37. [132] The full text of this inscription is given in Maudslay, 1889-1902: I, pls. 27-30. [133] Note the decoration on the numerical bar. [134] So far as known to the writer, this very unusual variant for the closing glyph of the Supplementary Series occurs in but two other inscriptions in the Maya territory, namely, on Stela N at Copan. See pl. 26, Glyph A14, and Inscription 6 of the Hieroglyphic Stairway at Naranjo, Glyph A1 (?). (Maler, 1908 b: pl. 27.) [135] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 105-107. [136] 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 0 uinals, and only after this has been read does B4a follow. [137] Texts illustrating the head-variant numerals in full will be presented later. [138] The preceding hotun ended with the day 9.12.5.0.0 3 Ahau 3 Xul and therefore the opening day of the next hotun, 1 day later, will be 9.12.5.0.1 4 Imix 4 Xul. [139] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 109, 110. [140] 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. [141] 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 monuments, which, the writer believes, were period-markers. 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 undeciphered. [142] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 17-19. [143] Although this date is considerably older than that on Stela 9 at Copan, its several glyphs present none of the marks of antiquity noted in connection with the preceding example (pl. 8, _B_). 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 Kayab, more than three hundred years later than the Initial Series 9.1.0.0.0 6 Ahau 13 Yaxkin 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 C was erected to mark, but some far earlier date in Maya history. [144] For the full text of this inscription see Maudslay, 1889-1902: I, pl. 74. [145] For the full text of this inscription see Maler, 1903: II, No. 2, pls. 74, 75. [146] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 79, 2. [147] For the full text of this inscription see Maler, 1911: V, No. 1, pl. 15. [148] As used throughout 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 2 Kan 2 Yax on Lintel 21 at Yaxchilan, 9.1.0.0.0 6 Ahau 13 Yazkin on the west side of Stela C at Quirigua, and 9.4.0.0.0 13 Ahau 18 Yax 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. [149] 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. [150] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 4-7. [151] For the full text of this inscription see Maudslay, 1889-1902: IV, pls. 80-82. [152] 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 civilization by upward of 3,000 years. [153] For the full text of this inscription see Maudslay, 1889-1902; IV, pls. 87-89. [154] For the full text of this inscription, see Maudslay, 1889-1902: IV, pl. 23. [155] It is clear that if all the period coefficients above the kin have been correctly identified, even though the kin coefficient is unknown, by designating it 0 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 0 as the kin coefficient, therefore, we can not be more than 19 days from the original date. [156] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 88, 89. [157] While at Copan the writer made a personal examination of this monument and found that Mr. Maudslay's drawing is incorrect as regards the coefficient of the day sign. The original has two numerical dots between two crescents, whereas the Maudslay drawing shows one numerical dot between two distinct pairs of crescents, each pair, however, of different shape. [158] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 41-44. [159] For the text of this monument see Spinden, 1913: VI, pl. 23, 2. [160] For the discussion of full-figure glyphs, see pp. 65-73. [161] The characteristics of the heads for 7, 14, 16, and 19 will be found in the heads for 17, 4, 6, and 9, respectively. [162] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 47, 48. [163] The student will note also in connection with this glyph that the pair of comblike appendages usually found are here replaced by a pair of fishes. As explained on pp. 65-66, the fish represents probably the original form from which the comblike element was derived in the process of glyph conventionalization. The full original form of this element is therefore in keeping with the other full-figure forms in this text. [164] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 66-71. [165] The student should remember that in this diagonal the direction of reading is from bottom to top. See pl. 15, _B_, glyphs 7, 8, 9, 10, 11, 12, etc. Consequently the upper half of 13 follows the lower half in this particular glyph. [166] For the full text of this inscription see Hewett, 1911: pl. XXII _B_. [167] A few monuments at Quirigua, namely, Stelæ F, D, E, and A, have two Initial Series each. In A both of the Initial Series have 0 for the coefficients of their uinal and kin glyphs, and in F, D, E, the Initial Series which shows the position of the monument in the Long Count, that is, the Initial Series showing the katun ending which it marks, has 0 for its uinal and kin coefficients. [168] 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 katun ending prior to the one on Stela H, i. e., 9.15.15.0.0 9 Ahau 18 Xul. [169] For the full text of this inscription see Holmes, 1907: pp. 691 et seq., and pls. 34-41. [170] For a full discussion of the Tuxtla Statuette, including the opinions of several writers as to its inscription, 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. [171] For the full text of these inscriptions, see Seler, 1902-1908: II, 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-10 Initial Series, namely, 10.2.0.0.0. 3 Ahau 3 Ceh. [172] Missing. [173] At Seibal a Period-ending date 10.1.0.0.0 5 Ahau 3 Kayab is clearly recorded, but this is some 30 years earlier than 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 shifting 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. [174] 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 connection with the date 6 Ahau 18 Kayab, 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. Bowditch (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, pls. 39-41. [175] For the full text of this inscription, see ibid.: II, pls. 16, 17, 19. [176] Table XVI contains only 80 Calendar Rounds (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. [177] Counting 13.0.0.0.0 backward from the starting point of Maya chronology, 4 Ahau 8 Cumhu, gives the date 4 Ahau 8 Zotz, which is no nearer the terminal date recorded in B5-A6 than the date 4 Ahau 3 Kankin reached by counting forward. [178] For the full text of this inscription, see Maudslay, 1889-1902: IV, pls. 73-77. [179] 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 giving 13. Usually the head for 13 is represented by a form peculiar to this number alone and is not built up by the combination of lower numbers as in this case. [180] Although at first sight the headdress resembles the tun sign, a closer examination shows that it is not this element. [181] Similarly, it could be shown that the use of every other possible value of the cycle coefficient will not give the terminal date actually recorded. [182] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 56. [183] 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. [184] 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. [185] The number 15.1.16.5 is equal to 108,685 days, or 297½ years. [186] It is interesting to note in this connection that the date 9.16.1.0.0 11 Ahau 8 Tzec, which is within 9 days of 9.16.1.0.9 7 Muluc 17 Tzec, is recorded in four different inscriptions at Yaxchilan, one of which (see pl. 9, _A_) has already been figured. [187] For the full text of this inscription see Maler, 1901: II, No. 1, pl. 12. [188] The month-sign indicator appears in B2 with a coefficient 10. [189] Not expressed. [190] The writer has recently established the date of this monument as 9.13.15.0.0 13 Ahau 18 Pax, or 99 days later than the above date. [191] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 47-49. [192] 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 probably Yax. See fig. 19, _q, r_. [193] Since the Maya New Year's day, 0 Pop, always fell on the 16th of July, the day 3 Yax always fell on Jan. 15th, at the commencement of the dry season. [194] Since 0 Pop fell on July 16th (Old Style), 18 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. [195] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 46. [196] Bracketed dates are those which are not actually recorded but which are reached by numbers appearing in the text. [197] Although not recorded, the number 1.14.6 is the distance from the date 9.15.5.0.0 reached by the Secondary Series on one side to the starting point of the Secondary Series on the other side, that is, 9.15.6.14.6 6 Cimi 4 Tzec. [198] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 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. [199] This is one of the two Initial Series which justified the assumptions made in the previous text that the date 12 Caban 5 Kayab, which was recorded there, had the Initial-series value 9.14.13.4.17, as here. [200] This is the text in which the Initial-series value 9.15.6.14.6 was found attached to the date 6 Cimi 4 Tzec. [201] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 38, 40. [202] 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. [203] See Maudslay, 1889-1902: I, pl. 102, west side, glyphs A5b-A7a. [204] See ibid.: IV, pl. 81, glyphs N15 O15. [205] See Maler, 1908 b: IV, No. 2, pl. 38, east side, glyphs A17-B18. [206] See ibid., 1911: V, pl. 26, glyphs A1-A4. [207] See Maudslay, 1889-1902: I, pl. 104, glyphs A7, B7. [208] See Maudslay, 1889-1902: IV, pl. 60, glyphs M1-N2. [209] Maler, 1911: V, pl. 17, east side, glyphs A4-A5. [210] See Maudslay, 1889-1902: II, pl. 19, west side, glyphs B10-A12. [211] See Maudslay, 1889-1902: IV, pl. 75, glyphs D3-C5. [212] See Maler, 1901: II, No. 1, pl. 8, glyphs A1-A2. [213] See Maudslay, op. cit., pl. 81, glyphs C7-D8. [214] It will be remembered that Uayeb was the name for the _xma kaba kin_, the 5 closing days of the year. Dates which fall in this period are exceedingly rare, and in the inscriptions, so far as the writer knows, have been found only at Palenque and Tikal. [215] See Maudslay, 1889-1902: IV, pl. 77, glyphs P14-R2. Glyphs Q15-P17 are omitted from pl. 22, _G_, as they appear to be uncalendrical. [216] See Maudslay, 1889-1902: I, pl. 100, glyphs C1 D1, A2. [217] This excludes Stela C, which has two Initial Series (see figs. 68 and 77), though neither of them, as explained on p. 175, footnote 1, records the date of this monument. The true date of this monument is declared by the Period-ending date figured in pl. 21, _H_, which is 9.17.0.0.0 6 Ahau 13 Kayab. (See p. 226.) [218] See Maudslay, 1889-1902: II, pl. 44, west side, glyphs G4 H4, F5. [219] The dates 10.2.5.0.0 9 Ahau 18 Yax and 10.2.10.0.0 2 Ahau 13 Chen on Stelæ 1 and 2, respectively, at Quen Santo, are purposely excluded from this statement. Quen Santo is in the highlands of Guatemala (see pl. 1) and is well to the south of 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 civilization. [220] See Maler, 1908 a: IV, No. 1, pl. 9, glyphs E2, F2, A3, and A4. [221] The student will note that the lower periods (the tun, uinal, and kin signs) are omitted and consequently are to be considered as having the coefficient 0. [222] The usual positions of the uinal and kin 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. [223] In this number also the positions of the uinal and kin coefficients are reversed. [224] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 28-32. [225] The student will note that 12, not 13, tuns are recorded in A5. As explained elsewhere (see 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. [226] This Secondary-series number is doubly irregular. In the first place, the kin and uinal coefficients are reversed, the latter standing to the left of its sign instead of above, and in the second place, the uinal coefficient, although it is 14, has an ornamental dot between the two middle dots. [227] Since we counted _backward_ 1.14.6 from 6 Cimi 4 Tzec to reach 10 Ahau 8 Chen, we must _subtract_ 1.14.6 from the Initial-series value of 6 Cimi 4 Tzec to reach the Initial-series value of 10 Ahau 8 Chen. [228] It is obvious that the kin and uinal coefficients are reversed in A17b since the coefficient above the uinal sign is very clearly 19, an impossible value for the uinal coefficient 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. [229] The first glyph of the Supplementary Series, B6a, very irregularly stands between the kin period glyph and the day part of the terminal date. [230] Incorrectly recorded as 12. See pp. 247, 248. [231] 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 contemporaneous 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 date in each text. [232] The Initial Series on the west side of Stela D at Quirigua is 9.16.13.4.17 8 Caban 5 Yaxkin, which was just 2 katuns later than 9.14.13.4.17 12 Caban 5 Kayab, or, in other words, the second katun anniversary, if the term anniversary may be thus used, of the latter date. [233] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 50. [234] For the full text of this inscription, see Maudslay, 1889-1902: I, pl. 112. [235] 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 Ahau 8 Zotz 9.16.10.0.0 1 Ahau 3 Zip 9.16.15.0.0 7 Ahau 18 Pop 9.17. 0.0.0 13 Ahau 18 Cumhu etc. [236] Maler, 1911: No. 1, p. 40. [237] For a seeming exception to this statement, in the codices, see p. 110, footnote 1. [238] 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. [239] 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. [240] As explained on p. 31, tonalamatls were probably used by the priests in making prophecies or divinations. This, however, is a matter apart from their composition, that is, length, divisions, dates, and method of counting, which more particularly concerns us here. [241] 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. [242] If there should be two or more columns of day signs the topmost sign of the left-hand column is to be read first. [243] 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. [244] This and similar outlines which follow are to be read down in columns. [245] 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. [246] The last sign Chuen, as mentioned above, is only a repetition of the first sign, indicating that the tonalamatl has re-entered itself. [247] As previously stated, the order of reading the glyphs in columns is from left to right and top to bottom. [248] The right-hand dot of the 13 is effaced. [249] The manuscript has incorrectly 7. [250] In the title of plate 30 the page number should read 102 instead of 113. [251] The manuscript incorrectly has 24. [252] Incorrectly recorded as 13 in the text. [253] Incorrectly recorded as 15 in the text. [254] _Bull. 28, Bur. Amer. Ethn._, p. 400. [255] The terminal dates reached have been omitted, since for comparative work the Initial-series numbers alone are sufficient to show the relative positions in the Long Count. [256] The manuscript incorrectly reads 10.13.3.13.2; that is, reversing the position of the tun and uinal coefficients. [257] The manuscript incorrectly reads 10.8.3.16.4. The katun coefficient is changed to 13, above. These corrections are all suggested by Professor Förstemann and are necessary if the calculations he suggests are correct, as seems probable. [258] The manuscript incorrectly reads 8.16.4.11.0. The uinal coefficient is changed to an 8, above. [259] The manuscript incorrectly reads 10.19.6.0.8. The uinal coefficient is changed to 1, above. [260] The manuscript incorrectly reads 9.16.4.10.18. The uinal coefficient is changed to 11, above. [261] The manuscript incorrectly reads 9.19.8.7.8. The tun coefficient is changed to 5, above. [262] Bowditch, 1909: p. 279. [263] The manuscript has incorrectly 16 Uo. It is obvious this can not be correct, since from Table VII 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. [264] 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. [265] Counting backward 8.2.0 (2,920) from 9 Ahau, 1 Ahau is reached. [266] Professor Förstemann restored the top terms of the four numbers in this row, so as to make them read as given above. [267] The manuscript reads 1.12.5.0, which Professor Förstemann corrects to 1.12.8.0; in other words, changing the uinal from 5 to 8. This correction is fully justified in the above calculations.