memoranda on the maya calendars used in the books of chilan balam by charles p. bowditch (from the american anthropologist (n. s.), vol. , january-march, ) new york g. p. putnam's sons 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) ymix, was the day on which ahpula died; and that the count may be known in numbers and years, it was the year . 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, imix was the day ahpulha died; it was the year . 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,[ ] nor whether the calendar was sufficiently perfected to prevent confusion in dates in the remote past. [ ] it should be noted that the grand cycle, which dr brinton refers to, is the period of × days = , days or periods of days; while the grand cycle according to goodman's method is × , days or periods of 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 to , 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 ahau, katun 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 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 × days. the followers of perez, however, insist that the length of the katun was × days. sr perez has indeed made this assertion,[ ] 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 ahau, katun ahau, katun ahau, katun ahau, etc., and that by starting with a katun which begins with ahau and counting forward a period of × days, we should reach another katun beginning with ahau. but the same result is brought about by considering the katun as a period of × 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 × or days. an objection to considering a katun as × 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 -day period, and that the books did not pretend to speak with scientific accuracy. [ ] stephens, _incidents of travel in yucatan_, p. 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 to . 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 ymix zip in the year kan. now this day and this year could recur only after the lapse of fifty-two years or , days. it should be noted here that in the inscriptions and in the dresden codex, the day ymix was always the day , , , or of any month, showing that the day of the month was eznab, akbal, lamat, or ben; while in landa and the books of chilan balam the day ymix was the day , , , or , showing that the day 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 days, a katun ahau could not recur until after the lapse of × or , 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 , and , . this is , , days, which is a period of calendar rounds of , days or of years each. this is equal to , years, and, in the method of reckoning shown in the initial dates of the inscriptions, would equal grand cycles, cycles, and katuns, or, to use the method of goodman, . . . . . . 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 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 or years. the day ahau 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 ahau cumhu is itself given. in this place (on stela c of quirigua) ahau cumhu is reckoned thus: "grand cycle glyph . . . . . .", 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 . i give here the first and last terms of a list of the beginning days of the katuns ahau in a complete round of , years occurring after the beginning of the grand cycle called by goodman grand cycle , which began with ahau 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 to the grand cycle glyphs common to copan, quirigua, etc. if . . . . . . or the beginning of the grand cycle, called grand cycle by goodman, begins with ahau cumhu, a katun ahau will appear two katuns after this or with the count of . . . . . . ahau mol year ix, and other katuns ahau will follow at intervals of katuns as here given: . . . . . . ahau pax year ix. . . " xul cauac. . . " kankin " . . . . . . . . . . . . . . . . . ahau ceh kan. . uo muluc. . . yax " . cumhu " . . . . . . ahau mol ix. but we are seeking a katun ahau in which tuns have elapsed and of which tuns still remain unexpired. we must, therefore, add tuns or × days = days to each of the dates given and we shall then have the following complete list of the beginning days of tun of katun ahau for the term of , years: . . . . . . ahau zotz kan. . ceh kan. . . uo muluc. . . yax muluc. . cumhu muluc. . . mol ix. . . pax ix. . xul cauac. . . kankin cauac. . zip kan. . . zac kan. . . pop muluc. . chen muluc. . . . . . . kayab muluc. . . yaxkin ix. . muan ix. . . tzec cauac. . . mac cauac. . uo kan. . . yax kan. . . . . . . cumhu kan. -------- . mol muluc. . . pax muluc. . . xul ix. . kankin ix. . . zotz cauac. . . ceh cauac. . pop kan. . . chen kan. . . kayab kan. . . yaxkin muluc. . . muan muluc. . tzec ix. . . mac ix. . . zip cauac. . zac cauac. -------- . . uayeb cauac. . . mol kan. . pax kan. . . xul muluc. . . . . . . kankin muluc. . zotz ix. . . ceh ix. . . uo cauac. . yax cauac. . . cumhu cauac. . . yaxkin kan. . muan kan. . . tzec muluc. . . mac muluc. . . zip ix. . . zac ix. . pop cauac. . . chen cauac. . . kayab cauac. . xul kan. . . kankin kan. . . zotz muluc. . ceh muluc. . . uo ix. . . . . . . yax ix. . cumhu ix. . . mol cauac. . . pax cauac. . tzec kan. -------- . . mac kan. . . zip muluc. . . zac muluc. . . pop ix. . . chen ix. . . kayab ix. . . yaxkin cauac. . muan cauac. . . zotz kan. the only places where a year kan appears are at the dates . . . . . .[ ] ahau cumhu year kan, and . . . . . . ahau tzec year kan. but as the words used are that years (or tuns) remained before the end of the katun, and as a slightly longer time than just 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 kan, it is quite possible that the beginning of the tun 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: . . . . . . ahau zac year cauac. [ ] it is necessary to remember that, by goodman's methods, these figures represent periods of past time. thus the number of the katun means that katuns have passed, and that the current katun is what we should call the third; and that . 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 ymix zip is said to be in the year kan, we shall find this date before the dates of the beginning of tun in the first two cases and after the beginning of tun in the last case. this date of ymix zip will then be numbered thus, placing the three dates in consecutive order: ) . . . . . . tuns days to end of katun ahau. ) . . . . . . " " " " " ) . . . . . . " " " " " in no one of the cases is the date ymix zip exactly tuns before the end of the katun ahau, but it is possible that the annalist took no account of fractions of tuns, either in excess of the 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 whole tuns remaining of the katun and i will call it ," or in the second case he may have said: "there are tuns remaining and days besides; i will call it 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 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 . . . . . . this precedes the above dates by the following periods: ) . . . . . . = , days = , years days. ) . . . . . = , , " = , " " ) . . . . . = , , " = , " " if, now, we accept the first date of . . . . . . as the date of ahpula's death, we shall have the date of stela of copan as a.d. , since the death occurred in . if we accept the second date, . . . . . ., as the true one, stela must represent a date of b.c. , and in the case of the third date, . . . . . . in which the period to elapse to the end of katun ahau is the nearest to an exact tuns, we should throw back copan to b.c. , . 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. 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 , . . . . a.d. . " n, . . . . = years later than a.d. a.d. . quirigua: " c, . . . . = + " earlier " " say b.c. . " k, . . . . = + " later " " a.d. . if this is correct, copan lasted, so far as the erection of stelæ is concerned, for about years, and quirigua for about 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. ) 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 ahau instead of katun ahau, while the last of the series was katun 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. 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. note: project gutenberg also has an html version of this file which includes the original illustrations. see -h.htm or -h.zip: (http://www.gutenberg.net/dirs/ / / / / / -h/ -h.htm) or (http://www.gutenberg.net/dirs/ / / / / / -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. representation of deities of the maya manuscripts by dr. paul schellhas second edition, revised with plate of figures and text illustrations translated by miss selma wesselhoeft and miss a. m. parker translation revised by the author cambridge, mass. published by the museum december, . 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, . preface. since the first edition of this pamphlet appeared in the year , 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 , kommentar zur madrider mayahandschrift, danzig , and kommentar zur pariser mayahandschrift, danzig ) 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, . 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. - ] god a is represented as a figure with an exposed, bony spine, truncated nose and grinning teeth.[ - ] 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. b 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. c 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. c) the visible vertebrae of the spine. several times (dr. b and b) 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. , 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. b and b), 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. [ - ] 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. a, they are fastened with bands wound around the forearm and around the leg; in dr. c 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. .* 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. to ). figs. and are the forms of the dresden manuscript and figs. and are those of the madrid manuscript. god a is almost always distinguished by two hieroglyphs, namely figs. and or and . moreover the hieroglyphs are always the same, have scarcely any variants. even in dr. c, 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. and and under it in fig. 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. 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. , 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. , 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. , the death-god wears a kind of breeches on which cross-bones are depicted, exactly as in dr. (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. and . elsewhere, on the other hand, this god is connected with other cardinal points, thus dr. a with the west or east (the hieroglyph is illegible, but it can be only west or east), and in dr. c 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 stands just in the place of the sign of the north; this is on tro. * (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. , 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. c, c, a and c and in other places, and the hieroglyphic group (fig. ) 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: . 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. . the moan bird. see beyond under mythological animals, no. . . the dog. see the same, no. . . a human figure, possibly representing the priest of the death-god (see dr. , centre, dr. b and a). 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. (centre). that this figure is related to the death-god is proved by the fact that on dr. a 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. . an isolated figure, dr. a (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. ). . another isolated figure is twice represented combined with the death-god in dr. c. 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. ( )a, clearly the picture of a beheaded prisoner. death symbols occur, too, with the curious picture of a hanged woman on dr. b, 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. . 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 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. . 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. c, c, a and c and elsewhere, and forms a regular attendant hieroglyph of the death-god in the group of three signs already mentioned (fig. ). 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. - ] 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. is the hieroglyph of this deity. in codex tro.-cortesianus it usually has the form of fig. . 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. b) staff in hand and a bundle on his back, and fettered (dr. a) 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. ). in dr. b, b and b, 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. , 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. b and a (compare no. of the mythological animals). he likewise occurs sitting on the serpent and in dr. a he is twice ( st and d figures) pictured with a snake in his hand. god b sits on the moan head in dr. c, on a head with the cauac-sign in dr. c, c, and on the dog in dr. a. 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. c, 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. ( ). his face with the large nose and the tongue (or fangs) hanging out on the side in dr. ( )a ( st 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. -cort. . compare förstemann, kommentar zur madrider handschrift, pp. , ). 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. c, c and . this is expressed in the hieroglyphs by the sign, fig. , 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. *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. , washington, ), 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. , no. ) and also by cyrus thomas (aids to the study of the maya codices, washington, ). 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, , p. ). 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. b), 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. b, a. on pages - 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. , no. ). c. the god with the ornamented face. [illustration: figs. - ] 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. , ). the circular design in front of the forehead of the hieroglyph head seems, as a variant from the codex tro. (fig. ) 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. *b; fig. , the symbol of the sacrificial knife, and instead of the prefix the numeral occurs in one instance! (tro. *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. (bottom) and tro. * (bottom). this deity does not occur very often in the dresden manuscript, the places where it is depicted are: dr. a, c, b, a, a, and as a subordinate figure on c, a. his hieroglyph occurs alone a few times, as in dr. ; it is more frequent in the madrid manuscript. it appears on pp. to 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. (bottom), his head is represented surrounded by a nimbus of rays, which can only mean a star (see fig. ). 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. , and (centre) fig. , in the familiar rectangular planet signs. tro. * (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. , with its continuation in the cort. p. , and in exactly the same manner in the allied passage of tro. (middle and bottom). in addition, his head is contained in the symbol for the north (fig. ); 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. , no. ), the fact that the figure of god c in the tonalamatl in dr. a- a 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. and , 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. , et seq., especially dr. c). 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. b, st and d pictures). according to förstemann, the day ruled by c seems to be chuen. d. the moon- and night-god. [illustration: figs. - ] 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. , and a second sign almost always follows (fig. ) 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. ). this character also has the significance of 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 . 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. ) 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. c). in a few other places the god is, curiously enough, depicted with a short beard, as dr. c, a, b. 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. c, 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. c and a he wears the snail on his head. he seems, therefore, like god a to be connected with birth. in dr. c 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. ), compare too dr. c, where the solitary tooth is also to be seen. in dr. a ( st figure) the god holds in his hand a kind of sprinkler with the rattles of the rattlesnake, as landa (cap. ) describes the god in connection with the rite of infant baptism (see also cort. , tro. *a and *c) a very remarkable passage is tro. *; 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, ) 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. - ] this god bears on his head the kan-sign and above it the ear of maize with leaves (fig. ); compare dr. b (left figure), b, a, etc. the hieroglyph is definitely determined (fig. ). 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. a, c, (bottom), tro. *b (figs. - ) and especially the representation in dr. a (fig. ), 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. b (fig. ) with the head ornament of the god in dr. b (fig. ), a, a; 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. - . that these gods with elongated heads are, in point of fact, identical with e is plainly seen from the passage in dr. ( )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. a and cort. a, a) 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. , 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. a) god e also holds a similar tall and slender vessel in his hands. according to all appearances the scene pictured in dr. a 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. ) 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. - ] 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. - ; it contains the number . a variant of this occurs on dr. b, where instead of the 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. - ). 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. . sometimes it encircles the eye only (dr. a) and again it is a dotted double line (dr. b). 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. a, st and d figures, in which the line likewise differs from the other forms (figs. - ). 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. , namely tro. *c. indeed, in tro. *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. ), 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. ); an exactly similar picture of the two gods of human sacrifice is given in codex tro. d; here, too, they sit opposite one another. the identity of this attendant of death with the deity, designated by the hieroglyph with the numeral , is proved by the following passages: tro. , bottom (on the extreme right hand without picture, only hieroglyph, see fig. ), dr. b, a, b, and c and many others. in some of the passages cited (dr. a and b) he is distinguished by an unusually large ear-peg. his hieroglyph occurs with the hieroglyph of the death-god in dr. c, where he is himself not pictured. as war-god, god f occurs combined with the death-god in the passages mentioned above (tro. *- *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. *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 ). spanish writers do not mention a deity of the kind described here as belonging to the maya pantheon. g. the sun-god. [illustration: figs. - ] god g's hieroglyph (fig. ) contains as its chief factor the sun-sign kin. it is one of the signs (of which there are about 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 b, c, 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. c. god g seems to be not wholly without relation to the powers of death; the owl-sign (fig. ) occurs once in connection with him (dr. c). besides the sun-sign kin, which the god bears on his body, his representations are distinguished by a peculiar nose ornament (fig. ) 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. b (middle figure), (centre), b, a, b; occasionally they also have the shape of a flower, for example b (centre), c (left), a. lastly it is worthy of note, that god g is sometimes represented with a snake-like tongue protruding from his mouth, as in dr. b and c. h. the chicchan-god. [illustration: figs. - ] 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. a, b and b. 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. and again that of fig. . the prefix likewise differs very much, having sometimes the form of fig. , and again that of fig. or of figs. and . 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. and and which leads him to assume that fig. 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. a. the crenelated, black border of the chicchan-spot in fig. passes in rapid cursive drawing almost of itself into the scallops of fig. , a transition to which there are distinct tendencies on the serpent's body in tro. a. 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. a 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. c, a, b, c, a, c. 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. , 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. *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. b, we see his hieroglyph belonging to the figure of a woman with the knotted serpent on her head, in dr. a to the god p, who there bears a serpent in his hand, and in dr. b 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. ] 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 , 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. , 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. b, b, a and . the figure corresponding to her in the madrid manuscript, in tro. and *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. . the well-known oblong signs, which förstemann (drei mayahieroglyphen, published in the zeitschrift für ethnologie, , pp. - ) 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. c, b, a, a, b and b. 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. c we find d's sign, in b that of h; on a, b and b we see only the general sign for a woman. in dr. a the signs are effaced. in the codex troano goddess i occurs on pp. b and ; there is also a woman with the knotted serpent on her head in tro. *c. in the codex cortesianus and in the paris manuscript these forms are wholly lacking. k. the god with the ornamented nose. [illustration: figs. - ] 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. ; fig. is the form in the madrid manuscript. he is closely related to god b. he is represented in dr. (centre) where he is perhaps conceived of as a priest wearing a mask with the face of the god, also in dr. a, a (with his own hieroglyph and that of e!), (bottom) with a variant of the sign. his figure without the hieroglyph occurs in dr. . very frequently the well-known group, oc, is given with him and in connection with his hieroglyph (in dr. , a, b (right); without picture, a). förstemann (drei mayahieroglyphen, zeitschrift für ethnologie, . pp - ) 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. b, (middle and bottom), (bottom, left), and tro. *b; with a variant of the attribute in dr. (third vertical row). a slight variation appears also in dr. (top, right). in dr. a (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. (bottom); the passage, however, is somewhat obliterated. the hieroglyph is lacking in this place; it is found, however, on the preceding page (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. , where b holds k's head in his hand; in dr. b, where he carries this head on his own and in dr. a where he appears to carry it in a rope. once, how ever, a variation of these plainly synonymous representations occurs, namely in dr. (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. , , , , and (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. -tro. ) 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 times on these pages with the days enumerated there. the two gods must, therefore, have either a parallel or an opposite astronomic and calendric meaning. the fact that in dr. and 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. ] god l's features are those of an old man with sunken, toothless mouth. his hieroglyph is fig. , 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. b and c and dr. b; the figure has the characteristic black face. he appears entirely black in dr. a. the hieroglyph alone occurs in dr. b and (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. b the god is pictured armed and in warlike attitude. both in dr. b and c 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 th annual report of the bureau of ethnology, washington, , p. ) 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. - ] god m's hieroglyph is figs. , ; 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. ). the god is found in the dresden manuscript only three times, namely in dr. b (with a bone in his hand) in picture and sign, in dr. c grouped with an animal, without the hieroglyph, and in dr. a (with his sign) while finally his hieroglyph alone appears in dr. (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 ( b) with his body striped black and white, and on p. a entirely white, he is always entirely black in the codex troano. his other distinguishing marks are the following: . the mouth encircled by a red-brown border. . the large, drooping under lip. by this he can be recognized with certainty also in dr. a. . 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. c, a, *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 b and a 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. , , , , always with the hieroglyph, then without it on pp. , , , *c, *b, *a, *b and again with the hieroglyph on pp. *a, *a, *a; finally it is found again without the hieroglyph on pp. *a, *a, *, *, *, *. in the codex cortesianus god m occurs in the following places: p. , where he strikes the sky with the axe and thus causes rain, p. (bottom), (bottom, second figure), (bottom) and (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. , , , *. tro. *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. *a, *a. besides his hieroglyph mentioned above, figs. and , another sign seems to refer to god m, namely fig. (compare for example tro. a and cort. , 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. , and in his commentary on the dresden manuscript, p. . he thinks the hieroglyph has relation to the revolution of venus, which is performed in 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. *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. , and (perhaps this is a black variant of b as god of the storm?) and on *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. , bottom). according to brinton (nagualism, philadelphia , pp. , ), 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. - ] we have here a deity with the features of an old man and wearing a peculiar head ornament reproduced in fig. , which contains the sign for the year of days. the god's hieroglyph is fig. , which consists of the numeral 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 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. , no. . 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. a, c (grouped with a woman) and a; also on c, but in this latter place with pronounced deviations from the usual representations. the figures in dr. c (first group) and a (third picture) are doubtful, especially since the hieroglyph of the god is lacking in both instances. the third group in dr. c 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. . 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. , where he holds k's head in his hands, and on p. . o. a goddess with the features of an old woman. [illustration: fig. ] 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. *c, *b, and *b, c and d, cort. b, a, a. in tro. * 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. ; 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. ] we call him the frog-god because in the codex tro. , 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 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. a and b, tro. (top, scattering seed) and cort. (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. a (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. . it occurs in tro. (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, , p. ) 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. b. it is designated in the text by two hieroglyphs, which belong together, figs. and , the latter occurring once with k (dr. a). it seems to represent blowing from the mouth, screaming or speaking. [illustration: figs. - ] ii. mythological animals. . the moan bird. [illustration: figs. - ] this bird[ - ] belongs to the death-god as his symbol and attendant. its hieroglyph (fig. ) contains the numeral ; other forms are figs. - . it is pictured in dr. c, a, a, c, b, and its hieroglyph without the picture is seen in dr. b. a realistic representation of the whole figure of the moan as a bird, occurs on the head of the woman in c ( st figure) and b. god b sits on the head of the moan in dr. c; the third hieroglyph of the accompanying text refers to this representation. just as in dr. and , the moan bird appears in tro. *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. a), 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. , also occurs frequently with it. [ - ] see plate for representations of the mythological animals, - . 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, ), 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_. . 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, ). 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: a, , , c, b, a, b, b , a, , , c a and . it is prominent also in the madrid manuscript, occurring for example in cort. - , - , tro. , , and elsewhere. . the dog. [illustration: fig. ] fig. 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. b where the god is distinguished by its hieroglyph. this animal is again represented in dr. a, c on the right, b with its hieroglyph, a, a (forming a part of a, where god b holds the bound dog by the tail), and a without the hieroglyph, (bottom) with a variant of the hieroglyph. in dr. a 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. (last line, nd sign) and once with the _death-god_ in dr. a. the dog as lightning-beast occurs with the akbal-sign in the eye instead of on the forehead in codex tro. *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. . according to förstemann his day is oc. . the vulture. [illustration: fig. ] this bird is distinctly pictured as a mythological figure in dr. a. it appears again, in feminine form, together with the dog, in dr. c and also in a. 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. b it is almost entirely black. the same passage displays a second hieroglyph for this figure (fig. ); this hieroglyph also occurs with the numeral in dr. b. in dr. b 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. a, b, b and b. mention should also be made of the realistic representations of the vulture, eating the eye of a human sacrifice (dr. , tro. *a and *a). according to förstemann his day is cib. . the jaguar. [illustration: fig. ] the jaguar is likewise an animal with mythological significance. it is represented in dr. a, where its hieroglyph is the third sign in the writing; it also occurs in dr. (at the top). it occurs in tro. (at the end) with a hieroglyph which represents the jaguar's head and contains the numeral (fig. ); again it appears without a hieroglyph on p. (bottom) and on and (bottom). its day is ix, and hence it also relates occasionally as year regent to the ix years, for example in dr. a. . the tortoise. [illustration: figs. - ] this animal, like the dog, appears as a lightning-beast (see dr. b, middle). its hieroglyph is figs. , . this sign also is connected with the numeral , 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. a, where the tortoise itself is also represented. it must have reference to the th month of the maya year, for the month kayab (and apparently also pop) contains the head of the tortoise (compare fig. ). it occurs several times in the cortesianus, thus on pp. , , , ; on p. with the hieroglyph (on the top of the lower half of the page, st line and at the right of the margin). in dr. (at the top) we see the sign of the tortoise with the kin-sign as its eye and the numeral ; 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 ). 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. a and tro. *a, *a, *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. , 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 ( * 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, , p. ) 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 times. following him in point of number in the same manuscript are the death-god a pictured times, god d times, and gods c and e and times respectively. in the madrid manuscript, god d, with pictures, is of most frequent occurrence. he is followed by the maize-god e with pictures, god b with , god a with , c with and m with pictures. in the paris manuscript, god e's picture can be verified times, those of c and b 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: . god b: pictured times. . " d: " " . " e: " " . " a: " " . " c: " " . " m: " " . " f: " " 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: . in the dresden manuscript: d and c, b and c, dog and vulture, bird and serpent, b and k. . 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. . 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. ] * * * * * * transcriber's note: typographical errors: page footnote missing final period serpent-and rain-deity should read serpent-and-rain-deity sentence ending with "and *c)" does not have a period manuuscripts should read manuscripts repsented should read represented pp - should read pp. - comma missing following b comma missing following c 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. indian notes and monographs edited by f. w. hodge vol. ix [illustration: logo] no. 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 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 the maya indians of yucatan in , by santiago mendez customs women dress language stature, physiognomy, color savage tribes note by antonio garcía y cubas notes on the superstitions of the indians of yucatan ( ), by pedro sanchez de aguilar of the religious beliefs of the indians of yucatan in . report of francisco hernandez glossary bibliography notes 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 , 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. - . it is on pages - , bears the date mérida, october , , and was written by santiago mendez, who states that he was governor of yucatan during the years - . 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, pp., august, . we have also had translated the notes on the superstitions of the indians of yucatan contained in the work of pedro sanchez de aguilar, , published by the museo nacional of mexico in (pp. - ), 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 , and is given by him in chapter cxxiii (pp. - ) of his apologetica historia de las indias, a work which did not appear in print until - , the first complete edition of which was edited by m. serrano y sanz, and printed at madrid in . 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 but not published until , when it appeared in the _registro yucateco_, tomo i, pp. - . 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 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 , ._ 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 and , 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_[ ]) to use it in order to force parents to send their children to the said schools. unfortunately, in 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_[ ]), 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_,[ ] 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 pesos, reals. in addition to this they have to give him two hours on saturdays for what they call _fagina_,[ ] 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_,[ ] the first clearing of a field by felling trees, cutting and burning undergrowth, etc., is meant; while the _milpa caña_[ ] 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_[ ] 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_[ ] 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[ ] 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 [ to pounds][ ] 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_,[ ] 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,[ ] _camote_ [sweet potatoes], and _jicama_,[ ] 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 , 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 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 th, _. 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 st, _. notes on the superstitions of the indians of yucatan informe contra idolorvm cvltores del obÍspado de yvcatan. madrid, 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_.[ ] 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 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_,[ ] and that he had created man and all things. the son's name was _bacab_,[ ] who was born from a maiden who had ever remained a virgin, whose name was _chibirias_,[ ] and who is in heaven with god. the holy ghost they called _echuac_.[ ] they say that _içona_ means the great father. _bacab_, who is the son, they say killed _eopuco_,[ ] 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_,[ ] 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_,[ ] 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_,[ ] 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 ), 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 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 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. - . this account was written in yaxcabá, april , . 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. - . this report is dated mexico, december , . carrillo, estanislao. papeles sueltos de p. carrillo. fantasmas. _registro yucateco_, tomo iv, pp. - . 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. , . this report is dated mérida, april , . carrillo, crescencio. estudio historico sobre la raza indigena de yucatan. vera cruz, , pp. bancroft, hubert howe. the native races of the pacific states. 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. brinton, daniel g. the folk-lore of yucatan. _folk-lore journal_, london, vol. , part viii, pp. - . 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, pp. the first edition was printed in . brinton, daniel g. a primer of mayan hieroglyphs. _publications of the university of pennsylvania, series in philology, literature, and archæology_, vol. iii, no. . rejÓn garcÍa, manuel. supersticiones y leyendas mayas. mérida, . notes [ ] for the meaning of this and of other indian words, consult the glossary. [ ] _fotuto_ is a musical instrument used by the carib indians and also by the negroes of the antilles. [ ] _luneros_ are monday-workers. [ ] _fagina_--_faena_, manual labor. [ ] _milpa roza_ is, literally, field cleared of underbrush and ready for planting. [ ] _milpa caña_, literally cane field. [ ] an _almud_ is a dry measure equivalent to twelve english bushels. there seems to be an error in the quantity here. [ ] the author here seems to have confused the meaning of the word _mitote_ (see glossary). in yucatan the instrument he describes is called _tunkul_. [ ] the _machete_ is the large knife which the indian men of yucatan invariably carry with them. [ ] the _arroba_ is the spanish measure of twenty-five pounds. [ ] we have been unable to find the meaning of the word _güero_. [ ] _calabaza_ is the spanish for pumpkin; but the mexican pumpkin is different from that raised in our latitudes. [ ] _jicama_ seems to be a local word not in the dictionary. [ ] _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 , 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. [ ] the names to which we call attention in notes to 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." [ ] according to brinton the _bacabs_, or _chacs_, were the offspring of _itzamna_ and his consort _ix-chel_ (spoken of by the caçique as _hischen_). [ ] _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." [ ] _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. [ ] _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. [ ] _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. [ ] _himis_ is _imix_, the name of the first day of the twenty-day month of the maya calendar. [ ] _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." 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 , . worcester: press of chas. hamilton, main street. . notes on the bibliography of yucatan and central america.[ ] 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 , and subsequently in the editions of , and of the latter book. it was also translated into the english language by richard eden, in the "historie of travayles," london, , 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," , by s^r j. g. icazbalceta, of méxico. * * * * * petrus martyr ab angleria. "enchiridion de insulis nuper repertis simulatque incolarum moribus," basel, . (separate print of the th 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, . 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 th and th decades), i merely quote: "novus orbis regionum ac insularum veteribus incognitarum, &c." by simon grynæus, basel, , embodying dec's , , , _and_ . [footnote : 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 .)--a french translation of the th decade, by simon de colines, paris, .--a german version, by hôniger of kônigshofen.--hackluyt's reprint of . "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, . 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 th july, , 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, .--folsom's translation of . "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. , edition of , and an abstract is found in prescott: "conquest of mexico," appendix ii., d 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 , by the "hackluyt society," vol. . juan cristÓbal calvet de estrella. "de rebus gestis ferdinandii cortèsii," written between and , 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, .) benedetto bordone. "libro di benedetto bordone.--nel qual si ragione tutte l'isole del mondo con li loro nomi antichi e moderni," .--later editions also. girolamo benzoni. "historia del mondo nuovo," venice, .--translated into german by nicolaus hoeniger: "die neue welt und indianischen kônigreichs, neue und wahrhaffte geschichte, &c., &c.," basel, .--incorporated in théodore de bry "grosse reisen," parts , , and .--of other prints i but mention the latest english translation, published by the hackluyt society in (vol. ,) 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 , french of , and latin of . bernal diez del castillo. "historia verdadera de la conquista de nueva españa," madrid, . (there may be two editions of the same year). of the spanish reprints i mention here (also contained in "historiadores primitivos de indias," vedia, , vol. ii.), the one of , paris, vols. ^o, and the other of , méxico, 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, .--"the memoirs of the conquistador, bernal diez del castillo," translated by john ingram lockhart, london, .--there is also a german translation, by p. j. rehfuss, bonn, .--bernal diez (not diaz) is very valuable as eye-witness, having been to yucatan with cordoba ( ), grijalva ( ), cortés ( ),--and finally with the latter to honduras, passing through peten. fray lorenzo de bienvida. letter to the infanto philip (ii.), dated yucatan, february, . original in ms. french translation by h. ternaux-compans in " ^{er} recueil de piéces concernant le méxique," vol. x. , 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 books.--the first books, and part of the th, were published by the author as early as ,--and the first books as early as ,--but the entire work has only been printed in , at madrid, 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, .--of this book i quote--e. g.--the following spanish editions: medina del campo, , antwerp, prints, --zaragoza, ,--and it is also contained in "historiadores primitivos de indias," by andrés gonzalez barcia, madrid, , vol. ii.--and in "historiadores primitivos de indias," by vedia, madrid, , vol. i.--there is an italian version, by augustino de cravaliz, rome, , ("la histoirie generale delle indie occidentali. &c., &c."), and french translations published respectively in , , , and .--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 .--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, and , by the marquis de la fuensanta del valle and don josé sancho rayon, in vols. the th vol. contains the famous "apologética historia."--another publication of the "historia de las indias," though not as complete, has appeared in mexico in vols., as the first series of sr. j. m. vigel's "biblioteca mexicana," and .--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, . of this polemic and strongly tinged memoir there are innumerable versions.--i know of spanish publications besides the above, and those of london, ,--philadelphia, ,--both due to dr. de mier,--madrid, j. a. llorente, , and méxico, .--latin translations: francfort, ; oppenheim, ; heidelberg, .--french translations: antwerp, ; amsterdam, ; rouen, ; lyon, ; paris, ; amsterdam, . (the last two contain each five papers of las casas), and paris, . "oeuvres de don bartolomé de las casas," by j. a. llorente.--of italian translations (with spanish text). i allude to those of . venice.-- , id.:-- , id., and also of .--there is a german translation of .--dutch translations: amsterdam, and , and .--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, ,--although dr. robertson mentions one of .--las casas must be used with great caution. diego de landa. "relacion de las cosas de yucatan." bishop landa was born in , and died in ; his work must therefore have been written between and the latter date. it was published by the abbé brasseur de bourbourg, in , with a french translation opposite to the spanish text, and under the title of "relation des choses de yucatan."--republished again in , 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. - ), 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, . these contain several letters and reports on yucatan, from the th century. i only refer to one, a complaint of four indian "gobernadores," dated april, , 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, . 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 ; printed in . gerÓnimo de mendieta. "historia ecclesiástica indiana," written about , but printed for the first time, by sr. j. g. icazbalceta, at mexico, in --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 , 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," . already noticed under petrus martyr. petrus apianus. "cosmographia," , , (dutch version), &c. abraham ortelius. "theatrum orbis terrarum," , , &c. thomaso porcacchi. "l'isole pio famose del mondo," , , , &c., &c. g. mercator. "atlas, six cosmographical meditations." duisburg, . conrad loew. "meer oder see-ansicht buch." cologne, . sebastian munster. "cosmographey," , &c. andrÉ thevet. "les singularites de la france antarctique, autrement nommé amérique, et de plusieurs terres et isles decouvertes de notre temps."--paris, ; antwerp, ; in italian, at venice, . 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 , 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 ). don francisco montejo. "carta al rey sobre la fundacion de la villa de san francisco de campeche, y de la ciudad de mérida," june, . (still at sevilla, leg. . "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, , , vols. folio. there are two other editions in the original language: madrid, and , and antwerp, . 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 twice, and a french translation of the st, d and d decades, at paris, .--a latin version of the "descripcion" was also published in , by colin, at amsterdam, and a very unreliable english rendering by john stephens, in vols. ^o, appeared at london in . 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." st edition, ; second edition, madrid, , 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." st edition, madrid, ; d edition, madrid, . barcia. augustin de vetancourt. "teatro mexicano." méxico, .-- d edition, in "biblioteca de la iberia," méxico, .--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, and .--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," , 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, , 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," . 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."-- st edition, madrid, ; d edition, mérida, ; d edition, .--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, . juan diaz de la calle. "memorial y resûmen breve de noticias de las indias occidentales." madrid, . * * * * * these constitute the most important sources on yucatan written during the th 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." . francisco cÁrdenas. "relacion de la conquista y succesos de yucatan," . (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 , and comprising 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 th 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, , and . (this forms the th volume of purchas' great works).--the great work of purchas, also known as "hackluytus posthumous," appeared in , and treats also of yucatan. o. dapper. "die unbekannte neue welt, oder beschreibung des welt-theils amerikas, &c." amsterdam, . 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, . mathias quad. "enchiridion cosmographicum: dass ist, ein handbüchlein, der gantzen welt gelegenheit, &c." cologne, and . joannes petrus maffei. "... historiarum indicarum libri xvi., &c." antwerp, --frequently reprinted and translated. jacobus viverus. (van de vijvere). "handbook: of cort begrijp der caerten ende beschryvinghen van allen landen des werelds." amsterdam, . (this is the d edition of an anonymous atlas). cornelius wytflict et anthoine magin. "histoire universelle des indes occidentales et orientales," douay, . gaspard ens. "west und ost-indischer lustgart.:...." cologne, . aubertus miraeus. "de statu religionés christianae...." cologne, . athanasius inga. "west-indische spiegel, &c." amsterdam, . johann philipp abelin. (gottfriedt). "neue welt und americanische historien." francfort, a. m. . a. o. exquemelin. "de amerikaensche zee-roovers." amsterdam, . (innumerable translations, &c. &c). eberhard werner happel. "thesaurus exoticorum." hamburg, . (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, . the first part only, composed of 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, , . spanish translations: london, ; méxico, , id. . english translation: london, . german version: leipzig, . (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, - . vols. ^o.--english translation by g. a. thompson. london, - . joseph antonio de villa-seÑor y sanchez. "teatro americano." méxico, .--of indirect value for yucatan. ( vols. folio). j. lafitan. s. j. "moeurs des sauvages américains, comparées aux moeurs des premiers temps." paris, . (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 . abbÉ guillaume thomas raynal. "histoire philosophique et politique des établissements et du commerce des européens dans les deux indes." paris, , and other editions. english translation. edinburgh, . 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, . 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 th century). "giro del mondo...." naples, .--french: "voyage du tour du monde." paris, . * * * * * 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." . * * * * * 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 th 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, , vols. ^o.--id. paris, , vols. ^o.--paris, - , vols. ^o. spanish translation: madrid, . english translation by john black. london, . 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, . splendid, but the drawings are mostly restorations,--therefore suspicious. antonio del rio. (the date of this report is: "palenque june, ," 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, .--there are two german translations: one "huehuetlapallan, amerika's grosse urstadt, &c." meiningen, , and v. minutoli's "beschreibung einer alten stadt in guatemala." .--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, . "incidents of travel in yucatan." n. york, . f. catherwood. "views of ancient monuments in central america, chiapas and yucatan." n. york, . b. m. norman. "rambles in yucatan." n. york, . charles st. john fancourt. "the history of yucatan." london, .--not of great value. emmanuel von friedrichsthal. letter of april, , in "registro yucateco," vol. ii., and "diccionario universal," vol. x.--"les monuments de l'yucatan," in "nouvelles annales des voyages," , vol. .--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.; ; 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, . carl bartholomÂus heller. "reisen in mexico." leipzig, .--rather fair and moderate. dÉsirÉ charnay, and viollet le duc. "cités et ruines américaines." paris, .--invaluable for its photographs. arthur morelet. "voyage dans l'amérique centrale, l'ile de cuba, et la yucatan." paris, . english translation by mrs. e. g. squier. "itza, or the unexplored regions of central america." london, .--a very attractive and valuable work. charles etienne brasseur de bourbourg. "histoire des nations civilisées du méxique et de l'amérique centrale." paris, - . "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, . (see landa and lizana). "quatre lettres sur le méxique." paris, . "manuscrit troano." paris, - . 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." . diccionario de la lengua haya. mérida, . manuel orozco y berra. "geografia de las lenguas y carta etnogrática de méxico." méxico, . american antiquarian society, worcester, mass. _proceedings no. ._ oct. , page . report of s. f. haven, ll.d. _proceedings no. ._ oct. , page . report of s. f. haven, ll.d. _proceedings no. ._ april, , page . report of s. f. haven, ll.d. _proceedings no. ._ april, , page . "the mayas," by stephen salisbury, jr. _proceedings no. ._ april. , page . "dr. le plongeon in yucatan," by stephen salisbury, jr. _proceedings no. ._ oct. , page . report of s. f. haven, ll.d. _proceedings no. ._ april, , page . "terra cotta figure from isla mujeres," by stephen salisbury, jr. page , "the mexican calendar stone," by philipp j. j. valentini, ph.d. _proceedings no. ._ oct. , page . "archæological communication on yucatan," by augustus le plongeon, m.d. page , "notes on yucatan," by mrs. alice d. le plongeon. proceedings no. ._ april, , page . "mexican copper tools," _by philipp j. j. valentini, ph.d. page , "letter from dr. augustus le plongeon." _proceedings no. ._ oct. , page . "the katunes of maya history," by philipp j. j. valentini, ph.d. _proceedings no. ._ april, , page . "the landa alphabet," by philipp j. j. valentini, ph.d. _proceedings no. ._ oct. , page . "mexican paper," by philipp j. j. valentini, ph.d. page , "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," . 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, . a. aubin. "mémoire sur la peinture didactique et l'écriture figurative des anciens méxicaines." paris, - . ( papers, published also in the "revue américaine et orientale." st series, vols. iii., iv. and v.) lÉon de rosny. "les écritures figuratives et hiéroglyphiques des peuples anciens et modernes." paris, . "mèmoire sur la numération dans la langue et dans l'écriture sacrée des anciens mayas." (compte-rendu du "congrés international des américanistes." , vol. ii.) "essai sur le déchiffrement de l'écriture hiératique de l'amérique centrale." paris, .--still continued. francisco pimentel. "cuadro descriptivo y comparativo de las lenguas indígenas de méxico." méxico, . german translation, by isidor epstein. n. york, . hyacinthe de charency. "recherches sur le codex troano." paris, . d. geronimo castillo. "diccionario historico, biografico y monumental de yucatan." mérida, . vols. serapio baqueiro. "ensayo historico sobre las revoluciones de yucatan, -- ." mérida, . vols. gustav klemm. "allgemeine culturgeschichte der menschheit." vols. leipzig, - . heinrich wÜttke. "die enstehung der schrift." edward king, lord kingsborough. "antiquities of mexico." - , london, vols. folio. special value of plates. de larenandiere. "méxique et guatemala," in "univers pittoresque." paris, . 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." . (no. of "smithsonian contributions to knowledge.") "american aboriginal architecture." johnson's encyclopedia, vol. i. "ancient society." new york, . hubert howe bancroft. "the native races of the pacific states." vols. n. york, . john d. baldwin. "ancient america." new york, . josÉ m. melgar y serrano. "exámen comparativo entre los signos simbólicos, &c." vera cruz, . gustav brÜhl. "die culturvölker alt-amerika's." new york, cincinnati, and st. louis, , , and . adolph bastian. "die culturlaender des alten america's." berlin, . vols. john t. short. "the north americans of antiquity." new york, . * * * * * i further refer to papers in "nouvelles annales des voyages." . 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, . vols. manuel larrainzar. "estudios sobre la historia de américa, sus ruinas y antigüedades." méxico, . 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."--( th and th 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. of the "proceedings of the american association for advancement of science." . 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 ^{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 d "_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 th 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 th 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 th 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, . _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." st edition, madrid, ; d edition, brussels, .--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 th 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 , 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, . 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, . 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 , 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 th book is at the "museo nacional" of guatemala. "historia de la provincia de predicadores de san vicente de chiapas y guatemala." written about ,--and possibly the same work as the above.--according to brasseur de bourbourg, 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 . 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, and , vols.--the library of guatemala ("museo nacional") still contains an anonymous ms. of 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 ." 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 , and is the first authentic report on the celebrated ruins. d. nÁxera. "vida portentosa del v. p. fr. antonio margil de jesús." méxico, . h. vilaplana. "vida portentosa del americano septentrional apóstol antonio margil de jesús...." méxico, . (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." nov. . (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 de diciembre de ." description of the ruins. mss. translated and published by brasseur in "ruines de palenque," . antonio bernasconi. other reports on the ruins, accompanied by plans and drawings. ms. in spain. date, june, . juan bautista muÑoz. letter to the marquis de sonora, written . translated by brasseur: "ruines de palenque." . 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 , 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 . guillermo dupaix and luciano castaÑeda. "relacion hecha al rey, sobre tres expediciones, &c." in , , and . they visited palenque late in .--their reports and drawings were first published in , 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, .--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 april, , in "antiquités méxicaines," vol. i.--english translation in the "literary gazette," no. , london, .--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 large plates, in "monuments anciens du méxique." paris, .--m. de waldeck had spent two years at palenque ( - ,)--his plates are magnificent, but they restore far too much. john l. stephens. "travels in central america, chiapas, and yucatan." n. york, . "incidents of travel in yucatan." . f. catherwood. (see yucatan.) arthur morelet. (see yucatan.) visited p. in . dÉsirÉ charnay. (see yucatan.) in . charles etienne brasseur de bourbourg. "ruines de palenque," in "monuments anciens du méxique," , 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 . to these reports i finally add: charles rau. "the palenque tablet in the united states national museum," washington, d. c., . (no. 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," -- .--english translation by j. bailly, london, . francisco de paula garcia l'elaez. "memorias para la historia del antiguo reyno de guatemala." vols. guatemala, .--an excellent work, full of valuable and reliable information. hyacinthe de charency. "le mythe de votan." alençon, .--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, . 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, . josÉ de garay. "reconocimiento del istmo de tehuantepec." méxico, . 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 , 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. ( th and th letter. casual mention.) pedro de alvarado. seventeen letters to hernan cortés, the first of which is dated: utlatlan, april, . 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 ( april and 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 d volume, editions of , , and . oviedÓ. "historia y natural de las indias." vol. iii. written between and , but printed only . madrid. andrÉs gonzalez barcia. "historiadores primitivos de indias." madrid, , vol. i. h. ternaux-compans. "premier recueil de piéces relatives à la conquéte du méxique." paris, .--french translation. enrique de vedia. "historiadores primitivos de indias." madrid, . (vol. i.) these letters, from the conqueror of guatemala, are very important, and the 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 feb'y, , to philip ii. published in french, by h. ternaux-compans, in ^{st} "recueil de piecés concernant le méxique," .--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 .--original at sevilla, printed for the first time by don martin fernandez de navarrete, in . 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. , .--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 , 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," .--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," , march th.--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 , "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 , in vol. vii. of "coleccion de documentos inéditos...."--a spanish copy, with english translation, by e. g. squier, in , as vol. i. of his "collection of rare and original documents, relations, &c., &c."--finally. dr. alexander von frantzius published a german translation in , under the heading of "san salvador and honduras im jahre, ,"--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 , and the fact is established through him that its buildings were in ruins at the time of the spanish conquest, that is about , 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 , and still continued. "_colección de documentos relativos al descubrimiento, conquista y colonizacion de las posesiones españolas en américa y oceanía._" commenced in , 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 to .) "colección de documentos antiguos del archivo del ayuntamiento de la ciudad de guatemala."--(both bound in one volume and published in and .) manuscripts. "libro segundo del cabildo de la ciudad de santiago de la provincia del guatemala." ( to .) "libro tercero de cabildo." ( to .) "historia de la provincia de san vicente de chiapa y guatemala." (fragmentary.) francisco hernandez, cacique of solola. (francisco ernandez arana xahila.) "memorial," written about .--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." may, . (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.) . francisco montero de miranda. "relacion dírigida al ill'mo señor palacio, &c., &c., sobre la provincia de la verapaz ó tierra de guerra." . (ms. of e. g. squier.) frayles: francisco viana, lucas gallego, and guillermo cadena. "relacion de la provincia y tierra de la vera paz," . (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 . fray tomÁs torre. "historia de los principios de la provincia de chiapas y guatemala, del orden de santo domingo."--written prior to . fray domingo vico. "historia de los indios, sus fábulas, supersticiones, costumbres, &c." "teologia para los indios, en lengua de vera paz." 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 .) 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 th however, was published under the title of "horribles crueldades de los conquistadores de méxico," as appendix to sahagun's "hist-general," vol. iii., in . from this, m. ternaux made a french translation, published by him in , 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 .--( d 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 . 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, .--whether and where it still exists i do not know. lionel wafer. "a new voyage and description of the isthmus of america."--london, . 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 .--robertson quotes an english edition of , and that of is the fourth edition. there are french editions of , - , , . dutch of , . german of . spanish, .--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, .--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, . d edition, by barcia, and . (important bibliographically.) "relácion que en el consejo real de las indias hizo el licenciado ..., sobre la pacificacion de las provincias del manché y lacandon," . 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, - .-- d edition, . "política indiana." madrid, .--subsequent editions, , - , . 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 ." "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 th 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 .) 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." . "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 . nicolas de valenzuela. (wrote about the expedition against lacandon,--in .) fray estevan verdelete. "noticias de la provincia de teguzigalpa." (written between and .) 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." . "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 , 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." . 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 th 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, . 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, . _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." - . fray francisco ximenez. "historia de la provincia de san vicente de chiapa y guatemala de la orden de los predicadores." 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 ."--anonymous. printed works: fray isidro fÉlix de espinosa. "el peregrino septentrional atlante." (life of fray antonio margil.) méxico, . fray cÁrlos cadena. "breve descripcion de la noble ciudad de santiago de los caballaros de guatemala, &c." mexico, .-- d edition, guatemala, . 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 . (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." . "relacion de la sublevacion de los zendales." . antonio rodriguez campas. "diario histórico de guatemala." fray juan cartajena. "la s^{ta} iglesia de guatemala, madre fecundísima de hijos ilustrissimos." méxico, . 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." - , guatemala. (relies too much on fuentes.) english translation by bailey. london, . "a statistical and commercial history of the kingdom of guatemala, in spanish america."--a second spanish edition appeared in . francisco de paula garcia pelaez. (see chiapas.). "memorias para la historia del antiguo reyno de guatemala." . 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, . 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 th volume of proceedings of the american association for the advancement of science, in .--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 .--this is developed utterly independent of the fact that the document hints at two data (p. ,) indicating the time of its composition to have been after , and prior to .--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 , 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 th 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 , 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 to , 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 , 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. , ) used similar means. fray pedro de angulo, who went with las casas to guatemala and was made provincial of chiapas in , 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 .--fray domingo vico, who was killed by the indians of lacandon, in , 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 . (remesal. lib. iii., cap. xi., p. .) 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 , 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, . 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. - . . "notions sur palenque," &c., &c., "transmises à la société géographique de france," in "antiquités méxicaines," vol. i., pp. - .--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, . "the states of central america: their geography, topography, &c., &c. aborigines," n. york, . "notes on central américa, particularly the states of honduras and san salvador." n. york, .--german translation, leipzig, .--french version, paris, .--spanish, paris, , (two different translations.) "honduras, descriptive, historical and statistical." london, . "honduras and guatemala." "the national intelligencer." n. york, . "the ruins of tenampua." although in honduras, they appear traditionally connected with copan. n. york, , in "proceedings of the historical society of new york." "monograph of authors who have written on the languages of central america." albany, .--a very valuable and important contribution to bibliography. * * * * * carl scherzer. "wanderungen durch die mittel-amerikanischen freistaaten." braunschweig, .--english version, london, . "narrative of the circumnavigation of the globe by the austrian frigate novara." london, . (the official reports on the results of the circumnavigation, &c., are very rare.) "die indianer von ixtlahuacan." vienna, . "ein besuch bei den ruinen von quirigua." vienna, . i omit here his linguistical writings, and his publication of the "historia del origen de los indios, &c.," in .--see ximenez. moritz wagner, and carl scherzer. "die republik costa-rica in central amerika." leipzig, .--describes the ruins of quirigua. manuel galvan rivera. "historia de méxico, guatemala, estados-unidos del norte, perú, &c." méxico, . "gaceta de guatemala." (from .) contains interesting notices, historical and ethnological. "periodico de la sociedad econÓmica de guatemala." (only numbers published in and .) may, , to april, . the padres: chica, abella, and escoto, and aguilar. "informes, al ill'mo señor arzobispo de guatemala, tocantes á la vera-paz." and . 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, . orlando n. roberts. "narrative of voyages and excursions on the east coast and in the interior of central america." edinburgh, . carl hermann berendt. "report of explorations in central america." smithsonian report, . "collection of historical documents on guatemala." smithsonian report, . "die indianer des isthmus von tehuantepec."--zeitschrift für ethnologie. berlin, , vol. v. "_analytical alphabet_ for the mexican and central american languages." published by the american ethnological society. new york, . "_cartilla en lengua maya_ para la enseñanza de los niños indigenes." mérida, . _el ramie._ tratado sobre el cultivo y algunas noticias de esta planta. mérida de yucatan, . (ed. de la revista de mérida.) _los escritos de d. joaquin garcia icazbalceta._ ed. de la revista de mérida. tomo ii., . "_articulo sobre el méxico_," se halla en el "deútsch amerikanisches conversations lexicon, barbeitet von. prof. alex. i. schem. lieferung , band vii., seite , pp. . (n. y. .) "_remarks on the centres of ancient civilization in central america_, and their geograpical distribution." address read before the am. geogr. society, n. y., july th, , 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. , september, . 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, ."--annotated also by berendt. gustav bernoulli. "reisen in der republik guatemala."--in "petermann's mittheilungen," - . baron der theil. "le guatemala." in "l'explorateur," vol. iii. . j. laferrier. "de paris au guatémala." paris, . george williamson. "antiquities in guatemala." smithsonian reports, . (very interesting and of great value for archæological studies.) j. w. boddam-wetham. "across central america." london, . adolph bastian. "die monumenta in santa lucia cozumalguapa."--"zeitschrift für ethnologie," . "die culturlaender des alten amerikas." (see yucatan.) gustav brÙhl. (see yucatan.) h. w. bates. "central america, west indies, and south america." london, . a. boncard. "le guatèmala."--in "l'explorateur," . no. . francisco pimentel. (see yucatan and chiapas.) manuel orozco y berra. (see yucatan, &c.) s. habel. "the sculptures of santa lucia cozumalguapa."--smithsonian contributions, no. .--washington, . 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." st edition, rome, . d edition, madrid, - . juan josÉ de eguiara y eguren. "biblioteca mexicana." méxico, . incomplete: only the first volume published. antonio de alcedo. "biblioteca americana." ms. original belonged to mr. jared sparks. méxico, . j. mariano bÈristain de souza. "biblioteca hispana americana. septentrional." méxico, and , volumes. (exceedingly rare.) brasseur de bourbourg. "bibliothéque méxico-guatemalienne." paris, . * * * * * 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. ( d 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 . 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 and .) diego durÁn. "historia de las indias de nueva-españa, é yslas de tierra firme."--(written between and , but only the first part of it printed, at mexico, , by s^r josé f^r ramirez.)--very important; mentions again mitla as a settlement inhabited about . "apéndice" por alfredo chavaro, méxico, . fernando de alvarado tezozomoc. "crónica mexicana."--written . 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, , 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. and of kingsborough.--the same book, under the title of "historia general, &c., &c." appeared at mexico, in vols., , 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, . "geográfica descripcion de la parte septentrional del polo artico de la américa." méxico, . 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, --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, . royal folio.--same, vols. ^o paris, . english version, by helen m. williams, london, . "essai politique sur la nouvelle-espagne." (see "yucatan.") mathieu de fossey. "le méxique." paris, .--very fair. eduard mÛhlenpfordt. "versuch einer getreuen schilderung der republik mejico." hannover, . vols. arthur von tempsky. "mitla, a narrative of incidents and personal adventures." london, .--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 . his photographs are very important.) josÉ maria garcia. (visited mitla in , according to "boletin de la sociedad mexicana de geografia y estadistica." vol. vii., pp. and .) brantz-mayer. "mexico as it was and as it is." new york, . very fair. "mexico, aztec, spanish and republican." hartford, . very good. "observations on mexican history and archæology." (smithsonian contributions. no. , washington, .) contains sawkins' drawings of mitla. j. w. von mÜller. "beitrage zur geschichte und ethnographie von mexico." leipzig, . "reisen in den vereinigten-staaten, canada, and mexico." leipzig, . carlos maria de bustamante. "memoria estadística de oajaca, y descripcion del valle del mismo nombre." vera-cruz, . 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, . 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...." . hernando de cervantes. "relacion de teotzacualco y amoltepec...." . augustin de salazar. "relacion del vicario de chilapa." juan lopez. "relacion del corregidor...." . 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, . numerous grammars, vocabularies, "doctrinas," sermonaries, &c., &c., were written in the course of the th century, of and in the language of oajaca. emilio hÉrbrÜger. "album de vistas fotográficas de las antiguas ruinas de los palacios de mitla." oaxaca, . 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. 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, , and was printed in the _penn monthly_, march, . 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.[ -*] 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.[ -+] 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.[ -++] 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 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."[ -*] 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.[ -+] "_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 , 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 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 - . 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 --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.[ -*] 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.[ -*] 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- ] 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 , 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.[ -*] 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- ] of the months, principally because he could not find them in the two codices at his command.[ -+] 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.[ -*] [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.[ -*] 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.[ -+] 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- ] who has written a good, and i believe the only, description of them which has yet appeared in print.[ -*] 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: [ -*] read before the numismatic and antiquarian society of philadelphia, at its twenty-fourth annual meeting, january th, . [ -+] 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 , when many natives were still living who had been born before the conquest ( ). 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 ). 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. [ -++] "_se les quemamos todos_," he writes, "_lo qual á maravilla sentian y les dava pena._"--"_relacion de las cosas de yucatan_," page . [ -*] "_relacion de las cosas de yucatan_," page . [ -+] "the names of the gods in the kiche myths of central america." proceedings of the american philosophical society, vol. xix., . 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 , note, merida, ,) 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. [ -*] for example, in the "_registro yucateco_," _tome iii._; "_diccionario universal de historia y geografia_," _tome viii._ (mexico, ); "_diccionario historico de yucatan_," _tome i._ (merida, ); in the appendix to landa's "_cosas de yucatan_" (paris, ), 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, ." [ -*] the abbé's criticism occurs in the note to page of his edition of landa's "_cosas de yucatan_." [ -*] it is described at length by don crescencio carrillo y ancona, in his "_disertacion sobre la historia de la lengua maya_" (merida, ). [ -+] "_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 (paris, ). by the "_codex peresianus_," he does not mean the "_codice perez_," but the maya manuscript in the bibliothêque[tn- ] nationale. the identity of the names is confusing and unfortunate. [ -*] "the manuscript troano," published in _the american naturalist_, august, , page . this manuscript or codex was published in chromo-lithograph, paris, , by the french government. [ -*] "_declarar las necesidades y sus remedios._"--"_relation de las cosas de yucatan_," page . like much of landa's spanish, this use of the word "_necesidad_" is colloquial, and not classical. [ -+] a "_medicina domestica_," under the name of "don ricardo ossado, (alias, _el judio_,)" was published at merida in ; 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." [ -*] in his "_disertacion sobre la historia de la lengua maya ó yucateca_" (merida, ). transcriber's note the following misspellings and typographical errors were maintained. page error tn- re should read are tn- hierogylphs should read hieroglyphs tn- an cona should read ancona tn- fn. -+ bibliothêque should read bibliothèque papers of the peabody museum of american archaeology and ethnology, harvard university vol. iv.--no. 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, * * * * * 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 , 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, . * * * * * 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 at leipsic and the second at dresden in . the edition in lord kingsborough's "mexican antiquities" (in volume iii of that work, london, ) 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, ), 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, ), 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 - . page . 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 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 and was thus divided into five sections of days each. in sections b and d, at least, these periods seem to be divided into equal halves of 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 . 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. a. this first tonalamatl has the following form:-- xiii v iv ii i 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 a, 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. b shows the bound prisoner with an axe behind him. then follows in tro. b 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:-- . of these , and - are wholly effaced and for the most part. the very first group refers to human sacrifice, for is a head with an axe affixed to it, 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 a, which on pages a- a and a, b, appears as prefix. 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 . sign signifies the death-god a = cimi, who appears again in . in like manner is repeated in and . , and (probably also ) are, however, the familiar cross _b_; 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. and are another unknown head. in we see the familiar kan-imix sign, which, for the present, i am inclined to regard as denoting a feast or a sacrificial meal. b--c. these two sections have something in common. first, b (as also d) is divided into but two parts and c into only three parts. second, in b and c the scribe intended to draw the hieroglyphs for days each, instead of 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 a, a and *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" ( ), p. , and "zauberei im alten mexiko" ( ), p. , by the same author. this clearly indicates the use of these tonalamatls in soothsaying. fourth and last, each of the five hieroglyph groups of b and c begin with the same sign, which must, therefore, denote the casting of lots. the tonalamatl b runs thus:-- xi vi 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 uayeyab days at the end of the year. this would account for the sign resembling an lying on its side, which appears on the god's head and which usually represents the change of the year (compare pages a, b, b, a and c). 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 hieroglyphs . the first, as stated, seems to refer to the casting of lots, is the sign for h, denotes the female figure pictured beneath it, and is the sign _q_ with the ben-ik on top of it. in the second group is the same as , is the cross _b_, and and are the hieroglyphs for a. c contains the following tonalamatl:-- iii x i 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 b. 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:-- . of these hieroglyphs , and are the head already numbered and on b; , and are the cross _b_; , and are three different heads, all, as it seems, having the akbal sign, and having also the numeral . is again (see on a above) the kan-imix sign, a kin with suffix (the east?) and the numeral as prefix; finally is cimi (a). do the numbers and refer to the th and th of the and days standing below them? the beginning of this tonalamatl iii oc seems to me to fall on an especially auspicious day (hieroglyph _a_). d has the following tonalamatl:-- xiii ii xiii lamat ahau eb kan cib. this refers probably to the section devoted to women, pages - . 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. *b. the hieroglyphs are . of these , and are one of the signs of a, another, and may be a third, recalling the moan, which, as on page c, rests on a hand held beneath it. and seem to signify a carpet or other fabric (or a lying-in bed?), on the one hand suggesting the occupation of the figures in b and c, and on the other the checkered hieroglyph, which is so common in the palenque inscriptions. finally is the woman pictured beneath. page . 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. - ; 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. *a and *a. this picture is surrounded by four gods, who, however, differ very much from the other four in the second sacrificial scene, page a. 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:-- . of these, - are wholly effaced and also the most essential part of . of these hieroglyphs four ( - , - , - and - ) clearly belong to each of the four deities, for , , and (the last again with the dot between two crosses as on page a) certainly belong to the picture. from this it seems to follow that hieroglyphs to refer to the sacrifice itself. as a matter of fact and , 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 and 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, and are cimi; , , and the cross _b_ and and the hieroglyph c. 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. is a similar head, again imix, the sign _o_ and 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 xi ii iv xiii i but cyrus thomas, "aids," p. , has i v xiii xi xiii i. either reading is dubious. the scribe divided the lower half of page 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 a-- a. 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 days into no less than parts of , or 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 , xii , iii , vi , viii , xii , i , iii , vii , ix , xi , xiii , iv , vi , ix , xi , i , iii , vi , viii , x. since the five sections on page a 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 = × + ), 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 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 ( b- b), 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. . day = 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 maya gods (cf. dres. ) 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" ( ) expresses this opinion on page of the separate edition. but possibly the ear-ornament may refer to ezanab. of the hieroglyphs, and 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 a. ( = _r_) i think is the sign for the week of days, which recurs in groups , , and , and hence is distributed times, though not regularly, among the × days. sign is the death bird. . day = 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 , is _p_ the third _q_ and the fourth _a_ with the usual before it; their relations to b are still unknown. . day = 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 c, b, a, c, and a. his hands are much deformed; perhaps indicating the bite of a serpent? of the hieroglyphs, , and are effaced; is surely the sign of the god, differing, it is true, from his usual hieroglyph, but recurring with a also on pages c and . this 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 th day of cumku, which should lie here (in the year kan), if i have begun the tonalamatl correctly. . day = manik; aztec mazatl. the significance is stag or roe, game or the chase. the first picture on page 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 , which is peculiar to the god f, probably stood before the second sign. did this god rule the eleventh of the months of days, as moan ruled the thirteenth? . day = 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_. . day = 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 as a prefix, is entirely destroyed, the third is the sign _u_, and the fourth, which is half obliterated, was _q_. . day = men; aztec quauhtli, eagle. the figure to which the first hieroglyph with the numeral belongs, is a form of the god f, but has the nose-ornament of the sun-god g. hieroglyph , which we shall find again on c, may refer especially to the eagle; the third is the sign of the day caban with a prefixed , and the fourth is the sign _o_. . day = 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" ( ), p. , calls him the young god. in the hieroglyphs we find the serpent sign chicchan twice, just as in the first group on page ; then follow _a_ and kan-imix. . day = 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 and are wholly obliterated, and partly; there is a lock of hair, the sign of femininity, before and . it is to be noted further that 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? . day = 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 , 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 days, and to the lords of the same. in addition to appearing with these th, th, th, and th days, an ahau is found with the st, th, th and th as regent of the year, and lastly, but especially, with the th, which bears the name ahau, and with the god d belonging to it. . day = 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 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. . day = muluc; aztec atl, water, cloud. with this corresponds the image of the storm deity k and his two hieroglyphs and , the first of which occurs frequently, and the second is found on pages b and , while (ahau) designates the day as regent of the year and is the hieroglyph a. the curious sign is also given on cort. b. . day = chuen; aztec ozomatli, ape. there is no agreement at all here, but everything points to the day lying 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 a), 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. . day = ix; aztec ocelotl, jaguar. here there is an admirable correspondence between the figure and the first hieroglyph, which on page , top, also refers to the jaguar represented there; the other three hieroglyphs are _r_, kan-imix and _q_. . day = 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. . day = cauac; aztec quiahuitl, meaning, as in the eighth group, rain, storm, summer. the figure, the first on page , 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. . day = 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 c. the third is cimi and the fourth _q_. . day = 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 c, c, c, b, a, b and a. . day = cimi; aztec miquiztli, death. the first figure on page 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. . day = 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 . 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 × + = days. the hieroglyph here, however, is _not_ the usual sign for 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 days. this is confirmed on pages , , and . in that case this hieroglyph would denote × + = 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 th day of the same ( cipactli), in february , the emperor ahuitzotzin died; compare especially brinton, "essays of an americanist" ( ), pp. - . should this association in our manuscript of cimi = death, x tochtli and the numeral , be considered accidental? or did the scribe, writing in the year after the event, actually record it in the year 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 gods in another way; see his "monumente von copan und quirigua" ( ), p. . (cf. his collected papers p. .) pages b-- b. 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 days into a large number of small parts ( ) and has the following form, if we adopt seler's correction in the last member:-- xii iii vii xi i v viii xii ii viii xi ii vi x 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," , pp. - ). there are two rows of hieroglyphs above the monster, the upper contains and the second , but the second hieroglyph in the upper row belongs in the lower. thus there are 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 groups; this likewise points to a close connection between the two tonalamatls. the remaining hieroglyphs should be considered as only , 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 c. this sign with the number has already been seen on page a. if in b this sign signifies the last day of the year, then this tonalamatl falls in the year xiii kan. the sign zac also appears in the tro-cort., _e.g._, cort. c, tro. *b and *b. now i shall proceed to examine all that has not yet been discussed to the end of page , taking up first the remainder of sections a and b and then all those of c- c. pages a-- a. xi x v iv xii xi lamat ahau eb kan cib. the period of days is thus divided into five sections of and days each, alternating regularly. a deity and four hieroglyphs belong to each of these sections, viz:-- . d sitting, with his right hand pointing upward and his left downward; on his head is the akbal sign as on page c. the hieroglyphs are destroyed with the exception of the third, which is the sign of d (ahau). the fact that the days happen to end with the day belonging to d (ahau) is accidental. . r, a human figure with the head of the moan (as on page c and a) and with the copal pouch around his neck. of the hieroglyphs only the fourth, one of the common signs of moan (_c_), is legible. . h, or, according to seler, "the young god," as on b and b, 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 b. 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. . 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. . 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 a. the scribe evidently wishing to carry out his material in some conclusive form in the top, middle and bottom sections of page , 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 days was divided, for the sake of brevity, into only two parts, viz:-- viii (ix) (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 . 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 b), seems to stand here also in place of e. in agreement with this, hieroglyph and probably also (_s_, which occurs again on page a, and also on page b) refers to k, while clearly refers to e and is the sign a. hieroglyphs - 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 b-- b. i iv xiii xii i manik cauac chuen akbal men. four hieroglyphs belong to each of the four subdivisions:-- . these four parts, however, form a whole, inasmuch as they all relate to making fire, as it is also represented in the troano , and *c. hence the upper row of hieroglyphs contains signs which are repeated. , and 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 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 ( , , , ), which i designate by _k_ and which, originally, doubtless consisted of two hands (double manik sign); the prefix is the same in and , and different in and . 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 belonging to this deity has an akbal as a prefix. pages b-- b. x x x x 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 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. d- d (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 and ). 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 b. viii viii 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:-- . 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 . the two hieroglyphs _e_ and _h_ must refer to this; they are repeated, as usual, in the two groups, _e_ in places and , and _h_ in and . signs and refer unquestionably to d and hence and (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 b and a, with the same person, and on pages a and b with entirely different persons. sign is an object, which also appears on b and a, held in the hands of women and may denote some special sacrificial offering; on b kan-imix appears in place of this sign, and on b beside it. it should be noted that sign stands here in exactly the same proximity to and as on page a. the hieroglyphs and 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 b. page b. here, for the first time in this manuscript, we have a tonalamatl in which the days are not divided into five fifths of days each, but into four quarters of days. this may be represented as follows, if we supply the iii, which is wanting at the beginning:-- iii x iii muluc ix cauac kan. in the first place, the close connection of this tonalamatl with that recorded on page b, just now discussed, is striking, for . here too we find a division into two equal parts is intended, but which, of course, as the number is , cannot be mathematically exact. . here too we not only find hieroglyphs, but we find them in the same order as on page b, and here too the sign _e_ stands in places and , and _h_ in and ; again , and are exactly the same hieroglyphs here as there, so that only , and are different. . 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 and , while those of d are and . it seems, therefore, that d is announcing to e the prophecy contained in the preceding tonalamatl. . two hieroglyphs, and , are again added, both relating to death-- to god a and 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. ), 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 moan in the preceding tonalamatl, while here it is f, will be of special significance in deciding the interpretation. page b. the manuscript gives the following:-- xiii iii oc ik ix cimi ezanab. this cannot be correct, for + is not , and from xiii to iii is not days, while the last roman numeral is wanting. i, therefore, propose to make a of the numeral , 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 xiii 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 a 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 and , are wanting here, and we find only the usual eight signs:-- . of these, , and , are the usual comprehensive heading; and are the manik sign, which must denote the offering, while and 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 a- a. 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 and probably denoting a good day. is the hieroglyph of f to which the sign in corresponds, while the prefixed arm in seems to refer to the presentation of the sacrifice. pages b-- b. viii iii xii viii v viii chuen akbal men manik cauac. i have corrected the in the manuscript by making it . hieroglyphs correspond regularly to the five sections in the following order:-- . this section seems to refer chiefly to the harvest. first the muluc sign with suffix and affix, which is repeated in , , , and at regular intervals, suggests rain as a preliminary condition of the harvest. next in 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 and . there is no picture belonging to this group; it ought to be the god k. the second group adds to the muluc in the glyph of the sun, which is the second preliminary condition of the harvest. this is followed in by the sign _u_ apparently denoting wind and cloud and having the prefix of the storm-god, and in 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 is e's hieroglyph, to which, as is so often the case, sign (imix-kan) is added and in the double manik (_i_). the last two groups are without figures of deities; the double manik ( and ), 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 is the hieroglyph of the vulture, that of the death-bird and 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 b. i i i i ix cimi ezanab oc ik. this is again a regular arrangement, half of the 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 hieroglyphs indicate the connection with the foregoing tonalamatl, for , and 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 c should be compared. the lock of hair before sign , the death hieroglyph, agrees with this as do also the familiar signs and . 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 a. 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 designates the deity h, (imix-kan) probably denotes the devouring of the flesh and sign , 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 , and fit here admirably. we will now turn back to page and consider the lowest section (c) of pages to , which like pages b- b (i omit b here because its contents are of an entirely different nature) contain tonalamatls, that is, five ritual years of days. if, however, we add b to these and bear in mind that c- c contain a double tonalamatl, we will have tonalamatls. we find a group of tonalamatls also on pages a- a. pages c- c. xii ix v iii xii cauac chuen akbal men manik. the incorrect of the manuscript has been changed to . the hieroglyphs are as follows:-- . 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 st, th, th and th hieroglyphs, but all the four gods hold it in their hands. placed after each of these signs are hieroglyphs , , and , 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 and . designates him rather as night and moon-god and 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 , with which, to be sure, the unusual sign (_v_) appears as a not very intelligible determinative. the fourth god is a and his usual signs are given in and . pages c-- c. this is the second example in our manuscript of a tonalamatl divided into four parts:-- xii ii xiii v xii ezanab akbal lamat ben ezanab. the repetition of the th day at the end is superfluous. here, then, we have the four days with which the uinals can begin; in the tonalamatl on page b, the four regents of the year were given instead. now, whether the beginning of these periods of 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 , , and . 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 b. his hieroglyphs are and , and sign _a_ is added as fourth. the next deity is a with his usual signs in , and . c follows with his hieroglyph in and lastly f with the sign which belongs to him. there still remain as the th and th 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 in the preceding tonalamatl). the th sign (_v_), which occurs in exactly the same place in the preceding tonalamatl, is no more intelligible to me here than there. pages c-- c. i v xi iv i chuen akbal men manik cauac. four sitting gods with the regular 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 , , and , 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 is his monogram and is that of his companion f and fits both deities. the second figure is d and his signs are hieroglyphs and to which is added quite superfluously. the sacrifice proper is denoted by , 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 days, it enhances the value to × = days. the third picture represents the god with the bird-head of the moan and his signs are hieroglyphs , and . one of these, signifying rising birds, is also the offering in . 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 . added to this is the sign _a_ in , and in it is _q_ again with the same superfix as in sign of the preceding tonalamatl. the sacrifice in is represented by a kan sign, which is equivalent to maize, maize bread or tortilla. repeatedly, as on page b or b- b 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 c. iii xii viii iv xiii ix 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 days into sections of 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 hieroglyphs must belong to each of the figures. i read the hieroglyphs in the following order:-- . 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 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 a, 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 corresponds in general to and to . in the first group and are the hieroglyphs of d and and are the signs _q_ and _v_; does one of these last signs refer to the god c? in the second group is the sign of f, who stands in front of the house and that of the god in the house, as perhaps is also , when we consider the closed eye; this is one of the many hieroglyphs having an uplifted arm as a prefix. on page a 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 ( × = days). page c. here for the first time the manuscript contains a tonalamatl, which is divided into × 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 cauac ben xi ii chuen chicchan akbal caban vi vii men muluc manik imix. i iii i read it thus:-- iii vi viii xi ii vi vii i 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 days or to the half of the whole, 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 and . the second god is a with a snail on his head and his signs are and . in addition to these, sign of the first group is _v_ and sign of the second group is c. pages c-- c. i xiii i vi iii iii v (in error ) xiii imix cimi ben ezanab chicchan oc caban ik muluc ix. here we have two independent tonalamatls as on page a. there are subdivisions only for the second; the first should be regarded either as entirely invalid or else its division has merely been omitted. gods with hieroglyphs each are represented on these pages:-- . here too hieroglyphs , , , , and are the common factor; they have the form of the month mol, but here, as on page c, they probably designate the particular object constituting the sacrifice. the following details are to be noted regarding the six divisions:-- . the god a with his two signs in and . . d with the signs and . . f with the signs and (the latter _c_). . e with the signs and , having on his head a structure, which is compounded apparently of a kan sign, a snail and the suggestion of the maize plant. . g, clad in the gala cloak and the copal bag. his sign is , while suggests rather the moan or k. . b, his headdress displays the little circles, which often occur in connection with him, _e.g._, pages c, a and a, and which may suggest the starry sky. his sign is ; the hieroglyph _m_ is added to it in as a determinative. as usual, the fourth sign of each group is the most puzzling. and are imix with the uplifted arm as a prefix, as on page a, is the hieroglyph _o_, is _a_, is _c_ and the principal part of is _r_. this sign _r_ seems to me to suggest the week of days (see above the explanation of page a); 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 c. xiii xiii xiii xiii chuen cib imix cimi chuen. this is another tonalamatl divided into × , 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 , and are the fist, familiar from the inscriptions, and which we also see on page b 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, , and 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 (ahau) refers to d; but what is the meaning of , 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 , apparently referring to the five uayeyab days, is his sign; we found it on page b and shall again find it on page c, and this time likewise with the old man. what is the meaning of the grain-goddess e denoted by sign ? 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 , while sign , which suggests the wind-god k and balled-up clouds, is as difficult to explain here as it was on page c. the signs and 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 the tonalamatls of the three sections of the page come to an end and a new part of the manuscript begins. page a. i shall here group together pages and , the top third of encroaches a little upon page . a has the following tonalamatl:-- imix ben chicchan caban muluc. i have supplied the first day, which is effaced. the week days are wanting. the days are divided into halves of days each. of the 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 b and a. hieroglyph , which is mostly destroyed, must have been b's monogram, has the ahau as its determinative, and is the elongated head _q_ with ben-ik. in the second group and are the signs of a, and is an imix with the uplifted arm prefixed, as on page c. pages a-- a. viii viii viii viii ahau eb kan cib lamat. the month days and 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 ). here, as in the preceding tonalamatl, the period is divided into equal parts. little can be said of the hieroglyphs, in number, since , , , , , , and are wholly or mostly destroyed. , and seem here to be a comprehensive element, as is also probably , but i am unable to refer this head to a particular god; , , and may also be alike, but this is very uncertain. , , and may have denoted the four cardinal points, at least suggests the south and the north. thus we have left for the four deities e, h, a and g, only the signs , , and ; surely belongs to e, and to h, but the other two are erased. pages b-- b. vi vi ii ix iii x vi ahau eb kan cib lamat. there are hieroglyphs for the divisions:-- . of these the upper row again contains the comprehensive signs, and the lower the discriminating characters. the closed eye in , , , , and suggests a, who also appears below as the first of the six gods, and the superfix of these signs suggests the south. , , , , and 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 a and b, 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 and are the common hieroglyphs for a; that for e, to which _o_ is added as a determinative; is c's hieroglyph with an _a_ added to it, and l is undoubtedly denoted by sign ; is _r_ (equal to days; it is meant here for the day iii cib). f appears quite according to rule in , which is appropriately followed by the sign _c_ in . finally the hieroglyphs for d in and are the usual ones. we come now to the large section extending to page , 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 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 * of the troano affords remarkable parallels to the dresdensis, even in details. pages c-- c. ii ii ix xii ii 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 c. the entire representation on c and c 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:-- . apparently, the first two pictures have only signs each, and the other two , but this is equalized by the fact, that hieroglyphs , , , and are clearly each composed of two signs. the comprehensive sign appearing in , , and , 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. . 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:-- , a combination of manik and chuen with a prefixed , just as on page b; , likewise a compound sign, with a prefixed , which occurs also on page c on the left, and which i do not venture to explain, but which seems to denote horns, and lastly the hieroglyph c. . the female figure is an animal (on page a 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 b. hieroglyph is composite and contains first the sign generally belonging to the dog and suggesting a skeleton, which also represents the th month, and secondly, a cimi closely related to it, precisely the same as in the parallel passage b. the well-known _q_ follows in the th place. . the god d holds in front of himself an animal, which may be a rabbit. his signs are hieroglyphs and , while , the principal part of which is a grasping hand, clutching a moan sign, seems to refer to the animal in the picture. is _b_ and is a. . lastly, two beings in human guise, showing thus a closer connection with what follows. they are the black god l with his hieroglyph in enlarged by an imix, and a woman holding a kan sign in her hand, hieroglyph likewise showing the ordinary combination of imix-kan. sign , however, refers to the woman, and lastly and are the signs _m_ and _r_; i note that _r_ ends a period of days. the contents of the following seem to suggest that we should first read page (including the middle section of ) from top to bottom, then pages - , partly from left to right and partly from top to bottom, according to the subject. page a. v xiii v ahau eb kan cib lamat. there are two pictures with 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 , and , which are all signs of d. further, 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 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 , the second part of which is illegible. is the sign of a and is effaced. pages b-- b. i i vi i i ik manik eb caban ik. that is × = days. hence the sign of ik repeated at the bottom, as is usual in such cases, is superfluous. the tonalamatl contains figures, of which and form one pair and and another. as on page a, 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. . hieroglyphs - belong to this pair. of these, , and and also refer to death, with the determinative sign, , added (which is the sign _q_ with a ben-ik), refers to b, while signs and 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 a for example; he holds a bone in his hand. hieroglyphs and 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 and of the preceding group, they seem to refer to a sacrifice offered to the death-god. and are again, strange to say, like and of the preceding group, the sign of d. is the hieroglyph of h, who is represented below as feminine, and that is a complement of 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 a with the same figure; compare also page b. is surely the hieroglyph of m, who is pictured below, as in the tro. a and *a where the same m appears with the same hieroglyph, and to him belongs in the sign _r_, which i am inclined to consider the week of days, and which here, as on c, ends a section of days. page c. iii iii ii 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 ; both hold in their hands a kin = sun. hieroglyphs and are also the kin sign, while and have the closed eye of a, but differ in their secondary parts, the sign suggesting the south being a suffix in and a superfix in ; , however, has an affix, while has as a prefix a sign differing from the affix in . and are the signs of a, that of d, next to which in one would expect to see an ahau, but instead of this there is again the sign of h (borrowed from page b?). 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 a. kan 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 hieroglyphs of which, however, the top row is almost entirely obliterated; and 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 which is the sign of the deity e, the grain-god. pages a-- a. in the following i will group together all the pages from page - 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 a- a, 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, 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 c. 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 th 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. and are not legible and perhaps may be supplemented by the third picture on page c. 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 a-- a. viii vii vi ii xii viii ik ix cimi ezanab oc. this is a tonalamatl of five parts with 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 b. 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 th 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 ?). compare pages c, c and b, and in the second part, b and c. 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 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 b, 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 a-- a. xi xi xi xi xi 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:-- . all that can be distinguished here is that the th and th have the same cross _b_ and that and 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 c. 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 . in the second and third pictures he is related to a or the moan and the first figure on page 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 has a serpent on her head and the third a bird. the bird's head resembles that on page c. pages a-- a. the cimi and eb of the second column have changed places in the manuscript. instead of the x there is an erroneous and there is no initial vii. vii vii x xii vi ii v vii oc ahau cib cimi ik eb lamat ezanab ix kan. we have here a tonalamatl consisting of × days, and the days are subdivided into six parts. i have just assumed that the is wrong and the initial vii is wanting over the first column, yet the 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 hieroglyphs, _i.e._, 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 , in the third a , in the fourth a and in the fifth a . what can these numbers mean? + + + = , and chuen with the meaning of (especially in the inscriptions) would be × = . 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 , 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 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 b. 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 ( , a, a, b, b, a, c, c) the prefix might have the meaning of . 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 a-- a. ii ii ii ii iv xii vi iii 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 days, all of which occur again here as on pages a- a, 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 days from the future caban, but days distant from the desired weekday of the same name (see my "erläuterungen," p. ). thus we have here a period of × days = , _i.e._, a three-fold tonalamatl. the three tonalamatls represented on the pages between the preceding passage (pages a- a), where all the days appear, and this, are of three _different_ kinds ( × , × , and × ). 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 . of the above the third hieroglyph of each group, _i.e._, , , , (probably also ) 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 at the beginning of this section. now, which were the other four deities? signs , , refer to a, h and c. 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 and the signs of f and b. is uncertain, 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 b-- b. 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 to . the first part, b to b and c to c, 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 b- b, runs as follows:-- muluc (or ) imix ben chicchan caban. the red numerals are wanting and were probably forgotten. the hieroglyphs stand thus:-- . of these , , and are the sign for women, , , and are likewise all the same sign, which is repeated in the same places on pages c to c. 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 and refer. the third woman would have carried d, which is plainly proved by hieroglyphs and , and the fourth, f, as follows from sign and probably also from (_q_). pages b-- b. eb . kan cib lamat ahau. here again there are no red numerals. the hieroglyphs of the six divisions stand thus:-- . 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 , , , , and , but in and the prefix is different from that of the rest. as from here on the women repeatedly carry a bird, the signs for this are , , , , and , which are the symbol of a rising bird, as in the sign of the th uinal (moan), which in my opinion generally coincides with the th month of 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 a. in regard to it see also schellhas, "göttergestalten," p. . the hieroglyph of the vulture, which we find repeated on page c, , b, , , , is here hieroglyph , usually regarded as the sign of the bat deity, and near it in is _q_. the second woman would have carried the black deity l (hieroglyph ), to which _q_ is added in . the third would have had the dog, _i.e._, the lightning dog, which we find in hieroglyph and in the month sign kankin; an _a_ is added to them in . the fourth woman carries a, as is proved by his signs in and . the fifth carries nothing; according to the hieroglyphs and she ought to carry d. lastly the sixth carries the moan as is proved by signs and . pages c-- c. muluc ix cauac kan muluc. this is a tonalamatl of × days. the muluc at the bottom is, therefore, superfluous. i have been obliged to correct the in the last column of the manuscript by changing it into a . 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:-- . signs , , , , and ( and have changed places) denote women. of the six women only the first three are here portrayed. the first carries the moan with which signs , and 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, and , with the added determinative are unfamiliar. in and the well-known determinatives _a_ and _c_ are added. judging by sign the fourth woman would have carried the same vulture, which we see in the middle section of this page; and are again signs _c_ and _q_. the fifth woman would have carried an unknown bird of prey, the signs of which are and , and = ; is again _q_, but with a superfix different from that in . finally the sixth woman, like the third in b, seems to have carried the dog, as is proved by sign , but in the symbol of a bird is again added. this passage ends in with the well-known imix-kan. pages c-- c. iv vi xiii 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 b- b and c- c is an evidence that i was right in proceeding directly from the former to the latter. of the hieroglyphs, , and have again the form which we found on pages b- b, and which seems to refer to a carrying-frame; compare, however, the explanation of pages - below. the women themselves are designated by hieroglyphs , and . the first woman carries the god a and hieroglyphs and 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 ; compare the upper section of the same page. that this hieroglyph is nothing else than a designation of god d follows from hieroglyph . finally the fourth woman carries a figure, which has a moan sign for a head and to which hieroglyphs and certainly refer. pages c-- c. xiii vi xiii ahau eb kan cib lamat. the first woman carries the god a, who is denoted by hieroglyphs and , though somewhat irregularly by the latter. is the carrying-frame and the woman herself. the second woman has again the yax-kin sign on her back as in the preceding tonalamatl, and hieroglyph is also a combination of these signs, but here in we find, not the sign of d, but that of e, to which also the imix-kan in corresponds. is again the carrying-frame, though, as is also the case in , more indistinctly drawn than in the earlier tonalamatls. pages c-- c. xiii xi ix vii iv xiii ahau eb kan cib lamat. this is a tonalamatl divided into five parts, to which hieroglyphs belong. the hieroglyphs are in the following order:-- . at places , ( and have changed places), , and we find again the sign which we think means a carrying-frame, while signs , , , and 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 and his determinative in . 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 a. this object is denoted by hieroglyph (_w_). its determinative is probably . 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 and hieroglyph accord. the fourth woman carries the maize deity e. is his sign and the food hieroglyphs, imix-kan in , 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 th sign. 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 c- c. page b. x xiii 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 and , the sign for woman in and , and their determinatives in and . the first woman has a deity facing her who is devoid of all characteristic marks, and sign is also nothing but the universal a. the second woman whose eyes are closed, sits facing a, whose hieroglyph is in . pages b-- b. vi viii vi cib lamat ahau eb kan. the arrangement of this tonalamatl is very similar to that of the preceding. hieroglyphs and are again the cross, and and the signs for woman. the first picture is wanting; hieroglyph with the number as a prefix denotes a deity with whom i am not familiar. the same sign is found on page , left, middle; in 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 c and b, with the nose-peg resembling a flower. his sign is to which in the familiar ahau is again added. page b. ii ix ii ii cauac chuen akbal men manik. the hieroglyphs stand thus:-- . the subject now passes into the province of astronomy. this is already proved by sign , 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 suggests the storm-god k (compare pages a and left) to which in the ahau might be appropriately added, inasmuch as it rules the year here under consideration as on pages b to c. on account of the ben-ik sign i see in one of the months of 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 and , 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 and , 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 days and, in fact, the interval between the two hieroglyphs is days. on the left is the inverted figure of a person in a squatting attitude, the head surrounded by stars as on pages b and b 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 - days) or disappearance into the light of the sun during this week, is the subject of this passage. and are the sign for d with the usual ahau, and and 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 b and b. page b. vii vii i viii ii vii oc ahau cib cimi ik eb lamat ezanab ix kan. this is also a tonalamatl of parts ( × ). the first column should be read first from top to bottom and then the second. the days are exactly the same as on page a, and here too cimi and eb have changed places. the hieroglyphs run thus:-- . the signs forming the hieroglyphs into groups are, in addition to the cross in , , and , the heads in , , and with an akbal sign (indistinct in ) which, by the lock of hair in , and , refer to a woman. this lock of hair is replaced by a hand in . sign , with which _m_ in 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 a. opposite her sits the dog which we saw on page c. here (in sign ), as on page c, the hieroglyph of the dog is combined with a cimi sign, and this hieroglyph is repeated in 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 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 , which is compounded of manik and chuen with a superfix, nor does the cimi added in shed light on the subject. as for we have already found it on page c with the prefixed , which i find prefixed in this way in at least different signs. pages c-- c. caban 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:-- . among these are hieroglyphs which are common to all the groups:--the cross in , and and the woman in , and . in this cross is replaced by another sign, perhaps that for the year of days, and in 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 to which an imix is added in , with the uplifted arm prefixed as in c and a. 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 c 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 c. further, there is no hieroglyph at all for d and instead we find in , zac, the regular sign of n. also sign 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 th hieroglyph, which is the head of an old man with a prefixed , referring to the four different forms of n in the kan, muluc, ix and cauac years. the ahau in , 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 , which applies to all the three groups, and by transferring to the first group n and the th sign of the third group. the fourth group has no picture. it should have, as hieroglyph shows, the god f, who represents death by violence in human sacrifice and the chase. the hieroglyph cimi in the th place is a suitable sign for this deity. pages c-- c. ii xii xi vii xiii vii ii oc ik ix cimi ezanab. the hieroglyphs are arranged in the following order:-- . 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 , and , and the cross _b_ only in and , 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 , the familiar _c_ in and the unknown sign in (= ) 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 c and b. the cimi sign in and the sign _c_ in are familiar, but the infrequent = 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, (cimi) and (_q_) afford no explanation, nor does the head with the uplifted arm in , which we find with the same hieroglyph on pages a and a. the most puzzling is the th 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 a, 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 , 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 , while imix-kan in , _b_ in and _a_ in are rather meaningless. the fifth group represents the woman united with a, who is designated by the cimi sign in . with its _b_ and with its _q_ display little that is characteristic, _r_ in , which i think is the sign for the week of 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 as imix-kan, as _a_ and as sign of femininity supply nothing in the way of explanation. as , and are the characteristic signs in the preceding groups, so here the characteristic sign is --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. * d. now of the entire woman section closing with page only the two tonalamatls on pages b- b remain. these tonalamatls again display very many peculiarities and seem to be but loosely connected with the five tonalamatls last discussed. page b. iii iii iii iii iii akbal men manik cauac chuen. this is a regular tonalamatl, in which the days are divided into four equal parts. the hieroglyphs are in the following order:-- . an ahau is added here as the th sign, which is very unusual. we find elements here forming the hieroglyphs into groups in three different ways. . the signs , , and 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. . the hieroglyphs , , and are all alike and are the head with the akbal eye, which in is closed. . 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 b. the first picture is b; his sign is the third with the _q_ in 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 th sign, not her hieroglyph, but merely the one generally used to denote a woman. 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 th, to which in is added the sign _q_, the sign for the bad days, with a superfix. the fourth picture is wanting. according to the th hieroglyph it should be the maize deity e. my theory that is the sign for the week of days is supported by the fact that the division into × days is the prevailing one. page b. viii vii vi v iv iii viii kan muluc ix cauac lamat. this is a tonalamatl of × days divided as evenly as possible into × + . the th day added after the th must be a mistake (suggested by the th day of the last section) for it is usually the first of the days, which is repeated superfluously. the hieroglyphs are:-- . contrary to practice the first section has six hieroglyphs, and the other five but four each. as the characteristic hieroglyph we find in , , , , and a sign, the meaning of which is still undetermined and which we shall meet again on page , 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 , , , and (in perhaps represented by _q_, the evil days). we shall find this sign on pages , , - , - and - , 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 , the mammal by and the bird by , and i believe, therefore, that the iguana with its spiny back is denoted by . we find the four animals, though in a different order, also on pages b- b, b- b and c- c, as well as in cort. - and , 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 th sign is an ahau, which is not quite intelligible here. sign = 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 c. according to the th sign, the second group might refer to the serpent deity h, and the th sign would not improperly denote the iguana. in the same way sign in the third group probably denotes the storm-god k, with whom the bird in accords very well. in the fourth group both the animal and the sign of fasting, belonging to it, are wanting, while and as well as the unlucky day in clearly refer to the death-deity a. the fifth passage belongs, as sign shows, to the maize deity e and to this is added the haunch of venison in . 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 . the five deities specified here may be compared with those on page , which are denoted by hieroglyphs - 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 . 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 - ). the first problem it presents is to find periods in which the solar year ( days) is brought into accord with the apparent venus year ( days). this takes place in a term of days = × = × . sequent to this is the still higher aim of bringing the tonalamatl ( ) into harmony with this period, which is accomplished in , days (= × = × = × ). the revolution of the moon ( ), the ritual year ( = × ) and the apparent revolution of mercury ( ) come in question as secondary matters. i will now give an approximate reproduction of the page:-- hieroglyphs. , , , , ( × , ) ( × , ) ( × , ) ( × ) i ahau i ahau i ahau i ahau , , , i ahau i ahau i ahau i ahau , , , , ( × ) ( × ) ( × ) ( × ) vi ahau xi ahau iii ahau viii ahau , , , , ( × ) ( × ) ( × ) ( × ) xiii ahau v ahau x ahau ii ahau , , , ( × ) ( × ) ( × ) vii ahau xii ahau iv ahau ix ahau , , , , , iv ahau i ahau i ahau cumhu kayab zip. first let me observe that i have restored the four large numbers at the top, which are almost entirely effaced, as follows:-- . 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 members, each being a multiple of . it begins with the date i ahau (which is always concealed in these series), regularly stops at the month day ahau (since = × ), but necessarily advances in the week days by days each (since = × + ), until , is reached, when the day i ahau again appears (since , = × ). according to my method of filling in the numbers, the top row of the page consists only of multiples of , . 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 , 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:-- ) , + , = , , which is just years of × = days, mars years of days, tonalamatls of days or months of days. ) , - , = , , _i.e._, precisely the highest number of the top row, = solar years of days each or venus years of days each, _i.e._, the product of the days of the tonalamatl multiplied by the venus years. we shall again find the , on page , and seler ("quetzalcoatl and kukulcan," p. ) finds this same period on a relief of chichen itza. ) , + = , , _i.e._, mars years or tonalamatls. the half of this number, or , , we shall find again on pages - by computation; also the whole , . ) , - = , , _i.e._, mercury years of days, or tonalamatls, or five times the period of , days, in which these two periods are united. by computation again we find the , on page . this period of , days is, however, to the period of , in the proportion of : , _i.e._, × : × . is the fifth part of the apparent mercury year, as 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):-- , , , , iv ahau i ahau i ahau cumhu kayab zip. the first thing to be done is to arrange and fill out these numbers to suit our purpose. the 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 , , . it would suit this date equally well if the number were higher or lower by , or a multiple of , ; 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 ix, in the case of the middle date, the year kan, and of that on the right hand, the year 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:-- , , , , , , i ahau i ahau iv ahau zip kayab cumhu kan kan ix. let us now consider the properties of the three numbers individually. ) , , = × , and = × , , hence it is divisible by the month days of the year of days and by the mercury year. at all events this is the least important of the three numbers. ) , , . this looks as if it referred particularly to the moon and to mercury; to the latter since it is equal to × , , and to the former if we assume that the lunar revolution has been fixed at - / days, in which case this number is exactly equal to , such lunations. if this last number be again divided by , the number of days required for a revolution of mercury, the quotient is , 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). , , , 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 - / days. ) , , . 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 ( × , ; this is, however, the first number of the top row), the tonalamatls ( × ), the old official years ( × ), the solar years ( × ), the venus years ( × ), the mars years ( × ), the venus-solar periods ( × ), the solar year-tonalamatls ( , × ), the venus, solar, tonalamatl periods ( , × ), and the periods which are generally designated ahau-katuns ( , × ). we have next to consider the intervals which elapse between the three dates. ) from , , to , , is , days, which period we have already found once on this page by computation. , , however, is equal to × and × , _i.e._, the mercury revolution and the tonalamatl combined. , is again equal to × + , and from the year kan to kan it is actually years, and from the date zip to kayab it is, in fact, days. the day i ahau must be common to both dates. ) from , , to , , is days, as the manuscript expressly states. , however, is equal to × + , and the distance from the day i ahau to iv ahau is in fact exactly days. further = × + ; from the year kan to ix it is years and from the date kayab to cumhu it is days. ) from these two statements the third follows. the distance from , , to , , is , . this contains first the , in which both the tonalamatl and the old official year of days meet, and second , which is again the interval between i ahau and iv ahau. but , is also equal to × + , and the interval between kan and ix is of course years, and from zip to cumhu it is days. the numbers with which we have had to do here will again occupy our attention further on, especially the and the , on pages - , the , and on pages - , and the , on page . that these computations are not confined to the dresden manuscript is proved by the cross of palenque, where we find in signs a b precisely the date i ahau zotz, a tonalamatl before kayab, in d c exactly the difference and in d c the date iv ahau 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 , , . the high numbers of our manuscript, so far as they are in question here, form first a group, which extends from about , , to , , , and then there is a blank, and next a large group extending from about , , to , , , then another blank and lastly a group extending from about , , to , , . 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 - 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 th century (see "weltall," vol. . pp. - ). now, however, the number , , contains the statement that years ago (each year having 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 cumhu? in my opinion this date is to be regarded only as the result of the far more important date i ahau kayab, lying days earlier. day , 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 as a basis, begins with i ahau, and the three series on pages - 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 days end each time with i ahau. why is precisely this day chosen here, which is the th day of the month kayab, therefore in the year kan, and lying days earlier than the historical date? day kayab is our june th. in my treatise "schildkröte und schnecke in der mayaliteratur" ( ), 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 th of june was regarded as the longest day. the middle one of the three series on pages - begins with exactly this date, i ahau kayab. but whence come the 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 , moon , mercury , venus , and mars days, these numbers added together give exactly . it will scarcely excite surprise that i should set down the lunar year at days (and not at the usual days) for there are × - / lunations in a year and we thought we had already found this period on this page, while discussing the number , , ; also on pages - , in addition to the half lunar year of days, we shall find one of days. were the planets therefore created days before the appearance of mankind? jupiter and saturn, of course, with their and days are probably not considered here, because their periods of revolution so nearly correspond to that of the sun, and on pages - they are also treated as of secondary importance. i confess i am quite unable to discover what may have happened , 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 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 - , which are mostly destroyed, can hardly denote anything other than the four quarters of the globe, at least we can still recognize in the sign for the east, which has also the fourth place in pages - . they stand thus together five times in the middle of the left side of pages - , which pertain to this subject. to are the sign for venus repeated times, probably denoting the four parts of its revolution as on pages - 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. c, though this manuscript contains little else that is astronomical, yet it also has the rectangular heavenly shields. . this is a well-known form of the moan sign. in the globus, volume lxv, , 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 , where the -period ends, the venus and moan signs appear at the top on the right-hand side. and are the same sign, being that of the th uinal (mac), with which 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 tonalamatls of the period of , days are doubled--thus obtaining the number , of such importance here--are the sun and venus periods brought into unison (with the whole system). . 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 , combined with kin and imix, as the sign for , days, is used here after the two tonalamatls to denote the doubling of this period. - . if the preceding signs led us to the venus-solar period and to the continuation of this subject on pages - , these five hieroglyphs bring us to the mercury-lunar period and later, on pages - , which are devoted to the same period, we shall find a parallel especially on the last page. first comes , which, as has been acknowledged, is the sign for × = days. , a hand holding a rectangle divided by a cross into four parts, is, i believe, the sign for the period of days augmented to by the in front of it. the much more distinct form of sign on the middle of page and also at the top of page , should be compared with the sign as given here. the top part is the familiar ben-ik sign denoting the th and th days, and the bottom is the sign of the th division of days, which make up the year. now, however, the th day, when it becomes the th of the next days, is distant from the first 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 ½ 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 × ½ = . 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 th hieroglyph becomes quite clear when it is compared with the parallel passage on page ; it is × = days, a third of the remarkable period of , days. thus we have hieroglyph = " = " = " = ----- , which is exactly the lunar-mercury period. the sign xul = conclusion, end, is fittingly added in to the end of this period, as also on page . this sign is very common on pages and at the end of the long periods. from signs and we see that the four parts of the venus year are also about to be treated of here, that is, the periods of , , and days respectively, which are discussed on pages - . for is the sign for venus, and is a hand with a knife as a superfix, which divides the venus revolution. this hand appears times in like manner on the pages mentioned above. signs - 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 - , both times at the beginning and end of the period of 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 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 , and 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 also has a prefix, which probably refers to the night-god d. i find exactly the same combination in signs a and b of the inscription on the cross of palenque, but i must leave to others the task of connecting and likewise with the north, which is very evident in (muluc). sign is entirely effaced. nevertheless, i am positive that it represented the day iv ahau, the beginning of maya chronology, for may still be identified as cumhu belonging to iv ahau, and sign is the same sign as , _i.e._, the sign xul = the end, and denoting here the end of the long period. the comprehensive hieroglyphs, - , stand here in the wrong place. a more suitable position for them would be before or just after . 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 is the black deity, l according to schellhas, here denoting the west, and is the venus sign with the prefix denoting division. in the same way we find these two signs together on page 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 in the middle of the page in the beginning, at the end of a period of days. on page 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 days. hence this sign may mean:--here begins the venus period of days. - . the sign for the south still remains to be found. sign is again the venus hieroglyph. in we should expect to find one of the five gods of the south, which are found on pages - , _e.g._, the moan, who is represented on page 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 , middle, right-hand, an actual date as the beginning of this short southern period of only eight days. it is the date zip (third month), the month sign of which does indeed suggest a hieroglyph of the moan. now, if we recall that in hieroglyph the god n is designated in exactly the same way by an actual date, viz:-- zac ( th month), then we see that the interval between zac and zip of the second year following, is exactly + + = 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 th and disappeared as the evening star on the d 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 years. - . the last five of the signs appear in the same order again on pages - , _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 each sign has the same prefix, which is wanting on pages - , where a similar hieroglyph always _follows_. from their position on pages - it follows that these are hieroglyphs of five gods, each of whom belongs to a whole venus year of days. i am not very sure in regard to these gods. i prefer to call k, f, e and a. sign with the person crouching, i am obliged to leave entirely unsettled. we shall find this hieroglyph again, _e.g._, on pages and right, middle. let it suffice that in these five signs we have a repetition of the venus-solar period of 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 - . pages -- . 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. . the columns of day-signs. on the left-hand side of each page two days are repeated times. they are as follows:--on page eb and ben, on page caban and ezanab, on page ik and akbal, and on page 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 -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 × years, that is, over a period of , 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, ). the transition from the muluc to the ix years is represented on page ; from the ix to the cauac years on page ; from the cauac to the kan years on page , and from the kan to the muluc years on page . the ix years are represented first, because the beginning of the historical chronology lies in an ix year (iv ahau; 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. . 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. , 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" ( ), 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 the god is b, on he has the form of a jaguar (ix), on he is undoubtedly e, and on page 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 - , 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 = ), and at the same time the period of days, then in this passage these three chuen signs would properly designate the days which elapse _before_ the last day of the year, which is the last day of the th month. in the same way we shall find the chuen bundle appropriately given this meaning on pages c- c. likewise the simple chuen sign at the top of page seems to denote 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 numbers and , on number , on number and on number . 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. . 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 on each page, and arranged as follows:-- . 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 signs in the top line only one is legible, and that is the first on page . this is the usual cross _b_; as a comprehensive heading it perhaps occupied places and on each page, alternating with another sign in and . in spite of this obliteration there are a few points which can be profitably discussed here. i would call attention first to signs and on page . the first seems to contain twice repeated the figure, which is thought to represent eagle feathers, and which we found on pages b and a, for example. as this double character is also used to change the -sign into a -sign, so it may also combine the years of this passage. the th sign on page 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 it appears three times. this page treats of the transition of the ix to the cauac years. in the th place the ix sign seems actually to be used as a prefix, in the prefix is plainly the kin-cauac sign, just as on page a, and in 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 c- c. on page , in the th place, the year sign has a prefix and a suffix, which seem to indicate that here it was intended to represent as separated into × or + . lastly, on page the th sign can be explained as meaning that the ritual year of days is separated into bacab periods of 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 b- b, b- b, c- c. we find it with slight variations once on each of the four pages - . it is the th on page ; the th on ; the th on ; the th on . its lower part, especially the (phallic?) sign added at the left, suggests the hieroglyphs of the bacabs, as we find them on pages , , , etc.; they might refer to the separation of the ritual year of days into × days. on the other hand it has been considered simply as the reproduction of the carrying-frame pictured below it (compare above under page c.) 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 as the th sign, on page as the th, on page as the th and on page as the th. to this sign are prefixed successively the numbers , , and . the second is unquestionably the hieroglyph for the numeral or for the moon. it is effaced on page and on pages and has a prefix, which on page is used as a superfix. this sign is the th on page , the th on page , the th on page and the th on page . the prefixed numbers are , , and . the meaning of these two signs and that of the apparently irregular numbers is still a mystery. the latter will be discussed presently. the th sign on all the four pages seems to refer to a period like the one hitherto discussed. on page the sign resembles that for the th uinal (mac) and hence appears to refer to the tonalamatl, as in the first column on page . 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 it ought to be b. sign , however, though it can with difficulty be identified, points rather to god k. sign on page 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 a; here its prefix is the sign for the west. on page we ought to see the grain-god e carried by the priest; his hieroglyph may be destroyed, but sign , which is kan-imix (food and drink) is his determinative. finally the th sign on page is, just as we should expect, the hieroglyph of a and, in addition, we find his determinative in . but what is to be said of the fact that the tiger appears again on page in sign , and this time with the sign for the east? the ahau on page , sign , refers to the god d of the middle section. there maybe some reference here to sacrifice, thus:--the th sign on page is kan-imix, the th on page is kan, which is followed in the th sign on page by another one with a yax and a suggestion of a second kan-imix. also the curious sign in the th place on page , which we have already discussed under page b, is used to denote the sacrifice on pages a and b. here its position with reference to sign is the same as on page b. on page the prefix of sign , which is half destroyed, may be recognized as a serpent. signs and on page are unintelligible. unfortunately the following signs are entirely effaced:--sign on pages , and , as well as on all the four pages, on page , and on all the four pages, on pages , and , on pages and , on page , on pages and , and on page . . 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 the god is k with his eyes apparently destroyed, and on page it is b with a kin sign on his head covering, hence designated here as a sun or day-god. on page the god is d, and on page , 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 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 c and cort. and c). the contents of the lower vessel on page 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 the lower vessel contains a fish and the upper the sign for the south. lastly, the single vessel on page 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 there is a with the lower vessel, and on page with the upper vessel two dots with a cross between them (perhaps this may mean - = , which is used in place of the usual clumsy numeral?). on page we see above the vessel a , 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. . the middle hieroglyphs. on each page these signs consist of but _one_ line containing , , and 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 , b as the sun-god on page , and d on page . the second sign on page , 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 in sign 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 and not the tiger, on page b or g and not e, on page d and not a, and on page a and not b. hence there is some confusion here. yet it seems to be in the nature of a correction, that on page the third sign, next to that of the sun-god, is actually the sign for e who is in the top section on page , and that the sixth sign is kan-imix belonging to this god. on pages and this line also refers to the past year, _i.e._, to the year set down in the top third. the fourth sign on page 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 , is, in fact, the tiger pictured above. the lunar hieroglyph as the third sign on page and the _a_ as the fourth on page 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 is the usual determinative of d, whose hieroglyph stands beside it. on page 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. . the bottom pictures. in the left-hand lower corner of each page we see the sign for the year of 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 , and , which probably refers to rain as the most desired event of the year. the tree on page 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 the god b, on the god k, on a and on 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 . there are besides, on every page, several small objects between the two pictures, just as in the middle section. on page the object is probably an altar, but instead of the flame it has the number . 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 as the contents of the lower vessel. on page 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 with a prefix, and above this a . at the bottom of page 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 and in that of the lower section of page . above these is again the sign for the moon or with a superfix, which is the same as the prefix on page , and beside it is a . page 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 with the same superfix and the numeral . i shall discuss below the numbers scattered over these four pages. . 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 - as the symbol of strength, and on page , but probably by mistake, the abbreviated sign for the west. the _third_ sign always represents one of the four cardinal points:--on page the east, on page the south, on page the west and on page 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 , with that for the east (kan), which belongs on page . the other three signs do not stand in the same order on every page. the _fifth_ sign on pages and and the _fourth_ on page show correspondence most clearly. this sign is always a head, undoubtedly that of the god pictured in the bottom third. but on page it is the hieroglyph of e, who is pictured on the top of page , instead of that of b. in the same way the th sign on page , the th on page , the th on page and the th on page have something in common. one element of the hieroglyph is always the sign for the year of days, combined on page with cross-bones and the cauac sign, on with yax and kan, and on and simply with yax. the most puzzling and divergent of these hieroglyphs are the remaining ones. the th on page has an oblique cross (or bones?) and the abbreviated glyph for the west, the th on page is the head of e, the th on page is the -day sign combined with kin and cauac, and the th on page is the usual kan-imix sign. here, too, there seems to have been a displacement. before i leave the four pages - , 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. , 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 and designates it like a duodeviginti by - . next, that in this passage as on pages a, c, c, b and c, 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 b close beside the picture of that god. assuming this as a known fact, we find scattered over these four pages the following numbers:-- : , , , , , : , , , , , : , , , , , : , , , , . it is very remarkable that the sum of the numbers on each of the first three pages is equal to , and as an accidental freak it would be most surprising; somewhere on the fourth page six units may have been omitted; but perhaps the , which stands above the _two_ chuen signs in the centre, is to be counted twice. the , however, designates the very years, which are treated of on these four pages. as yet i know no reason to account for the fact that the 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 _days_, perhaps those which follow a tonalamatl coming in the middle of the year? page 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 years. pages - (_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 . 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 a-- a. xi xi xi xi xi xi lamat ben ezanab akbal. this is a tonalamatl of × days, each part subdivided into × 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 ; 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 th 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 b and perhaps on page . there are a number of small dots around b's head, which on page c 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 - as ruler of the four cardinal points and in as the ruler of the earth in general. pages a-- a. this passage looks like an amplification of the middle picture on page a. 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 b. 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 , probably a is effaced and the sum should be , the sum which so often occurs in the cod. troano - 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 a-- a. in my article "zur entzifferung, etc., vi," published in the year , 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 days:-- . the ritual year of days, and consequently also a quarter of it, the bacab period of days. . the period of 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, ) 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, ) 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 a 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 years, furthermore a series which shows the same difference of 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 × , _i.e._, days = tonalamatls, like a similar representation of tonalamatls on page . above these days, and to the left of them, numbers are set down rather irregularly, which begin with 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:-- , , , ( ), ( ), ( ), ( ), ( ), ( ), ( ). then with a bound follow and ; with the last number akbal is reached in the natural way, which day the scribe had erroneously set down again with in place of cauac. the number already united the numbers , and , but did not include the number . this inclusion is accomplished by the number on page , quite on the left where we find the numbers and , under which only a has been omitted. with the usual hiatuses this series seems to end on page , where i think the numbers , , and ought to stand, but they are almost wholly effaced; this would then be × , × , × , × = , . 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 , , , the close of the eleventh ahau-katun, and the latter in the neighborhood of , , , the close of the thirteenth ahau-katun. the manuscript presents the following:-- , , , , , , . xiii akbal xiii akbal xiii akbal , iv ahau iv ahau cumhu cumhu iv ahau. in connection with this it should be noted first that i have restored the in the statement of the months, and second that the two numbers on the right were found with the aid of page only by an easy conjecture. for with the reading of the manuscript , , , , , i do not agree, but read instead , , , , ; the number below, however, is given in the manuscript as , and then a black joined to a red ; i read this , , , . 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 kan years, is given; also the differences of the series and , therefore also in the proportion of to . if we combine these last two numbers by addition and then by multiplication with , the result is ( + ) × = . if, however, , and be combined by multiplication the product is × × = , = × = × = × = × = × ( + ). we have already met with the , on page , which was obtained by the addition of , + , . my opinion is as follows:--first ahau-katuns = , , , were taken as a point of departure, and to this sum was added , = × , and as the interval between the normal date iv ahau and xiii akbal. the result was , , . the position of this day, however, is xiii akbal xul ( ix). then the mentioned above was added to this number and the result was , , = xiii akbal pop ( muluc). then to the , , was added the , and the sum was , , = xiii akbal kankin ( kan), the very place in that year where a tonalamatl ends. the following numbers were thus obtained:-- , , , , , , . these numbers are suppressed in the manuscript. but if the encircled numbers are added to them, viz:-- (interval between xiii akbal and iv kan), (interval between xiii akbal and iv ahau), and , (= × + ; , 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:-- ) , , = iv kan xul ( muluc). this number = , × = , × = × . it also = × + , the interval between iv ahau and iv kan. ) , , = iv ahau mol ( ix) = × = × = , × . is the interval between xiii akbal and iv ahau. ) , , = iv ik zac ( muluc). it also = × + . the , however, the half of the ritual year of 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 , , _i.e._, of × + (there are days between xiii akbal and iv ik). but it was evidently desirable to obtain as large a number as this. on page a number of nearly similar value is associated with it, viz:-- , , . it is set down almost in the middle between the th and th ahau-katuns, for it is , days greater than , , , and , days less than , , . now, however, the manuscript presents in the last column but one of page a number, , , , 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 muluc, and to the date iv ahau mol. it has many remarkable properties, for it is:-- ) = , × ) = , × ( = iv kan - iv ahau). ) = , × ( = iv ik - iv ahau and iv kan - iv ik). ) = × . we have already met with this above. now, however, the , , by virtue of its magnitude creates the suspicion that it may be composed of two ordinary large numbers. it might be ) , , + , , , therefore , ( + ). ) , , + , , , therefore , ( + ). that is to say, the important multiplied by the days of the lunar year and also by those of the solar year, hence the , referred to under , separates into these two parts. the lunar year of = × + × days was not unknown to the mayas. we shall find its half, days, several times on pages - . we might also use the two important numbers , and , , the first of which is divisible by and , and the second by and , without remainder. then we have the large number desired:-- ) × , + , . ) × , - . 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 , 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. - . in the top sign i recognize an imix with a prefix and probably also a superfix. i think this denotes the period of , days. i am forced to pass over the second entirely, inasmuch as a red inserted in it remains a mystery ( × , = , ?). as i stated in the above-named work, i think the third is three times the sacred period of , _i.e._, days. finally, the fourth sign certainly denotes the period of 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 we find the third in the th place in the second column, the first in the th place in the same column, and the fourth in the th place in the first column. page has the first sign in the middle of the th column; the second somewhat lower down in the d column and the th two places below. finally all three signs appear in succession on the top of page in the same order as on page . the fifth column on page 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 a-- a. 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 xii i xiii xiii xii v x xi v iv x v x iv iii viii iii i. there are thus divisions, the different lengths of which reveal no rule. they embrace days, _i.e._, × , which may well be considered as a continuation of the computation in the preceding section, of which the 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 - . i assume that the scribe has set down the th, d and nd 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. . i would note in addition that a period such as this, consisting of days = weeks, might be explained in an entirely different way, if there were a column of five days at the left having a difference of 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 , but for about subdivisions. it may, therefore, be assumed that about four subdivisions averaging days are not specified, in which case this passage would extend not over , but over 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 subdivisions. . pages a- a. here at the very beginning it is uncertain whether the signs at the end of page and at the beginning of page are to be regarded as a single group of hieroglyphs, as seems to follow from the numbers, or as two groups of hieroglyphs each. at the end of page 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, , and (the last probably the god c) seem to have the sign for the west as a prefix, while the prefix of (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 , 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. . the rest of a 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 hieroglyphs belonging to this picture, only the following are distinguishable:--the st containing an akbal, the d, which is the common cross _b_ with a , the th, an imix also with , and of the th only the prefix yax. the d and th appear again on page a, days later. . page , like page , 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 , 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. ), 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 b and b. 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. and . page a. 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. b- b, 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 c and c. and quite on the right sits b with foot-prints pictured below him and on his clothing. the hieroglyphs on page , when they were all legible, numbered and were arranged in two rows. of the upper row are preserved, the lower part of the first is a year-sign (?), similar to that which often appears on pages - , 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 , 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 (sign of the second or third month?). these two signs with the prefixed are perhaps to be read as a calendar date ix imix zip ( ix), as on page a. ix, however, belongs to the west, which is the predominant cardinal point from a 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 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. . page a. here the head of b forms the head of a serpent (cf. pages and ) represented in pouring rain, while on page b it is emerging from the water. of the four hieroglyphs and are entirely and for the most part destroyed, and is the usual kan-imix. . 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, is effaced, is a compound of kan and kin, a head with akbal and kin (d?) with the uplifted arm as a prefix, and , corresponding with the picture, is the compound of the rain sign cauac with the prefix of the storm-god k. . 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 b and b; the first and second signs are rather indistinct. . page a. unless i am entirely mistaken, b is here represented with his arms bound behind his back. cf. the pictures on page , top, and , bottom. are the ends of the rope fluttering in front of the god intended to render this still more plain? hieroglyph contains the sign _t_, which resembles, but is not the same as, the year sign. this sign has already occurred frequently, especially on pages a- a, and the last time on page in the first hieroglyph. as on page , hieroglyph 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 a. is again cauac and is the hieroglyph for b. . rain is falling from the heavenly shield, already seen on page , 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 c, a and c. 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 a, 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 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 , left, middle. the third hieroglyph contains caban signs, the first and second cannot be clearly identified. . this is a deity which i hardly think appears elsewhere. it has an animal's head resembling that of a bear, thus recalling page a, and it also has the paws of a bear. of the hieroglyphs only a kin-akbal is recognizable. . page a. 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 a. hieroglyphs to are wholly and , which is a head, is for the most part destroyed. . b is here represented in very close connection with a female figure. cf. pages c- c. the representation on page b 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. . 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. , i stated that this was the sign for the change of the year, which is its meaning on pages b, b and a. the kan year follows here after the cauac year of page . 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. . page . 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. . 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 a. 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. . 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 , and shall meet with again on pages , , , , 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. . the entire section ends with a picture of b, who carries the hatchet and probably the copal pouch. the hieroglyphs are wholly obliterated. pages a-- a. the following tonalamatl, one of the form of × , has suffered much from the carelessness of the scribe and from injury. i have attempted to restore it as follows:-- x x iv viii xii i ii 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 × 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. . b is traversing the water in a canoe, as on pages c and c, with the paddle in his hand. all the hieroglyphs belonging to him are obliterated. . b is sitting on the laterally elongated head _q_, which here, as on page , is enlarged and drawn with special care. seler ("charakter der aztekischen, etc. handschrift" in the zeitschrift für ethnologie, , p. ) 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. . as on pages a and c, and again just as on page a, 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 days on pages - ; the prefix of also suggests this meaning. . 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 b- b, and which in the treatise, "zur maya-chronologie" (zeitschrift für ethnologie xxiii, p. ), 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 days ("zur entzifferung" v, ); still the red numeral 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. . 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. . the god is sitting on a mat in a house. all the hieroglyphs except his own are obliterated. pages a-- a. another tonalamatl of the form of × ; i have restored the effaced day-signs as follows:-- xiii xiii iii v vii xiii ii iv vi 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 subdivisions has hieroglyphs, and the order is as follows:-- . 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 c- c. 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 and which we shall meet again on pages - no less than times, with regular intervals of 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 st, d, th, and th groups, and in the third of the th group; in the th group it is destroyed. in the nd and th 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. . 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 - . it is remarkable that the flourish, which usually appears as the nose-ornament of the sun-god g (_e.g._, pages b 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. . 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. . page . 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. . 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. . 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 zac, which belongs to n. cauac, however, belongs to the south, and therefore corresponds with the north of the second group on page . sign , a kan, corresponds exactly with the same sign in the fifth place of the preceding group. . page . 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. . 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 a. this passage recalls page a, where b is seated on the laterally elongated head _q_. nothing more can be said of the hieroglyphs, than that is the head without an underjaw. . b is sitting here in a house; his sign in the third place has yax as a prefix. hieroglyph , with the number prefixed, recalls the one which we found on page c belonging to the baldheaded old man. hieroglyph is the common kan-imix. page a. 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 a- a. 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 , , and . but the two series gain this end by different means. on page the series begins with , and at first has only as a difference, until with a multiple of and is obtained, then it returns to the simple difference , in it obtains again the and , loses these two last numbers once more in and finally in obtains the desired multiple of all four numbers, which is retained in , , , , and , . the series on page a proceeds much more briefly. it begins at once with ( , , ), loses the in , gains the and loses the in , arrives at divisibility by all four numbers in the , loses the again in , but then comes to a standstill after having obtained the same multiples (double at that) of , 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 , and , 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 days apart from each other, and here they are separated by , _i.e._, xiii ezanab, xiii ik, xiii cimi, xiii oc. the initial days of the two series, xiii oc-xiii akbal, are separated by days, and the reversed series, xiii akbal-xiii oc, by days. hence the subject of both passages is essentially the week of thirteen days, _i.e._, the year of ( × ) days. now this series is also accompanied by a number amounting to millions. it is in the second column of page ; only, in order to understand it, we must add a zero as the bottom figure; then it becomes , , . xiii oc stands below this number as the beginning of the series. the first column has 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 , the interval between iv ahau and xiii oc, to this was added × = , , the sum being , . the result of this number added to ahau-katuns = , , , was , , , which number is not revealed in the manuscript. it is concealed in xiii oc mol ( muluc). but , , = , × , _i.e._, it is divisible by the interval xiii oc-iv ahau. now if we add to this large number the set down in the manuscript, the result will be the above-mentioned , , . this number in the manuscript has the date iv ahau chen. ( muluc). it is, of course, divisible by and by , hence = , × and × . it corresponds not merely in this respect with the largest number on page a, viz:-- , , , but also with regard to its divisibility by , , , which are all multiples of . on page a, 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 days; see page of my treatise "zur entzifferung v." pages b-- b. we come now to the middle section of pages - , 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 iii iii iii iii ix cimi ezanab oc ik. that is to say, the days divided into four equal parts. to these four divisions, as on page b, 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:-- . of these, , , and are the cardinal points just mentioned; , , and are the sign for b, and , , and 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, , , and , although they are not exactly alike, have something in common, the th 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 a. 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 c, a, a. pages b-- b. 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 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 , , and ; 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 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 b-- b. 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 days each, but the remarkable thing about it is that these divisions of days are each subdivided into two periods of and days, and the days again into eight unequal parts, which are exactly the same each time, while the days run their course without further subdivision. on pages , and this is always on the left at the bottom, on page 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 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 vi ii xi xiii iv xiii iv 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):-- ( ) x ben ( ) vi ik ( ) ii chuen ( ) xi ahau ( ) xiii ik ( ) iv cimi ( ) xiii men ( ) iv cauac ( ). ( ) x ezanab ( ) vi manik ( ) ii cib ( ) xi chicchan ( ) xiii manik ( ) iv chuen ( ) xiii ahau ( ) iv kan ( ). ( ) x akbal ( ) vi eb ( ) ii imix ( ) xi oc ( ) xiii eb ( ) iv cib ( ) xiii chicchan ( ) iv muluc ( ). ( ) x lamat ( ) vi caban ( ) ii cimi ( ) xi men ( ) xiii caban ( ) iv imix ( ) xiii oc ( ) iv ix ( ). 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 of the 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 days, the first of these pictures referring to the divided period of days and the second to the undivided one of . it is also in agreement with this that on pages and 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 . as the hieroglyphs belonging to the periods of days are allied to one another, and as this is also true of those belonging to the periods of 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 ( , , and ) on the right side of the pages:-- . 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. . 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. . he is walking and holding the reversed torch in his left hand and the hatchet in his right. . 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:-- . the first hieroglyph on each page certainly represents one of the cardinal points. they are in the usual order:--east, north, south and west. 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 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 , and the end alone eight times at the bottom of pages - . on page , is b's sign, on page b's with the prefix of the north, on page it is b's sign again and although quite indistinct its is plainly joined with the east. on page 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 and ; on page it is the laterally elongated head _q_ with the ben-ik superfix, and on page 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 - . on page it is a cauac, the prefix of which here, however, suggests k, on it is certainly the hieroglyph of e and on possibly of a, on 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 , , and and to the hieroglyphs belonging to them, which are on the left side of the pages and belong to the periods of days. . b is pictured walking, raising the hatchet in his right hand, and holding an uncertain object in his left; the serpent with the set down in its coils does not appear here. the nd, d and th pictures belong together. in each picture on these three pages there is a serpent with water in its coils and the number in the water, denoting the number of days belonging here. as on pages and 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 nd and d b wears the copal pouch, second, that only in the d and th 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 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 it has a prefix and on pages - 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 b- b. on page it has an akbal as a superfix, on - a prefix, which is familiar and in keeping with the sign and probably also the same suffix, though it is indistinct on page . the fourth sign shows, as do several other things, that the representation on page differs from that on pages - . on the first of these pages we see an imix with a puzzling prefixed. if the numbering of the days really begins with kan, as is probable in this manuscript, then imix is the th day and + might denote the , which is not set down here. on pages - 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 prefixed three times to the spiral. this number is rarely a prefix, but it occurs, for example, on pages a and a before the cross _b_ and on page right, middle, prefixed to xul (= end). the interval occurs in this tonalamatl times, including therefore of the days. the fifth sign each time contains the head without the under jaw, just as it recurs regularly in the preceding passage, pages - . 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 . pages b-- b. i xii v i v xii viii i caban muluc imix ben chicchan. that is, a regular tonalamatl of five parts, × . that the days are divided into two halves ( + + = + + + ), may only be accidental. i will designate the hieroglyphs of the seven divisions thus:-- | | | | . 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 th, th, st and th hieroglyphs, but, for an unknown reason, c's sign is joined to b's in the th, probably also in the th and perhaps in the th, and in and c's sign forms an integral part of a hieroglyph. now in discussing the great tonalamatl, pages a- a, 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 to , 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 and we find an inscribed; in hieroglyph it is joined to an imix, exactly as on page c; on page a it is joined to kin, and on a and a to a hand. is it possible that here also the 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:-- . a serpent in the water, with b emerging from its head, exactly as on pages a, tro. and cort. . 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. . 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. . b is traversing the water in a boat, exactly as on pages c, a and c, and c. 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 we see with kan a sign which may suggest the usual hieroglyph denoting a year. . a serpent is pictured here, with a bird sitting upon it. we met with the same bird on page b. schellhas, "maya-handschr.," p. , 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 a. 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? . 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. . 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 a. 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 c, b, , on the right, with a superfix suggesting k. . 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 at the left ends the series of twenty gods. the twenty-seventh sign (with yax) is still undetermined. pages b-- b. vi ix iv ii xii xiii xii v iv ii xiii vi cauac akbal manik chuen men. the sum of the black numbers is , the whole is, therefore, a double tonalamatl = × = . while the series on pages a- a primarily brought the and the together, and the series on page a accomplished the same result with the and the , here, though the process is a different one, the is combined with the 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 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. . 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 a and c. hieroglyphs and 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. . 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. . 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. . page . 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 b and on the last page, . 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. . 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 b. . b is again sitting in the rain and under the same astronomical signs as before on page . 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. . page . b is plunging down headfirst from the same astronomical signs and is brandishing the hatchet. hieroglyph is the cross _b_, is b's sign, probably that of the grain-god e, and being kan-imix refers to grain. favorable weather seems to have set in. . 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 (_w_) with the superfix suggesting k still puzzles me. is the cross _b_, is the tortoise-head with the number , which probably refers to the kan, muluc, ix and cauac years, as the sometimes appears prefixed to n's hieroglyph. in exactly the same way the tortoise-head with the tortoise itself occurs frequently in the cortesianus. is the sign of the year with prefixed kin and cauac, _i.e._, day-cauac-year. . 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 b, a, b, a, and possibly on pages b, - a, b. . page . 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 b), 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. , 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 th 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. . 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 , 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 is b's, is the sun between a dark and a bright sky, and 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 days extends from april th to august nd, which, with the addition of the five days not counted at the end of the year, does indeed make days. all this, however, is only true on the supposition that i have not seen more in these representations than they contain. pages b-- b. vi v xii v xiii 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 and , in the sixth of group and might perhaps be intended also in the fourth of and . the usual kan-imix is in the third sign of group , in the fifth of , and the fourth of ; possibly also in the fifth of ; the third hieroglyph in group , at any rate, contains imix. let us now consider the five groups individually:-- . 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 - . 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. . page . 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 b. the first, fifth and sixth hieroglyphs are not finished, and the third is kan-imix. . 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?). . 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. . page . 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 b, 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 days between the second and fourth groups and of days between the second and fifth, this would be found to correspond with the interval between the months pax and cumhu. pages b-- b. this is the fourth and last series of the first part of the manuscript; the first is on page , the second on pages a to a, and the third on page a. 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 :-- , and , equal to , , and × . all three aim and arrive at numbers which are common factors of , and , and therefore also of , 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 , the week day numbers remain the same, while those of the month days must advance by 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 × , _i.e._, × and thus comes again to the day iii lamat. from onward this number is itself always the difference of the higher terms of the present series. at the same time days are the duration of the apparent revolution of mars, which is here supplementary, as it were, since page 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 , , and , always accompanied by the day iii lamat. the larger numbers require a few corrections; i read them , ( × ), , ( × ), , ( × ), , ( × ) and , ( × ). the very largest again are correctly set down; first , equal to × , but here also equal to × and × , so that in this series the goal aimed at is not reached until later than it is in the two preceding series. then follows , = × , × , × , but finally , , which number = × and × , but is not divisible by . detached in the usual way from this series on the left of page is the number , , . above and below it is the day iii lamat, further down iv ahau, and between them is 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 , added to it × = , , and subtracted the result , from ahau-katuns = , , . the remainder was , , , which number would correspond to the date iii lamat zotz ( kan), which, however, is suppressed in the manuscript. the = + was added to this sum, and the result was the , , written out in the manuscript, _i.e._, a day iv ahau zip ( muluc). now this number is the one sought; it is × = × = × , and hence must also be equal to × , since the and are united in . 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 b-- b. this section supplements the pictures and hieroglyphs belonging to the series just examined. therefore it likewise extends over days and divides them as follows:-- iii ix ii viii 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 - , 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 st, the moon and saturn, nd, mars and mercury, d, the moon and mars, and th, 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. . 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. *b we also find the pierced ear; a pierced _tongue_ (tro. *b), however, does not occur in the dresdensis. the second place always contains the sign of the beast like the one instance on page . 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 d- nd); the second might very well be the month yax (january th- st). this is quite in keeping with the distances + = set down below. in my "tagegöttern der mayas" (globus lxxiii, ) and above in my discussion of the great tonalamatl under pages a- a, 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:-- st, group , sign , where it may be joined to the month mol belonging here; nd, group , sign , joined to the akbal, which also belongs here; d, group , sign , with a usual prefix. in the second group it may be included in the very similar month sign of mol. four hieroglyphs remain:-- st, akbal in group , sign , hence probably denoting the darker time of the year in general; nd, a in , sign ; d, e in , sign ; _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); th, kan-imix in , sign , 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 in order to examine the lower sections. pages c-- c. iii vi ix xii iii ix cauac kan muluc. here is a tonalamatl of four quarters, × . in the manuscript is again erroneously set down for and the iii following it is omitted. the initial day is exactly the same iii ix, as in section b 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 b. 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 c to c 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:-- . b is rowing a boat, as we have already seen him several times ( b, a, _c_, and c). 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. . 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. . 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 , where the fish and kan are also combined. . holding a hunting-spear, he is sitting on an animal slain in the chase, as on page c. finally, i have remarked that pages c- c, the last part of the first division of the manuscript, look like an enlargement or amendment of the section just considered. pages c-- c. 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 days distant from the preceding, but in reality the interval is days, since the same week-day is always implied. the hieroglyphs seem to indicate that these days are divided into three distinct parts, , and . days, however, are equal to × and hence in what follows we find a black set down 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 such sections of days, the duration of this calendar is days or tonalamatl. consequently we find nine pictures of the same god b. in five of them (in groups - and ) he is sitting before or on a sacrificial tree or tree of life; cf. b. 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, , and he is seated on various supports, in on an object, which is not completed and which cannot, therefore, be explained, in on astronomical figures (mars and venus?) and in on agave leaves. in and his head is again surrounded by those dots suggesting stars, in there seems to be a bird (quetzal?) seated upon it and in it bears what may be the kin sign. in and he has the pouch for incense in his hand, while in alone he wears the gala mantle and is painted black, just as he appears in connection with the same hieroglyphs on page c. he carries a hatchet in repose in , and , and raised for a blow in and . in 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 and of group , 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 there are two signs for the north; in group that for the east with the sign for the west beside it erroneously given for the east, and in group two signs for the south. in groups , and we find in the th place the head of c, and the same sign in group in the d place, where it is joined to another head, which may be that of a woman. the d sign of group is incomplete and cannot be determined. the d sign of group displays a repetition of the astronomical signs represented below. there still remain the d and th signs of groups and . of these the d in group is _w_, which is as yet unexplained. the th might be interpreted either as oc (day ) or as xul (end). its prefix is a yax sign. finally, in group the d sign is manik (day ), the th the elongated head _q_ with the ben-ik superfix, which seler assigns to men (day ). pages c-- c. the beginning of this tonalamatl is indicated by a large red dot on page . it resembles the tonalamatl almost exactly above it on pages b- b, 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 ix vii i xi 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 ( ) ix muluc ( ) vii ahau ( ) i ahau ( ) xi oc ( ) xiii chicchan ( ) ix ix ( ) vii chicchan ( ) i chicchan ( ) xi men ( ) xiii oc ( ) ix cauac ( ) vii oc ( ) i oc ( ) xi ahau ( ) xiii men ( ) ix kan ( ) vii men ( ) i men ( ) xi chicchan ( ) i have arranged the whole series in four parallel periods of days each, for the appears throughout the computation, although the entire tonalamatl is written out in _one_ continuous line. on the right of page the scribe seems to have wished to erase an entirely incongruous , and in writing the last , on page , 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 month days do not occur at all. also the intervening periods + (= ), , , 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 times, usually appears in the second place, in the first and second groups in the third place, and in the th and th his sign does not appear at all. i will discuss the remaining hieroglyphs in their place in each of the groups. . 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 th 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 b, c, b, b, a and a. the fourth sign is a combination of cauac and manik. . 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 as a prefix (cf. the same sign with the on page , 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 th to the th day of the tonalamatl. the rest of the hieroglyph is unintelligible. in the th place we see a vessel with imix, probably denoting pulque. . b is sitting in water, the hatchet raised in his right hand and his face turned upward. the d hieroglyph is again imix and the th a compound of ik and muluc:--wind and clouds. . b is seated on a reproduction of his own head or d's, beating a drum with his hand. the d hieroglyph denotes the serpent-god h with the number as a prefix. the th hieroglyph is a chuen with the sign for the south prefixed,--at any rate the upper part of that sign. . b is standing in the pouring rain and looking backward. the d sign here is a caban apparently in a vessel. following this in is the hieroglyph which i have proposed to interpret as the sign for _beginning_ (globus, vol. lxvi, page ). this sign occurs again in groups , , , and , and must therefore be connected with the principal idea embodied in this tonalamatl. . 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 - , and which very much resembles the familiar sign for a year of days. we shall meet it again in the continuation of this tonalamatl on pages and . the three passages refer to the th, th, and th days of the tonalamatl, and hence are days apart. the th sign is the cross _b_, with possibly the sign of the east as a prefix. . 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 th hieroglyph. we have already seen it in the th hieroglyph on page , 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 c, 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. ). this figure is represented independently only on the right of page . in the passage under present consideration this personage appears again on page . the two figures are connected one with the th and the other with the th day, and are, therefore, divided by exactly half a tonalamatl or days. here we find it as a prefix of the supposed sign for _beginning_ of which mention was made in discussing the th group. the d 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. . 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 rd sign is manik, with a prefix. the th is an indistinct head, which may be c's, with an imix sign as a prefix. . b is walking with the pouch hanging from his neck, and the hatchet in his hand. the d sign, which is unusual, is very obscure, but suggests the fish on page c or that on page b. the th sign with the prefix of the north is very indistinct. . 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 th part merely indicated, occurs days later on page . the th sign is the familiar compound kin-akbal. . 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 th 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 . the component at the right, top, is indistinct. . 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 , which is days earlier. the fourth is the sign of the year of 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. . _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 b 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 . the fourth sign is a kin-akbal. . 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. . 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 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 ( days earlier). . 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 ( 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. . 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, days earlier. the fourth hieroglyph is again the sign for beginning, which we have already often met with, as, for example, days earlier in the twelfth group. . 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 , which we found on pages b and b, and has the imix sign as a prefix, as in the first of these two passages. the same compound appears on pages a- a. . 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. . 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 days, correspond in certain respects with one another, _viz_:-- . pictures , , and . in all, and _only_ in these, b is sitting in a house or tent, in and with his arms folded. . pictures , , and . 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. . pictures , , and . here in the last two b is sitting _beneath_ astronomical signs. in all four pictures water, clouds and rain are represented. . pictures , , and . 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_. . pictures , , and . 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 c-- c. i xi viii v ii v 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. . 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 ( × ). the fourth sign is a fish forming a connecting link between the water represented below and the rest of the group. . 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 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? . 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 b. it is drawn in precisely the same curious fashion in cort. and c; hence it is represented in the picture by the serpent. . 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 b. the second sign might be the abbreviation for the south. . 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 c and a similar one on c. 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. . 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 days begin, and if the prefixed 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 + , with the second , with the third + , with the fourth + , with the fifth + , and with the sixth + , _i.e._, with the exception of the second, or , two multiples of . 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 . 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 , and ik is the th day, if we count from kan as the starting-point. pages c-- c. this is a tonalamatl consisting of × days. if written out in the usual way it would run as follows:-- xiii iv xii vii ii x v 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 b- b and c- c. 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 ( ) iv ahau ( ) xii lamat ( ) vii cib ( ) ii kan ( ) x eb ( ) v ahau ( ) xiii lamat ( ) iv chicchan ( ) xii ben ( ) vii imix ( ) ii muluc ( ) x caban ( ) v chicchan( ) xiii ben ( ) iv oc ( ) xii ezanab ( ) vii cimi ( ) ii ix ( ) x ik ( ) v oc ( ) xiii ezanab ( ) iv men ( ) xii akbal ( ) vii chuen ( ) ii cauac ( ) x manik ( ) v men ( ) thus the days chicchan, lamat, oc, ben, men, ezanab, ahau, and akbal are repeated here twice, and the others occur but once. the ( + ) strongly recalls the ( + ) on pages b- b. 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 . from this it follows, as we have already found on pages - , that chuen really denotes days and that the count of the days in the "dresdensis" begins with kan. but the numbers , , and are entirely unexplained. they show no recognizable order and always stand near the bundle of chuen signs. they recall the numbers on pages - , 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 c- c. the meaning is simply as follows:--every 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. . page . 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 , 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. . page 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 ( c), and muluc, the north, has certainly a close relation to water. we see here two kinds of food, while none is represented on page . the same bird's head, which we find at the bottom of the corresponding page , is placed in front of the canoe, and on c 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. . page likewise refers to the introduction of the new cardinal point, west, which is represented on page 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 b and b and also the nose of the storm-god k, who occurs on the corresponding pages and 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 ? or of hunting with snares? page 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 a and c 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 . . . . south ( ) east ( ) north ( ) west ( ). it ends ( ) ( ) ( ) ( ) b ( ) ( ) ( ) ( ) the time of the cauac ( ), kan ( ), muluc ( ), ix ( ), while kan ( ), muluc ( ), ix ( ), cauac ( ) begins ( ) ( ) ( ) ( ). if that which is actually set down in the manuscript be compared with this, it will be seen that in of the places the manuscript corresponds to my hypothesis:-- , and are the familiar signs for the three cardinal points, and are the sign xul = end, which i have already frequently mentioned, and are the sign for b, is muluc, 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 and . finally the two agree in and , 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 to , from to , the north from to , the xul from to , to , the e (kan) from to and and cauac from to , _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 th, th and nd, and probably also in the half destroyed th sign, the scribe thoughtlessly put down a sign for e, which is proper only with kan and should come after or . finally in the th place he put a sign for a, as if it were the intention that this passage should end exactly like its parallel on page . 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 -- . 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 is nothing more than an amplification of page . the contents of pages - are of a more independent nature, but special attention should be called to the relation of a- a to - . pages -- . the entire contents of these pages must be represented as a unit, for what is in the main true of page is also true of these pages, namely that they treat exclusively of the period of days, in which five venus years of days each are brought into accord with eight solar or terrestrial years of days each. each page is a direct continuation of the preceding one. each period of days is taken times, the result being , days, which are equal to 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:-- . 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. . the venus hieroglyph three lines below, repeated twenty times with the sign of the knife, to denote the _division_ of the venus revolution. . the _akbal_ sign occurring further down, four times on each page, except on pages and . 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. . the sixteen venus signs also occurring below, except on page . 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 . 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 yaxkin zac zec xul north. west south east gods. [ ] zac [ ] muan yax yax gods east north west south kayab zotz pax kayab page . 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 cumhu zotz pax kayab north west south east gods. zotz mol uo zip gods east north west south yax pax chen chen page . 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 yax pax chen yax[ ] north west south east gods pax pop mac kankin gods east north west south zip yaxkin uo uo page . 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 zip mol uo uo north west south east gods yaxkin ceh xul xul gods east north west south kankin cumhu mac mac page . 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 kankin cumhu[ ] mac mac north west south east gods cumhu zec[ ] kayab kayab gods east north west south xul zac zec xul let us first examine the numbers which are regularly repeated in the lowest line:-- , , , and , and we shall find that the days of the apparent venus revolution are divided into these four periods. the number denotes the time of the western elongation, when venus is the morning star, the time of the invisibility of the planet, during its superior conjunction, that of its eastern elongation, when venus is the evening star, and the time of its invisibility during inferior conjunction. the disproportion between and is somewhat striking. these periods which need not of course be exactly equal are usually computed at 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, (mex. ), 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 th and th 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 th and th lines must follow the same course. the numbers in the th line indicate to which day of the period of days the position has advanced. but now we see that the indication of days in the lines - , the indication of months in lines , and , and the numbers in line 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 a iii cib yaxkin, a iii cib zac, a iii cib kayab must be formed. all the × × = day indications combined with three month indications each, show therefore that this whole passage is a huge abbreviation for calendar dates and that the whole refers to × , days = , days. but , which we already found on page , is equal to × , × , × , × . i am inclined to think that i also found , on page . but the × , = , days do not form the entire period treated of here. for the three periods begin and end with the days:-- i ahau mac ( muluc), i ahau kayab ( kan), i ahau xul ( cauac). hence these three dates, the second of which was found on page , prove that the three periods of , are not consecutive, but that there is an interval between them. now between the first and second of the three dates the interval is years + days = days, and between the second and third, the interval is years + days = days. if these two periods be added to the , days, the sum is the whole period treated of here, viz:-- , = × 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 xul ( cauac) to i ahau kayab ( kan) there is a lapse of days or apparent mars years of days, such as we shall find as the principal subject of page . , however, equals × + days. we shall meet with this again as a difference on page . but from i ahau kayab ( kan) to i ahau mac ( muluc) there are , days, _i.e._, the mercury years, which we found on page , and which we shall find again as the principal period on pages - . but this is equal to years + or years - days. now if , , , , are added together, we have for the entire period under discussion here, , days, and this is equal to × × 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:-- , - , = , = tonalamatls, , - , = = tonalamatls. but if we subtract × , = , from , , the remainder is , , _i.e._, an extraordinary number which often occurs and is equal to × , × and × . 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 , days, is the date i ahau kayab ( kan). now, however, page furnished us with a day number for this date, , , , and from this the beginnings of the other two periods may be computed in the following way:-- i ahau xul ( cauac) = , , , i ahau kayab ( kan) = , , , i ahau mac ( muluc) = , , . between the first number and the second there are , days = ^ × × × ^ , and between the second and third , days = ^ × × × days. but, according to what has been stated above, , = , + , and , = , + , . the whole period is therefore divided as follows:-- it begins with a venus-solar-tonalamatl-period followed by mars years, then the great period again followed by × = mercury years, and lastly, apparently about the present time, comes the third great period, which, as already stated, ends , days after the first date. the case assumes a different aspect, if we insert between the three dates the other two from page :-- , , = i ahau, , , = i ahau, , , = i ahau, , , = iv ahau, , , = i ahau. here we have again, as examination of page showed, the difference , between the second and third numbers, while there is no longer any connection with the periods of , 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 ; the lower in line , 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 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 , hieroglyph . page . the first sign is probably k; compare the third picture on page a with its hieroglyph; the second is c's hieroglyph with an akbal appropriate to it; the third sign is moan with the belonging to it; the fourth sign is n's with a prefixed ; the year-sign in the lower series is replaced by zac, which agrees equally well; compare page , hieroglyph . page . 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 . this same sign in the line below has a , 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 , hieroglyph . page . the first sign is b's; the second, a's; the d, k's; compare page , hieroglyph ; the fourth is h's with a prefixed ; compare page , hieroglyphs and perhaps . page . the first sign is e's; compare page , hieroglyph ; the second is l, the black deity; compare page , hieroglyph ; the third is an unknown hieroglyph with a prefixed , which also occurs on page a and b; the fourth is the bat-god; compare page , hieroglyph . 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. ), 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 is like the fourteenth on page (a), and perhaps the two following refer to the same god k; the first two are separated by days and the latter by 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 - 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 b's head accompanies these signs. on pages and the deity is undoubtedly the old woman with tiger claws, who usually pours streams of water from a jug (compare pages , and ). i cannot identify the personage on pages and . the object in the deity's hand seems invariably to be a cup of foaming pulque. on page another object is placed above the cup, which i am unable to determine. the fifth, page , 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 is doubtless a representation of the sun-glyph; and on 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 it is a jaguar; at any rate it is the same animal found on pages a, c and c; a very similar creature pierced by arrows is given in the cod. vat. b.; compare also the pictures in seler's "venus-periode," page . on the other four pages this creature is in human guise. on page 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 and the tortoise on page . 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 we see the venus sign and e's hieroglyph; on page 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 , prefixed to an obliterated sign on page , 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 :--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 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 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 . 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:-- . unquestionably these × 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 , sign ; , ; , ; , ; and that of the death-bird on page , sign ; , , , , , and , _i.e._, only in places , and , which indicates that the signs are divided each time into three times four. it is further to be noted that the five gods, who are represented on page by hieroglyphs - , always recur in the ninth place in the order of the pages:--the god represented on page by sign is the th on page ; the th on the same page is the th on page and the th on page ; the th is the th on page , and the th may be the th on page , though this is hardly possible. on page the th hieroglyph seems to be the th on page 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 occupies the th place, and the th on page , also occurs as the th on page and the th on page . it is doubtless of special significance that the sign of the first of the twenty deities on the left side of page is repeated on the right as the tenth sign on all the pages (on page also in the eleventh place where it has a prefixed ). 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 th deity of the left side, the st of page , reappears in the th place on page ; the th deity, the nd on page , in the th on page ; the th deity, the d on page , in the th on page and the th on page (as already stated); the th, the nd on page , in the th on page . the nd of these deities is suggested by the th on page , perhaps also by the th on page ; the d and th seem to be a and to recur in the d place on page . 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 th sign on page contains a chuen, which in the th sign on page is probably combined with a muluc, in the th on page with yax and a prefixed , and in the th sign on page with c's sign, _i.e._, as a rule chuen stands in the th place in a line. as the gods e and k already mentioned also appear on pages - in connection with the change of the year, so we find the tiger on the top of page , and i believe this animal occurs again in the th sign on page . of the day-signs i take the th on page to be kan, the th on page to be caban, and the next sign, the th on page , 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 th (the middle) line is the most important, owing to its ending, 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 on page 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 and . i shall examine the remaining signs in the order of the pages. sign on page is the same compound of yax and kin having as a superfix the sign assumed by me to be the numeral , which occurs again in the lower group on page and also on page . in the number prefixed to the fifth sign on page , the seems to be indistinct and may not belong here. if we correctly assume that this number is , then the sign is the same as the th on page , to the discussion of which i beg to refer my readers. sign on page is an indistinct compound, the first part of which i supposed above to be the sign of the second deity on page . i cannot explain and on page . as yet i do not understand sign on page , which we seem to have met before on page c. sign on page is the moon, which is very curious here. i would like to call special attention to signs to on page . 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 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, ). sign is recognized as very appropriate to the change of year; compare the first sign of the middle section on pages - . all this points to the day 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:-- . 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 days, which is the fifth part of the days of the solar year and the eighth part of the days of the venus year:-- it is combined with chuen in all four cases (pages , , and ). but i attribute the meaning of eight days to this chuen sign, as i did on pages - and c- c, though i am doubtful in these as in other cases. page contains the sign for with a chuen under it, and a prefixed to each sign; _i.e._, × × = expiration of the first venus year. on page chuen follows the sign for and each sign has a prefixed to it; _i.e._, × × , expiration of the third venus year. on page the two signs again stand side by side, but the prefix is a instead of the expected . by an error this has been added to the of the preceding page, but, for a wholly unintelligible reason, prefixed to the crouching person below the chuen, as if to correct the . page again has the sign for above and the chuen below. a prefixed would seem to be in order; instead of it, there is a , one for the and another for the days. in this connection let me say that i believe i have found on page , top left, the year of days divided into × . page 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 in the fifth place, which i ventured to refer to the summer solstice. there is a 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 th sign on page and page , and the latter is the d and th on page , the th on page and finally the nd and th on page . the moon is represented in the th sign on page and in the d on page and indistinctly in the th on page . the cardinal points occur here several times. the d and th signs on page have at least the superfix of the south as a prefix; the th on page apparently has the east, but with the familiar cross-hatched sign prefixed; the th on page plainly has the east, the d on page the prefix of the north prefixed to the cross _b_, and the th on page the west, thus approximating the usual order and distribution. of the gods i note the akbal head, perhaps intended for d, in the th place on page , also in the d on page , and lastly in the th on page , the first two times with the ben-ik superfix, and in the nd place on page the sign for a. in the th place on page we have the tortoise as the sign of the month kayab or of the summer solstice, in the th on page 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 th sign on page . it is hard to decide whether the sign on page represents the god f owing to the line through the eye, or a female by reason of the prefixed lock. sign on page represents the deity whose sign began the series of twenty gods on the left of page 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 on page is a kin combined with an unfamiliar sign. sign on page contains a kin with a yax and probably with as a superfix (as on pages and middle). sign on page contains a crouching person with a which is probably out of place here and to be regarded as a correction of the above it. sign on page 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 on page merits special attention, because it contains the duplication of the sign, which, at the end of the first part of the manuscript, pages - , always began the groups of hieroglyphs on the lower third of the pages. i do not understand the second hieroglyph on page and the th on page . in conclusion i would call attention to the fact that the last hieroglyph on page is very peculiar. as on pages , , and it has the meaning of , days and consists of an imix with a comprehensive superfix; its prefix is a . but what is the meaning here of × , = , ? when we recall the statement made above that the whole section of pages - embraces , days, or, according to another calculation , days, it is a striking fact that , is exactly the mean of the two numbers, being separated from each by days = × . can it be an accident that on the next page (page ) the fourth venus revolution is reached, for × = , _i.e._, almost ? the hieroglyph discussed here would not be so extraordinary on page . i will not venture to assert as to the in , = × , that it is connected with the which will appear as the difference on page . 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 , and , in the middle groups on pages , , and twice on page , in the lower groups on page , twice on page , once on , twice again on , making 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 and , in the middle of pages , , and , and in the lowest on pages and , 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 has already referred (see page of this book). the inner meaning of these pages is of course still enveloped in mystery. pages a-- a. i shall begin the discussion of this very peculiar section with the remarkable fourth column on page , which, very possibly, the scribe ought to have placed at the beginning; for it looks like a repetition of the section on pages - , 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:-- chuen , . since, as is frequently the case, the chuen will here have the value of days and the with the sign for may be regarded as , this group might denote × = , but actually be × , = , . both numbers are the basis of the section included on pages - . and in the same way the repeated times seems to me to refer to the series of days on those pages, which begin with the th 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 the signs for end and beginning, which we often find in the vicinity of numbers; in the second and third columns of page , the sun and moon; in the fourth column, the days of such significance here and in the fifth and sixth, the normal date iv ahau cumhu repeated twice. as the problem on pages - was to bring into accord the solar year with the venus year and consequently also the tonalamatl, _i.e._, to combine , and , so the aim here is first of all to bring the tonalamatl into unison with the mercury year ( ). for this purpose the number , is employed. this is equal to × = × , including, therefore just as many mercury years as there were solar years in the preceding section. , is also × , and this is significant here, for, as we shall see directly, the day forming the basis of this calculation is xii lamat, which comes days after the normal date iv ahau. the series given here is based, therefore, on , 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 st and th multiples of , , which are separated from each other by × , , viz:-- , and , . 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 , and the last of one row and the first of the next on the left are days apart, hence the whole is equal to × = days. from xii lamat begins also the peresianus, pages - . now these dates are connected with the four large numbers, which we find on page , 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:-- , , = xii lamat i muan ( muluc). , , = i akbal muan ( muluc). , , = iii ezanab pax ( muluc). , , = vii lamat i muan ( muluc). it is curious that while the first three are separated from each other by , between the d and th, or rather between the missing th and th, × days are inserted in excess of the required , _i.e._, , . this, however, is not accidental, but is due to the fact that between the first number and the last exactly , = × days have elapsed. this number is, however, = , + , 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 -place of the third, i have put a instead of , while in the -place of the fourth, i have omitted the three dots, _i.e._, set down a instead of the . 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 we again find a day xii lamat, as is expressly stated beneath it. it has the number , , and the corresponding date is xii lamat cumhu ( kan). this day, however, is separated from the same day on page ( , , = xii lamat i muan muluc) by , days, that is by × , + , = × , _i.e._, by so-called katuns increased by tonalamatls. here × = , seems to have been added to (xii lamat - iv ahau) and the sum subtracted from ahau-katuns = , , . i could obtain this number only by substituting for in the -place. in the manuscript the sign xii lamat is set down above and below this number. i must leave undetermined whether the directly above the number and combined with kin and the katun sign refers only to the katuns or at the same time also to the days from iv ahau to xii lamat. it is also to be noted here that once before on page of this manuscript (which forms the basis of this section) × , = , days was found to be the difference between , and , , and that there, too, if my restoration is correct, it was the highest term of the series = × , . finally, in the first column of page , we have the complete normal date ahau cumhu ( ix). but below this, between red numerals denoting the , , mentioned above, there is set down in black the number , , . this corresponds to the date iv ahau zip ( cauac). it may have been formed by adding , = × to ahau-katuns = , , . it is, however, not only equal to × , but also to , × , therefore also divisible by the interval between iv ahau xii lamat, as well as by = × , while on the contrary it is not as we should expect, divisible by , . i have changed the , in the × , to 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 , which is only less, and that on page . finally it should be noted that the two large numbers on page are separated from one another by , days = years and 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 , , . pages -- . thus far we have examined only the upper halves of pages and and have still to consider the lower, but not until we have finished the upper parts of pages - of which the former are the continuation. we have first to consider the series, then the pictures and lastly the hieroglyphs. as on page we found multiples of the number (= × = × ), while on pages - it was divided into four unequal parts, so on pages - we find multiples of the number , ( × = × ) while on pages - it is divided into unequal parts. on pages - 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 . 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 as numerator, or beyond these at most with / (see hultsch, "die elemente der ägyptischen teilungsrechnung," , page ). now the mayas had determined the lunar revolution so exactly that they perceived the incompatibility of the period of , days with a multiple of lunar revolutions. they found that lunar revolutions amounted approximately to , days, which is, in fact, the largest number on the second half of page . in order not to drop the significant , altogether, they made use of a very shrewd artifice. they took as the starting-point the day xii lamat, corresponding to the number , , 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 , . 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 , days was doubtless first divided into three equal periods of days. and in order still further to subdivide these shorter periods, the term of days was employed as far as it would go; , however, is the half of a lunar year of days, made up of months of days and of days, thus allowing . days in round numbers for each month. now is = × + × . the average, . , 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:-- = × + × , = × + × . = months of . days, while = months of - / days. now let us see in what _proportion_ these and days were distributed among the periods of . first we see that the period of days (_i.e._, a third of the whole) was divided into sections of , and days, as follows:-- = × + + = × + + = × + ---------------------------- = × + × + × . this is equal to months of . 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:-- + ½ + / + / . the _whole_ period of , days was divided as follows:-- × = × + × + × × = × + × + × × = × + × --------------------------------------- × = × + × + × . thus for every parts of days there was consequently of and to every parts of , of . since and include months each, while equals months, the entire length of the period is months, which are divided into 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 days, and the two horizontal lines divide the periods of , and days. page a: | . * | . . | . | . . * | . * | . . | page a: | . * . * | . | page b: . | . | . . * * | . * | . * page a: | . | . . | page b: | . . | . | . . | . | . . * | . | -----------------+-------------------+----------------- . | . | . . * | . | . * * . * | . | page b: page a: | page b: | . * . * | . * | . * . * | . | . . | . | . -----------------+-------------------+----------------- . | . | page b: . | page b: | . page a: | . | . . | . | . . | . | . . | . | . . | . | page b: page a: | page b: | . . * | . | . no one acquainted with the cursoriness of the maya manuscripts will be surprised that among numbers i have declared to be wrong. furthermore the errors are lessened by the fact that six of them are really only one, for in all cases where the difference is , the scribe has overlooked this and written down the usual , although the numbers and the days of the series very correctly indicate . again the three errors in groups and are also only one, for the author had confused the differences and and had, therefore, to write down , instead of , . in group the error is merely the omission of a line meaning . 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 and . in the three periods of days the always occupies the th place and in the periods of it is always in the th place. this difference appears, therefore, in groups , , , , and , _i.e._, , , , and groups apart; but it is entirely lacking in the periods of days. and in all nine sections the occupies the third place, _i.e._, directly in front of the pictures, which will be discussed immediately, therefore in groups , , , , , , , , , _i.e._, at intervals of , , , , , , and groups. but i must point out an error fraught with consequences. groups and quite correctly have the difference , but in this single instance the scribe has written down 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 group 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, , numbers and ). 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 days as on pages - . let us attempt to advance a step further in the darkness which still surrounds us here. one of these pictures, the th, which is on page b, is in the wrong place, owing to the error in computation in groups and to which i called attention above. it belongs not _before_ but _after_ group , the first on page b. this is indicated in the manuscript itself. for in group 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 ), 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:-- . a . a . a . a . b . b . b . b . b . b . 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 (= × + ) days. the pictures are thus separated from one another by , and days, which intervals correspond exactly to the length of the nine sections. but the last picture is separated from the preceding one by days, and as it has a character quite its own, it must be discussed separately. but these days with the days of the beginning quite regularly amount to 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 as its zero-point. in that case, we shall have to subtract every time from the days set down in the manuscript. this new series may be represented thus:-- . a . a . a . a . b . b . b . b . b . it is certainly remarkable that the last number, , corresponds so closely to the time of the revolution of saturn, which is computed at 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 ( 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 , 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 days. the mayas, i think, computed it at days. in the passage alluded to i regarded the following as the sign for jupiter:-- [illustration] we find these signs in pictures , , and . the corresponding numbers reduced for the revolution of saturn are , , and , . i assume that the third picture, _i.e._, the number , is another zero-point, in consequence of which the sign is here suppressed, and that still another is the tenth picture with the number , , which has no relation to the revolution of saturn. if we compare these numbers with the , _i.e._, the apparent revolution of jupiter, we have the following:-- . = × - . = × + . = × - . = × + . = × + . = × + the differences , , , , and are so small in comparison with , that the numbers , 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:-- + a multiple of , by which this remainder would be reduced to - . 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:-- + × - = , , or even + × = , . the regular progression from the th multiple to the th, th, th, th, and th 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:-- . = + . = × + . = × + . = × + . let us now try to interpret the meaning of the remaining rectangles (always omitting the saturn sign as a matter of course.) in pictures and the rectangle also contains the sign of the moon or of the twenty days. beside it in picture is the sign, which in my "erläuterungen," page , i regarded as the sign for mercury. hence we have here + × = , _i.e._, only units more than the required . 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._, , and i take the required number to be in the form of + × + . above the third picture i see a mercury and a venus sign and i read + × = , which is only units less than the required . the fifth picture still remains to be discussed, but i do not know how to unite the mercury revolution here with the . 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 , page a, 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 , page a, 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 , page a, 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 , page b, represents a hanged woman, which schellhas, "göttergestalten," page , takes to be the maya goddess ixtab, the goddess of the halter, _i.e._, of the hanged. the centre of picture on page a, 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 , , and , pages b, b, b and b. in all four cases there is on either side of kin a black and white surface, such as we have already seen in picture and similar to that in picture . pictures and are vomited up, as it were, by a serpent placed below them, in the same way as b is represented on pages b and b. in pictures and , 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 , page b, but only on the black and not on the white surface. i will postpone discussing picture 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 - , and also with the more elaborate last picture . with pictures and 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 , and , and h with picture , and with pictures , , , , and 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 , and and occurs twice each with pictures and . i am inclined to see the sign for mercury in the crouching figure belonging to pictures and , which is drawn upside down and combined with the half venus sign ( = × - ). hands grasping a hieroglyph (a sign for days?) are represented in pictures , , and . the enigmatical numbers, prefixed to the hieroglyphs, occur several times, thus a with pictures and , and a twice with picture and a with picture . now let us examine picture somewhat in detail and also the signs standing above it, since both are of special significance here. this representation treats of the period of , days in which the mercury and lunar revolutions meet. and this is proved by the ten hieroglyphs, which i will number as follows:-- . i can omit signs and , sun and moon, since they refer to a period of time only in a general way. sign seems to me, as i have already stated, to have reference to the revolutions of mercury. then follows sign , 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 - showed that it was the year muluc. the mat (pop) is very properly the symbol of beginning, since the first month of the year was likewise called pop. sign , 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 , the length of the period is stated here by signs , , and , but the dot before the fifth should be placed before the fourth, as is actually the case on page . therefore:-- = = = = ----- . 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 is doubtless xul = end, as it so often is, for example, on pages - below. but i have not solved the meaning of the two prefixes. the end would be xii lamat yax ( 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. , 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 ( × = , ). and the two venus signs can mean nothing more than that this period of , also serves the purpose of filling up the gap between the two large venus-solar periods of , days, like the similar process which we saw on pages - . 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 . | . | . | . . . . . . .| . . . .| . . . . . .| . . . . . . . | | . . . . . | . . . . . page . | . | . | . . . . . . | . . . .| . . . . | . . . . . . . . . . .| . . . .| . . . . .| . . since each group contains two hieroglyphs, this makes . in all. of these, however, about 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 is entirely lacking or rather group , in the place of which the th has been set down. the eighth picture was probably already drawn, when the artist saw that there was not room enough left for the th and th groups. hence he omitted the th, setting down in place of it the th 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 b (i will designate the upper hieroglyphs by _a_ and the lower by _b_). it is placed in the period indicated in which - days elapse, and in which, therefore, venus has finished a revolution of 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 days with its four bacab periods of days each is referred to here, as we have already found it referred to on pages a- a and on page a, and shall find it again on pages - and - . in that case the single groups would be separated from one another by one maya week = days. i will now arrange the sixty-nine groups in the following order (the reason for which will become clear directly):-- i ii iii iv v vi vii . the groups in a horizontal row are separated from one another by or a multiple of . 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 × days probably merely for the purpose of filling up the space. i. in b, b, b and b, _i.e._, after every seven groups, perhaps also in b, 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 b the sign is replaced by that for venus. in b, b, b and b we find other signs, it is true, nevertheless the regularity stated above cannot be accidental. the upper signs of groups a, a, a and a contain an imix and corroborate the connection. ii. b and b (after × 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 b, b and b. then b, b and b correspond, _i.e._, after six groups of days and one more of the same length, but the same sign appears also in b, b and b. iii. b and a are xul = end and are therefore separated by × = × days, _i.e._, the length of a year. it is singular that both signs of are like those of ; if we assume that was set down one group too soon, it would be in excellent keeping with the rest. the xul also appears in b and b. b and b correspond after × days, as already mentioned under ii. iv. a and b both contain the sign for the sun between clouds. v. b and b agree after × days; the same sign appears again in b and b. a and a correspond after × days; we shall continue the examination of this sign under pages - . vi. a and a agree, _i.e._, after × 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 days later than this. vii. a and a agree, _i.e._, after × days. the sign is composed of the crouching figure prefixed to the cross, which we also find in b, a and b; it is prefixed to a different hieroglyph in a. in b, b and b ( in the manuscript) we see bird-like heads resembling the bacab sign. we should expect to find a familiar sign in , 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 a, a and a we again see an imix, and i consider it a corroboration of my theory that all the four signs of groups and are repeated in and after × days. i believe a further corroboration is the fact that though many of these hieroglyphs have no connection with these periods of × , _i.e._, with the divisions of the ritual year, they do correspond with the usual divisions of the tonalamatl, _i.e._, × and × days. after × or a multiple of it the signs recur in b, b, b, b- b, b, b- b, b, b- b, b- a, a- a, a- b, b- b and b. as examples of × i would mention b, b- a, a, a- b, b- b, b- b, b- b, b, b. finally, i must mention two more hieroglyphs, which are limited almost entirely to these pages:-- [illustration] in the first sign, which occurred on page a, i thought i recognized the lunar month of days. it occurs in this section in connection with the third picture on page , and besides in the following groups of hieroglyphs:-- b, b and b, 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 th, th and th groups and again in the next, the st. 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 b and b which may have been the same hieroglyph. the eleven places in which it occurs are as follows:-- b, b, b, b, b, b, b, b, a, b and b. 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, and , and are groups apart, and , and , and are groups apart, and are groups apart, and hence and are separated by groups or year. group 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 , and on pages b and b, seems to me to refer to the conjunctions of the sun with certain stars, which occur at intervals of thirteen days. pages -- . this section is also based on a series occupying the whole of page , which contains nothing but number and day signs. this series has the difference , which we found once before on page . there the starting-point was iii lamat, here it is the day xiii muluc, probably coming in the year xiii muluc, as in cort. b, 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 , in again reach the day xiii muluc, at which point the succeeding members remain stationary, since from here on the difference is always or a multiple of it. 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 - having been venus and the sun, and of pages - , mercury and the moon with incidental treatment of saturn and jupiter. with as its difference, the series ascends to × = , , 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 , , 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 and the series ends with . 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 and days. the interval from ix ik to xiii muluc is and in reversed order days. it can hardly be assumed that the of the ix or ix ik is connected with the × mentioned above or with the + + + into which the is divided on pages - , or finally with the , which four times forms the principal part of the sub-divisions of on pages - . numbers amounting to millions accompany this series in the usual way. two of these are on page , viz:-- , , and , , ; 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 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 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 with a black inserted, below this a black and below this again, enclosed in a red band, a black , 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 . . . = and . . = . but = + and is the interval between xiii muluc and iv ahau. with the day xiii muluc and the interval 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 where, in like manner, numbers were first formed for day xiii akbal. i assume that to begin with, tonalamatls (= , ) were added to this and then tonalamatls (= , ), the being = × and the , including revolutions of mars. the result in one case was , and in the other , . if the ahau-katuns, which are specified as , , on page b be added here, we have the following numbers:-- , , = xiii muluc mol ( muluc), , , = xiii muluc zip ( muluc), and if the two encircled numbers of the manuscript:-- and be added, the sums are , , and , , , _i.e._, the two large numbers of the manuscript. the dates corresponding to these numbers are as follows:-- , , = iv ahau muan ( muluc), , , = iv ahau muan ( ix). if we compare the two numbers with the normal date, the curious result follows that:-- ) , , - , , = , . this number is equal to × , including therefore the ritual year of days. ) , , - , , = , . this number is five times , days, which is assumed to be the time in which the lunar and mercury revolutions accord. this , was found once before on page as the suppressed difference between , and , . 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 , . this is equal first to mars revolutions of days, and second to × , _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 , apart from the matter-of-course calendar date at the top, which is repeated at the bottom. one column contains hieroglyphs and the other . 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 × days, i believe that each group of three tonalamatls treated of on page , is divided into of these parts; that each hieroglyph, therefore, denotes 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 days, always form a separate group. is the th part of . with the omission of the first and fifth signs, the passage, i think, stands thus:-- xiii muluc kankin ( muluc). ) - xiii imix pax. ) - xiii ben pop ( ix). ) - xiii chicchan zip. -------------------------------------- ) - xiii caban xul. ) - xiii muluc mol. ) - xiii imix zac. -------------------------------------- ) - xiii ben kankin. ) - xiii chicchan pax. ) - xiii caban cumhu. -------------------------------------- ) - xiii muluc zip ( cauac). ) - xiii imix xul. ) - xiii ben mol. -------------------------------------- ) - xiii chicchan zac. ) - xiii caban mac. ) - xiii muluc 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:-- . the zero-point lies , days later than the normal date iv ahau cumhu ( ix). this is equal to × or × increased by the interval between iv ahau and xiii muluc = . there are days between kankin and cumhu _i.e._, , = × - , and from ix to muluc it is years. . the same zero-point, muluc, lies in the year with the same name, that is, the very point where a tonalamatl of the year ends. . in this arrangement the first as well as the last day of the year 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. . also the fact that it is the first of the two columns, which closes with this year-end, seems to show a purpose. . several instances of similarity appear among the hieroglyphs in these groups of three:--an akbal sign in and suggests the god d, the superfix and prefix of and the god k and and the screech-owl and therefore a. little else is to be said of these hieroglyphs. c might be denoted by ( zip) and ( zip). group , 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 as the revolution of mercury, which requires days:-- is × + or × - . is a sign, as yet unknown, for the year of days? looks like two signs for the month mac, placed back to back, which here designates the tonalamatl as it does on page . the superfix of three parts might denote three tonalamatls = 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 . 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 . 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 b. 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 is set down between the two combatants, and there may also have been a red , 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 and a black between the two groups. we see that the reference here is to combat, just as it was on the right side of pages - . and since the subject of these pages like that of - 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 . 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 - and perhaps also in the on page . 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:-- | | | ----------------- | | | these signs can have no relation to mythology. there is not a hieroglyph of a god among them, for if sign 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 were intended to denote the bacab, then it would refer to chronology rather than to mythology. also the cimi in 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 and , they might denote the normal date iv ahau cumhu, which always occupies the first place. signs and are plainly the same, xul (sixth month) and sign is yaxkin (seventh month). sign might be caban combined with uo (second month) and a ten. in sign we again see yaxkin without a number. signs and are zec (fifth month) and signs and 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 , the rest of which is effaced, but the familiar compound of caban and muluc appears in and and cimi is in , as we have seen. in sign , 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 yaxkin near by, for ahau is never the tenth day of a month. can be the sign of the twelfth month, ceh, combined with that for ? hieroglyphs and are effaced and i do not understand , and . there are no parallels in the kindred passages - , unless it be zec on the bottom of page and here in signs and , but without a number. cf. my paper on this page in the "weltall," year , pages - . page -- . on examining the reverse of the second part of our manuscript, _i.e._, pages - , we find an empty page on the left, the back of which is occupied by page . this may be explained by assuming that the scribe wrote pages - and possibly even pages - 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 . nevertheless, it is advisable to continue with the original numbering in order to avoid confusion. aside from the concluding (or beginning) page , this whole section of pages - consists of three parts:-- - , - and - . 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 . its primary difference is always that which we found on pages - , viz:--the bacab period of days, the quarter of the ritual year of days = weeks of days each. it ascends by until it reaches , which number is a multiple of both and and is also divisible by , the number of weeks in a year. just as on page the series continues with the new difference as far as , 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 , = × , which would then become the fourth difference and the series would close at the top of page with , = × , _i.e._, with the numbers . . . . . of which the is entirely and the half effaced. the series on pages - , however, closed with , = × , but there is still room for a higher series. under this largest number ( × ) there is on page a large red number consisting of . . . . which is crowded into a very small space between the figures of . i can only understand it by replacing the first by a , for then it is , = × 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 , 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 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 . from 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 , and , _i.e._, × , × and × , are likewise not set down here by mere accident. we come now to the five columns, three on page and two on page , 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 , one with red numbers and the other with black. of these black numbers, i take the second from the top to be not but , assuming that a line is omitted. the normal date iv ahau 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:-- , , ; iv ik zac ( muluc). , , ; vii kan chen ( kan). , , ; iv ahau mol ( ix). , , ; iv ahau kayab ( kan). , , ; iv kan yaxkin ( muluc). , , ; iv imix mol ( ix). the first, third and fifth numbers are already known from page a, 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:-- , , = iii chicchan zac ( cauac). , , = iii chicchan kankin ( cauac). , , = iii chicchan zip ( muluc). the second date in the manuscript is kankin and the third is zip; hence there is one line too many in the former number and one too few in the latter. while on page a 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 , , which is the same number we found with the corresponding day xiii akbal; the second has and the third = + . the , was × + ; but is the interval from iii chicchan to vii kan, just as it is from xiii akbal to iv ik. the is the interval between iii chicchan and iv ahau and the that from iii chicchan and iv imix. by the addition of these differences, the numbers written out in the manuscript are obtained:-- , , + , = , , (vii kan). , , + = , , (iv ahau). , , + = , , (iv imix). keeping in mind what was said in reference to page a, 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:-- days. hence the distance from iii chicchan to vii kan is also exactly equal to that between xiii akbal to iv ik, viz:-- days. finally, the distance from vii kan to iii chicchan is exactly equal to that between iv ik and xiii akbal, viz:-- days. iv imix and iv kan are separated from the normal date iv ahau by × = and × = days. regarding the encircled numbers, so far as they are independent of , i would note the following:-- = xiii akbal to iv ahau. = xiii akbal to iv kan. = iii chicchan to iv imix. = iii chicchan to vii kan and xiii akbal to iv ik. = iii chicchan to iv ahau. in addition let me remark that = vii kan to iv ahau, = iv imix to iv ahau and = 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:-- × , = , , (iv ahau), × , = , , (iv ahau), × , = , , (vii kan), × , = , , (iv imix), × , = , , (iv kan). but the highest number, , , , was formed in a different way; it = , × ; but the interval from iv ahau to iv ik = = × , and from iv ik to iv ahau = = × . 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:-- , , , xiii akbal. , , , iii chicchan. difference = × + (vii kan to iv ik, iii chicchan to xiii akbal). , , , xiii akbal. , , , iii chicchan. difference , = × + (as above). , , , xiii akbal. , , , iii chicchan. difference (which is - ); = iv kan to iv imix. on the other hand the three pairs specified in the manuscript are as follows:-- , , , iv ik. , , , vii kan. difference = × + as above, by reason of the encircled number , which is common to both numbers. , , , iv ahau. , , , iv ahau. difference , = × , on account of the same day. , , , iv kan. , , , iv imix. difference = iv kan to iv imix; strictly speaking = + . 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 the date xiii imix uo. it comes in the year ix and represents the number , , (or a number separated from it by a multiple of , ). now , , = × + and = × + . this agrees with the lower number inserted in red:-- , , = iv ik zac ( muluc), which comes later by , = × + and = × + . , 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 . if we set down with these two numbers, those of the normal date just preceding and the normal date next following, we have , , = × . , , , , , , , , = × . this is a period of , = × , 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 we find ceh, and on page , xul, but nothing further is to be learned from this than that one or the other of the day-signs, , , , , 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 , and and the goddess in and ; 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 . in the passage on page , which is so closely related to the present one, a timid attempt has already been made with the number , , 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 , _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 and the right of page . 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 - . 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:-- . of these and in the first and fourth groups form the date ix kan kayab, which is in the year 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 , where this date occurs again in the lowest place. the last three large numbers are not computed from the normal date iv ahau 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 - , suggesting that the series here is closely connected with the one which had the difference . 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 and at the top; and over it in the second place of the fourth group is b's hieroglyph, which is also repeated on pages and 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 b 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 ), 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 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 b, the red number belonging to the first serpent. i assume that a line is wanting in the lowest figure, _i.e._, it should be instead of , and that the conspicuously large 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 in the date b i add a dot, and read it . 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:-- a: , , ; xi kan kankin ( ix); iii chicchan xul ( muluc). b: , , ; xi kan muan ( ix); iii chicchan pax ( ix). a: , , ; ix kan kankin ( cauac); iii chicchan yaxkin ( ix). b: , , ; ix kan chen ( kan); iii kan ceh ( ix). a: , , ; ix kan xul ( ix); iii ix zac ( muluc). b: , , ; ix kan kayab ( ix); iii cimi kayab ( ix). a: , , ; ix kan kayab ( ix); xiii akbal kankin ( kan). b: , , ; ix kan kayab ( ix); iii kan uo ( muluc). see my treatise, "die schlangenzahlen in der dresdener mayahandschrift" (weltall, year , pages - ). several details show how this number-structure forms a definite, closely connected whole. . the beginning day in each case is the day kan, which thereby indicates its position as the first. . 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. . the two numbers b and b are exactly the same. . the first three numbers are each divisible without a remainder by , the interval from xiii akbal to iv ahau, which was true also of the , , in the second column on page , 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, days between ix kan and xi kan. hence the numbers a and b are separated from each other by , = × + , although they have the same end iii chicchan. further it is to be noted that the largest of the eight numbers, , , , is separated from the lowest, , , , _i.e._, the black number from the red one of the first serpent, by only , , _i.e._, by not a full one per cent of the entire magnitude. , = × , + × or × or × . it is to be noted also that the differences between the black and red numbers in the second and third serpents ( , and , ) are divisible by ( × and × ). 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 we found a , (not , ) 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 × . at first i thought it possible that this , had been again multiplied by , the real basal number of this section; for we had found a second power once before (on pages - ) by computation, viz:-- × × . the result of multiplication in this case would be , , , and the differences between the eight numbers in the serpents would be as follows:-- a + , , b - , , a + , b and b - , , a - , , b + , , a - . 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 , , , _i.e._, it is times the so-called ahau-katun of , 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:-- a) , , b) , , , , , , ---------- ---------- , = × + - , = × + xi kan - iii chicchan = . iii chicchan - xi kan = . a) , , b) , , , , , , ---------- ---------- , = × + - , = × + ix kan - iii chicchan = . iii kan - ix kan = . a) , , b) , , , , , , ---------- ---------- , = × + , = × + ix kan - iii ix = . ix kan - iii cimi = . a) , , b) = b , , ---------- , = × + ix kan - xiii akbal = . where the serpent number is less than , , , 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 ; and the choice of the multiple seems to have been quite arbitrary. the number thus obtained he added to , , , unless it was the smaller, in which case he subtracted it from , , , and the result he wrote down in the serpents. we shall find the same process, only somewhat amplified, with the serpent on page . 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 , which we will now examine and at the same time compare them with the corresponding column of page , the upper part of which is exactly the same, and the lower very nearly so. each column consists of 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:-- , , , , , , but in the first column we find faces belonging to them. in his work "the archaic maya inscriptions," , 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. a and b are effaced on page ; they probably contained a sort of superscription as on the inscriptions. a is effaced on page , but the sign may be recognized from page as that with which on page the series of the twenty deities begins after ( × ) days. on pages and it takes the place of a face, to which i am inclined to assign the numerical value . in b, which is c's head, i am inclined to look for the value , , = × × × 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 ab as × , , = , , . b, it seems to me, resembles the sign for , , which i found in the inscriptions and which is repeated in a. it must, however, be left undecided by what this same number in a is to be multiplied; a is repeated besides in a and b. a contains the head of e, and b that of the moan. a seems to refer to a, and b to b. but a and b are the same sign, which, inserted between the , and the , can scarcely mean anything else than the so-called ahau-katun of × , = , days. have we two such periods here? were they designated by consecutive numbers? now comes the in a, and the number with e's head and the inserted sign for days in b (on page without e's head), therefore × = . seler also thinks a has the numerical value (einiges mehr über die monumente von copan, etc., page ); b belongs to a. b, a kin with a i and a suffix and a leaf-shaped prefix, is inserted between the and . what can it mean? hardly the , for this is represented elsewhere (_e.g._, page ) by the thirteenth month mac. or can it possibly refer to the month yaxkin (days - )? b is a chuen sign, which, with its prefix (superfix on page ) always denotes twenty days in the inscriptions. it is multiplied with the same unknown head in a, which we have already met with in a. a contains h's head, and b 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 cumhu then follows in ab. if it refers to the signs just now discussed, then they must denote a number of about the same magnitude as the serpent numbers. or times , 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 ab and ab. i look upon a as denoting , and with regard to b i have already expressed the surmise in the zeitschrift für ethnologie xxiii, page , that it may mean = × , _i.e._, three venus-solar periods. that would be × = × = , . the moan in a may have the value , for this number is so often combined with the moan. as we saw under page , b is = , ; × , = , . accordingly the four signs taken together may mean , = × . the second group, from a to b, refers, on the other hand, to the year of days. first a = , , having in b the unknown multiplier, which we have already seen in a and a. then follows in a, × = , ; in b, × = ; in a, a with a prefixed ( ?); and in b, three days. it would be more correct to place the beside the following . the whole sum would then end with the number , which would agree with the day kan, the date specified below. in the third group the a = × , = , , remains a mystery; an empty outline of a sign is added in b. ab also forms a group by itself. a contains a sign, which rather suggests the bacab, upon whose period of days the series belonging here is based. the imix in b with a superfix is still unintelligible. the columns end in with the date ix kan xii kayab, the starting-point of the serpent numbers. pages -- . i think it very likely that this section bears the same relation to pages - as pages - do to and as - to - . for here, too, a period of time forming the basis of the earlier section seems to be divided into smaller parts. on page we recognize as the basis of the series the number , the quarter of the ritual year of days; here we have to do with the fourfold division of into 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:-- xii, iv, v, ii, viii, x, viii, ii, v, iv, xii, iii, iii. i, i, xii, xiii, viii, i, v, vii, vii, xiii, vi, i, iii. xi, xi, ix, x, v, xi, ii, iv, iv, x, iii, xi, xiii. ix, i, ii, xii, v, vii, v, xii, ii, i, ix, xiii, xiii. the first two lines, forming together a single period of 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 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 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 to , 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 days present the following appearance:-- iii . . . xii ix . . iv cauac . . v ahau . . ii oc . . viii cib . . x eznab . . viii muluc . . ii cib . . v cauac . . iv chuen . . xii cauac . . iii akbal . . iii cib . . i manik . . i ahau . . xii chuen . . xiii eb. . . viii ahau . . i cimi . . v oc . . vii eb . . vii chicchan . . xiii chuen . . v caban . . i chicchan . . iii manik in the same way i will tabulate the second group of 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 . . . ix eb . . i caban . . ii ezanab . . xii lamat . . v ix . . vii cib . . v manik . . xii ix . . ii caban . . i muluc . . ix caban . . xiii imix . . xiii ix . . xi chicchan . . xi ezanab . . ix muluc . . x oc . . v ezanab . . xi kan . . ii lamat . . iv oc . . iv akbal . . x muluc . . iii men . . xi akbal . . 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 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 contains the sign 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 st day of the year. hence i will again set down the twenty-six dates, but add to them the position in the year. . xiii akbal i zac ( kan) . . ix eb zac . . i caban zac . . ii ezanab zac . . xii lamat ceh . . v ix ceh . . vii cib ceh . . v manik mac . . xii ix mac . . ii caban mac . . i muluc kankin . . ix caban kankin . . xiii imix kankin . . xiii ix muan . . xi chicchan pax . . xi ezanab pax . . ix muluc kayab . . x oc kayab . . v ezanab kayab . . xi kan cumhu . . ii lamat cumhu . . iv oc cumhu . . iv akbal cumhu . . x muluc pop ( muluc) . . iii men pop . . xi akbal pop . . xiii chicchan pop let us now prove the correctness of my theory by an examination of groups and . in the th day of this period, the st day of the year is reached, _i.e._, the first of the five uayeyab days. the year kan is ended and the year 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 d group the th day has passed and the second of the year 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 a we saw that k is the ruler of the day muluc ( ). 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 , and , and represents the god in the most varied positions and activities. these pictures are very similar to those on pages - and we shall therefore make frequent reference to the section there represented. second, the first hieroglyph in groups to , 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 c- c. 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 . third, the head with no underjaw, which is the sixth hieroglyph in groups to , but does not occur in groups to . it is repeated in a very similar fashion in the last hieroglyph but one on page b. i propose to attribute to it the meaning of fasting. now for the single groups:-- . b is seated rowing in a boat, as he is represented also on pages c, b, c and c. a creature is swimming beneath him, which may be a crocodile. the fifth hieroglyph is the important kan already discussed, the fourth is _a_ and the second the cross _b_ combined with caban. the day is the th of the year. . b is walking with the atlatl in his hand, and armed with javelins. hieroglyph , manik, denotes the chase, but has a prefix, which often seems to have the meaning of . is the elongated head _q_ with the prefix of the east belonging to the kan years. 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. . b is walking, carrying a large stick like that for tilling the field, as on pages b and b, and he bears a carrying-frame; there are footprints below him. hieroglyph is the compound of the signs for south and east, (_r_) may denote rain, and is two elongated heads with an unknown prefix. . b, is seated on astronomical signs as on page c. the copal pouch is hanging from his neck and he is brandishing his hatchet. sign is _b_, is _a_ and is _r_, but all three signs have unusual prefixes; the first of these prefixes appears again in the tenth group, days later. . 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 c and a). i do not venture to decide what he holds in his hand nor what are the other objects which he carries. sign is _r_ with a prefix, is imix perhaps with a knife as a prefix, is the skeleton which sometimes belongs to the lightning beast, but also to the th month; its prefix is unknown. . 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 is the crouching naked personage, with the cross _b_ prefixed, is the elongated head with a prefixed yax, and is kan with a vessel as a prefix (instead of imix) from which steam or froth is rising. the day is the th of the year, _i.e._, the end of a week of × days. . b is sitting on a tree at the root of which his own head appears (compare with this the representations on pages c, c, and especially a, and also b and b). the second sign is yax with a prefix; is kin within which there is a , as is several times the case, for example, on pages and . 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 . . b is seated in a house, on the roof, wall and floor of which are several caban signs, just as on page a; he seems to be pointing forward. sign is caban with a prefix, the th and also the th is kan with two unusual prefixes. . water is pictured at the bottom of this picture, and in it are a fish, a mussel and a snail (possibly page b 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 b). sign is composed of _b_, imix, the mouth and nose of c and the object which apparently is a beak, previously met with in sign . is kan-imix, and is kan with prefix and suffix. . b is seated in an expectant attitude, his hands resting on his knees. we see a very similar representation of him on page a, where he faces himself, and in general the remaining pictures of that passage furnish a striking parallel to the present one. sign is a head (e's?) with a call seemingly issuing from its mouth. is the elongated head _q_ with the ben-ik superfix and an unusual prefix, which we found on page c prefixed to the cross _b_; is kan with the same prefix, which i regarded as denoting a call in sign , and which is probably answered here by an affirmative cry. . the expectation has been fulfilled. b is seated on a mat holding a woman in the same position as on page a. sign is the cross _b_ with the prefixed beak as in , and also with another prefix, which seems sometimes to denote the number . is exactly the same kin with and the leaf-shaped prefix, which occurred in the same place with the seventh picture. contains the sign for days; a new period of this length begins here on the th day. . as in the parallel passage on page 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 . is kin-akbal, and is a kan with the prefix which generally belongs to the south as a superfix. . b is seated on the elongated head _q_ with a superfix and a prefix, exactly as on pages c and a, and this sign is repeated in the hieroglyphs (in ) 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 c. is b represented here as the preventer of evil? hieroglyph is _a_, while is kan, apparently with the sign of the south as a prefix. a bacab period of days ends here. we come now to the upper series of pictures. . 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 and are effaced, is indistinct, seems to be a xul (end, close) and is e's head. . 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 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. 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 th day of this section is reached here, corresponding with the apparent revolution of mercury = days. similarly sign invites computation; it is a face resembling an ahau sign, with a as a superfix and a as a prefix; compare the other places containing the same face, with c. after the fashion of the inscriptions this would denote + × = , which by the way is three fifths of the mercury revolution. is a compound of akbal and imix and a compound of a moan sign (_c_) with a. . 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 . i do not know how to explain , unless it is the bat-god; is a xul = end (but of what?) combined with imix, and is the usual kan-imix. is a kin with an back of it (as b, b, a, a) and over it is a hand pointing to the right, just like those in groups and . this looks as if we ought to count forward days, but what can be the purpose of doing so? . b is walking armed with spear and shield. sign is _b_, the face resembling an ahau, which occupied the second place in group , is probably xul again, but with an effaced prefix; of also only an imix remains; while is the usual compound of muluc-caban. . we have now reached the day kayab, a day very close to the day kayab, which on page 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 cumhu it may also have denoted the end of a lunar year, as on pages - 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 c and particularly on c; the sun and moon are also represented, but below the planets. the hieroglyphs likewise contain the sun and moon in and , in , ahau and xul with a prefix, as if this were the end of the increase of the sun's power; is kin-akbal, day and night, and is caban with the cross b. . b is walking armed with hatchet and shield. he holds a serpent in his hand as on page c, but here with the head downward. hieroglyphs and are destroyed, is the cross _b_ with a suffix and the horse-shoe prefix _e_, known to us from pages and . is imix combined with chuen and probably with yax, and is e's head. . this is the old red woman with the tiger claws, whom we saw on pages b and b and shall see again on page ; she reinforces the water falling from the planets by pouring a stream from her jug. the first three hieroglyphs are effaced, is the elongated head _q_, is kin-akbal, , as in group , is again the enigmatical with a hand pointing to the right. . b is walking and bears pouch, spear and shield. hieroglyph is a hand holding the sign of the rising moan, just as in a hand holds the head of k; is again k, whose sign is probably effaced several times in the last groups of this series. is e with the sign of the east; is compounded of imix, chuen and _b_, and 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 ix. . we come now to the representation of the change of the year, which we have already mentioned. hieroglyph is curious, consisting of the moon with a stripe running around it like a strap; and are not clear to me and are doubtless closely connected with one another; also contains a trace of k and is perhaps a determinative of the same. is again e, and suggests the tilling of the fields. . this picture as well as the first two hieroglyphs have already been discussed above. the crouching personage, repeated again in as a prefix to the cross _b_, is curious. is again e and is imix, referring to grain and honey. . 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 and . sign is e's hieroglyph, is kan-imix and is the wind-beast. b is superfluously added in and the same is true of the cross _b_ in , while kin-akbal in seems to fit almost everywhere. pages a, a and c show the lightning-beast in a different form. . 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 , and , the latter apparently representing c, are effaced. the other three are enigmatical, is again xul with a prefixed , a caban, but with an unintelligible prefix, and is again the mysterious . . 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 , and are effaced; is b's sign, might be xul and is _a_ with _c_ added and thus referring to the moan. and here the half of the ritual year ends with the nd day, which is xiii chicchan pop ( 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 days, which, however, seems sometimes (as on pages , and in the upper sections) to be raised to the value of half a tonalamatl = days. this may be explained by the fact that it is difficult to determine exactly the length of the revolution of mercury. in group this figure appears exactly on the th day of this section, but in group on the th day of the year, _i.e._, approximately at the expiration of two mercury periods after the beginning of the year. but now for group . 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 -- . 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 - , 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 - , 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 - . 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 b- b, where a period of days is considered with reference to the wind-deities. the first and sixth columns of pages - 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 days, though × , 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 b- b and may be one of the effaced signs on pages - . 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 , and from it i will borrow the following. this second passage fills the middle and lower thirds of pages - , 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 - . but the scribe, misled by the direction of the numeral series, began on page 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 . page . page . | | | | the number shows that we have to do here with weeks of days each, _i.e._, with a ritual year of days, as was the case on pages - , - and - . this year, however, is divided into four parts of x = days, _i.e._, into four so-called bacab periods. this is very plainly indicated here, for groups , , and , _i.e._, those separated by seven groups each, are exactly alike, but in group b (i will designate the three hieroglyphs of each group from top to bottom by _a_, _b_ and _c_) there is a prefixed which refers to the four bacabs as does the same prefixed to the bacab sign at the top of page . now the question arises as to when this ritual year began. undoubtedly its beginning day was very different from that of the civil year ( days) and from that of the astronomical year ( 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 , 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._, days, which were preceded and followed by 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 th 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 -day periods which agree in general with the dates. . - march - ceh. . - march -april mac. . - april - } kankin. . - april -may } . - may - moan. . - may - , pax. . - may -june } kayab. . - june - } . - june -july } cumhu. . - july - } . - july - pop. . - august - } uo. . - august - } . - august -september zip. . - september - } zotz. . - september -october } . - october - zec. . - october - } xul. . - october -november } . - november - yaxkin. . - november -december } mol. . - december - } . - december -january } chen. . - january - } . - january - yax. . - january -february } zac. . - february - } . - february -march ceh. in the following i will call attention to a few points by which this arrangement is justified. hieroglyph a 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 a thus:--the day of the change of year in the month ceh. the sign b 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 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:-- , , and , 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 c and c, 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 c and c, 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 (second picture). the serpent b 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 days. i have some other ideas on this subject, which, however, are mere conjectures, advanced with some hesitation. if the chuen sign in a 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 b we find a crouching figure with the sign which is usually considered that of the death-bird. in another place (zur entzifferung iv, ) i have regarded the naked human figure placed upside down on page as the sign for mercury, and on page at the bottom, left, i also regarded the crouching figure as representing mercury vanquished by venus. but in b, which belongs to the th- th days of the year, a day revolution of mercury is computed. a crouching figure, like that in b, likewise appears on page a in the second series of days after + = days of this series have elapsed, _i.e._, directly after the days of the apparent revolution of mercury. in b, 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 th). in group , 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 , but there was no room for it, since it was necessary that the signs for the period of days should be set down there. signs a and the combined signs bc are almost alike and suggest a. is it intended to designate here the ritual year, the time of the autumnal equinox (september th?). in a 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 in front of them signify the third quarter of the year? b 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 a 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 th group, in the th it is combined with the apparent mercury sign, and in the th with the year sign. the second bird with the prefixed yax is in the nd 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 , and and also probably in 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, , and ). 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. . the -series of the day ix ix. as with the other series, we begin here at the right, _i.e._, with page . 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 a discussed above. the fourth is an akbal with a prefixed arm as on pages a, a, and the fifth is an ik with a prefix. below these are three numbers:-- , , and , which are in the proportion of , and , so that the , is a tonalamatl, as it were, of periods of days each. the fact that is chosen here as the difference of the following series is curious, because usually only parts of or of are selected. but is probably only a secondary matter, while , , with its marvellous property of divisibility into the most varied and important periods, is the chief subject. there is a 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 are connected with the "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 , in the next to the last column; it is continued on page and on page 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):-- xi lamat xiii ik ii cib iv oc vi kan viii ezanab x eb xii cimi i ahau iii ix v lamat vii ik. the series must now continue with the already specified on page , which it proceeds to do from right to left in the middle of page , and continues from there on with regularly added dates and with the itself as the difference. at the same time, since = × , the week-days are forced to come to a standstill on the ix, while each of the month days ascends by two ( = × + ). the = × is obtained in the next to the last column of page . on page the is incorrectly set down as . . . instead of . . . the series continues on page in the same way beyond the , until in a number is obtained which is also divisible by , so that now the accompanying day must be ix ix. now we ought to expect to see here the double of , the very , abovementioned, but it is omitted just because it was set down on page . nevertheless this very number forms the new difference with which the series returns from page to the top line of page , where the numbers are mostly effaced, but enough remains to enable us to assume that the last number on page is the th multiple of , , and this may be followed by the th and th multiples, the last number being , . . the -series of the day iv eb. this series begins in the middle of page with the day iv caban, the zero-point therefore being iv eb. it then advances to the left across members, until on page it reaches the number = years of days = tonalamatls. from there on, itself is the difference, and the accompanying day therefore remains iv eb. then, in the two lowest sections of pages and , the fourth multiple of , _i.e._, , is the third difference and thus the series advances to × = , on page , after which on page the omitted × = , is written out. close beside this number are the figures . . . . and a below the latter, which was not successfully erased; this would be the number of which i can make nothing at all. the initial dates of the two series, ix ix and iv eb, are days apart and reversely days. . 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 - ; its first top line is completely effaced. the remainder i will designate by the following numbers:-- . the date ix kan kayab, set down under and does not belong there but to the serpent below and will be discussed later. i take sign to be that of a bacab, i do not understand and it is half obliterated; it seems to occur again on page in the column to the extreme right. and are the elongated head _q_ with an unusual superfix, and correspond with one another, but i cannot explain them. , and denote the beginning, , and , the end. and both designate the th day of the month kayab and over them iv ahau must have been set down twice. and are two heads of gods, is probably d's with the sign for west and , b's with that of the east. on page , 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:-- ) pax ) pop or cumhu ) viii ahau ) yaxkin ) muan ) , ) ) zec. the following is to be noted in this connection:-- 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. , a compound of imix and the superfix denoting multiplication, is the sign for , , and its prefix seems to me to denote duplication. we have long known how important the , = × = × is, and, if my theory is correct, we shall see directly that it occurs again here. seems really to be 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 and ought to be read together as viii ahau yaxkin, then this date would come in the year muluc. in the zeitschrift für ethnologie i explained the five hieroglyphs in the third column at the bottom of page (the third group) as civil years of and astronomical years of days:-- ) , = × = × ) , = × = × ) , = × ) , = × = × ) ------ , . this, it is true, is a striking explanation and certainly a surprising one! now the date ix ix kayab is at the very bottom of the fourth column. this, without apparent reason, would refer to the year kan. should it not be read ix kan kayab ( 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 , above the two numbers , and , , 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, , page , i have endeavored to explain these three signs on the right above , , by suggesting for them the values , = × , = × , = × ------ , and calling special attention to the fact that between iv eb and iv ahau there are days, and that the , placed below them in the manuscript, increased by , is equal to , . this group then seems really to belong to the day iv eb and to the -series, while manifold problems are still to be encountered in interpreting the other groups. . the large numbers. the manuscript offers material with which to work, beginning on page :-- , , , , , , , , ( ) ( ) iv eb ix ix iv ahau iv ahau viii ahau; yaxkin ( muluc). cumhu cumhu ix ix iv eb , , , , , , ( ) ( ) iv ahau iv ahau cumhu cumhu this is followed at the right top of page by , , ix ix iv eb. two of the numbers and two of the dates are conjectural:-- i read the , , as . . . . . while the manuscript has instead of . i read the , as . . . . the manuscript has instead of the second . and in two places in the third column of page , i have restored the day iv eb, where the manuscript incorrectly repeats the ix ix, and does the same thing on page . let us now first consider the construction of those large numbers, which are connected with the day ix ix and thus with the -series. these numbers are the two upper ones of columns and and the lower one of column on page . 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 to . (iv ahau - ix ix = .) the th, th and th multiples of have been added to ; 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:-- , , = ix ix muan ( kan). , , = ix ix chen ( cauac). , , = ix ix mac ( muluc). when we add to the above the three encircled numbers , , and , the resulting sums are the three numbers found in the manuscript:-- , , = iv ahau chen ( ix). , , = iv ahau cumhu ( cauac). , , = iv ahau kayab ( muluc). i am placing the first two not far from the present and the third in the past. as multiples of these three numbers have the following form:-- , , = × . , , = × . , , = × . some curious facts come to light with regard to their magnitude and their mutual relation. the two largest numbers are × = × apart; this recalls the -series. the third lowest number is × and thus contains not only the but = × × . the ritual year ( ) and its excess over the tonalamatl ( ) is likewise contained in these numbers, at least in the first and third:-- , , = × = , × . , , = × = , × . the three encircled numbers are connected with one another because the first = × + , the second = × + and the third is itself. the larger encircled numbers are, therefore, = × apart, and this is also the interval between the two numbers near the bottom. , however, also = × , and is the interval from iv eb to iv ahau. now it is curious that the two numbers below are × and × , though the third belongs to day ix ix and the fourth to iv eb. one result of this is that , , = × and , , = × . as these three numbers relate to day ix ix and the -series, so the fourth relates to iv eb and the -series. here the starting-point is the number , which belongs to day iv eb and this is separated from iv ahau by days _i.e._, it divides the tonalamatl in the proportion of to . to the number then, for unknown reasons was added × = , , , and thus the number , , , suppressed in the manuscript, was obtained for the day iv eb. to this sum the encircled number was then added and the result was , , , the number in the manuscript. the number = , × = × , which is self-evident, but it also = × , _i.e._, it is a multiple of the encircled number. it consequently also = , × , and thus it is related to the first and third numbers just now discussed. the position of this number is iv ahau kankin ( kan) and the position of the suppressed number is iv eb zotz (also kan). we ought now to discuss the last two numbers of this section amounting to millions:-- , , and , , , which are in the third and fourth columns at the top of page . but before going further, we must examine four other numbers, two of which, , and (with my correction) , , are in column on the lower part of page , and the other two, , and , , are on the top of page . 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. , - , is , the very same number which we shall afterward find as the difference of the serpent numbers on page . , - , = , . if be subtracted from this, the remainder is exactly , = tonalamatls = revolutions of mars. i have already found this number on page a, and also the double of it, , , on page , and this i found by using , + for my computation. , - , = , , _i.e._, exactly the double of the important , , which is recorded on page . , - , = , , _i.e._, = tonalamatls or revolutions of mars. , - , = , ; if , the interval from iv eb to ix ix be subtracted from this, the remainder is , = tonalamatls. , - , = , ; if , the interval from ix ix to iv eb, be subtracted from , , the remainder is , = tonalamatls = ritual years of days each, _i.e._, exactly the double of the specified on page . now we also have the following equations for the four numbers:-- , = × + . , = × + . , = × + . , = × + . a day viii ahau is days back of the day ix ix, and another viii ahau is 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 and days, which are in the proportion of to , _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 , for , , and , , are both divisible by , 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):-- , , = × --------- , , = viii ahau yax ( cauac). , --------- , , = ix ix zip ( muluc). , , = × --------- , , = viii ahau mol ( kan). , --------- , , = ix ix zip ( muluc). , , = × --------- , , = viii ahau uo ( ix). , --------- , , = iv eb pop ( muluc). , , = × --------- , , = viii ahau pax ( muluc). , --------- , , = iv eb pop ( muluc). the last record of the date of viii ahau seems to throw light on the date pax (page , column ), 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 yaxkin. this would point to a year 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 and , or these numbers increased by a multiple of . this passage would then read about as follows:-- , , (iv ahau) , , (iv ahau) (iv eb) (ix ix). these two numbers for iv ahau are equal to and tonalamatls. if × be subtracted from these, the remainders are and tonalamatls respectively, _i.e._, , and , , and these are in the proportion of to . now the two large numbers have the difference , = × + ; 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 ):-- in the first case we see the following:-- , , - , , = , = × , - . yax ( cauac) to uo ( ix) = , = , - . , - , = , = × , . while in the second case:-- , , - , , = , = × , - . mol ( kan) to pax ( muluc) = . , - = , = × , . . the serpent. as in the section occupying pages - , 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 kayab ( 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 c); 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 . 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 . the first of the two also occupies the same place on page above the fourth serpent. but here at the bottom we find the date ix kan kayab ( 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 is barely visible in the red number. the black number here has the figures . . . . . . and the red . . . . . . the black is therefore , , , and the red , , . 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 = × + ; but is the interval between days iv eb and ix ix. now this is the same which we found on page , as the difference between , and , . in order not merely to examine these numbers, but also to understand them, we will again make use of ahau-katuns = , , , as we did in the first four serpents, and we shall have the following:-- black red , , , , , , , , ---------- ---------- - , = × + - , = × + iv eb - ix kan = ix ix - ix kan = 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 -series, is given for the black number, and therefore also the interval between iv eb and ix kan = . to this was added a multiple of , not an arbitrary choice, but one which combined with resulted in a number divisible by , the interval from ix kan to iv eb. , = × = × + was thus obtained. the subtraction of this number from , , resulted in the serpent number , , . in addition to all this the day ix ix, the starting-point of the -series, is given for the red number; consequently also the interval between ix ix and ix kan = , which, at the same time, is reversely the interval from ix kan to ix ix. to this was added a multiple of , which _must_ in every case be a multiple also of . thus we obtain the , = × + . the subtraction of this number from , , results in the serpent number , , . reckoned from the starting-point ix kan kayab ( ix) the black number corresponds to the date iv eb chen ( muluc) and the red to ix ix zip ( 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 and the red by . 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 we believed were connected with the creation of the world. thus here, too, we have the genesis and the apocalypse of all the mythologies. . the columns of hieroglyphs. the last portion of this section is formed by the two middle columns of hieroglyphs on page . they bear an extraordinary resemblance to those discussed under page even in regard to the fact that each column contains signs. besides, the upper lines, _i.e._, the upper signs, are exactly alike on the two pages, aside from slight variations, and differ only in so far as the passage on page is written on blue ground and the one on page on white. but also the lower part, with eight signs in each column, shows many points in common with page . here as there the whole is divided into several groups. with the four signs ab and ab, which formed the first group there, i can compose only the two signs ab here. in the cross a, as on pages and of the manuscript, i see the sign for with the prefixed making . in b we find the sign for , days, which we have already met with several times. hence ab would have the value of × , = , days, as on page the corresponding four signs seemed to form , . and as the number there was × , so on page we have × . i believe there is a disarrangement in what follows, inasmuch as i assume that the two signs b and a ought to be placed _before_ and not _after_ a. assuming that the two little crosses on either side of the are meaningless, we should assign the value of to the chuen, 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 , column , 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 and on pages - the two most important days, iv eb and ix ix, are days apart, and is the second multiple of . i can now put the , of a in the place of the a. then, secondly, the four signs from a to b in the one section are exactly like those in the other section, and therefore need not be discussed here. only ab differs from the signs in the other passages inasmuch as on page we find × + × . the last 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 corresponds to the signs in ab and ab of page . on the contrary, the initial date of the serpent ix kan kayab, which on page does not appear until ab is set down in ab. on the other hand on page the four signs ab and ab are added, a being a sign as yet unknown with as a superfix. i feel inclined, though with many misgivings, to treat ab like a and b of page and to assign to them the value of an ahau-katun of , days. for then they would denote the th ahau-katun, which extends from the day , , (page ) to , , and which contains the two large numbers on page , left, top, while the two lower numbers in the first and second columns of that page belong to the th ahau-katun, and the two in the third and fourth belong to the th ahau-katun. the th would be the present and the th and th the past and future; but all this could only be confirmed by further research. at all events, the signs for beginning in b and for end in a refer to past and future. unfortunately, b is entirely effaced. page .[ ] besides the picture, this page contains only 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 - 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 , and 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 a and b, 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. | | a | | a- a | | | a- a | | a | | | a- a | | b- b | a- a | | a- a | | b- b | b- b | | a- a | | b- b | a- a | | a- a | | b- b | a | | b- b | | b- b | b- b | | b- b | | b- b | b- b | | c- c | | b- b | b | | c- c | | b- b | b | | c- c | | c- c | b | | c- c | | c- c | b- b | | b | | c- c | b | | b- b | | c- c | c- c | | b | | c- c | c- c | | b | | c- c | | c- c | | second part. c | | c- c | | c | | b | | - | c- c | | b | | a- a | c | | | | - | a | | - | | - | b- b | | a- a | | | c- c | | a- a | | - | a- a | | a- a | | - | a | | a- a | | - | b- b | | a- a | | | c | | | | | * * * * * [illustration: glyphs referred to in the text.] [illustration: cardinal points.] * * * * * notes [ ] the manuscript has incorrectly and . [ ] = chen. [ ] the sign denotes the end of the -day year. [ ] = zotz. [ ] compare the peresianus, page . smithsonian institution bureau of american ethnology bulletin an introduction to the study of the maya hieroglyphs by sylvanus griswold morley [illustration] washington government printing office * * * * * {iii} letter of transmittal smithsonian institution, bureau of american ethnology, _washington, d. c., january , ._ 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 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 ), 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 , , followed by unknown characters; april , , by others; and march , , 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: ( ) 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 ( ) 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 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 habitat history manners and customs ii. the maya hieroglyphic writing iii. how the maya reckoned time the tonalamatl, or -day period the haab, or year of days the calendar round, or , -day period the long count initial series the introducing glyph the cycle glyph the katun glyph the tun glyph the uinal glyph the kin glyph secondary series calendar-round dates period-ending dates u kahlay katunob iv. maya arithmetic bar and dot numerals head-variant numerals first method of numeration number of cycles in a great cycle second method of numeration first step in solving maya numbers second step in solving maya numbers third step in solving maya numbers fourth step in solving maya numbers fifth step in solving maya numbers v. the inscriptions texts recording initial series texts recording initial series and secondary series texts recording period endings texts recording initial series, secondary series, and period endings errors in the originals vi. the codices texts recording tonalamatls texts recording initial series texts recording serpent numbers texts recording ascending series * * * * * {x} list of tables page table i. the twenty maya day names ii. sequence of maya days iii. the divisions of the maya year iv. positions of days at the end of a year v. relative positions of days beginning maya years vi. positions of days in divisions of maya year vii. positions of days in divisions of maya year according to maya notation viii. the maya time-periods ix. sequence of katuns in u kahlay katunob x. characteristics of head-variant numerals - , inclusive xi. sequence of twenty consecutive dates in the month pop xii. comparison of the two methods of numeration xiii. values of higher periods in terms of lowest, in inscriptions xiv. values of higher periods in terms of lowest, in codices xv. the positions in the maya year xvi. calendar rounds expressed in arabic and maya notation xvii. interrelationship of dates on stelæ e, f, and j and zoömorph g, quirigua {xi} illustrations page plate . the maya territory, showing locations of principal cities (map) . diagram showing periods of occupancy of principal southern cities . page of the dresden codex, showing the end of the world (according to förstemann) . diagram showing occurrence of dates recorded in cycle . tonalamatl wheel, showing sequence of the differently named days . glyphs representing initial series, showing use of bar and dot numerals and normal-form period glyphs . glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs . glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs . glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs . glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs--stela , tikal . glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs--stela a (east side), quirigua . glyphs representing initial series, showing use of head-variant numerals and period glyphs . oldest initial series at copan--stela . initial series on stela d, copan, showing full-figure numeral glyphs and period glyphs . initial series on stela j, copan . initial series and secondary series on lintel , yaxchilan . initial series and secondary series on stela , piedras negras . initial series and secondary series on stela k, quirigua . initial series and secondary series on stela f (west side), quirigua . initial series on stela f (east side), quirigua . examples of period-ending dates in cycle . examples of period-ending dates in cycles other than cycle . initial series, secondary series, and period-ending dates on stela , piedras negras . initial series, secondary series, and period-ending dates on stela e (west side), quirigua . calendar-round dates on altar , tikal . initial series on stela n, copan, showing error in month coefficient . page of the dresden codex, showing tonalamatls in all three divisions . page of the dresden codex, showing tonalamatls in all three divisions . middle divisions of pages and of the tro-cortesiano, showing one tonalamatl extending across the two pages . page of the codex tro-cortesiano, showing tonalamatls in the lower three divisions {xii} . page of the dresden codex, showing initial series . page of the dresden codex, showing the serpent numbers figure . itzamna, chief deity of the maya pantheon . kukulcan, god of learning . ahpuch, god of death . the god of war . ek ahau, the black captain, war deity . yum kaax, lord of the harvest . xaman ek, the north star god . conflict between the gods of life and death (kukulcan and ahpuch) . outlines of the glyphs . examples of glyph elision, showing elimination of all parts except essential element . normal-form and head-variant glyphs, showing retention of essential element in each . normal-form and head-variant glyphs, showing absence of common essential element . glyphs built up on a phonetic basis . a rebus. aztec, and probably maya, personal and place names were written in a corresponding manner . aztec place names . the day signs in the inscriptions . the day signs in the codices . sign for the tonalamatl (according to goodman) . the month signs in the inscriptions . the month signs in the codices . diagram showing engagement of tonalamatl wheel of days and haab wheel of positions; the combination of the two giving the calendar round, or -year period . signs for the calendar round . diagram showing section of calendar-round wheel . initial-series "introducing glyph" . signs for the cycle . full-figure variant of cycle sign . signs for the katun . full-figure variant of katun sign . signs for the tun . full-figure variant of tun sign . signs for the uinal . full-figure variant of uinal sign on zoömorph b, quirigua . full-figure variant of uinal sign on stela d, copan . signs for the kin . full-figure variant of kin sign . period glyphs, from widely separated sites and of different epochs, showing persistence of essential elements . ending signs and elements . "snake" or "knot" element as used with day sign ahau, possibly indicating presence of the u kahlay katunob in the inscriptions . normal forms of numerals to , inclusive, in the codices . normal forms of numerals to , inclusive, in the inscriptions . examples of bar and dot numeral , showing the ornamentation which the bar underwent without affecting its numerical value {xiii} . examples showing the way in which numerals , , , , , , , and are _not_ used with period, day, or month signs . examples showing the way in which numerals , , , , , , , and _are_ used with period, day, or month signs . normal forms of numerals to , inclusive, in the books of chilan balam . sign for in the codices . sign for in the codices . sign for in the inscriptions . figure showing possible derivation of the sign for in the inscriptions . special sign for used exclusively as a month coefficient . examples of the use of bar and dot numerals with period, day, or month signs . head-variant numerals to , inclusive . head-variant numerals to , inclusive . head-variant numerals to , inclusive, and . a sign for , used also to express the idea "ending" or "end of" in period-ending dates . examples of the use of head-variant numerals with period, day, or month signs . examples of the first method of numeration, used almost exclusively in the inscriptions . signs for the cycle showing coefficients above . part of the inscription on stela n, copan, showing a number composed of six periods . part of the inscription in the temple of the inscriptions, palenque, showing a number composed of seven periods . part of the inscription on stela , tikal (probably an initial series), showing a number composed of eight periods . signs for the great cycle and the great-great cycle . glyphs showing misplacement of the kin coefficient or elimination of a period glyph . examples of the second method of numeration, used exclusively in the codices . figure showing the use of the "minus" or "backward" sign in the codices . sign for the "month indicator" . diagram showing the method of designating particular glyphs in a text . signs representing the hotun, or -tun, period . initial series showing bar and dot numerals and head-variant period glyphs . initial series showing head-variant numerals and period glyphs . initial series showing head-variant numerals and period glyphs . initial series on stela h, quirigua . the tun, uinal, and kin coefficients on stela h, quirigua . the initial series on the tuxtla statuette, the oldest initial series known (in the early part of cycle ) . the introducing glyph (?) of the initial series on the tuxtla statuette . drawings of the initial series: _a_, on the leyden plate; _b_, on a lintel from the temple of the initial series, chichen itza {xiv} . the cycle- initial series from quen santo . initial series which proceed from a date prior to ahau cumhu, the starting point of maya chronology . the initial series on stela j, quirigua . the secondary series on stela j, quirigua . glyphs which may disclose the nature of the events that happened at quirigua on the dates: _a_, . . . . caban kayab; _b_, . . . . cimi tzec . the initial series, secondary series, and period-ending date on altar s, copan . the initial series on stela e (east side), quirigua . calendar-round dates . texts showing actual errors in the originals . example of first method of numeration in the codices (part of page of the dresden codex) * * * * * {xv} bibliography aguilar, sanchez de. . informe contra idolorum cultores del obispado de yucatan. madrid. (reprint in _anales mus. nac. de mexico_, vi, pp. - , mexico, .) bowditch, charles p. a. memoranda on the maya calendars used in the books of chilan balam. _amer. anthr._, n. s., iii, no. , pp. - , new york. ---- . the temples of the cross, of the foliated cross, and of the sun at palenque. cambridge, mass. ---- . dates and numbers in the dresden codex. _putnam anniversary volume_, pp. - , new york. ---- . the numeration, calendar systems, and astronomical knowledge of the mayas. cambridge, mass. brasseur de bourbourg, c. e. - . manuscrit troano. Études sur le système graphique et la langue des mayas. vols. paris. brinton, daniel g. b. the maya chronicles. philadelphia. (no. of _brinton's library of aboriginal american literature_.) ---- b. a primer of mayan hieroglyphics. _pubs. univ. of pa._, ser. in philol., lit., and archeol., iii, no. . bulletin of the bureau of american ethnology, : 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. . historia de yucathan. madrid. cresson, h. t. . the antennæ and sting of yikilcab as components in the maya day-signs. _science_, xx, pp. - , new york. dieseldorff, e. p. see bulletin . fÖrstemann, e. . commentary on the maya manuscript in the royal public library of dresden. _papers peabody mus._, iv, no. , pp. - , cambridge. _see also_ bulletin . gates, w. e. . commentary upon the maya-tzental perez codex, with a concluding note upon the linguistic problem of the maya glyphs. _papers peabody mus._, vi, no. , pp. - , cambridge. goodman, j. t. . the archaic maya inscriptions. (biologia centrali-americana, archæology, part xviii. london.) [_see_ maudslay, - .] ---- . maya dates. _amer. anthr._, n. s., vii, pp. - , lancaster, pa. hewett, edgar l. . two seasons' work in guatemala. _bull. archæol. inst. of america_, ii, pp. - , norwood, mass. holmes, w. h. . on a nephrite statuette from san andrés tuxtla, vera cruz, mexico. _amer. anthr._, n. s., ix, no. , pp. - , lancaster, pa. landa, diego de. . relacion de las cosas de yucatan. paris. le plongeon, a. . the maya alphabet. supplement to _scientific american_, vol. xix, jan. , pp. - , new york. maler, teobert. . researches in the central portion of the usumatsintla valley. _memoirs peabody mus._, ii, no. , pp. - , cambridge. ---- . researches in the central portion of the usumatsintla valley. [continued.] ibid., no. , pp. - . ---- a. explorations of the upper usumatsintla and adjacent region. ibid., iv, no. , pp. - . {xvi} maler, teobert. b. explorations in the department of peten, guatemala, and adjacent region. ibid., no. , pp. - . ---- . explorations in the department of peten, guatemala, and adjacent region. [continued.] ibid., no. , pp. - . ---- . explorations in the department of peten, guatemala. tikal. ibid., v, no. , pp. - , pls. - . maudslay, a. p. - . biologia centrali-americana, or contributions to the knowledge of the flora and fauna of mexico and central america. archæology. vols. of text and plates. london. morley, s. g. b. correlation of maya and christian chronology. _amer. journ. archeol._, d ser., xiv, pp. - , norwood, mass. ---- . the historical value of the books of chilan balam. ibid., xv, pp. - . ponce, fray alonzo. . 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. . essai sur le déchiffrement de l'écriture hiératique de l'amérique centrale. paris. sapper, carl. _see_ bulletin . schellhas, paul. _see_ bulletin . seler, eduard. c. die alten ansiedelungen von chaculá im distrikte nenton des departements huehuetenango der republik guatemala. berlin. ---- - . gesammelte abhandlungen zur amerikanischen sprach- und alterthumskunde. vols. berlin. _see also_ bulletin . spinden, h. j. . a study of maya art, its subject-matter and historical development. _memoirs peabody mus._, vi, pp. - , cambridge. stephens, j. l. . incidents of travel in central america, chiapas, and yucatan. vols. new york. ---- . incidents of travel in yucatan. vols. new york. thomas, cyrus. . are the maya hieroglyphs phonetic? _amer. anthr._, vi, no. , pp. - , washington. villagutierre, sotomayor j. . 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] * * * * * { } 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. .) 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 , 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,[ ] but to-day they are a dwindling { } 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.[ ] 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,[ ] 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 years, or until about the close of the sixth century, may be called { } 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 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[ ] 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 { } 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.[ ] 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. ), the first settlement in the north, was occupied for only 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 years, until the destruction of chakanputun by fire about 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 these three cities--chichen itza, uxmal, and mayapan--formed a confederacy,[ ] in which each was to share equally in the government of the country. under the peaceful conditions which { } followed the formation of this confederacy for the next 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 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,[ ] 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[ ] 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 { } subjects in check.[ ] this unrest finally reached its culmination about the middle of the fifteenth century, when the maya nobility, unable longer to endure such tyranny, banded themselves together under the leadership of the lord of uxmal, sacked mayapan, and slew its ruler. 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 francisco de cordoba landed the first spanish expedition[ ] on the shores of yucatan. the natives were so hostile, however, that he returned to cuba, having accomplished 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 ( ) 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 , 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 ships and 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 { } 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 years later, on june , (old style), that, the spaniards having defeated a coalition of maya chieftains near the city of ichcanzihoo, the conquest was finally brought to a close and the pacification of the country accomplished. with this event ends the independent history of the maya. manners and customs according to bishop landa,[ ] who wrote his remarkable history of yucatan in , 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 { } 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 , 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 { } 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 { } 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 { } 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[ ] 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.[ ] when the deceased { } 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 ( - 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 { } 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 { } [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.[ ] 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] { } 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. ) indicates that many of them were contemporaneous, and that a few, namely, tikal, naranjo, palenque, and copan were occupied approximately years, a much longer period than any of the others.[ ] these four would seem to have been centers of population for a long time, and at least three of them, tikal, palenque, and copan, attained considerable size. indeed they may well have been, like chichen itza, uxmal, and mayapan, at a later epoch in the north, the seats of halach uincil, or overlords, to whom all the surrounding chiefs were tributary. geographically considered, the country was well apportioned among these cities: tikal dominating the north, palenque, the west, and copan, the south. the architecture, sculpture, and hieroglyphic writing of all the southern centers is practically identical, even to the borrowing of unessential details, a condition which indicates a homogeneity only to be accounted for by long-continued and frequent intercourse. this characteristic of the 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 { } southern. there is some ground for believing that the highest office in the south may have been elective, the term being a _hotun_[ ] ( , 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,[ ] rests on very slender evidence, however, so far as the maya are concerned and is mentioned here simply by way of suggestion. [illustration: fig. . 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 . his characteristics here are: the aged face, roman nose, and sunken toothless mouth. [illustration: fig. . 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 { } 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. ), 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. . 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. ), 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. ) suggests the dread idea for which he stood. note the eye closed in death. [illustration: fig. . 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. ) 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. ). another unpropitious deity was ek ahau, the black captain, also a war god, being represented (fig. ) in the picture-writings as armed { } 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. ). [illustration: fig. . 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. ). 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. ) embodies the same idea, the god's head merging into the conventionalized ear of corn surrounded by leaves. [illustration: fig. . 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. ). 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 { } 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. ); 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. . 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. . 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 { } 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 { } 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. { } chapter ii. the maya hieroglyphic writing the inscriptions herein described are found throughout the region formerly occupied by the maya people (pl. ), 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. . 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. , _c_). those in the codices, on the other hand, approximate more nearly in form rhomboids or even ovals (fig. , _a_, _b_). this difference in outline, however, is only superficial in significance and involves no corresponding difference in meaning between { } 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 ( b: p. ) 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. . 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 { } 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. . normal-form and head-variant glyphs, showing retention of essential element in each.] the element shown in figure , _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 , _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 , _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 { } 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 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 , 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 , 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. . 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 { } 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: ( ) astronomical, calendary, and numerical signs, that is, glyphs used in counting time; and ( ) 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.[ ] 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: . that the glyphs are phonetic, each representing some sound, and entirely dissociated from the representation of any thought or idea. . that the glyphs are ideographic, each representing in itself some complete thought or idea. . that the glyphs are both phonetic and ideographic, that is, a combination of and . 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 { } 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 , within years of the spanish conquest, landa was able to obtain characters for 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 by abbé brasseur de bourbourg (see landa, ), 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[ ] 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 ( b: p. ), 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: ( ) 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 ( ) 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 , 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_ { } and _chikin_ (see _e_ and _f_, respectively, fig. ), 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 . 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. . 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 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 { } 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."[ ] 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 , _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 , _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. . 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. { } 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 ( : p. ) 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. . aztec place names: _a_, the sign for the town toltitlan; _b_, the sign for the town acatzinco.] doctor brinton ( b: p. ) 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. { } 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 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 -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 -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. ). 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 -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 - of the dresden manuscript. here, to begin with, a period of , days is represented, which exactly contains five venus years of [ ] days each (one on each page) as well as eight solar years of days each. each of the venus years is divided into four parts, respectively, , , , and days. the { } 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 , days was taken as the basis from which the number , was formed. this contains venus-solar periods, venus-years, solar years, and _tonalamatls_, or sacred years of days each. finally, the last number ( , ) with all the subdivisions above given was thrice repeated, so that these five pages of the manuscript record the passage of , days, or solar years. again, on pages - of the same manuscript, revolutions of the moon are set down; and so accurate are the calculations involved that although they cover a period of nearly years the total number of days recorded ( , ) is only / of a day less than the true time computed by the best modern method[ ]--certainly a remarkable achievement for the aboriginal mind. it is probable that the 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. ), 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 of the dresden codex, showing the end of the world (according to fÖrstemann)] { } much less progress has been made toward discovering the meaning of the inscriptions. doctor brinton ( b: p. ) 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 ( : p. ) 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 -day year, into harmony with the true solar year of . days.[ ] 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 , 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 , 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 , days, or four times the { } 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.[ ] 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.[ ] 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 , 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 ] { } . at first there was a long period of slow growth represented by few monuments, which, however, increased in number toward the end. . this was followed without interruption by a period of increased activity, the period from which the great majority of the monuments date. . 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[ ] 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[ ] 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. ]. 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. ], "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, : p. ): "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 { } 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. ) who visited yucatan as early as , 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 ( ), 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 , some of these historical codices were in the possession of the last great independent maya ruler, one canek. says villagutierre ( : 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. { } 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 -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 { } 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. . the day signs in the inscriptions.] [illustration: fig. . the day signs in the codices.] the glyphs for these twenty days are shown in figures and . the forms in figure are from the inscriptions and those in figure 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 { } day in each. the sign for the first day, imix, is practically identical in both. compare figure , _a_ and _b_, with figure , _a_ and b. the usual form for the day ik in the inscriptions (see fig. , _c_), however, is unlike the glyph for the same day in the codices (fig. , _c_, _d_). the forms for akbal and kan are practically the same in each (see fig. , _d_, _e_, and _f_, and fig. , _e_ and _f_, respectively). the day chicchan, figure , _g_, occurs rarely in the inscriptions; when present, it takes the { } form of a grotesque head. in the codices the common form for this day is very different (fig. , _g_). the head variant, however (fig. , _h_), shows a slightly closer similarity to the form from the inscriptions. the forms in both figure , _h_, _i_, and figure , _i_, _j_, for the day cimi show little resemblance to each other. although figure , _i_, represents the common form in the codices, the variant in _j_ more closely resembles the form in figure , _h_, _i_. the day manik is practically the same in both (see figs. , _j_, and , _k_), as is also lamat (figs. , _k_, _l_, and , _l_, _m_). the day muluc occurs rarely in the inscriptions (fig. , _m_, _n_). of these two variants _m_ more closely resembles the form from the codices (fig. , _n_). the glyph for the day oc (fig. , _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 , _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. , _r_). this form bears a general resemblance to the glyph for this day in the codices (fig. , _p_, _q_). the forms for the day eb in both figures , _s_, _t_, _u_, and , _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. , _v_) is practically identical with that in the codices (see fig. , _s_). the day ix in the inscriptions appears as in figure , _w_, _x_. the form in the codices is shown in figure , _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 , _y_, is a grotesque head not unlike the sign for this day in the codices (fig. , _u_). the signs for the day cib in the inscriptions and the codices (figs. , _z_, and , _v_, _w_), respectively, are very dissimilar. indeed, the form for cib (fig. , _v_) in the codices resembles more closely the sign for the day caban (fig. , _a'_, _b'_) than it does the form for cib in the inscriptions (see fig. , _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 , _a'_, _b'_, and , _x_, _y_, show a satisfactory resemblance to each other. the forms for the day eznab are also practically identical (see figs. , _c'_, and , _z_, _a'_). the forms for the day cauac, on the other hand, are very dissimilar; compare figures , _d'_, and , _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 { } 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. , _e'-k'_, and , _c'_, _d'_). the latter form is the only one found in the codices, and is identical with _e'_, _f'_, figure , the usual sign for this day in the inscriptions. the variants in figure , _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 and 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 -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 to , inclusive, as imix or 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, to , inclusive, were joined to the twenty names of table i was as follows: selecting { } any one of the twenty names[ ] as a starting point, kan for example, the number 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 ( ), namely, chicchan. the next name, cimi, was given the next number ( ), namely, cimi, and so on as follows: manik, lamat, muluc, oc, chuen, eb, ben, ix, men, cib. table ii. sequence of maya days imix ik akbal * kan chicchan cimi manik lamat muluc oc chuen eb ben ix men cib caban eznab cauac ahau instead of giving to the next name in table ii (caban) the number , the number was prefixed; for, as previously stated, the numerical coefficients of the days did not rise above the number . following the day caban, the sequence continued as before: eznab, cauac, ahau. after the day ahau, the last in table ii, the next number in order, in this case , was prefixed to the next name in order--that is, imix, the first name in table ii--and the count continued without interruption: imix, ik, 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., , and the day following akbal in table ii would be, therefore, kan, and the sequence would continue to be formed in the same way: kan, chicchan, cimi, manik, lamat, muluc, oc, chuen, 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 ._ the sequence of the day names repeats itself again and again without interruption. [illustration: tonalamatl wheel, showing sequence of the differently named days] { } _rule ._ the sequence of the numerical coefficients to , inclusive, repeats itself again and again without interruption, following immediately . _rule ._ the numerical coefficients are attached to the names, so that after a start has been made by prefixing any one of the numbers to any one of the 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 numbers and names, and since each of the numbers must be attached in turn to each one of the names before a given number can return to a given name, we must find the least common multiple of and . as these two numbers, contain no common factor, their least common multiple is their product ( ), which is the number sought. therefore, any given day can not reappear in the sequence until after the days immediately following it shall have elapsed. or, in other words, the st day will have the same designation as the st, the d the same as the d, and so on. this is graphically shown in the wheel figured in plate , where the sequence of the days, commencing with 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 imix, is shown in parenthesis. now, if the star opposite the day 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 -day sequence. it appears from this diagram also that the day imix can not recur until after days shall have passed, and that it always follows the day ahau. this must be true since _ahau_ is the name immediately preceding imix in the sequence of the day names and is the number immediately preceding . after the day ahau (the th from the starting point) is reached, the day imix, the st, recurs and the sequence, having entered into itself again, begins anew as before. [illustration: fig. . sign for the tonalamatl (according to goodman).] this round of the differently named days was called by the aztec the _tonalamatl_, or "book of days." the maya name for this period is unknown[ ] and students have accepted the aztec name for it. the tonalamatl is frequently represented in the maya codices, there being more than 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, { } namely, × , × , × , × , and × . tonalamatls divided into , , and equal parts of , , and 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 as the sign for the -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 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 -day year, though they doubtless knew that the true length of the year exceeds this by hours. indeed, bishop landa very explicitly states that such knowledge was current among them. "they had," he says, "their perfect year, like ours, of days and hours;" and again, "the entire year had of these [ -day periods] and besides days and hours." in spite of landa's statements, however, it is equally clear that had the maya attempted to take note of these 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. ), 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 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, { } 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 ( : 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 days. it was divided into periods of days each, designated in maya _uinal_, and a closing period of days known as the _xma kaba kin_, or "days without name." the sum of these ( × + ) 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 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 ( : p. ) included, always fell on the th of july.[ ] uayeb, the last division of the year, contained only days, the last day of uayeb being at the same time the th 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, : p. ) 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] { } 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 o'clock, in reality the first hour after noon, that is, the hour between noon and p. m., has passed and the second hour after noon is about to commence. when we say it is 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 is written: ^{hr.} ^{min.} ^{sec.}, and quarter of , ^{hr.} ^{min.} ^{sec.}. indeed one hour can not be written until the first hour after midnight is completed, or until it is o'clock, namely, ^{hr.} ^{min.} ^{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 st day of january immediately after midnight december . it was the first year of the eleventh century immediately after midnight december , a. d. and finally, it was the twentieth century immediately after midnight december , 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. { } it will be seen that in the first method of counting time, in speaking of o'clock, hour, minutes, we use only the cardinal forms of our numbers; but in the second method we say the st 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: ( ) all periods less than the day, as hours, minutes, and seconds, are referred to in terms of past time; and ( ) 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, ( pop) for not until one whole day of pop had passed could the day 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 pop; the third day, pop; the fourth day, pop; and so on through the 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 instead of . this appears in table iv, in which the last days of one year and the first 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 days, whereas all the other periods (the uinals) had 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.[ ] the { } glyphs which represent the different uinals and the xma kaba kin, however, are shown in figures and . the forms in figure are taken from the inscriptions and those in figure from the codices. table iv. positions of days at the end of a year th day of the year cumhu last day of the month cumhu. st day of the year uayeb first day of uayeb. d day of the year uayeb d day of the year uayeb th day of the year uayeb th day of the year uayeb last day of uayeb and of the year. st day of next year pop first day of the month pop, and of the next year. d day of next year pop d day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop th day of next year pop last day of the month pop. st day of next year uo first day of the month uo. d day of next year 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. , _a_, and , _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 , a. uo has two forms in the inscriptions (see fig. , _b_, _c_),[ ] which are, however, very similar to each other as well as to the corresponding forms in the codices (fig. , _b_, _c_). the glyphs for the month zip are identical in both figures , _d_, and , d. the grotesque heads for zotz in figures , _e_, _f_,[ ] and , _e_, are also similar to each other. the essential { } characteristic seems to be the prominent upturned and flaring nose. the forms for tzec (figs. , _g_, _h_, and , _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. , _i_, _j_) bears very little resemblance to the common form for this month in the codices (fig. , _g_), though it is not unlike the variant in _h_, figure . 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. . the month signs in the inscriptions.] { } [illustration: fig. . the month signs in the codices.] the sign for the month yaxkin is identical in both figures , _k_, _l_, and , _i_, _j_. the sign for the month mol in figures , _m_, _n_, and , _k_ exhibits the same close similarity. the forms for the month chen in figures , _o_, _p_, and , _l_, _m_, on the other hand, bear only a slight resemblance to each other. the forms for the months yax (figs. , _q_, _r_, and , _n_), zac (figs. , _s_, _t_, and , _o_), and ceh (figs. , _u_, _v_, and { } , _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. , _w_) bearing absolutely no resemblance to that shown in figure , _q_, _r_, the only form for this month in the codices. the very unusual variant (fig. , _x_), from stela 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 , _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 . the sign for the month kankin (figs. , _y_, _z_, and , _s_, _t_) and the signs for the month muan (figs. , _a'_, _b'_, and , _u_, _v_) show only a general similarity. the signs for the last three months of the year, pax (figs. , _c'_, and , _w_), kayab (figs. , _d'-f'_, and , _x_, _y_), and cumhu (figs. , _g'_, _h'_, and , _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 , _i'_, with figure , _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 , , , and , since his progress will depend largely on his ability to recognize these glyphs when he encounters them in the texts. the calendar round, or -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. ) three things: ( ) the number of differently named days; ( ) the names of these days; ( ) 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: ( ) the length of the year; ( ) the number, length, and names of the several periods into which it was divided; ( ) the order in which these periods invariably followed one another; ( ) 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 { } 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. ) that the complete designation or name of any day in the tonalamatl consisted of two equally essential parts: ( ) the name glyph, and ( ) 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: . 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. . 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. . when the sums of the units in the two sequences contain a common factor (except in those cases which fall under ( ), 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 names in table i and the 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 names in endless repetition, it is evident that the st will be the same as the st, since = × . therefore the d will be the same as the d, the d as the d, the th as the th, and the as the th. but the th, or th, name is the name of the last day of the year, consequently the st day of the following year (the th from the beginning) will have the th name in the sequence. following out this same idea, it appears that the st day of the _second year_ will have the same name as that with which it began, that is, the th name in the sequence, the d day the th name, the d the th, the th the th, and the th, or last day of the _second year_, the th name. therefore the st day of the _third year_ (the st from the beginning) will have the th name in the sequence. similarly it could be shown { } that the _third year_, beginning with the th name, would necessarily end with the th name; and the _fourth year_, beginning with the th name (the th from the beginning) would necessarily end with the th, or last name, in the sequence. it results, therefore, from the foregoing progression that the _fifth year_ will have to begin with the st name (the st from the beginning), or the same name with which the _first year_ also began. this is capable of mathematical proof, since the st day of the _fifth year_ has the st name from the beginning of the sequence, for = × + = × + . the _ _ in the second term of this equation indicates that the beginning day of the _fifth year_ has been reached; and the _ _ in the third term indicates that the name-part of this day is the st 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 days distant, the next, eb, another five days, the next, caban, another days, and the next, ik, the name with which the table started, another 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 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 divisions of the year, with the exception of the last, each contained 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 days, the name of the first day of the following year; as well as { } the names of the first days of all of its divisions, was shifted forward in the sequence another 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 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 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 st name, manik will be the th, eb the th, and caban the th, and in the years when manik is the st, eb will be the th, caban the th, and ik the th, and in the years when eb is the st, caban will be the th, ik the th, and manik the th, and in the years when caban is the st, ik will be the th, manik the th, and eb the th, 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 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 th, th, and th positions as well. similarly kan, muluc, ix, and cauac will fill the d, th, th, and th positions, and so on. this enables us to formulate a third-- _rule._ the 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. { } table vi. positions of days in divisions of maya year --------------------------------------------------------------------+ | | { st, | d, | d, | th, | th, | | positions held | { th, | th, | th, | th, | th, | | by days | { th, | th, | th, | th, | th, | | | { th | th | th | th | th | |----------------+----------+---------+---------+---------+---------+ | | { 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 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 pop, but pop, and similarly the second day of pop was written not pop, but pop, and the last day, not pop, but pop. consequently, before we can use the names in table vi as the maya used them, we must make this shift, keeping in mind, however, that ik, manik, eb, and caban (the only four of the twenty names which could begin the year and which were written pop, pop, pop, or pop) would be written in our notation st pop, th pop, th pop, and th 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 |{ , , | , , | , , | , , | , , | | mayan notation |{ , | , | , | , | , | |--------------------+----------+---------+---------+---------+---------+ | | { 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 { } _the name parts of the days and not their complete designations_. bearing this in mind, we may state the following facts concerning the day-names and their positions in the divisions of the year: . the maya year and its several divisions could begin only with one of these four day-names: ik, manik, eb, and caban. . consequently, any particular position in the divisions of the year could be occupied only by one of four day-names. . consequently, every fifth year any particular day-name returned to the same position in the divisions of the year. . 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. . 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. . 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 maya days, to the haab, which gives the positions of the days in the divisions of the year, in such a way that any one of the days whose name-part is ik, manik, eb, or caban shall occupy the first position of the first division of the year; that is, pop, or, as we should write it, the first day of pop. it matters little which one of these four name parts we choose first, since in four years each one of them in succession will have appeared in the position pop. perhaps the easiest way to visualize the combination of the 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. ), has teeth, or cogs, each one of which is named after one of the days of the tonalamatl and follows the sequence shown in plate . the second wheel, b (fig. ), is somewhat larger, having cogs. each of the spaces or sockets between these represents one of the positions of the days in the divisions of the year, beginning with pop and ending with 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 ik in a shall fit into the socket named { } pop in b, after which both wheels start to revolve in the directions indicated by the arrows. [illustration: fig. . diagram showing engagement of tonalamatl wheel of days (a), and haab wheel of positions (b); the combination of the two giving the calendar round, or -year period.] the first day of the year whose beginning is shown at the point of contact of the two wheels in figure is ik pop, that is, the day ik which occupies the first position in the month pop. the next day in succession will be akbal pop, the next kan pop, the next chicchan pop, the next cimi 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, 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, pop, the corresponding cog in b will not be ik, but another day ( manik), since by that time the smaller wheel will have progressed cogs, or days, farther, to the cog manik. the question now arises, how many revolutions will each wheel have to make before the day ik will return to the position pop. the solution of this problem depends on the application of one sequence to another, and the possibilities concerning the numbers or names which stand at the head of the resulting sequence, a subject already discussed on page . in the present case the numbers in question, and , contain a common factor, therefore our problem falls under the third contingency there presented. consequently, only certain of the days can occupy the position pop, or, in other words, cog ik in a will return to the position pop in b in fewer than revolutions of a. the actual solution of the problem { } is a simple question of arithmetic. since the day ik can not return to its original position in a until after days shall have passed, and since the day pop can not return to its original position in b until after days shall have passed, it is clear that the day ik pop can not recur until after a number of days shall have passed equal to the least common multiple of these numbers, which is ( / )×( / )× , or × × = , days. but , days = × = × ; in other words the day ik pop can not recur until after revolutions of b, or years of days each, and revolutions of a, or tonalamatls of days each. the maya name for this -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_.[ ] the calendar round was the real basis of maya chronology, since its , dates included all the possible combinations of the days with the 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 , years, this truly remarkable feat was accomplished only by using a sequence of calendar rounds, or -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 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 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:[ ] 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. { } 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. . 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 , _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 -year period among the maya. the sign in figure , _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 , dates, and the glyphs which composed these are found repeatedly in both the codices and the inscriptions (see figs. , , , ). 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 , 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 years. { } the long count we have seen: . how the maya distinguished day from the others in the tonalamatl; . how they distinguished the position of day from the others in the haab, or year; and, finally, . how by combining ( ) and ( ) they distinguished day from the other , of the calendar round. it remains to explain how the maya insured absolute accuracy in fixing a day within a period of , years, as stated above, or how they distinguished day from , , others. the calendar round, as we have seen, determined the position of a given day within a period of only 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 b. c., which were won by a certain coroebus. the romans took as their starting point the supposed date of the foundation of rome, b. c. the babylonians counted time as beginning with the era of nabonassar, b. c. the death of alexander the great, in b. c., ushered in the era of alexander. with the occupation of babylon in b. c. by seleucus nicator began the so-called era of seleucidæ. the conquest of spain by augustus cæsar in 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 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 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, { } commences with that event, supposed to have occurred in b. c. the jews reckoned the same event as having taken place in 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 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, ahau cumhu,[ ] that is, a day named ahau, which occupied the th 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[ ] 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[ ] refer to a time fully , years later than the starting point ( ahau cumhu) from which each is reckoned. in other words, maya history is a blank for more than , 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 ahau 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: . that, as stated, after the starting point of maya chronology there is a silence of more than , years, unbroken by a single contemporaneous record, and { } . that after this long period had elapsed all the dated monuments[ ] had their origin in the comparatively short period of four centuries. consequently, it is safe to conclude that no matter what the maya may have believed took place on this date ahau 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 , years simply by using so unwieldy a unit as the -year period or its multiples? a numerical system based on as its primary unit immediately gives rise to exceedingly awkward numbers for its higher terms; that is, , , , , , , etc. indeed, the expression of really large numbers in terms of 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 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 , 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 kin = day kins = uinal = days uinals = tun = days tuns = katun = , days katuns = cycle = , days [ ] cycles = great cycle = , , 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 d place (uinals), { } in which units instead of make unit of the d place, or order next higher (tuns). the break in the regularity of the vigesimal progression in the d place was due probably to the desire to bring the unit of this order (the tun) into agreement with the solar year of days, the number being much closer to than , the third term of a constant vigesimal progression. we have seen on page that the uinals of the haab were equivalent to 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 days more than the tun, thus causing a discrepancy of days as compared with the third place of the chronological system, may have given to these closing days of the haab--that is, the xma kaba kin--the unlucky character they were reputed to possess. the periods were numbered from to , inclusive, units of any order (except the d) always appearing as unit of the order next higher. for example, a number involving the use of kins was written uinal instead. we are now in possession of all the different factors which the maya utilized in recording their dates and in counting time: . the names of their dates, of which there could be only , (the number of dates in the calendar round). . the date, or starting point, ahau cumhu, from which time was reckoned. . 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 , , and , , days; and this number is followed by one of the , 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, ahau cumhu, the date invariably[ ] reached will be found to be the date written at the end of the long number. this method of dating has been called the _initial series_, because when inscribed on a monument it invariably stands _at the head_ of the inscription. the student will better comprehend this initial-series method of dating if he will imagine the calendar round represented by a large cogwheel a, figure , having , teeth, each one of which is { } 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 ahau 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. . diagram showing section of calendar-round wheel.] it is clear that after one complete revolution of a, , days will have passed the starting point b, and that after two revolutions , days will have passed, and after three, , , and so on. indeed, it is only a question of the number of revolutions of a until as many as , , , 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, ahau 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 , , , and that the date recorded by this number of days is akbal cumhu. referring to figure , it is evident that revolutions of the cogwheel a, that is, calendar rounds, will use up , , of the , , days, since × , = , , . consequently, when calendar rounds shall have passed we shall still have left days ( , , - , , = ), which must be carried forward into the next calendar round. the , , st day will be imix cumhu, that is, the day following ahau cumhu (see fig. ); the , , d day will be ik cumhu, and the , , d day, the last of the days in our initial series, akbal 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. { } several examples of this glyph are shown in figure . this sign is composed of four constant elements: . the trinal superfix. . the pair of comblike lateral appendages. . the tun sign (see fig. , _a_, _b_). . the trinal subfix. [illustration: fig. . 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 , _a_, _b_, _e_, this is a grotesque head; in _c_, a natural head; and in _d_, one of the day-signs, ik. this element varies greatly throughout the inscriptions, and, judging from its central position in the "introducing glyph" (itself the most prominent character in every inscription in which it occurs), it must have had an exceedingly important meaning.[ ] a variant of the comblike appendages is shown in figure , _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: ( ) on stela d at copan, where only full-figure glyphs are presented,[ ] the two comblike appendages of the "introducing glyph" appear unmistakably as two fishes. ( ) in some of the earliest stelæ at copan, as stelæ 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 { } stelæ 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. ( ) 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 , _a_, _b_, _e_, and , _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 , the comblike element stands for the sound _ca_ (_c_ hard); while _kal_ in maya means . also the element () stands for the sound _tun_. therefore _catun_ or _katun_ means 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 , 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 , _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. ). it is composed of the trinal superfix and a conventionalized fish (?). mr. goodman calls this glyph (fig. , _a-e_) the sign for the great cycle or unit of the th place (see table viii). he bases this identification on the fact that in the codices units of the th place stand immediately above[ ] units of the th place (cycles), and consequently since this glyph stands immediately above the units of the th place in the inscriptions it must stand for the units of the th place. while admitting that the analogy here is close, the writer nevertheless is inclined to reject mr. goodman's identification on the following grounds: ( ) 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. ( ) units of the th order in the codices invariably have a numerical coefficient, as do all the other orders. ( ) in the only three places in the inscriptions[ ] in which six periods are seemingly recorded, though not as initial series, the th period has a numerical coefficient just as have the other five, and, { } moreover, the glyph in the th position is unlike the forms in figure . ( ) five periods, not six, in every initial series express the distance from the starting point, ahau 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, ahau 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 , , 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 , _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 th order, let us next examine the signs for the remaining orders or periods of the chronological system (cycles, katuns, tuns, uinals, and kins), constantly bearing in mind that these five periods alone express the long numbers of an initial series.[ ] each of the above periods has two entirely different glyphs which may express it. these have been called ( ) the normal form; ( ) 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 { } 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: ( ) on stela d at copan; ( ) on zoömorph b at quirigua; ( ) on east side stela d at quirigua; ( ) on west side stela d at quirigua; ( ) 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 as a period glyph of an initial series. the cycle glyph [illustration: fig. . signs for the cycle: _a-c_, normal forms; _d-f_, head variants.] [illustration: fig. . full-figure variant of cycle sign.] the maya name for the period of the th 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 , _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. , _o-v_, , _l-p_). this has been called the _cauac_ element because it is similar to the sign for the day cauac in the codices (fig. , _b'_), though on rather inadequate grounds the writer is inclined to believe. the head variant of the cycle glyph is shown in figure , _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. ). 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. . signs for the katun: _a-d_, normal forms; _e-h_, head variants.] [illustration: fig. . full-figure variant of katun sign.] the period of the th place or order was called by the maya the _katun_; that is to say, tuns, since it contained units of the d { } order (see table viii). the normal form of the katun glyph is shown in figure , _a-d_. it is composed of the normal form of the tun sign (fig. , _a_, _b_) surmounted by the pair of comblike appendages, which we have elsewhere seen meant , and which were probably derived from the representation of a fish. the whole glyph thus graphically portrays the concept tuns, which according to table viii is equal to katun. the normal form of the katun glyph in the codices (fig. , _c_, _d_) is identical with the normal form in the inscriptions (fig. , _a_, _b_). several head variants are found. the most easily recognized, though not the most common, is shown in figure , _e_, in which the superfix is the same as in the normal form; that is, the element (), which probably signifies 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. , _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 , _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 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. { } the tun glyph [illustration: fig. . signs for the tun: _a-d_, normal forms; _e-h_, head variants.] [illustration: fig. . full-figure variant of tun sign.] the period of the d place or order was called by the maya the _tun_, which means "stone," possibly because a stone was set up every days or each tun or some multiple thereof. compare so-called hotun or katun stones described on page . the normal sign for the tun in the inscriptions (see fig. , _a_, _b_) is identical with the form found in the codices (see fig. , _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 , _d_, e. the determining characteristic of the head variant of the tun glyph, however, is the fleshless lower jaw (), as shown in figure _f_, _g_, though even this is lacking in some few cases. the form shown in figure , _h_, is found at palenque, where it seems to represent the tun period in several places. the head of the full-figure form (fig. ) has the same fleshless lower jaw for its essential characteristic as the head-variant forms in figure . 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. . signs for the uinal: _a-c_, normal forms; _d-f_, head variants.] [illustration: fig. . full-figure variant of uinal sign on zoömorph b, quirigua.] [illustration: fig. . full-figure variant of uinal sign on stela d, copan.] the period occupying the d 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 days in each lunation may account for the application of its name to the -day period. the normal form of the uinal glyph in the inscriptions (see fig. , _a_, _b_) is practically identical with the form in the codices (see fig. , _c_). { } sometimes the subfixial element () is omitted in the inscriptions, as in figure , a. the head variant of the uinal glyph (fig. , _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. ,) 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 . 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 ( : p. ) 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 -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 -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. { } the kin glyph [illustration: fig. . signs for the kin: _a_, _b_, normal forms; _c_, _d_, miscellaneous; _e-k_, head variants.] the period of the st, 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 , _a_, which is practically identical with the form in the codices (fig. , _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 , _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 , 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 , _d_; indeed, the writer recalls but two places where it occurs: stela 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. , _e'_) inverted and a subfixial element which varies in each of the two cases. these variants (fig. , _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 , _e_, may be readily recognized by its subfixial element () and the element (+), { } both of which appear in the normal form, figure , a. in some cases, as in figure , _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. , _i_, _j_) has as its essential element the banded headdress. a very unusual head variant is that shown in figure , _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 , _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, eb pop and ben 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. ), the head of which is similar to the one in figure , _i_, _j_, having the same banded headdress.[ ] [illustration: fig. . 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: . _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 per cent of the total[ ] against per cent, the periods in the remaining 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. . _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 years, while in initial series normal-form period glyphs do not occur until nearly years later, or about years after the first use of head variants for the same purpose. . _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 { } nearly years apart in point of time, the early form of the tun sign in figure , _a_, closely resembles the late form shown in _b_ of the same figure, as to its essentials. or again, although years apart, the early form of the katun sign in figure , _c_, is practically identical with the form in figure , 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 , _e_, precedes the one in figure , _f_, by some years, the same essential element--the large mouth curl--appears in both. again, although years separate the cycle signs shown in _g_ and _h_, figure , the essential characteristic of the early form (fig. , _g_), the hand, is still retained as the essential part of the late form (_h_). [illustration: fig. . period glyphs, from widely separated sites and of different epochs, showing persistence of essential elements.] . _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 ( ), 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,[ ] was nevertheless somewhat lengthy, since in order to express a single date by means of it eight distinct glyphs were required, namely: ( ) the introducing glyph; ( ) the cycle glyph; { } ( ) the katun glyph; ( ) the tun glyph; ( ) the uinal glyph; ( ) the kin glyph; ( ) the day glyph; ( ) 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 , 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 d, , a. d., may th, , a. d., july th, , a. d., december th, , a. d.; or in other words, repeating in each case the designation of time elapsed from the starting point of christian chronology. the maya obviated this needless repetition by recording but one initial series date on a monument;[ ] and from this date as a new point of departure they proceeded to reckon the number of days to the next date recorded; from this date the numbers of days to the next; and so on throughout that inscription. by this device the position of any date in the long count (its initial series) could be calculated, since it could be referred back to a date, the initial series of which was expressed. for example, the terminal day of the initial series given on page is akbal cumhu, and its position in the long count is fixed by the statement in cycles, katuns, tuns, etc., that , , days separate it from the starting point, ahau cumhu. now let us suppose we have the date cimi cumhu, which is recorded as being days later than the day akbal cumhu,[ ] the initial series of which is known to be , , . it is clear that the initial series corresponding to the date cimi cumhu, although not actually expressed, will also be known since it must equal , , (initial series of akbal cumhu) + (distance from akbal cumhu to cimi cumhu), or , , . therefore it matters not whether we count three days forward from akbal cumhu, or whether we count , , days forward from the starting point of maya chronology, ahau cumhu since in each case the date reached will be the same, namely, cimi 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 { } 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 kins and the date cimi 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 at piedras negras) does not occur until some 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 , dates of the calendar round, and will recur at intervals of every 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 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. { } 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.[ ] it is clear also that in this method only the name ahau out of the 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: . the higher periods, as the uinal, tun, katun, and cycle are exactly divisible by in every case (see table viii), and-- . they are all counted from a day, ahau, that is, ahau 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: . a particular period of the long count, as cycle , or katun , etc. . the date which ends the particular period recorded, as ahau ceh, or ahau muan, the closing dates respectively of cycle and katun of cycle ; and . 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: ( ) the element shown as the prefix or superfix in figure , _a-h_, _t_, all of which are forms of the same variant; ( ) the flattened grotesque head appearing either as the prefix or superfix in _i_, _r_, _u_, _v_ of the same figure; and ( ) the hand, which appears as the main element in the forms shown in figure , _j-q_. the two first of these never stand by themselves but always modify some other sign. the first (fig. , _a-h_, _t_) is always attached to the sign of the period whose end is recorded either as a { } superfix (see fig. , _a_, whereby the end of cycle is indicated[ ]), or as a prefix (see _t_, whereby the end of katun is recorded). the second form is seen as a prefix in _u_, whereby the end of katun is recorded, and in _i_, whereby the end of katun is shown. this latter sign is found also as a superfix in _r_. [illustration: fig. . 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. , _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. , _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. { } the use of the hand as expressing the meaning "ending" is quite natural. the aztec, we have seen, called their -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 , years in round numbers, as against , years in the other methods. for all practical purposes, however, , years was as accurate as , 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 ( : pp. 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 , -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 , 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 { } which they occupied in the cycle, as katun , for example, but by the different days ahau with which they ended, as katun ahau, katun ahau, etc. see table ix. table ix.--sequence of katuns in u kahlay katunob katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau katun ahau, etc. the peculiar retrograding sequence of the numerical coefficients in table ix, decreasing by from katun to katun, as , , , , , , , , , etc., results directly from the number of days which the katun contains. since the possible numerical coefficients, to , inclusive, succeed each other in endless repetition, following immediately after , 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 s possible from the number to be counted forward. the mathematical demonstration of this fact follows. if we count forward from any given coefficient, the same coefficient will be reached as if we had counted forward but . this is true because, ( ) there are only numerical coefficients, and ( ) these follow each other without interruption, following immediately after ; hence, when has been reached, the next coefficient is , not ; therefore or any multiple thereof may be counted forward or backward from any one of the numerical coefficients without changing its value. this truth enables us to formulate the following rule for finding numerical coefficients: deduct all the multiples of possible from the number to be counted forward, and then count forward the remainder from the known coefficient, subtracting if the resulting number is above , since 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 ahau, is named after its ending day, ahau. now let us see whether the application of this rule will give us ahau as the ending day of the next katun. the number to be counted forward from ahau is , , the number of days in one katun; therefore we must first deduct from , all the s possible. , ÷ = - / . in other words, after we have deducted all the 's possible, that is, { } of them, there is a remainder of . this the rule says is to be added (or counted forward) from the known coefficient (in this case ) in order to reach the resulting coefficient. + = . since this number is not above , is not to be deducted from it; therefore the coefficient of the ending day of the second katun is , 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 . again, we have , to count forward from the known coefficient, in this case (the coefficient of the ending day of the second katun). but we have seen above that if we deduct all the s possible from , there will be a remainder of ; consequently this remainder must be added to , the known coefficient. + = ; but since this number is above , we must deduct from it in order to find out the resulting coefficient. - = , and 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 , is always the number of days in any katun, after deducting all the s possible the remainder will always be , which has to be added to the known coefficient to find the unknown. but since has to be deducted from the resulting number when it is above , subtracting will always give us exactly the same coefficient as adding ; consequently we may formulate for determining the numerical coefficients of the ending days of katuns the following simple rule: subtract 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 -day year, are not mentioned. for example, the first katun was not called katun ahau zac, but simply katun 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 ahau, it might occur anywhere within a period of , days, or nearly years, and yet fulfill the given conditions. in other words, no matter how accurately this katun ahau itself might be fixed in a _long_ stretch of time, there was always the possibility of a maximum error of about years in { } such dating, since the statement of the katun did not fix a date any closer than as occurring somewhere within a certain -year period. when greater accuracy was desired the particular tun in which the date occurred was also given, as tun of katun ahau. this fixed a date as falling somewhere within a certain 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 imix zip of tun of katun ahau. a date thus described satisfying all the given conditions could not recur until after the lapse of at least , years. the great majority of events, however, recorded by this method are described only as occurring in some particular katun, as katun 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 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 ahau, for example, in table ix would recur in the sequence after the lapse of thirteen katuns, or about 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[ ] 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 years, within a period of more than , 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 ( : pp. et seq.) has pointed out { } 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 (_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 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 , _a-d_, are all from palenque; the knot variants (_e-h_ of the same figure) are found at both copan and quirigua. [illustration: fig. . "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 , 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,[ ] 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 { } katun ending days and the events which were connected more or less closely with it. in other words, the monuments were erected at short intervals[ ] and probably recorded events contemporaneous with their erection, while the u kahlay katunob, on the other hand, were historical summaries reaching back to a remote time. the former were the 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 , _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. ) 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, ahau, ahau, 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 ( : p. ) 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 ( : lib. iv, cap. v, p. ) 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 { } 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 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 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 { } 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 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: ( ) initial-series dating; ( ) secondary-series dating; ( ) calendar-round dating; ( ) period-ending dating; ( ) 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 and (that is, ) with the solar year conceived as containing days, and all were recorded by the same vigesimal system of numeration; that is: . all used precisely the same dates, the , dates of the calendar round; . all may be reduced to the same fundamental unit, the day; and . 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: . the absolute continuity of all sequences which had to do with the counting of time: the numerical coefficients of the day names, the day names, the days of the tonalamatl, the positions of the haab, the , 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. . all maya periods expressed not current time, but passed time, as in the case of our hours, minutes, and seconds. on these two facts rests the whole maya conception of time. { } chapter iv maya arithmetic the present chapter will be devoted to the consideration of maya arithmetic in its relation to the calendar. it will be shown how the maya expressed their numbers and how they used their several time periods. in short, their arithmetical processes will be explained, and the calculations resulting from their application to the calendar will be set forth. the maya had two different ways of writing their numerals,[ ] namely: ( ) with normal forms, and ( ) with head variants; that is, each of the numerals up to and including 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 , , , , , , and , , 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 , 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 , , , , , and by applying the essential characteristic of the head variant for to the head variants for , , , , , and , respectively, just as the sign for --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 to , inclusive. both of these notations occur in the inscriptions, but with very few exceptions[ ] no head-variant numerals have yet been found in the codices. bar and dot numerals the maya "roman numerals"--that is, the normal-form numerals, up to and including --were expressed by varying combinations of two elements, the dot (.) which represented the numeral, or numerical value, , and the bar, or line (--) which represented the numeral, or numerical value, . by various combinations of these two { } elements alone the maya expressed all the numerals from to , inclusive. the normal forms of the numerals in the codices are shown in figure , in which one dot stands for , two dots for , three dots for , four dots for , one bar for , one bar and one dot for , one bar and two dots for , one bar and three dots for , one bar and four dots for , two bars for , and so on up to three bars and four dots for . the normal forms of the numerals, in the inscriptions (see fig. ) 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. ). all these decorations, however, in no way affect the numerical value of the bar and the dot, which remain and , 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. . normal forms of numerals to , inclusive, in the codices.] [illustration: fig. . normal forms of numerals to , inclusive, in the inscriptions.] [illustration: fig. . examples of bar and dot numeral , 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 , , , , , , , and , that is, all which involve the use of _one_ or _two_ dots in their composition.[ ] in the inscriptions, as we have seen in chapter ii, every glyph was a balanced picture, exactly fitting its allotted space, even at the cost of occasionally losing some of its elements. to have expressed the numbers , , , , , , , and 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. , _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 , , , and , respectively) the single dot does not fill the space on the left-hand[ ] side of the bar, or bars, as the case may be, and consequently { } the left-hand edge of the glyph block in each case is ragged. similarly in _b_, _d_, _f_, and _h_, the numbers , , , and , 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 ( , , , , , , , and ) had to be recorded, other elements of a purely ornamental character were introduced to fill the empty spaces. in figure , _a_, _c_, _e_, _g_, the spaces on each side of the single dot have been filled with ornamental { } 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 . [illustration: fig. . examples showing the way in which the numerals , , , , , , , and are _not_ used with period, day, or month signs.] [illustration: fig. . examples showing the way in which the numerals , , , , , , , and _are_ used with period, day, or month signs. note the filling of the otherwise vacant spaces with ornamental elements.] [illustration: fig. . normal forms of numerals to , 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 , , , , , , , and , 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 , , are frequently mistaken for one another, as are also , , and ; , , and ; and , , and . the student must exercise the greatest caution at all times in identifying these { } 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 ( b: p. ) gives this extract, accompanied by the drawing shown in figure , 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. , footnote , for the single exception to this rule). by the development of a special character to represent the number 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 . 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 ,[ ] because { } ( ) as we have seen in table viii, units of any order (except the d, in which only were required) were equal to unit of the order next higher, and consequently could not be attached to any period-glyph, since this number of periods (with the above exception) was always recorded as period of the order next higher; and ( ) although there were positions in each period except the uinal, as kins in each uinal, tuns in each katun, katuns in each cycle, these positions were numbered not from to , but on the contrary from to , a system which eliminated the need for a character expressing . [illustration: fig. . sign for in the codices.] in spite of the foregoing fact, however, the number has been found in the codices (see fig. ). a peculiar condition there, however, accounts satisfactorily for its presence. in the codices the sign for 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,[ ] according to the maya point of view, and consequently some sign was necessary which should stand for regardless of its position or relation to others. the sign shown in figure 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. . sign for in the codices.] if the maya numerical system had no vital need for a character to express the number , a sign to represent zero was absolutely { } 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 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. ) is lenticular; it presents an interior decoration which does not follow any fixed scheme.[ ] only a very few variants occur. the last one in figure 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 d, or uinal, place in the texts in which they occur, though whether this fact has influenced their variation is unknown. [illustration: fig. . sign for in the inscriptions.] [illustration: fig. . figure showing possible derivation of the sign for 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 shown in fig. .] 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 . they are common and are unmistakable. an interesting origin for this sign has been suggested by mr. a. p. maudslay. on pages and of the codex tro-cortesiano[ ] the days of a tonalamatl are graphically represented as forming the outline shown in figure , a. half of this (see fig. , _b_) is the sign which stands for zero (compare with fig. ). 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 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 { } 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. ), which occurs throughout the inscriptions and in the dresden codex,[ ] 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 divisions of the haab, or year, and for no other. in other words, it denotes the positions pop, uo, zip, etc., which, as we have seen (pp. , ), corresponded with our first days of the months. the forms shown in figure , _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. , _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 , _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 ( ) can be attached only to the glyphs for the divisions of the haab, or year, that is, the uinals and the xma kaba kin; in other words, it is found only with the glyphs shown in figures and , the signs for the months in the inscriptions and codices, respectively. [illustration: fig. . special sign for used exclusively as a month coefficient.] ( ) it can occur only in connection with one of the four day-signs, ik, manik, eb, and caban (see figs. , _c_, _j_, _s_, _t_, _u_, _a'_, _b'_, and , _c_, _d_, _k_, _r_, _x_, _y_, respectively), since these four alone, as appears in table vii, can occupy the (zero) positions in the several divisions of the haab. { } [illustration: fig. . 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 . under each is given its meaning in english.[ ] 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 in figure and the sign for zero in figure . 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. { } 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.[ ] 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 , 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, , , , , , , , , , , , , , [ ] 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 and up to but _not including_ , the head numerals are expressed by the application of the essential characteristic of the head for to the heads for to , inclusive. no head forms for the numeral 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 , , and , 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. { } [illustration: fig. . head-variant numerals to , inclusive.] the head-variant numerals are shown in figures - . taking these up in their numerical order, let us commence with the head signifying ; see figure , _a-e_. the essential element of this head is its forehead ornament, which, to signify the number , 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 (fig. , _a-f_). except for their forehead ornaments the heads for and are almost identical, and great care must be exercised in order to avoid mistaking one for the other. { } the head for (fig. , _f_, _g_) has been found only twice in the inscriptions--on lintel 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 , admitting at the same time that the evidence is insufficient. [illustration: fig. . head-variant numerals to , inclusive.] the head for is shown in figure , _h_, _i_. its determining characteristic is the fillet, or headdress. the head for is shown in figure , _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_). { } the head for (fig. , _n-s_) is always to be identified by its peculiar headdress (), which is the normal form of the tun sign. compare figure , _a_, b. the same element appears also in the head for (see fig. , _b-e_). the head for is one of the most constant of all the head numerals. [illustration: fig. . head-variant numerals to , inclusive, and .] the head for (fig. , _t-v_) is similarly unmistakable. it is always characterized by the so-called hatchet eye (), which appears also in the head for (fig. , _f-i_). the head for (fig. , _w_) is found only once in the inscriptions--on the east side of stela d at quirigua. its essential characteristic, { } the large ornamental scroll passing under the eye and curling up in front of the forehead (), is better seen in the head for (fig. , _j-m_). the head for is shown in figure , _a-f_. it is very similar to the head for , as previously explained (compare figs. , _a-e_ and , _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 , _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 (fig. , _n-q_) follow the first variants (fig. , _a_, _b_), having the large curl, except _q_, which is similar to _d_ in having a flaring element instead. the head for 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 , but before the completion of cycle . consequently, is the coefficient attached to the cycle glyph in almost all initial series.[ ] the head for is shown in figure , _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 head has a beard, though this is not a constant element as are the dots, which appear also in the head for . compare figure , _r_. the head for (fig. , _m-r_) is extremely important since its essential element, the fleshless lower jaw (), stands for the numerical value , in composition with the heads for , , , , , , and , to form the heads for , , , , , , and , respectively. the head is clearly the fleshless skull, having the truncated nose and fleshless jaws (see fig. , _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 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 . the head for (fig. , _s_) has been found only once in the inscriptions, namely, on lintel 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 and . similarly, the head for (fig. , _t-v_) has no fleshless lower jaw, and consequently can not be composed of the heads for and . 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. { } the head for is shown in figure , _w-b'_. only the first of these forms, _w_, however, is built on the + basis. here we see the characteristic head with its banded headdress or fillet (compare _h_ and _i_, fig. ), to which has been added the essential element of the head, the fleshless lower jaw, the combination of the two giving the head for . the other form for seems to be a special character, and not a composition of the essential elements of the heads for and , as in the preceding example. this form of the head (fig. , _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 (fig. , _a_) is found but once--in the inscriptions on the west side of stela f at quirigua. it has the fleshless lower jaw denoting , while the rest of the head shows the characteristics of --the bulging eye and snaglike tooth (compare fig. , _j-m_). the curl protruding from the back part of the mouth is wanting because the whole lower part of the head has been replaced by the fleshless lower jaw. the head for (fig. , _b-e_) is composed of the essential element of the head (the tun sign; see fig. , _n-s_) and the fleshless lower jaw of the head for . the head for (fig. , _f-i_) is characterized by the fleshless lower jaw and the hatchet eye of the head. compare figures , _t-v_, and , _m-r_, which together form ( + ). the head for (fig. , _j-m_) is composed of the essential element of the head (the scroll projecting above the nose; see fig. , _w_) and the fleshless lower jaw of the head for . the head for (fig. , _n-q_) has the characteristic forehead ornament of the head (compare fig. , _a-f_) and the fleshless lower jaw denoting . only one example (fig. , _r_) of the 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 head and the fleshless lower jaw of the head appearing. the head for (zero), figure , _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 { } 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 , the head variant for zero in figure , _s-w_, and the form for zero shown in figure 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. , _s-w_) receives striking corroboration from the rather unusual sign for zero shown in figure , to which attention was called above. the essential elements of this sign are[ ] ( ) the clasped hand, identical with the hand in the head-variant forms for zero, and ( ) 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 , _l_, _m_, _n_, the first two of which accompany the closing date of katun , and the last the closing date of cycle . the resemblance of these three "ending signs" to the last three forms in figure 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. . a sign for , used also to express the idea "ending" or "end of" in period-ending dates. (see figs. and _s-w_, for forms used interchangeably in the inscriptions to express the idea of 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 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 { } 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 to , inclusive +-------------+---------------------------------------------------------+ | forms | characteristics | +-------------+---------------------------------------------------------+ | head for | clasped hand across lower part of face. | | head for | forehead ornament composed of _more than one part_. | | head for | oval in upper part of head. (?) | | head for | banded headdress or fillet. | | head for | bulging eye with square irid, snaglike front tooth, | | | curling fang from back of mouth. | | head for | normal form of tun sign as headdress. | | head for | "hatchet eye." | | head for | large scroll passing under eye and curling up in | | | front of forehead. | | head for | forehead ornament composed of _one part_. | | head for | dots on lower cheek or around mouth and in some | | | cases beard. | | head for | fleshless lower jaw and in some cases other | | | death's-head characteristics, truncated nose, etc. | | head for | undetermined. | | head for | undetermined; type of head known, however. | | head for | (_a_) long pendulous nose, bulging eye, and curling | | | fang from back of mouth. | | | (_b_) head for with fleshless lower jaw of head | | | for . | | head for | head for with fleshless lower jaw of head for . | | head for | head for with fleshless lower jaw of head for . | | head for | head for with fleshless lower jaw of head for . | | head for | head for with fleshless lower jaw of head for . | | head for | head for with fleshless lower jaw of head for . | | head for | head for with fleshless lower jaw of head for . | +-------------+---------------------------------------------------------+ mention should be made here of a numerical form which can not be classified either as a bar and dot numeral or a head variant. this is the thumb (), which has a numerical value of one. we have seen in the foregoing pages the different characters which stood for the numerals to , inclusive. the next point claiming our attention is, how were the higher numbers written, numbers which in the codices are in excess of , , , and in the inscriptions, in excess of , , ? in short, how were numbers so large expressed by the foregoing twenty ( to , 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: . by using the numbers to , inclusive, as multipliers with the several periods of table viii (reduced in each case to units of the lowest order) as the multiplicands, and-- . by using the same numbers[ ] 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. { } 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. . 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. { } first method of numeration [illustration: fig. . examples of the first method of numeration, used almost exclusively in the inscriptions.] in the first of the above methods the numbers to , inclusive, were expressed by multiplying the kin sign by the numerals[ ] to in turn. thus, for example, days was written as shown in figure , _a_, days as shown in _b_, and days as shown in _c_ of the same { } figure. in other words, up to and including the numbers were expressed by prefixing the sign for the number desired to the kin sign, that is, the sign for day.[ ] the numbers to , inclusive, were expressed by multiplying both the kin and uinal signs by the numerical forms to , and adding together the resulting products. for example, the number was written as shown in figure , d. we have seen in table viii that uinal = kins, consequently uinals (the being indicated by bars and dots) = kins. however, as this number falls short of by kins, it is necessary to express these by kins, which are written immediately below the uinals. the sum of these two products = . again, the number is written as in figure , e. the uinals (three bars attached to the uinal sign) = × = 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 kins, or "no kins" is written immediately below the uinals, and + = . one more example will suffice to show how the numbers to were expressed. in figure , _f_, the number is shown. the uinals = × = kins. but this number falls short of by , which is therefore expressed by kins written immediately below the uinals: and the sum of these two products is , the number to be recorded. the numbers to , , inclusive, are indicated by multiplying the kin, uinal, and tun signs by the numerals to , and adding together the resulting products. for example, the number is shown in figure , _g_. we have seen in table viii that tun = uinals; but uinals = kins ( × = ); therefore tun also = 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 uinals immediately below the tun, and kins immediately below the uinals. the sum of these three products equals ( + + = ). again, the number , is shown in figure , _h_. the tuns = × = , kins. this falls short of , by only units of the first order ( kins), therefore no uinals are involved in forming this number, a fact which is shown by the use of uinals between the tuns and kins. the sum of these three products = , ( , + + ). again, in figure , _i_, the number , is recorded. the tuns = × = , kins, which falls short of , kins by , - , = kins. but kins = uinals with no kins { } remaining. consequently, the sum of these products equals , ( , + + ). the numbers , to , were expressed by multiplying the kin, uinal, tun, and katun signs by the numerals to , inclusive, and adding together the resulting products. for example, figure , _j_, shows the number , . we have seen in table viii that katun = tuns, and we have seen that tuns = , kins ( × ); therefore katun = , kins. this number falls short of the number recorded by exactly kins, or in other words, no tuns or uinals are involved in its composition, a fact shown by the tuns and uinals between the katun and the kins. the sum of these four products = , ( , + + + ). the number , is shown in figure , _k_. the katuns = , ; the tuns, , ; the uinals, ; and the kins, . the sum of these four products = , ( , + , + + ). again, the number , is shown in figure , _l_. the katuns = , ; the tuns, , ; the uinals, ; and the kins, . the sum of these four products = , ( , + , + + ). the numbers , to , , (the highest number, according to some authorities, which has been found[ ] in the inscriptions) were expressed by multiplying the kin, uinal, tun, katun, and cycle signs by the numerals to , inclusive, and adding together the resulting products. for example, the number , is shown in figure , _m_. we have seen in table viii that cycle = katuns, but katuns = , kins; therefore cycles = , kins; and katuns = , kins; and tuns, kins; and uinals, kins; and the kins, kins. the sum of these five products equals the number recorded, , ( , + , + + + ). the highest number in the inscriptions upon which all are agreed is , , , as shown in figure , _n_. it equals cycles ( × , ), and consequently all the periods below--the katun, tun, uinal, and kin--are indicated as being used times. number of cycles in a great cycle this brings us to the consideration of an extremely important point concerning which maya students entertain two widely different 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 , and so far as the codices are concerned, as we shall presently see, this { } number was in fact the only unit of progression used, except in the d order, in which instead of units were required to make unit of the d 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 d place, just noted. see table viii. in the inscriptions, however, there is some ground for believing that only units of the th order (cycles), not , were required to make unit of the th order, or great cycle. both mr. bowditch ( : app. ix, - ) and mr. goodman ( : p. ) 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: . that the cycles in the inscriptions are numbered from to , inclusive, and not from to , inclusive, as in the case of all the other periods except the uinal, which is numbered from to , inclusive. . that the only two initial series which are not counted from the date ahau cumhu, the starting point of maya chronology, are counted from a date ahau zotz, which is exactly cycles in advance of the former date. let us examine the passages in the inscriptions upon which these points rest. in three places[ ] in the inscriptions the date ahau cumhu is declared to have occurred at the end of a cycle ; that is, in these three places this date is accompanied by an "ending sign" and a cycle . in another place in the inscriptions, although the starting point ahau cumhu is not itself expressed, the second cycle thereafter is declared to have been a cycle , not a cycle , as it would have been had the cycles been numbered from to , inclusive, like all the other periods.[ ] in still another place the ninth cycle after the starting point (that is, the end of a cycle ) is not a cycle in the _following_ great cycle, as would be the case if the cycles were numbered from to , inclusive, but a cycle , as if the cycles were numbered from to . again, the end of the tenth cycle after the starting point is recorded in several places, but not as cycle of the following great cycle, as if the cycles were numbered from to , inclusive, but as cycle , as would be the case if the cycles were numbered from to . the above examples leave little doubt that the cycles were numbered from to , inclusive, and not from to , 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. { } but because this is true it does not necessarily follow that cycles made great cycle. before deciding this point let us examine the two initial series mentioned above, as _not_ proceeding from the date ahau cumhu, but from a date ahau zotz, exactly 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 ahau 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 ahau 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 ahau cumhu.[ ] however, by counting _backward_ each of these long numbers from their respective terminal days, ahau tzec, in the case of the palenque initial series, and ahau 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 ahau zotz, exactly 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 cycles later than the starting point of these two. because of this fact and the fact that the cycles were numbered from to , inclusive, as shown above, mr. bowditch and mr. goodman have reached the conclusion that in the inscriptions only cycles were required to make 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 ( ) as in the codices: . in the codices where six orders (great cycles) are recorded it takes of the th order (cycles) to make of the th 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 th order in the inscriptions was formed in the same way. . the numerical system in both the codices and inscriptions is identical even to the slight irregularity in the second place, where only instead of units were required to make of the third place. it would seem probable, therefore, that had there been any irregularity in the th place in the inscriptions (for such the use of in a vigesimal system must be called), it would have been found also in the codices. { } . moreover, in the inscriptions themselves the cycle glyph occurs at least twice (see fig. , _a_, _b_) with a coefficient greater than , which would seem to imply that more than cycles could be recorded, and consequently that it required more than to make of the period next higher. the writer knows of no place in the inscriptions where kins, uinals, tuns, or katuns are recorded, each of these being expressed as uinal, tun, katun, and cycle, respectively.[ ] therefore, if cycles had made great cycle, cycles would not have been recorded, as in figure , _a_, but as great cycle and cycle; and cycles would not have been recorded, as in _b_ of the same figure, but as great cycle and cycles. the fact that they were not recorded in this latter manner would seem to indicate, therefore, that more than cycles were required to make a great cycle, or unit of the th place, in the inscriptions as well as in the codices. [illustration: fig. . signs for the cycle showing coefficients above : _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 ( ) on pages - . 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 cycles. assuming for the moment that there were cycles in a great cycle; it is clear that if this were the case cycles could never be recorded in the inscriptions, for the reason that, being equal to 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, uinal never appears as kins; tun is never written as its equivalent, uinals; katun is never recorded as tuns, etc. consequently, if a great cycle composed of cycles had come to its end with the end of a cycle , which fell on a day ahau cumhu, such a cycle 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 cycles in a great cycle, the cycles would have been numbered from to , inclusive, and the last, cycle , would have been recorded instead as completing some great cycle. it is necessary to { } 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 ahau cumhu, which an "ending sign" and a cycle further declare fell at the close of a cycle , this does not indicate that there were 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 , 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 cycles in a great cycle, we have equal grounds for saying that the great cycle contained only cycles. for example, on zoömorph g at quirigua the date ahau zip is accompanied by an "ending sign" and cycle , which on this basis of interpretation would signify that a great cycle had only cycles. similarly, it could be shown by such an interpretation that in some cases a cycle had katuns, that is, where the end of a katun was recorded, or katuns, where the end of a katun was recorded. all such places, including the date ahau cumhu, which closed a cycle 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 , or a certain cycle , or a certain katun , or a certain katun , 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 to , inclusive, and then began again with . 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 ik pop akbal pop kan pop chicchan pop cimi pop manik pop lamat pop muluc pop oc pop chuen pop eb pop ben pop ix pop men pop cib pop caban pop eznab pop cauac pop ahau pop imix pop the numerical coefficients of the days, as we have seen, were numbered from to , inclusive, and then began again with . see { } table xi, in which the 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 , the numbers showing the positions of these days in the month continue up through . in other words, two different sets of numerals were used in describing the maya days: ( ) the numerals to , inclusive, the coefficients of the days, and an integral part of their names; and ( ) the numerals to , 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 ( ) 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 to , inclusive, it does not necessarily follow that the next higher period (the uinal) contained only days. similarly, the writer believes that while the cycles were undoubtedly numbered--that is, named--from to , inclusive, like the coefficients of the days, it took of them to make a great cycle, just as it took 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 ahau, although it occupied the _first_ position in the cycle. again, the name of the second katun in the sequence is katun 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 to , inclusive, we may interpret them as follows: when we find the date ahau cumhu in the inscriptions, accompanied by an "ending sign" and a cycle , that "cycle ," even granting that it stands at the end of some great cycle, does not signify that there were only cycles in the great cycle of which it was a part. on the contrary, it records only the end of a particular cycle , being a period-ending date pure and simple. such passages no more fix the length of the great cycle as containing cycles than does the coefficient of the day name ix in table xi limit the number of days in a uinal to , or, again, the of the katun name ahau in table ix limit the number of katuns in a cycle to . this explanation not only accounts for the use of the cycles or cycles, as { } shown in figure , _a_, _b_, but also satisfactorily provides for the enumeration of the cycles from to , inclusive. if the date " ahau cumhu ending cycle " be regarded as a period-ending date, not as indicating that the number of cycles in a great cycle was restricted to , the next question is--did a great cycle also come to an end on the date ahau cumhu--the starting point of maya chronology and the closing date of a cycle ? that it did the writer is firmly convinced, although final proof of the point can not be presented until numerical series containing more than terms shall have been considered. (see pp. - for this discussion.) the following points, however, which may be introduced here, tend to prove this condition: . 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. . moreover, it would seem as though the natural cycle with which to commence counting time would be a _cycle _, and if this were done time would have to be counted from a _cycle _, since a cycle could follow only a cycle . on these two probabilities, together with the discussion on pages - , 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 , which was reckoned from the close of a great cycle whose ending cycle was a cycle and whose ending day fell on the date ahau cumhu. the second point (see p. ) on which rests the hypothesis of " 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 cycles in advance of the other, or more than , years earlier than the beginning of their chronology, and more than , years earlier than the beginning of their historic period. that this remoter starting point, ahau 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 - . on the contrary, the material given there tends to show that although the cycle which ended on the day ahau zotz was also named cycle ,[ ] it was the th division of the grand cycle which ended on the day ahau cumhu, { } 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 cycles. let us return to the discussion interrupted on page , where the first method of expressing the higher numbers was being explained. we saw there how the higher numbers up to and including , , were written, and the digression just concluded had for its purpose ascertaining how the numbers above this were expressed; that is, whether or units of the th order were equal to unit of the th order. it was explained also that this number, , , , was perhaps the highest which has been found in the inscriptions. three possible exceptions, however, to this statement should be noted here: ( ) on the east side of stela n at copan six periods are recorded (see fig. ); ( ) on the west panel from the temple of the inscriptions at palenque six and probably _seven_ periods occur (see fig. ); and ( ) on stela at tikal eight and perhaps _nine_ periods are found (see fig. ). 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 , , . 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. , ) 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. ), 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 ( ahau cumhu) in a much grander chronological scheme, as will appear presently. [illustration: fig. . part of the inscription on stela n, copan, showing a number composed of six periods.] [illustration: fig. . part of the inscription in the temple of the inscriptions, palenque, showing a number composed of seven periods.] [illustration: fig. . part of the inscription on stela , tikal (probably an initial series), showing a number composed of eight periods.] the first of these three numbers (see fig. ), if all its six periods belong to the same series, equals , , . although the order of the several periods is just the reverse of that in the numbers in figure , 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 with the highest period involved and reading up, a ,[ ] the great cycles = , , kins (see table viii, in which great cycle = , , , and consequently = × , , = { } , , ); a , the cycles = , , kins ( × , ); a , the katuns = , kins ( × , ); a , the tuns = , kins ( × ); a , the uinals, kins; and the kins, kins. the sum of these products = , , + , , + , + , + + = , , . the second of these three numbers (see fig. ), if all of its seven terms belong to one and the same number, equals , , . commencing at the bottom as in figure , the first term a , has the coefficient . 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 { } great cycle = , , ; therefore the great-great cycle = twenty times this number, or , , . our text shows, however, that seven of these great-great cycles are used in the number in question, therefore our first term = , , . the rest may be reduced by means of table viii as follows: b , great cycles = , , ; a , cycles = , ; b , katuns = , ; a , tun = ; b , uinals = ; b , kin = . the sum of these ( , , + , , + , + , + + + ) = , , . the third of these numbers (see fig. ), if all of its terms belong to one and the same number, equals , , , . commencing with a , this has a coefficient of . since it immediately follows the great-great cycle, which we found above consisted of , , , we may assume that it is the great-great-great cycle, and that it consisted of great-great cycles, or , , , . since its coefficient is only , this large number itself will be the first term in our series. the rest may readily be reduced as follows: a , great-great cycles = , , ; a , great cycles = , , ; a , cycles = , , ; a , katuns = , ; a , tuns = , ; a , uinals = ; a , kins = .[ ] the sum of these ( , , , + , , + , , + , , + , + , + + ) = , , , , the highest number found anywhere in the maya writings, equivalent to about , , 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 cycles of the first number (see a , fig. ) would then prove conclusively that more than cycles were required to make a great cycle in the inscriptions as well as in the codices. and furthermore, the great cycles in a , figure , the in b , figure , and the in a , figure , would also prove that more than 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 ( : p. ) has suggested in the case of the copan inscription (fig. ) that only the lowest four periods--the katuns, the tuns, the uinals, and the kins--a , a , and a ,[ ] here form the number; and that if this number is counted backward from the initial series of the inscription, it will reach a katun of the preceding cycle. finally, mr. goodman { } believes this katun is declared in the glyph following the katuns (a ), which the writer identifies as cycles, and consequently according to the goodman interpretation the whole passage is a period-ending date. mr. bowditch ( : p. ) 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 (a ). 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 . this glyph (a ) 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 , _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 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. and , 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 , a , and , b (see fig. , _a_, _b_), and the head variant in figure , a . (see fig. , _d-f_.) below the uinal sign in a , figure , and a , figure , and above a , in figure 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 , _d-g_. in the copan inscription (fig. ) the katun glyph, a , 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 , _e-h_. in the palenque and tikal texts (see { } figs. , b , and , a , respectively), on the other hand, the katun is expressed by its normal form, which is identical with the normal form shown in figure , _a_, b. in figures , a , and , a , the cycle is expressed by its head variant, and the determining characteristic, the clasped hand, appears in both. compare the cycle signs in figures , a , and , a , with the head variant for the cycle shown in figure ; _d-f_. the cycle glyph in the tikal text (fig. , a ) is clearly the normal form. (see fig. , _a-c_.) the glyph following the cycle sign in these three texts (standing above the cycle sign in figure at a ) probably stands for the period of the sixth order, the so-called great cycle. these three glyphs are redrawn in figure , _a-c_, respectively. in the copan inscription this glyph (fig. , _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 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 , _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. . 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 , 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 , _a_, the head variant has the same clasped hand as the head-variant cycle sign in the same text (see fig. , a ), which, as we have seen elsewhere, is the determining characteristic of the head variant for the cycle. in figure , _b_, _c_, the normal forms there presented contain the entire normal form for the cycle sign; compare figure , _a_, c. indeed, except for its superfix, the glyphs in figure , _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 , _b_, the superfix is very clear. just inside the outline and parallel to it there is a line of smaller circles, { } 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 , _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 as forms for the great cycle, or period of the sixth order, may be summarized as follows: . 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. . 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. . 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. , .) the two glyphs which may possibly be identified as the sign for this period are shown in figure , _d_, e. a comparison of these two forms shows that both are composed of the same elements: ( ) the cycle sign; ( ) a superfix in which the hand is the principal element. the superfix in figure , _d_, consists of a hand and a tassel-like postfix, not unlike the upper half of the ending signs in figure , _l-q_. however, in the present case, if we accept the hypothesis that _d_ of figure 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 , _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 { } 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: . 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. . 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. . 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 a in figure 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 th order, is composed of two parts, just like the signs for the great cycle and the great-great cycle already described. these are: ( ) the cycle sign; ( ) 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 shows that the glyphs which we have identified as the signs for the higher periods (a , a , a , and a ,) contain one element common to all--the sign for the cycle, or period of , days. indeed, a is composed of this sign alone with its usual coefficient of . moreover, the next glyphs (a , a , a , and a [ ]) are the signs for the katun, tun, uinal, and kin, respectively, and, together with a , form a regular descending series of 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: ( ) the cycle sign; ( ) 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 , thus showing that in all probability , not , cycles made great cycle. therefore, since the great-cycle signs in figure , _a-c_, are composed of the cycle sign plus a superfix (), this superfix must have the value of in order to make the whole glyph have the value of { } cycles, or great cycle (that is, × , = , , ). in other words, it may be accepted ( ) that the glyphs in figure , _a-c_, are signs for the great cycle, or period of the sixth place; and ( ) that the great cycle was composed of cycles shown graphically by two elements, one being the cycle sign itself and the other a superfix having the value of . it has been shown that the last six glyphs in figure (a , a , a , a , a , and a ) all belong to the same series. let us next examine the seventh glyph or term from the bottom (a ) 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. , _d_, _e_) are composed of the same elements in each: ( ) the cycle sign; ( ) 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. , _a-c_) the coefficient in every case is greater than , thus showing that in all probability , not , great cycles made great-great cycle. therefore, since the great-great cycle signs in figure , _d_, _e_, are composed of the cycle sign plus a superfix (), this superfix must have the value of ( × ) in order to make the whole glyph have the value of great cycles, or great-great cycle ( × , , = , , ). in other words, it seems highly probable ( ) that the glyphs in figure , _d_, _e_, are signs for the great-great cycle or period of the seventh place, and ( ) that the great-great cycle was composed of great cycles, shown graphically by two elements, one being the cycle sign itself and the other a hand having the value of . it has been shown that the first seven glyphs (a , a , a , a , a , a , and a ) probably all belong to the same series. let us next examine the eighth term (a ) 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 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 ( ) that the sixth term was composed of the fifth term plus a superfix which increased the fifth times, and ( ) that the seventh term was composed of the fifth term plus a superfix which increased the fifth times, or the sixth times. now let us examine the only known example of a sign for the eighth term (a , fig. ). this glyph is composed of ( ) the cycle sign; ( ) a superfix of two elements, (_a_) the hand, and (_b_) a semicircular element in which dots appear. { } but this same hand in the super-fix of the great-great cycle increased the cycle sign times ( × ; see a , fig. ). therefore we must assume the same condition obtains here. and finally, since the eighth term = × × × cycle, we must recognize in the second element of the superfix () a sign which means . a close study of this element shows that it has two important points of resemblance to the superfix of the great-cycle glyph (see a , fig. ), which was shown to have the value : ( ) both elements have the same outline, roughly semicircular; ( ) both elements have the same chain of dots around their edges. compare this element in a , figure , with the superfixes in figure , _a_, _b_, bearing in mind that there is more than years' difference in time between the carving of a , figure , and _a_, figure , and more than years between the former and figure , b. the writer believes both are variants of the same element, and consequently a , figure , is probably composed of elements which signify × ( × ) × 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: . the eight periods[ ] in figure are consecutive, their sequence being uninterrupted throughout. consequently it seems probable that all belong to one and the same number. . it has been shown that the highest three period glyphs are composed of elements which multiply the cycle sign by , , and , , respectively, which has to be the case if they are the sixth, seventh, and eighth terms, respectively, of the maya vigesimal system of numeration. . 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. . in the two texts which alone can furnish comparative data for this sixth term, the sixth-period glyph in each is identical with a , figure , thus showing the existence of a sixth period in the inscriptions and a generally[ ] accepted sign for it. . in the only other text which can furnish comparative data for the seventh term, the period glyph in its seventh place is identical { } with a , figure ; thus showing the existence of a seventh period in the inscriptions and a generally accepted sign for it. . 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. . 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. . finally, the two occurrences of the cycle sign with a coefficient above , and the three occurrences of the great-cycle sign with a coefficient above , indicate that , not , 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 at tikal are not illustrated in figure . the sixth glyph is a in figure , 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 manik, though it is somewhat effaced. the remaining three are unknown. the next glyph, a , figure , is very clearly another initial-series introducing glyph, having all of the five elements common to that sign. compare a with the forms for the initial series introducing glyph in figure . this certainly would seem to indicate that an initial series is to follow. moreover, the fourth glyph of the eight-term number following in a -a , inclusive (that is, a ), records "cycle ," the cycle in which practically all initial-series dates fall. indeed, if a , a , and a were omitted and a , a , a , a , and a were recorded immediately after a , the record would be that of a regular initial-series number ( . . . . ). can this be a matter of chance? if not, what effect can a , a , and a have on the initial-series date in a , a -a ? the writer believes that the only possible effect they could have would be to fix cycle of maya chronology in a far more comprehensive and elaborate chronological conception, a conception which { } 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 , the first historic period of the maya civilization, was cycle of great cycle of great-great cycle of great-great-great cycle . in other words, the starting point of maya chronology, which we have seen was the date ahau cumhu, cycles before the close of a cycle , was in reality . . . . . . . . ahau cumhu, or simply a fixed point in a far vaster chronological conception. furthermore, it proves, as contended by the writer on page , that a great cycle came to an end on this date, ahau cumhu. this is true because on the above date ( . . . . . . . . ahau cumhu) all the five periods lower than the great cycle are at . it proves, furthermore, as the writer also contended, that the date ahau zotz, cycles in advance of the date ahau cumhu, did not end a great cycle-- . . . . . . . . ahau cumhu . . . . . . . . . . . . . ahau zotz but, on the contrary, was a cycle of great cycle , the end of which ( . . . . . . ahau 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 a -a , figure , 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 ) was itself the closing great cycle of a great-great cycle, namely, great-great cycle : . . . . . . . . . . . . . . . . . . . . . . that is to say, that when great cycle had completed itself, great-great cycle would be ushered in. we have seen on pages - that the names of the cycles followed one another in this sequence: cycle , cycle , cycle , etc., to cycle , which was followed by cycle , 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 ; that is, it was counted from the end of a cycle . therefore, the { } closing cycle of great cycle of great-great cycle of great-great-great cycle was a cycle , that is to say, . . . . . . . . ahau cumhu concluded a great cycle, the closing cycle of which was named cycle . this large number, composed of _one_ great-great-great cycle, _eleven_ great-great cycles, and _nineteen_ great cycles, contains exactly , cycles, as below: great-great-great cycle = × × × cycles = , cycles great-great cycles = × × cycles = , cycles great cycles = × cycles = cycles ----- , cycles but the closing cycle of this number was named cycle , and by deducting all the multiples of possible ( ) we can find the name of the first cycle of great-great-great cycle , the highest maya time period of which we have any knowledge: × = , . and deducting this from the number of cycles involved ( , ), we have-- , , ------ this counted backward from cycle , brings us again to a cycle 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 , not with the beginning of a cycle , as they did their chronology. we have still to explain a , figure . 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: ( ) trinal superfix; ( ) pair of comb-like lateral appendages; ( ) the tun sign; ( ) the trinal subfix; ( ) the variable central element, here represented by a grotesque head. of these, the first only claims our attention here. the trinal superfix in a (fig. ), 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 . the question at once arises, can the two flanking parts be merely ornamental and the whole element stand for the number ? 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 a , or is it not a term of the series in glyphs a -a ? { } 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 a 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 , 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 glyphs denoted what particular day of time was designated in the inscription. but why, even admitting the correctness of this interpretation of a , 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- dates actually recorded, as well as a half a dozen cycle- dates. that is, the cycle, which changed its coefficient every 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 , 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 years, and the maya are known to have recorded dates in at least three cycles--nos. , , and . hence, it was great cycle for , years, great-great cycle for , , and great-great-great cycle for , , years, whereas it was cycle for only 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. { } 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 at tikal ( . . . . ) 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 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, , but in later times this middle dot lost its numerical characteristics and frequently appears as a scroll itself. the early date of stela 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 a , figure , 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 - will lead to the following conclusions: ( ) 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 ( ) 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 (footnote ), 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 , for example, the uinal and the kin coefficients are both . in this case, however, the on the left of the uinal sign is to be understood as belonging to the kin sign, which is omitted, while the above the uinal sign is the uinal's own coefficient . again in figure , the kin sign is omitted and the kin coefficient is prefixed to the uinal sign, while the uinal's own coefficient stands above the uinal sign. similarly, the uinals and kins recorded in figure , _d_, might as well have been written as in _o_ of the same figure, that is, with the kin sign omitted and its coefficient prefixed to the uinal sign, while the uinal's own coefficient appears above. or again, the uinals and kins recorded in _f_ also might have been written as in _p_, that is, with the kin sign omitted and the kin coefficient prefixed to the uinal sign while the uinal's own coefficient 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, { } 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 , _a_, had the kin coefficient been placed on the left of the uinal sign, the uinal coefficient 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 _above_ and the 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. . 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 , b. here a tun sign appears with the coefficient above and to the left. since there are only two coefficients ( and ) and three time periods (tun, uinal, and kin), it is clear that the signs of both the lower periods have been omitted as well as the coefficient of one of them. in _c_ of the last-mentioned figure a somewhat different practice was followed. here, although three time periods are recorded--tuns, uinals and kins--one period (the uinal) and its coefficient have been omitted, and there is nothing between the kins and 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 was just the reverse of that in the numbers shown in figures and ; 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 { } lowest period, so long as its several periods always stand in the same relation to each other. for example, in figure , _q_, cycles, katuns, tuns, uinals, and kins represent exactly the same number as kins, uinals, tuns, katuns, and cycles; that is, with the lowest term first. it was explained on page 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. ) 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 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 . , the second from the decimal point, counting from right to left, has a value ten times greater than the first , since it stands for tens ( ); the third from the decimal point similarly has a value ten times greater than the second , since it stands for hundreds ( ); finally, the fourth has a value ten times greater than the third , since it stands for thousands ( , ). 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 in all positions except the third. the value of these positions increased { } with their distance from the bottom, according to the terms of the vigesimal system shown in table viii. this second method, or "numeration by position," as it may be called, was a distinct advance over the first, since it required for its expression only the signs for the numerals to , 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 and 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. ). 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 to , inclusive, are expressed in this method, as shown in figure , and the number as shown in figure . as all of these numbers are below , they are expressed as units of the first place or order, and consequently each should be regarded as having been multiplied by , the numerical value of the first or lowest position. the number was expressed in two different ways: ( ) by the sign shown in figure ; and ( ) by the numeral in the bottom place and the numeral in the next place above it, as in figure , 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 (see fig. ) was necessary. see chapter vi. the numbers from to , 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 and , respectively. for example, the number was expressed as shown in figure , b. the in the kin place has a value of ( × ) and the in the uinal, or second, place a value of ( (the numeral) × (the fixed numerical value of the second place)). the sum of these two products equals . again, was written as in figure , c. the in the kin place has the value ( × ), and the in the second place has the value of ( × ), and the sum of these products equals . to express the numbers to , , inclusive, three places or terms were necessary--kins, uinals, and tuns--of which the last had a numerical value of . (see table viii.) for example, the number is shown in figure , d. the in the lowest place indicates that kins are involved, the in the second place indicates that uinals or 's are involved, while the in the third place shows that there is tun, or , kins recorded ( (the numeral) × (the fixed numerical value of the third position)); the sum of these three products equals . again, the number , is expressed as shown in figure , e. { } the in the lowest place equals ( × ); the in the second place, ( × ); and the in the third place, , ( × ). the sum of these three products equals , ( + + , ), [illustration: fig. . examples of the second method of numeration, used exclusively in the codices.] the numbers from , to , , 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 , . (see table viii.) for example, the number , is recorded in figure , _f_. { } the in the first place equals ( × ); the in the second place, ( × ); the in the third place, ( × ); and the in the fourth place, , ( × , ). the sum of these four products equals , ( + + + , ). again, the number , is recorded in figure , _g_. here the in the first place equals ( × ); the in the second place, ( × ); the in the third place, ( × ); and the in the fourth place, , ( × , ). the sum of these four products equals , ( + + + , ). the numbers from , to , , , 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 , . (see table viii.) for example, the number , is recorded in figure , _h_. the in the first place equals ( × ); the in the second place, ( × ); the in the third place, , ( × ); the in the fourth place, , ( × , ); and the in the fifth place, , ( × , ). the sum of these five products equals , ( + + , + , + , ). again, the number , , is recorded in figure , _i_. the in the first place equals ( × ); the in the second place, ( × ); the in the third place, , ( × ); the in the fourth place, , ( × , ); and the in the fifth place, , , ( x , ). the sum of these five products equals , , ( + + , + , + , , ). the writing of numbers above , , up to and including , , (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 , , . it will be remembered that some have held that the sixth place in the inscriptions contained only units of the fifth place, or , , 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 units of the fifth place. for example, the number , , is expressed as in figure , _j_. the in the first place equals ( × ); the in the second place, ( × ); the in the third place, ( × ); the in the fourth place, , ( × , ); the in the fifth place, ( × , ); and the in the sixth place, , , ( × , , ). the sum of these six terms equals , , ( + + + , + + , , ). the highest number in the codices, as explained above, is , , , which is recorded on page of the dresden codex. this number is expressed as in figure , _k_. the in the first place equals ( × ); the in the second place, ( × ); the in the third place, , ( × ); the in the fourth place, , ( × , ); the in the fifth place, , ( × , ); and the in the sixth place, , , ( × , , ). the sum of these six products equals , , ( + + , + , + , + , , ). { } 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[ ] with their corresponding multipliers--the numerals to , 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[ ] 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 | . use confined almost exclusively | . use confined exclusively to to the inscriptions. | the codices. | . numerals represented by both | . numerals represented by normal forms and head variants. | normal forms exclusively. | . numbers expressed by using | . numbers expressed by using the numerals to , inclusive, | the numerals to , as multipliers with the period | inclusive, as multipliers in glyphs as multiplicands. | certain positions the | fixed numerical values of | which served as | multiplicands. | . numbers presented as | . numbers presented as ascending or descending series. | ascending series | exclusively. | . direction of reading either | . direction of reading from from bottom to top, or vice | bottom to top exclusively. versa. we have seen in the foregoing pages ( ) how the maya wrote their { } numerals, and ( ) 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_.[ ] 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.[ ] 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 - , 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. { } table xiii. values of higher periods in terms of lowest, in inscriptions great cycle = [ ] , , cycle , katun , tun uinal kin table xiv. values of higher periods in terms of lowest, in codices unit of the th place = , , unit of the th place , unit of the th place , unit of the d place unit of the d place unit of the st place 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 attached to the katun sign reduces to , units of the first order ( × , ). again, attached to the uinal sign reduces to units of the first order ( × ). 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 in the third place indicates that the 's multiplicand is , the numerical value of the third place, and such a term reduces to , units of the first place ( × = , ). again, a in the fourth place indicates that the 's multiplicand is , , the numerical value corresponding to the fourth place, and such a term reduces to , units of the first place. having reduced all the terms of a number to units of the st 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 ._ when the starting point or date is expressed, usually, though not invariably, it precedes[ ] the number counted from it. it should be noted, however, in connection with this rule, that the starting date hardly ever immediately precedes the number from which it is counted, but that several glyphs nearly always stand { } between.[ ] certain exceptions to the above rule are by no means rare, and the student must be continually on the lookout for such reversals of the regular order. these exceptions are cases in which the starting date ( ) follows the number counted from it, and ( ) 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 _. 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 ahau cumhu.[ ] this rule is particularly useful in deciphering numbers in the inscriptions. for example, when the student finds a number which he can identify as an initial series,[ ] he may assume at once that such a number in all probability is counted from the date ahau 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. { } [illustration: fig. . 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[ ] by a special character. this character, although attached only to the lowest term[ ] of the number which is to be counted backward, is to be interpreted as applying to all the other terms as well, its effect extending to the number as a whole. this "backward sign" (shown in fig. ) 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 . although the "backward sign" in this figure surrounds only the numeral in the first place, , it is to be interpreted, as we have seen, as applying to the in the second place and the in the third place. this number, expressed as tuns, uinals, and kins, reduces to , 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 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 , recorded in figure is counted will be found to be below it, that is, the date ahau cumhu[ ] (second step). finally, the red circle and knot surrounding the lowest ( ) term of this , indicates that this number is to be counted _backward_ from its starting point, not forward (third step). on the other hand, in the inscriptions no special character seems to have been used with a number to indicate that it was to be counted backward; at least no such sign has yet been discovered. in the inscriptions, therefore, with the single exception[ ] mentioned below, the student can only apply the general rule given on page , 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 _. 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 { } 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 , , or . . . as it would be expressed in maya notation,[ ] from any date, as ahau cumhu, there are four unknown elements which have to be determined before we can write the date which the count reaches. these are: . the day coefficient, which must be one of the numerals to , inclusive. . the day name, which must be one of the twenty given in table i. . the position of the day in some division of the year, which must be one of the numerals to , inclusive. . 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 ( ) the starting date, and ( ) 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. - ) and also shown graphically in the tonalamatl wheel (pl. ) that after the day coefficients had reached the number they returned to , following each other indefinitely in this order without interruption. it is clear, therefore, that the highest multiple of 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 will always bring the count back to the same day coefficient. { } taking up the number, , , which we have chosen for our first example, let us deduct from it the highest multiple of which it contains. this will be found by dividing the number by , and multiplying the _whole-number part_ of the resulting quotient by : , ÷ = , - / . multiplying , by , we have , , which is the highest multiple of that , contains; consequently it may be deducted from , without affecting the value of the resulting day coefficient: , - , = . in the example under consideration, therefore, 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 the only part of the resulting quotient which is used in determining the new day coefficient is the _numerator_ of the fractional part.[ ] hence the following rule for determining the first unknown on page (the day coefficient): _rule ._ to find the new day coefficient divide the given number by , 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 in either case from the resulting number if it should exceed . applying this rule to , , we have seen above that its division by gives as the fractional part of the quotient / . assuming that the count is forward from the starting point, ahau cumhu, if (the numerator of the fractional part of the quotient) be counted forward from , the day coefficient of the starting point ( ahau cumhu), the day coefficient of the resulting date will be ( + ). since this number is below , the last sentence of the above rule has no application in this case. in counting forward , from the date ahau cumhu, therefore, the day coefficient of the resulting date will be ; thus we have determined our first unknown. let us next find the second unknown, the day sign to which this is prefixed. it was explained on page 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 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 will always bring the count back to the same day sign. { } returning to the number , , let us deduct from it the highest multiple of which it contains, found by dividing the number by and multiplying the whole number part of the resulting quotient by ; , ÷ = , - / . multiplying , by , we have , , which is the highest multiple of that , contains, and which may be deducted from , without affecting the resulting day sign; , - , = . therefore in the present example is the number which, if counted forward from the day sign of the starting point in the sequence of the day signs given in table i, will reach the day sign of the resulting date. in other words, after dividing by 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 (the day sign): _rule ._ to find the new day sign, divide the given number by , 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 , , we have seen above that its division by gives us as the fractional part of the quotient, / . since the count was forward from the starting point, if (the numerator of the fractional part of the quotient) be counted forward in the sequence of the day signs in table i from the day sign of the starting point, ahau ( ahau cumhu), the day sign reached will be the day sign of the resulting date. counting forward 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 for the first unknown and imix for the second, we can now say that in counting forward , from the date ahau cumhu, the day reached will be imix. it remains to find what position this particular day occupied in the -day year, or haab, and thus to determine the third and fourth unknowns on page . both of these may be found at one time by the same operation. it was explained on pages - that the maya year, at least in so far as the calendar was concerned, contained only days, divided into uinals of days each, and the _xma kaba kin_ of days; and further, that when the last position in the last division of the year ( uayeb) was reached, it was followed without interruption by the first position of the first division of the next year ( pop); and, finally, that this sequence was continued indefinitely. consequently it is clear that the highest multiple of 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 { } 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 will bring the count back again to the same position in the year. returning again to the number , , let us deduct from it the highest multiple of which it contains. this will be found by dividing the number by and multiplying the whole number part of the resulting quotient by : , ÷ = - / . multiplying by , we have , , which is the highest multiple that , contains. hence it may be deducted from , without affecting the position in the year of the resulting day; , - , = . therefore, in the present example, is the number which, if counted forward from the year position of the starting date in the sequence of the 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 (the position in the year of the day of the resulting date): _rule ._ to find the position in the year of the new day, divide the given number by 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 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 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 | | | | | | | | | | | | | | | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | | | +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ | do | | | | | | | | | | | | | | | | | | |--| +-----+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ { } applying this rule to the number , , we have seen above that its division by gives 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 forward in table xv from the position cumhu, the position of the day of the starting point, ahau cumhu. a glance at the month of cumhu in table xv shows that after the position cumhu there are positions in that month; adding to these the in uayeb, the last division of the year, there will be in all more positions before the first of the next year. subtracting these from , the total number to be counted forward, there remains the number ( - ), which must be counted forward in table xv from the beginning of the year. since each of the months has positions, it is clear that months will be used before the month is reached in which will fall the th position from the beginning of the year. in other words, positions of our will exactly use up all the positions of the first 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 th month (kayab) with still more positions to count forward. if the student will refer to this month in table xv he will see that positions counted forward in this month will reach the position kayab, which is also the position reached by counting forward , positions from the starting position cumhu. having determined values for all of the unknowns on page , we can now say that if the number , be counted forward from the date ahau cumhu, the date imix 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. ) 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 - that in maya chronology there were possible only , different dates--that is, combinations of the days and the positions of the year--and further, that any given day of the could return to any given position of the only after the lapse of , days, or years. { } since the foregoing is true, it follows, that this number , 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 , , all others being divided by , , and directly, as indicated in rules , , and , respectively. this enables us to formulate another rule, which should be applied to the number to be counted before proceeding with rules , , and above, if that number is above , . _rule_. if the number to be counted is above , , first deduct from it the highest multiple of , 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 calendar rounds, that is, multiples of , , 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 , , which was selected for our first example, it is seen by table xvi that calendar round, or , days, may be deducted from it; , - , = , . in other words, we can count the number , forward (or backward had the count been backward in our example) from the starting point ahau cumhu, and reach exactly the same terminal date as though we had counted forward , , as in the first case. mathematical proof of this point follows: , ÷ = - / , ÷ = - / , ÷ = - / the numerators of the fractions in these three quotients are , , and ; these are identical with the numerators of the fractions in the quotients obtained by dividing , by the same divisors, those indicated in rules , , and , respectively. consequently, if these three numerators be counted forward from the corresponding parts of the starting point, ahau cumhu, the resulting terms together will form the corresponding parts of the same terminal date, imix kayab. similarly it could be shown that , or , counted forward or backward from any starting point would both reach this same terminal date, since subtracting calendar rounds, , (see table xvi), from the first, and calendar rounds, , (see table xvi), from the second, there would remain in each case , . 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. { } table xvi. calendar rounds expressed in arabic and maya notation +--------+---------+-----------------+ |calendar| days| cycles, etc.| | rounds| | | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ | | , , | . . . . | +--------+---------+-----------------+ { } let us count forward the number , from the starting point kan tzec. it is apparent at the outset that, since this number is less than , , or calendar round, the preliminary rule given on page does not apply in this case. therefore we may proceed with the first rule given on page , by means of which the new day coefficient may be determined. dividing the given number by we have: , ÷ = - / . counting forward the numerator of the fractional part of the resulting quotient ( ) from the day coefficient of the starting point ( ), we reach as the day coefficient of the terminal date. the second rule given on page tells how to find the day sign of the terminal date. dividing the given number by , we have: , ÷ = - / . counting forward the numerator of the fractional part of the resulting quotient ( ) 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 akbal. the third rule, given on page , tells how to find the position which the day of the terminal date occupied in the -day year. dividing the given number by , we have: , ÷ = - / . counting forward the numerator of the fractional part of the resulting quotient, , from the year position of the starting date, tzec, in the sequence of the year positions given in table xv, the position 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 zip is determined is given in detail. after the year position of the starting point, tzec, it requires more positions (nos. - , inclusive) before the close of that month (see table xv) will be reached. and after the close of tzec, uinals and the xma kaba kin must pass before the end of the year; × + = , and + = . this latter number subtracted from , 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: - = . counting forward in the new year, we find that it will use up the months pop and uo ( + = ) and extend positions into the month zip, or to zip. therefore, gathering together the values determined for the several parts of the terminal date, we may say that in counting forward , from the starting point kan tzec, the terminal date reached will be akbal zip. for the next example let us select a much higher number, say , , which we will assume is to be counted forward from the starting point ik zip. since this number is above , , we may apply our preliminary rule (p. ) and deduct all the calendar { } rounds possible. by turning to table xvi we see that calendar rounds, or , , may be deducted from our number: , - , = . in other words, we can use exactly as though it were , . dividing by , we have ÷ = . since there is no fraction in the quotient, the numerator of the fraction will be , and counting forward from the day coefficient of the starting point, , we have as the day coefficient of the terminal date (rule , p. ). dividing by we have ÷ = . since there is no fraction in the quotient, the numerator of the fraction will be , and counting forward from the day sign of the starting point, ik in table i, the day sign ik will remain the day sign of the terminal date (rule , p. ). combining the two values just determined, we see that the day of the terminal date will be 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 differently named days (see pp. - ) and any given day will have to recur, therefore, after the lapse of days.[ ] dividing by we have: ÷ = / . counting forward the numerator of the fraction, , from the year position of the starting point, zip, in table xv, the position in the year of the day of the terminal date will be found to be pax. since days equal just uinals, we have only to count forward from zip uinals in order to reach the year position; that is, zotz is uinal; to tzec uinals, to xul uinals, and so on in table xv to pax, which will complete the last of the uinals (rule , p. ). combining the above values, we find that in counting forward , (or ) from the starting point ik zip, the terminal date reached is ik 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 , from the starting point imix uayeb. since this number is below , , no calendar round can be deducted from it. dividing the given number by , we have: , ÷ = - / . counting the numerator of the fractional part of this quotient, , _backward_ from the day coefficient of the starting point, , we reach as the day coefficient of the terminal date, that is, , , , (rule , p. ). dividing the given number by , we have: , ÷ = - / . counting the numerator of the fractional part of this quotient, , _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 eznab. dividing the given number by , we have { } , ÷ = - / . counting _backward_ the numerator of the fractional part of this quotient, , from the year position of the starting point, uayeb, the year position of the terminal date will be found to be yax. before position uayeb (see table xv) there are positions in that division of the year ( , , , ). counting these _backward_ to the end of the month cumhu (see table xv), we have left positions ( - = ); this equals uinals and days extra. therefore, beginning with the end of cumhu, we may count _backward_ 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 days out of our original , these must be counted backward from position zac, that is, beginning with position yax: , , , , , , , , ; so 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 , _backward_ from the starting point, imix uayeb, the terminal date is eznab 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 years, by the time their historic period had been reached, more than , years after the starting point of their chronology, the maya had upward of distinct dates of exactly the same name to distinguish from one another. it was stated on page that the , or starting point of maya chronology, was the date ahau cumhu, from which all subsequent dates were reckoned; and further, on page , 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: . . . . . ahau ceh the particular initial-series written here is to be interpreted thus: "counting forward cycles, katuns, tuns, uinals, and kins { } from ahau cumhu, the starting point of maya chronology (always unexpressed in initial series), the terminal date reached will be ahau ceh."[ ] or again: . . . . . caban kayab this inital series reads thus: "counting forward cycles, katuns, tuns, uinals, and kins from ahau cumhu, the starting point of maya chronology (unexpressed), the terminal date reached will be caban kayab." the time which separates any date from ahau cumhu may be called that date's initial-series value. for example, in the first of the above cases the number . . . . is the initial-series value of the date ahau ceh, and in the second the number . . . . is the initial-series value of the date caban kayab. it is clear from the foregoing that although the date ahau ceh, for example, had recurred upward of times since the beginning of their chronology, the maya were able to distinguish any particular ahau 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 . . . . . in the present case. similarly, any particular caban kayab, by the addition of its corresponding initial-series value, as . . . . in the case above cited, was absolutely fixed in the long count--that is, in a period of , 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[ ] 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 . . . is to be counted forward from the initial series . . . . ahau ceh. by multiplying the values of the katuns, tuns, uinals, and kins given in table xiii by their corresponding coefficients, in this case , , , and , respectively, and adding the resulting products together, we find that . . . reduces to , units of the first order. counting this forward from ahau ceh as indicated by the rules on pages - , the terminal date imix yaxkin will be reached. { } moreover, since the initial-series value of the starting point ahau ceh was . . . . , the initial-series value of imix yaxkin, the terminal date, may be calculated by adding its distance from ahau ceh to the initial-series value of that date: . . . . (initial-series value of starting point) ahau ceh . . . (distance from ahau ceh to imix yaxkin) . . . . (initial-series value of terminal date) imix yaxkin that is, by calculation we have determined the initial-series value of the particular imix yaxkin, which was distant . . . from . . . . ahau ceh, to be . . . . , notwithstanding that this fact was not recorded. the student may prove the accuracy of this calculation by treating . . . . imix yaxkin as a new initial series and counting forward . . . . from ahau 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 . . . from . . . . ahau ceh. in the above example the distance number . . . and the date imix yaxkin to which it reaches, together are called a secondary series. this method of dating already described (see pp. - 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-- . . . . cib yaxkin . . [ . . . . ][ ] chuen kankin [ . . . . ] cib kankin . . . [ . . . . ] imix zac the only parts actually recorded are the initial series . . . . { } cib yaxkin, and the secondary series . . leading to chuen kankin; the secondary series leading to cib kankin; and the secondary series . . . leading to imix zac. the initial-series values: . . . . ; . . . . ; and . . . . , 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 chuen kankin, becomes the starting point for the next number, . again, the terminal date reached by counting from chuen kankin, that is, cib kankin, becomes the starting point from which the next number, . . . , 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 . is to be counted forward from the initial series . . . . ahau uo. reducing uinals and kins to kins, we have units of the first order. counting forward from ahau uo, as indicated by the rules on pages - , it is found that the terminal date will be ik tzec. since the initial-series value of the starting point ahau uo is known, namely, . . . . , the initial series corresponding to the terminal date may be calculated from it as before: . . . . (initial-series value of the starting point) ahau uo . (distance from ahau uo forward to ik tzec) [ . . . . ] (initial-series value of the terminal date) ik tzec the bracketed . . . . in the initial-series value corresponding to the date ik tzec does not appear in the record but was reached by calculation. the student may prove the accuracy of this result by treating . . . . ik tzec as a new initial series, and counting forward . . . . from ahau cumhu (the starting point of maya chronology, unexpressed in initial series). if our calculations are correct, the same date, ik tzec, will be reached, as though we had counted only . forward from the initial series . . . . ahau uo. one more example presenting a "backward count" will suffice to illustrate this method. let us count the number . . . _backward_ from the initial series . . . . caban kayab. reducing . . . to units of the st order, we have , . counting this number _backward_ from caban kayab, as indicated in the rules on pages - , we find that the terminal date will be ahau ceh. moreover, since the initial-series value of the starting point caban kayab is known, namely, . . . . , the initial-series value of { } the terminal date may be calculated by _subtracting_ the distance number . . . from the initial series of the starting point: . . . . (initial-series value of the starting point) caban kayab . . . (distance from caban kayab backward to ahau ceh) [ . . . . ] (initial-series value of the terminal date) ahau ceh the bracketed parts are not expressed. we have seen elsewhere that the initial series . . . . has for its terminal date ahau 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 - . 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. - ), 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 ahau 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. { } 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, ahau ceh, caban kayab, etc. in initial series, on the other hand, the day parts of the dates, as ahau and caban, in the above examples, are almost invariably separated from their corresponding month parts, ceh or 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, ahau 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.[ ] the month glyph in the great majority of cases follows immediately the closing[ ] glyph of the supplementary series. the form of this latter sign is always unmistakable (see fig. ), and it is further characterized by its numerical coefficient, which can never be anything but or .[ ] 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 . . . . ahau zotz that the number . . . . has been counted forward { } from ahau cumhu (the unexpressed starting point), and has been found by calculation to reach the terminal date ahau zotz; and further, let us suppose that on inspecting the text the day part of this date ( ahau) has been found to be recorded immediately after the kins of the number . . . . . now, if the student will follow the next six or seven glyphs until he finds one like any of the forms in figure , the glyph immediately following the latter sign will be in all probability the month part, 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. . 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[ ] usually follow immediately the days signs to which they belong. the most notable exception[ ] to this general rule occurs in connection with the venus-solar periods represented on pages - 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 ahau stands above three different month signs-- cumhu, zotz, and yax--with each of which it is used to form a { } different date-- ahau cumhu, ahau zotz, and ahau 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 ahau with each of the two lower month signs, zotz and yax, by writing it once above the upper month sign, 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 ahau. with the exception of the initial-series dates in the inscriptions and the venus-solar dates on pages - 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 - (pp. - ) 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 , we must accept one of the following alternatives: . there is an error in our own calculations; or . there is an error in the original text; or . 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 { } have been given under step , page , and step , page . 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 for , or for or , 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 - to reach the terminal dates recorded as under 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. { } 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[ ] of the material presented in chapters iii and iv. [illustration: fig. . 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. ) that the maya glyphs were presented in parallel columns, which are to be read two columns at a time, the order of the individual glyph-blocks[ ] in each pair of columns being from left to right and from top to bottom. for convenience in 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, , , , , etc. for example, in figure the glyph-blocks in columns a and b are read together from left to right and top to bottom, thus, a b , a b , a b , etc. when glyph-block b is reached the next in order is c , which is followed by d , c d , c d , etc. again, when d is reached the next in order is e , which is followed by f , e f , e f , 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 n in figure . 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 glyph [alpha] is referred to as d ; glyph [beta] as f ; glyph [gamma] as k ; glyph [delta] as n . 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, , , , etc. in two copan texts, altar s (fig. ) and stela j (pl. ), 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] { } 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.[ ] in plate is figured the drawing of the initial series[ ] 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, a -b .[ ] analysis of this form shows that it possesses all the elements mentioned on page 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: ( ) the trinal { } superfix, ( ) the pair of comblike lateral appendages, ( ) the normal form of the tun sign, ( ) the trinal subfix, and ( ) the variable central element. as stated above, all these appear in the large glyph a -b . moreover, a comparison of a -b with the introducing glyphs given in figure shows that these forms are variants of one and the same sign. consequently, in a -b 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.[ ] exceptions to this rule are so very rare (see p. ) 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[ ]. the cycle sign in the present example appears in a with the coefficient ( bar and 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 , _a-c_. the outline of the repeated cauac sign appears in both places. we have then, in this glyph, the record of cycles[ ]. the glyph following the cycle sign in an initial series is always the katun sign, and this should appear in b , the glyph next in order. this glyph is quite clearly the normal form of the katun sign, as a comparison of it with figure , _a, b_, the normal form for the katun, will show. it has the normal-form numeral ( bars and dots) prefixed to it, and this whole glyph therefore signifies katuns. the next glyph should record the tuns, and a comparison of the glyph in a with the normal form of the tun sign in figure , _a, b_, shows this to be the case. the numeral ( bar prefixed to the tun sign) shows that this period is to be used times; that is, multiplied by . the next glyph (b ) should be the uinal sign, and a comparison of b with figure , _a-c_, the normal form of the uinal sign, shows the identity of these two glyphs. the coefficient of the uinal sign contains as its most conspicuous element the clasped hand, which suggests that we may have uinals recorded in b . a comparison of this coefficient with the sign for zero in figure proves this to be the case. the next glyph (a ) should be the kin sign, the lowest period involved in recording initial series. a comparison of a with the normal form of the kin sign in figure , _a_, shows that these two forms are identical. the coefficient of a is, moreover, exactly like the coefficient of b , which, we have seen, meant zero, hence glyph a stands for kins. summarizing the above, we may say that glyphs a -a record an initial-series number consisting of cycles, katuns, tuns, uinals, and kins, which we may write thus: . . . . (see p. , footnote ). { } 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 was to reduce the given number, in this case . . . . , 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 , a are given below: a = × , = , , b = × , = , a = × = , b = × = a = × = ---------- , , therefore , , will be the number used in the following calculations. the second step (see step , p. ) is to determine the starting point from which this number is counted. according to rule , page , if the number is an initial series the starting point, although never recorded, is practically always the date ahau 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 , , is to be counted from the date ahau cumhu. the third step (see step , p. £ ) 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 , the count is always forward, consequently , , is to be counted _forward_ from ahau cumhu. the fourth step (see step , p. ) is to count the given number from its starting point; and the rules governing this process will be found on pages - . since our given number ( , , ) is greater than , , or calendar round, the preliminary rule on page applies in the present case, and we may therefore subtract from , , all the calendar rounds possible before proceeding to count it from the starting point. by referring to table xvi, it appears that , , contains complete calendar rounds, or , , ; hence, the latter number may be subtracted { } from , , without affecting the value of the resulting terminal date: , , - , , = , . in other words, in counting forward , from ahau cumhu, the same terminal date will be reached as though we had counted forward , , .[ ] in order to find the coefficient of the day of the terminal date, it is necessary, by rule , page , to divide the given number or its equivalent by ; , ÷ = . now since there is no fractional part in the resulting quotient, the numerator of an assumed fractional part will be ; counting forward from the coefficient of the day of the starting point, (that is, ahau cumhu), we reach 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 , page , to divide the given number or its equivalent by ; , ÷ = . since there is no fractional part in the resulting quotient, the numerator of an assumed fractional part will be ; counting forward in table i, from ahau, the day sign of the starting point ( ahau cumhu), we reach ahau as the day sign of the terminal date. in other words, in counting forward either , or , , from ahau cumhu, the day reached will be ahau. it remains to show what position in the year this day ahau distant , , from the date ahau cumhu, occupied. in order to find the position in the year which the day of the terminal date occupied, it is necessary, under rule , page , to divide the given number or its equivalent by ; , ÷ = - / . since the numerator of the fractional part of the resulting quotient is , to reach the year position of the day of the terminal date desired it is necessary to count forward from cumhu, the year position of the day of the starting point ahau cumhu. it appears from table xv, in which the positions of the year are given, that after position cumhu there are only positions in the year-- more in cumhu and in uayeb. these must be subtracted, therefore, from in order to bring the count to the end of the year; - = , so is the number of positions we must count forward in the new year. it is clear that the first uinals in the year will use up exactly of our positions ( × = ), and that positions will be left, which must be counted in the next uinal, the th. but the th uinal of the year is ceh (see table xv); counting forward positions in ceh, we reach ceh, which is, therefore, the month glyph of our terminal date. in other words, counting forward from cumhu, position ceh is reached. assembling the above values, we find that by calculation we have determined the terminal date of the initial series in plate , _a_, to be ahau ceh. { } 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 , the difference between and ( + = ) is counted forward from position ceh, position cumhu will be reached if our calculations were correct. this is true because there are only positions in the year, and having reached ceh in counting forward from cumhu, counting the remaining days forward from day reached by , that is, ceh, we should reach our starting point ( cumhu) again. another good check in the present case would be to count _backward_ from ceh; if our calculations have been correct, the starting point 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 , , , or in the divisions of the year;[ ] hence, if in the above case the coefficient of ceh had been any other number but one of these four, our calculations would have been incorrect. we come now to the final step (see step , p. ), 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 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. , _a_), we find that the kins are recorded in a , therefore the day part of the terminal date should appear in b . the glyph in b quite clearly records the day ahau by means of dots prefixed to the sign shown in figure , _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, a -c a, which record the supplementary series,[ ] we reach in c a a sign similar to the forms shown in figure . this glyph, which always has a coefficient of or , was designated on page the month-sign "indicator," since it usually immediately precedes the month sign in initial-series terminal dates. in c a it has the coefficient ( dots and bar) and is followed in c b by the month part { } of the terminal date, ceh. the bar and dot numeral appears very clearly above the month sign, which, though partially effaced, yet bears sufficient resemblance to the sign for ceh in figure , _u, v,_ to enable us to identify it as such. our complete initial series, therefore, reads: . . . . ahau ceh, and since the terminal date recorded in b , c b agrees with the terminal date determined by calculation, we may conclude that this text is without error and, furthermore, that it records a date, ahau ceh, which was distant . . . . from the starting point of maya chronology. the writer interprets this text as signifying that . . . . ahau 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 -tun period, which came to a close on the date . . . . ahau ceh of maya chronology.[ ] in plate , _b_, is figured a drawing of the initial series on stela at naranjo.[ ] the text opens in a with the initial-series introducing glyph, which is followed in b b by the initial-series number . . . . . 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 st 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 , p. ), follows: b = × , = , , a = × , = , b = × = , a = × = b = × = --------- , , and , , will be the number used in the following calculations. the next step is to find the starting point from which , , is counted (see step , p. ). since this number is an initial series, in all probability its starting point will be the date ahau 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 , p. ); since our number is an initial series, the count can only be forward (see rule , p. ).[ ] { } 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 , p. ). since , , is greater than , ( calendar round), we may deduct from the former number all the calendar rounds possible (see preliminary rule, page ). according to table xvi it appears that , , contains calendar rounds, or , , ; after deducting this from the given number we have left , ( , , - , , ), a far more convenient number to handle than , , . applying rule (p. ) to , , we have: , ÷ = - / , and counting forward , the numerator of the fractional part of the quotient, from , the day coefficient of the starting point, ahau cumhu, we reach as the day coefficient of the terminal date. applying rule (p. ) to , , we have: , ÷ = - / ; and counting forward , the numerator of the fractional part of the quotient, from ahau, the day sign of our starting point, ahau cumhu, in table i, we reach manik as the day sign of the terminal date. therefore, the day of the terminal date will be manik. applying rule (p. ) to , , we have: , ÷ = - / ; and counting forward , the numerator of the fractional part of the quotient, from cumhu, the year position of the starting point, ahau cumhu, in table xv, we reach kayab as the year position of the terminal date. the calculations by means of which kayab is reached are as follows: after cumhu there are positions in the year, which we must subtract from ; - = , which is to be counted forward in the new year. this number contains just more than uinals, that is, = ( × ) + ; hence it will reach through the first uinals in table xv and to the first position in the th uinal, kayab. combining this with the day obtained above, we have for our terminal date determined by calculation, manik kayab. the next and last step (see step , p. ) is to find the above date in the text. in initial series (see p. ) 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 , _b_, the last period glyph, as we have seen, is recorded in b ; therefore the day should appear in a . comparing the glyph in a with the sign for manik in figure , _j_, the two forms are seen to be identical. moreover, a has the bar and dot coefficient attached to it, that is, dots and bar; consequently it is clear that in a we have recorded the day 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; { } indeed, in the text here under discussion, so far as we can judge from the badly effaced glyphs, no supplementary series seems to have been recorded. however, reversing our operation, we know by calculation that the month part should be kayab, and by referring to figure we find the only form which can be used to express the position with the month signs--the so-called "spectacles" glyph--which must be recorded somewhere in this text to express the idea with the month sign kayab. further, by referring to figure , _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 . returning to our text once more and following along the glyphs after the day in a , we pass over b , a , and b without finding a glyph resembling one of the forms in figure joined to figure , _d'-f'_; that is, kayab. however, in a 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 a , a the same terminal date, manik kayab, as determined by calculation, and may conclude, therefore, that our text records without error the date . . . . manik kayab[ ] of maya chronology. the next text presented (pl. , c) shows the initial series from stela i at quirigua.[ ] again, as in plate , a, the introducing glyph occupies the space of four glyph-blocks, namely, a -b . immediately after this, in a -a , is recorded the initial-series number . . . . , all the period glyphs and coefficients of which are expressed by normal forms. the student's attention is called to the form for used with the uinal and kin signs in a a and a b, respectively, which differs from the form for recorded with the uinal and kin signs in plate , a, b , and a , respectively. in the latter text the uinals and kins were expressed by the hand and curl form for zero shown in figure ; in the present text, however, the uinals and kins are expressed by the form for shown in figure , a new feature. reducing the above number to units of the st order by means of table xiii, we have: a = × , = , , b a = × , = , b b = × = , a a = × = a b = × = --------- , , deducting from this number all the calendar rounds possible, { } (see table xvi), it may be reduced to , without affecting its value in the present connection. applying rules and (pp. and , respectively) to this number, the day reached will be found to be ahau; and by applying rule (p. ), the position of this day in the year will be found to be zac. therefore, by calculation we have determined that the terminal date reached by this initial series is ahau 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 a b. therefore the day glyph should be b a. an inspection of this latter glyph will show that it records the day ahau, both the day sign and the coefficient being unusually clear, and practically unmistakable. compare b a with figure , _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 , footnote , occurs out of its regular position, following immediately the day of the terminal date. as mentioned on page , 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, ahau, was recorded in b a; hence, since the month glyph was not recorded in its regular position, it must be in b b, immediately following the day glyph. by comparing the glyph in b b with the month signs in figure , 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 b b is quite clearly and the month part therefore reads, zac. combining this with the day recorded in b a, we have the date ahau zac, which corresponds with the terminal date determined by calculation. the whole text therefore reads . . . . ahau zac. [illustration: fig. . signs representing the hotun, or -tun, period.] it will be noted that this date . . . . ahau zac is just . . ( tuns) later than the date recorded by the initial series on zoömorph p at quirigua (see pl. , _a_). as explained in chapter ii (pp. - ), the interval between succeeding monuments at quirigua is in every case , days, or 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 -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 -tun period ending . . . . ahau ceh, and stela i, the -tun period next following, that ending . . . . { } ahau 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 -tun period so conspicuously recorded in the inscriptions from the older maya cities the writer would suggest the name _hotun_, _ho_ meaning in maya and _tun_ being the name of the -day period. this word has an etymological parallel in the maya word for the -tun period, _katun_, which we have seen may have been named directly from its numerical value, _kal_ being the word for in maya and _kaltun_ contracted to katun, thus meaning tuns. although no glyph for the _hotun_ has as yet been identified,[ ] the writer is inclined to believe that the sign in figure , _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 , surely signifies ; therefore the glyph itself must mean " tun." this form recalls the very unusual variant of the tun from palenque (see fig. , _h_). both have the wing and the () element. the next initial series presented (see pl. , _d_) is from stela at naranjo.[ ] the text opens with the introducing glyph, which is in the same relative position as the introducing glyph in the other naranjo text (pl. , _b_) at a . then follows regularly in b -b the number . . . . , 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 , page , the following result should be obtained: b = × , = , , a = × , = , b = × = , a = × = b = × = --------- , , deducting[ ] from this number all the calendar rounds possible, (see preliminary rule, p. , and table xvi), we may reduce it to without affecting its value in so far as the present calculations are concerned ( , , - , , ). first applying rule , page , and next rule , page , to this number ( ), the student will find the day reached to be eb. and applying rule , page , he will find that the year position reached will be yax;[ ] hence, the terminal date as determined by calculation will be eb yax. [illustration: glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs] { } turning again to the text (pl. , _d_), the next step (see step , p. ) 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 a , therefore, should record the day reached. comparing this form with the several day signs in figure , it appears that a more closely resembles the sign for eb (fig. , _s-u_) than any of the others, hence the student may accept eb as the day sign recorded in a . the dots prefixed to this sign show that the day eb is here indicated. the month sign, as stated on page , usually follows the last glyph of the supplementary series; passing over b , a , b , and a , we reach the latter glyph in b . compare the left half of b with the forms given in figure . the coefficient or is expressed by a considerably effaced head numeral. immediately following the month-sign "indicator" is the month sign itself in a . the student will have little difficulty in tracing its resemblance to the month yax in figure , _q, r_, although in a 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 ,[ ] and the whole terminal date recorded will read eb yax, which corresponds exactly with the terminal date determined by calculation. we may accept this text, therefore, as recording the initial-series date . . . . eb 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 , is figured the initial series from stela b at copan.[ ] the introducing glyph appears at the head of the inscription in a { } and is followed by a head-variant glyph in a , to which is prefixed a bar and dot coefficient of . by its position, immediately following the introducing glyph, we are justified in assuming that a records cycles, and after comparing it with _d-f_, figure , 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 , is the essential element of the cycle head; therefore, a records cycles. the next glyph, a , should be the katun sign, and a comparison of this form with the head variant for katun in _e-h_, figure , shows this to be the case. the determining characteristic (see p. ) is probably the oval in the top of the head, which appears in both of these forms for the katun. the katun coefficient is ( bars). the next glyph, a , should record the tuns, and by comparing this form with the head variant for the tun sign in _e-g_, figure , this also is found to be the case. both heads show the same essential characteristic--the fleshless lower jaw (see p. ). the coefficient is (compare fig. ). the uinal head in a is equally unmistakable. note the large curl protruding from the back part of the mouth, which was said (p. ) to be the essential element of this sign. compare figure , _d-f_, where the head variant for the uinal is given. the coefficient of a is like the coefficient of a ( ), and we have recorded, therefore, uinals. the closing period glyph of the initial series in a is the head variant for the kin sign. compare this form with figure , _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. , _a_). again, the coefficient of a is like the coefficient of a and a , hence we have recorded here kins. the number recorded by the head-variant period glyphs and normal-form numerals in a -a is therefore . . . . ; reducing this by means of table xiii, we have: a = × , = , , a = × , = , a = × = a = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), it may be reduced to , . applying to this number rules and (pp. and , respectively), the day reached will be found to be ahau. applying rule (p. ), the position of ahau in the year will be found to be yax. therefore the terminal date determined by calculation will be ahau yax. { } according to step (p. ), the day reached should follow immediately the last period glyph, which in this case was in a ; hence the day should be recorded in a . this glyph has a coefficient , but the glyph does not resemble either of the forms for ahau shown in b , plate , _a_, or in b a, _c_ of the same plate. however, by comparing this glyph with the second variant for the day sign ahau in figure , _h'-i'_, the two forms will be found to be identical, and we may accept a as recording the day ahau. immediately following in a is the month sign, again out of its usual place as in plate , _c_. comparing it with the month signs in figure , it will be found to exactly correspond with the sign for yax in _q-r_. the coefficient is . therefore the terminal date recorded, ahau yax, agrees with the terminal date reached by calculation, and the whole initial series reads . . . . ahau yax. this date marks the close not only of a hotun in the long count, but of a katun as well. in _b_, plate , is figured the initial series from stela a at copan.[ ] the introducing glyph appears in a b , and is followed by the initial-series number in a -a . the student will have no difficulty in picking out the clasped hand in a , the oval in the top of the head in b , the fleshless lower jaw in a , the large mouth curl in b , and the flaring subfix in a , which are the essential elements of the head variants for the cycle, katun, tun, uinal, and kin, respectively. compare these glyphs with figures , _d-f_, , _e-h_, , _e-g_, , _d-f_, and , _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 . . . . .[ ] reducing this by means of table xiii to units of the st order, we have: a = × , = , , b = × , = , a = × = , b = × = a = × = --------- , , deducting from this all the calendar rounds possible, (see table xvi), and applying rules and (pp. and , respectively), to the remainder, the day reached will be ahau. and applying rule (p. ), the month reached will be cumhu, giving for the terminal date as reached by calculation ahau cumhu. the day should be recorded in b , and an examination of this glyph shows that its coefficient is , the day coefficient reached by calculation. the glyph itself, however, is unlike the forms for ahau previously encountered in plate , _a_, b and _c_, b b, and in plate , _a_, a . turning { } now to the forms for the day sign ahau in figure , it is seen that the form in a resembles the third variant _j_' or _k'_, the grotesque head, and it is clear that the day ahau is here recorded. at first sight the student might think that the month glyph follows in a , 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 , , , or , not , as recorded (see table vii), and, in the second place, the glyph itself in a bears no resemblance whatsoever to any of the month signs in figure . 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 a a glyph with a coefficient , although the sign itself bears no resemblance to the month-glyph "indicators" heretofore encountered (see fig. ). the glyph following, however, in a b is quite clearly cumhu (see fig. , _g'-h'_), which is the month part of the terminal date as reached by calculation. therefore, since a a has the coefficient it is probable that it is a variant of the month-glyph "indicator";[ ] and consequently that the month glyph itself follows, as we have seen, in b . in other words, the terminal date recorded, ahau cumhu, agrees with the terminal date reached by calculation, and the whole text, so far as it can be deciphered, reads . . . . ahau cumhu. the student will note that this initial series precedes the initial series in plate , _a_ by exactly uinals, or days. compare _a_ and _b_, plate . in plate , _a_, is figured the initial series from stela at copan.[ ] the introducing glyph occupies the space of four glyph-blocks, a -b , and there follows in a -b a the initial-series number . . . . . the cycle glyph in a is partially effaced; the clasped hand, however, the determining characteristic of the cycle head, may still be distinguished. the katun head in b 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 , but the two middle crescents are purely decorative and have no numerical value, and the numeral recorded here is (see pp. - ). although the tun and uinal period glyphs in a a and a b,[ ] respectively, are effaced, their coefficients may be distinguished as and , respectively. in such a case the student is perfectly justified in assuming that the tun and uinal signs originally stood here. in b a 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 (see fig. , _s-w_).[ ] the number here recorded is . . . . . [illustration: glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs] { } reducing this to units of the st order by means of table xiii, we have: a = × , = , , b = × , = , a a = × = , a b = × = b a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying to the remainder rules , , and (pp. - ), respectively, the date reached by the resulting calculations will be ahau zotz. turning to our text again, the student will have little difficulty in identifying b b as 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 . following the next glyphs in order, a -a , the closing glyph of the supplementary series is reached in b a. compare this glyph with the forms in figure . the coefficient of b a is again a head-variant numeral, as in the case of the kin period glyph in b a, above. the fleshless lower jaw and other skull-like characteristics indicate that the numeral is here recorded. compare b a with figure , _m-r_. since b a is the last glyph of the supplementary series, the next glyph b b should represent the month sign. by comparing the latter form with the month signs in figure the student will readily recognize that the sign for zotz in _e_ or _f_ is the month sign here recorded. the coefficient stands above. consequently, b b and b b represent the same terminal date, ahau zotz, as reached by calculation. this whole initial series reads . . . . ahau zotz, and according to the writer's view, the monument upon which it occurs (stela at copan) was the period stone for the hotun which began with the day . . . . imix xul[ ] and ended with the day . . . . ahau zotz, here recorded. in plate , _b_, is figured the initial series from stela at copan.[ ] the introducing glyph stands in a -b and is followed by the five period glyphs in a -a . the cycle is very clearly recorded in a , the clasped hand being of a particularly realistic form. although { } the coefficient is partially effaced, enough remains to show that it was above , having had originally more than the one bar which remains, and less than , there being space for only one more bar or row of dots. in all the previous initial series the cycle coefficient was , consequently it is reasonable to assume that dots originally occupied the effaced part of this glyph. if the use of cycles in this number gives a terminal date which agrees with the terminal date recorded, the above assumption becomes a certainty. in b six katuns are recorded. note the ornamental dotted ovals on each side of the dot in the numeral . although the head for the tun in a is partially effaced, we are warranted in assuming that this was the period originally recorded here. the coefficient appears clearly. the uinal head in b is totally unfamiliar and seems to have the fleshless lower jaw properly belonging to the tun head; from its position, however, the th in the number, we are justified in calling this glyph the uinal sign. its coefficient denotes that uinals are recorded here. although the period glyph in a is also entirely effaced, the coefficient appears clearly as , and from position again, th in the number, we are justified once more in assuming that kins were originally recorded, here. it seems at first glance that the above reading of the number a -a rests on several assumptions: . that the cycle coefficient was originally . . that the effaced glyph in a was a tun head. . that the irregular head in b is a uinal head. . that the effaced glyph in a 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 d, th, and th 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 , when, so far as the appearance of a is concerned, it might have been either , , , , or . the reason for choosing 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 , our assumption becomes a certainty. designating the above number as . . . . then and reducing this by means of table xiii, we obtain: a = × , = , , b = × , = , a = × = , b = × = a = × = --------- , , { } deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the date determined by the resulting calculations will be ahau pax. turning to our text again, the student will have little difficulty in recognizing the first part of this date, the day ahau, in b . the numeral appears clearly, and the day sign is the profile-head _h'_ or _i'_, the second variant for ahau in figure . the significance of the element standing between the numeral and the day sign is unknown. following along through a , b , a , b , the closing glyph of the supplementary series is reached in a . 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 , and the latter with the head variant for in figure , _m-r_. note the fleshless lower jaw in the head numeral in both places. the following glyph, b , is one of the clearest in the entire text. the numeral is , and the month sign on comparison with figure unmistakably proves itself to be the sign for pax in _c'_. therefore the terminal date recorded in b , b , namely, ahau pax, agrees with the terminal date determined by calculation; it follows, further, that the effaced cycle coefficient in a must have been , the value tentatively ascribed to it in the above calculations. the whole initial series reads . . . . ahau 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 , records the next to earliest initial series[ ] yet deciphered at copan.[ ] evidences of antiquity appear in the glyphs in several different ways. the bars denoting 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. { } [illustration: fig. . initial series showing bar and dot numerals and head-variant period glyphs: _a_, stela c (west side), quirigua; _b_, stela m, copan.] in figure , _a_, is figured the initial series on the west side of stela c at quirigua.[ ] the introducing glyph in a -b is followed by the number in a -a , which the student will have no difficulty in reading except for the head-variant numeral attached to the kin sign in a . the clasped hand in this glyph, however, suggests that kins are recorded here, and a comparison of this form with figure , _s-w_, confirms the suggestion. the number therefore reads . . . . . reducing this number by means of table xiii to units of the st order, we obtain: a = × , = , , b = × , = , a = × = b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, we reach for the terminal date ahau yaxkin. looking for the day part of this date in b , we find that the form there recorded bears no resemblance to ahau, the day determined by calculation. moreover, comparison of it with the day signs in figure shows that it is unlike all of them; further, there is { } no bar and dot coefficient. these several points indicate that the day sign is not the glyph in b , also that the day sign is, therefore, out of its regular position. the next glyph in the text, a , instead of being one of the supplementary series is the day glyph ahau, which should have been recorded in b . the student will readily make the same identification after comparing a with figure , _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 b . the form in b has a coefficient , one of the four ( , , , ) which the month must have, since the day sign is ahau (see table vii). a comparison of the form in b with the month signs in figure 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 . . . . ahau yaxkin.[ ] in figure , _b_, is shown the initial series on stela m at copan.[ ] the introducing glyph appears in a and the initial-series number in b a-b a. the student will note the use of both normal-form and head-variant period glyphs in this text, the cycle, tun, and uinal in b a, a a, and a b, respectively, being expressed by the latter, and the katun and kin in b b and b a, respectively, by the former. the number recorded is . . . . , and this reduces to units of the first order, as follows (see table xiii): b a = × , = , , b b = × , = , a a = × = , a b = × = b a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached by the resulting calculations will be ahau zotz. turning to our text, the student will have no difficulty in recognizing in b b the day ahau. the month glyph in this inscription irregularly follows immediately { } the day glyph. compare the form in a a with the month signs in figure and it will be found to be the sign for zotz (see fig. , _e-f_). the coefficient is and the whole glyph represents the month part zotz, the same as determined by calculation. this whole initial series reads . . . . ahau 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 , _a_, is figured a photograph of the initial series on the front of stela at yaxchilan.[ ] the introducing glyph appears in a b ; cycles in a ; katuns in b , tun in a , uinals in b , and kins in b . 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 . . . . , and reducing this to units of the first order by means of table xiii, we have: a = × , = , , b = × , = , a = × = b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively), to the remainder, the terminal date reached by the resulting calculations will be ahau tzec. the day part of this date is very clearly recorded in b immediately after the last period glyph, and the student will readily recognize the day ahau in this form. following along the glyphs of the supplementary series in c d , c d , the closing glyph is reached in c b. it is very clear and has a coefficient of . the glyph following (d ) should record the month sign. a comparison of this form with the several month signs in figure shows that tzec is the month here recorded. compare d with figure , _g-h_. the month coefficient is . the terminal date, therefore, recorded in b and d ( ahau tzec) agrees with the terminal date determined by calculation, and this whole text reads . . . . ahau tzec. the meaning of the element between the tun coefficient and the tun sign in a , which is repeated again in d 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] { } in plate , _b_, is figured the initial series on an altar in front of structure at yaxchilan.[ ] the introducing glyph appears in a b and is followed by the number in a -a . the period glyphs are all expressed as head variants and the coefficients as bar and dot numerals. excepting the kin coefficient in a , the number is quite easily read as . . . .? an inspection of our text shows that the coefficient must be , , , or . let us work out the terminal dates for all four of these values, commencing with , and then see which of the resulting terminal days is the one actually recorded in a . reducing the number . . . . to units of the first order by means of table xiii, we have: a = × , = , , b = × , = , a = × = , b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively), to the remainder, the terminal day reached will be ahau pop. therefore the initial-series numbers . . . . , . . . . , and . . . . will lead to the three days immediately following . . . . ahau pop. therefore our four possible terminal dates will be: . . . . ahau pop . . . . imix pop <------ . . . . ik pop . . . . akbal 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 b . this glyph probably has the coefficient ( bars and numerical dots), the oblong element between probably being ornamental only. this number must be either or , since if it were the dots would all be of the same size, which is not the case. an inspection of the coefficient in b eliminates from consideration, therefore, the last two of the above four possible terminal dates, and reduces the possible values for the kin coefficient in a to or . comparing the glyph in b with the day signs in figure , the form here recorded will be found to be identical with the sign for imix in figure , a. this eliminates the first terminal date above and leaves the second, the day part of which { } we have just seen appears in b . this further proves that the kin coefficient in a is . the final confirmation of this identification will come from the month glyph, which must be pop if we have correctly identified the day as imix. if, on the other hand, the day were ahau, the month glyph would be pop. passing over a b , a b , c d , and c , we, reach in d a the closing glyph of the supplementary series, here showing the coefficient . compare this form with figure . the month glyph, therefore, should appear in d b. the coefficient of this glyph is very clearly , thus confirming our identification of b as imix. (see table vii.) and finally, the month glyph itself is pop. compare d b with figure , a. the whole initial series in plate , _b_, therefore reads . . . . imix pop. in plate , is figured the initial series from stela at tikal.[ ] the introducing glyph, though somewhat effaced, may still be recognized in a . the initial-series number follows in b -b . the head-variant period glyphs are too badly weathered to show the determining characteristic in each case, except the uinal head in a , 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 a had not proved that the uinal was recorded here, we should have assumed this to be the case because this glyph, a , 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 b -b as . . . . . reducing this number by means of table xiii to units of the first order, we obtain: b = × , = , , a = × , = , b = × = , a = × = b = × = --------- , , deducting all the calendar rounds possible from this number, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau kayab. it remains to find this date in the text. the glyph in a , 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 , _h', i'_. the coefficient of a is very clearly dots, that is, , and consequently this glyph agrees with the day as determined by calculation, ahau. passing over b , a , b , and a , we reach in b the closing glyph of the supplementary series, here recorded with a coefficient of . compare b with figure . the month glyph follows in a with the coefficient . comparing this latter glyph with the month signs in figure , it is evident that the month kayab (fig. , _d'-f'_) is recorded in a , which reads, therefore, kayab. hence the whole text records the initial series . . . . ahau kayab. [illustration: glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs--stela , tikal] [illustration: glyphs representing initial series, showing use of bar and dot numerals and head-variant period glyphs--stela a (east side), quirigua] { } this initial series is extremely important, because it records the earliest contemporaneous[ ] date yet found on a monument[ ] in the maya territory. in plate is figured the initial series from the east side of stela a at quirigua.[ ] the introducing glyph appears in a -b and the initial-series number in a -a . the student will have little difficulty in picking out the clasped hand in a , the oval in the top of the head in b , the fleshless lower jaw in a , the mouth curl in b , as the essential characteristic of the cycle, katun, tun, and uinal heads, respectively. the kin head in a is the banded-headdress variant (compare fig. , _i, j_), and this completes the number, which is . . . . . reducing this by means of table xiii to units of the first order, we have: a = × , = , , b = × , = , a = × = , b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , { } respectively) to the remainder, the terminal day reached will be found to be ahau kayab. in b the profile variant of the day sign, ahau, is clearly recorded (fig. , _h', i'_), and to it is attached a head-variant numeral. comparing this with the head-variant numerals in figures - , the student will have little difficulty in identifying it as the head for (see fig. , _t-v_). note the so-called "hatchet eye" in a , which is the determining characteristic of the head for (see p. ). passing over a b , a b , a b , we reach in a the closing glyph of the supplementary series, here showing the head-variant coefficient (see fig. , _m-r_). in b , the next glyph, is recorded the month kayab (see fig. , _d'-f'_). the whole initial series therefore reads . . . . ahau 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 , _a_, is figured the initial series on the tablet from the temple of the foliated cross at palenque.[ ] the introducing glyph appears in a b , and is followed by the initial-series number in a -b . the student will have little difficulty in identifying the heads in b , b , b , b , and b as the head variants for the cycle, katun, tun, uinal, and kin, respectively. the head in a prefixed to the cycle glyph in b has for its determining characteristic the forehead ornament composed of _more than one part_ (here, of two parts). as explained on page , this is the essential element of the head for . compare a with figure , _a-e_, and the two glyphs will be found to be identical. we may conclude, therefore, that in place of the usual cycles heretofore encountered in initial series, we have recorded in a -b cycle.[ ] the katun coefficient in a resembles closely the cycle coefficient except that its forehead ornament is composed of but a single part, a large curl. as explained on page , the heads for and 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 a , and the latter a forehead ornament composed of but one part, as here in a . this head, moreover, is very similar to the head for in figure , _a-f_; indeed, the only difference is that the former has a fleshless lower jaw. this is the essential element of the head for (see p. ); when applied to the head for any other numeral it increases the value of the resulting head by . therefore we have recorded in a b , ( + ) katuns. the tun coefficient in a has for its determining characteristic the tun headdress, which, as explained on page , is the essential element of the head for (see fig. , _n-s_). therefore a represents , and a b , tuns. the uinal coefficient in a has for its essential elements the large bulging eye, square irid, and snaglike front tooth. as stated on page , these characterize the head for , examples of which are given in figure , _j-m_. consequently, a b records uinals. the kin coefficient in a is quite clearly . the student will readily recognize the clasped hand, which is the determining characteristic of the head (see p. and fig. , _s-w_). the number recorded in a -b is, therefore, . . . . . reducing this number to units of the st order by means of table xiii, we obtain: [illustration: glyphs representing initial series, showing use of head-variant numerals and period glyphs] { } a b = × , = , a b = × , = , a b = × = , a b = × = a b = × = ------- , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively), the terminal date reached will be ahau mac. of this date, the day part, ahau, is recorded very clearly in a b . compare the head in a with the head in a , which, we have seen, stood for and also with figure , _a-e_, and the head in b with figure , _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 a . the glyph in a has a coefficient , which agrees with the month coefficient determined by calculation, and a comparison of b with the forms for the months in figure shows that the month mac (fig. , _w, x_) is here recorded. the whole initial series therefore reads . . . . ahau mac. in plate , _b_, is figured the initial series on the tablet from the temple of the sun at palenque.[ ] the introducing glyph appears in a -b and is followed by the initial-series number in a -b . the student will have no difficulty in identifying the period glyphs in b , b , b , b , and b ; and the cycle, katun, and tun coefficients in a , a , and a , respectively, will be found to be exactly like the corresponding coefficients in the preceding initial series (pl. , _a_, a , a , a ), which, as we have seen, record the numbers , , and , respectively. the uinal coefficient in a , however, presents a new form. here the determining characteristic is the banded headdress, or fillet, which distinguishes the head for , as explained on page (see fig. _h, i_). we have then in a b record of { } uinals. the kin coefficient in a is very clearly . note the "hatchet eye," which, as explained on page , is the essential element of this head numeral, and also compare it with figure , _t-v_. the number recorded in a -b therefore is . . . . . reducing this to units of the first order by means of table xiii, we obtain: a b = × , = , a b = × , = , a b = × = , a b = × = a b = × = ------- , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and ), respectively, to the remainder, the terminal date reached will be cimi ceh. if this inscription is regular, the day part of the above date should follow in a b , the former expressing the coefficient and the latter the day sign. comparing a with the head numerals in figures - , it will be found to be like the second variant for in figure , _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 b with the day signs in figure , it will be seen that the form here recorded is the day sign cimi (fig. , _h, i_). therefore a b expresses the day 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 b . a comparison of this form with figure , _u-v_, shows that the month ceh is recorded here. the coefficient is . why the glyph in a 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 . . . . cimi ceh. the student will note that this initial series records a date days earlier than the preceding initial series (pl. , _a_). that two dates should be recorded which were within days of each other, and yet were more than , 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 ( ). 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. { } [illustration: fig. . 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 , _a_, is shown the initial series inscribed on the rises and treads of the stairway leading to house c in the palace at palenque.[ ] the introducing glyph is recorded in a , and the initial-series number follows in b -b . the student will readily recognize the period glyphs in b b, a b, b b, a b, and b b. the head expressing the cycle coefficient in b a has for its essential element the dots centering around the corner of the mouth. as explained on page , this characterizes the head for (see fig. , _g-l_, where variants for the head are figured). in b , therefore, we have recorded cycles, the number almost always found in initial series as the cycle coefficient. the essential element of the katun coefficient in a a is the forehead ornament composed of a single part. this denotes the head for (see p. , and fig. , _a-f_; also compare a a with the heads denoting in the two preceding examples, pl. , _a_, a , and pl. , _b_, a , each of which shows the same forehead ornament). the tun coefficient in b a is exactly like the cycle coefficient just above it in b a; that is, , having the same dotting of the face near the corner of the mouth. the uinal coefficient in a a is . compare this head numeral with a , plate , _b_, which also denotes , and also with figure , _x-b'_. the essential elements (see p. ) { } 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 b a is somewhat effaced, let us call it for the present[ ] and proceed to reduce our number . . . . to units of the first order by means of table xiii: b = × , = , , a = × , = , b = × = , a = × = b = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, we reach as the terminal date ahau pop. now let us examine the text and see what is the terminal date actually recorded. in a b the student will have little difficulty in recognizing the profile variant of the day sign ahau (see fig. , _h', i'_). this at once gives us the missing value for the kin coefficient in b , for the day ahau can never be reached in an initial series if the kin coefficient is other than . similarly, the day imix can never be reached in initial series if the kin coefficient is other than , etc. every one of the possible kin coefficients, to , 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 , 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 (p. ), though, as the student will see, both are applications of the same principle, that is, deducting all of the s possible and counting forward only the remainder. returning to our text, we can now say without hesitation that our number is . . . . and that the day sign in a b is ahau. the day coefficient in a a is just like the katun coefficient in a a, 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 in a a will show that the two forms are identical. the bifurcate ornament surmounting the head in a a 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 { } a a as the head for , that is, having a forehead ornament composed of more than one part, instead of the head for . the month glyph, which follows in b b, is unfortunately effaced, though its coefficient in b a is clearly the head for . compare b a with the uinal coefficient in a a and with the heads for in figure , _x-b'_. as recorded, therefore, the terminal date reads ahau ?, thus agreeing in every particular so far as it goes with the terminal date reached by calculation, ahau pop. in all probability the effaced sign in b b originally was the month pop. the whole initial series therefore reads . . . . ahau pop. in figure , _b_, is shown the initial series from stela p at copan.[ ] the introducing glyph appears in a -b and is followed by the initial-series number in a -b . the student will readily identify a , b , and a as cycles, katuns, and tuns, respectively. note the beard on the head representing the number in both a a and b a. as explained on page , this characteristic of the head for is not always present (see fig. , _g-i_). the uinal and kin glyphs have been crowded together into one glyph-block, b , the uinal appearing in b a and the kin in b b. both their coefficients are , which is expressed in each case by the form shown in figure . the whole number recorded is . . . . ; reducing this to units of the first order by means of table xiii, we obtain: a = × , = , , b = × , = , a = × = , b a = × = b b = × = --------- , , deducting from this number all of the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau pop. in a a the day ahau is very clearly recorded, the day sign being expressed by the profile variant and the by two dots (incorrectly shown as one dot in the accompanying drawing).[ ] passing over a b, b , and a we reach in b a the closing glyph of the supplementary series, and in the following glyph, b b, the month part of this terminal date. the coefficient is , and comparing the sign itself with the month signs in figure , it will be seen that the form in _a_ (pop) is the month recorded here. the whole initial series therefore reads . . . . ahau pop. { } [illustration: fig. . initial series, showing head-variant numerals and period glyphs, from zoömorph g at quirigua.] in figure is illustrated the initial series from zoömorph g at quirigua.[ ] the introducing glyph appears in a -b and is followed in c -h by the initial-series number. glyphs c d record cycles. the dots on the head for in c are partially effaced. in c is the katun coefficient and in d the katun sign. the determining characteristic of the head for appears in c , namely, the scroll passing under the eye and projecting upward and in front of the forehead. see page and figure , _w_. it would seem, then, at first sight that katuns were recorded in c d . that this was not the case, however, a closer examination of c 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 . consequently, instead of having katuns in c d we have ( + ) katuns. compare c with figure , _j-m_. in e f , tuns are recorded. the tun headdress in e gives the value to the head there depicted (see fig. , _n-s_) and the fleshless lower jaw adds , making the value of e . compare figure , _b-e_, where examples of the head for are given. glyphs e and f represent uinals and g h kins; note the clasped hand in e and g , which denotes the in each case. this whole number therefore reads . . . . . reducing this to units of the first order by means of table xiii, we have: c d = × , = , , c d = × , = , e f = × = , e f = × = g h = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively), to the remainder, the terminal day reached will be ahau muan. the day is recorded in g h . the day sign in h is quite clearly the grotesque head variant for ahau in figure , _j'-k'_. the presence of the tun headdress in g indicates that the coefficient here recorded must have been either or , 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 g is a day coefficient, and day coefficients as stated in chapter iii, can never rise above . consequently the number can not be recorded in g , and this form must stand for the number . [illustration: oldest initial series at copan--stela ] { } passing over i j , i j , k ll, k l , we reach in m the closing glyph of the supplementary series, here shown with a coefficient of , the head having a fleshless lower jaw. the month sign follows in n . the coefficient is and by comparing the sign itself with the month glyphs in figure , it will be apparent that the sign for muan in _a'_ or _b'_ is recorded here. the initial series of this monument therefore is . . . . ahau 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 at copan, because it is not only the oldest initial series at copan, but also the oldest one known in which head-variant numerals are used[ ] (see pl. ). the introducing glyph appears at a -b . there follows in a a number too much effaced to read, but which, on the basis of all our previous experience, we are justified in calling . similarly b must be the head variant of the cycle sign. the numeral is clearly recorded in a . note the square irid, protruding fang, and mouth curl. compare a with figure , _j-m_. although the glyph in b is too much effaced to read, we are justified in assuming that it is the head variant of the katun sign. the glyph in a is the numeral . note the fleshless lower jaw and other characteristics of the death's-head. again we are justified in assuming that b must be the head variant of the tun sign. the glyphs a , b clearly record uinals. note the clasped hand denoting zero in a , and the curling mouth fang of the uinal period glyph in b . this latter glyph is the full-figure form of the uinal sign[ ] (a frog). compare b with figure , 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 . . . .?. calling the missing kin coefficient , and reducing this number to units of the first order by means of table xiii, we have: a b = × , = , , a b = × , = , a b = × = , a b = × = × = --------- , , deducting from this number all the calendar rounds possible, { } (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau 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 , , , or (as here) and the uinal coefficient is (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, , the writer was shown a fragment of a stela which he was told was a part of this monument (stela ). this showed the top parts of two consecutive glyphs, the first of which very clearly had a coefficient of and the one following of . the glyphs to which these coefficients belonged were missing, but the coincidence of the two numbers (?) (?) 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 which showed the terminal date. this whole initial series therefore reads: . . . . ahau mol. it is chiefly interesting because it shows the earliest use of head-variant numerals known. in the foregoing texts plate , _a_, _b_, figure , _a_, _b_, and figure , the head-variant numerals , , , , , , , , , , , , , and have been given, and, excepting the forms for , , and , these include examples of all the head numerals.[ ] no more texts specially illustrating this type of numeral will be presented, but when any of the head numerals not figured above ( , , , , , and ) 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 , 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 is figured the initial series from stela d at copan.[ ] the introducing glyph is recorded in a . 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.[ ] [illustration: initial series on stela d, copan, showing full-figure numeral glyphs and period glyphs] { } the initial-series number itself appears in b -b . 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 , _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 . compare this head with figure , _g-l_, or with any other head variants for the numeral already figured. bearing in mind that the heads only present the determining characteristics of full-figure glyphs, the student will easily identify b as recording cycles. the katun and its coefficient are represented in a , 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 , the tun headdress. it has also the fleshless lower jaw of the head for . the combination of these two elements in one head, as we have seen, indicates the numeral , and a therefore records katuns. compare the head of this anthropomorphic figure with figure , _b-e_. the tun and its coefficient are represented in b . 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 , _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 (a ), except that in b the head has no fleshless lower jaw. since the head in a with the fleshless lower jaw and the tun headdress represents the numeral , the head in b without the former but with the latter represents the numeral . compare the head of the anthropomorphic figure in b with figure , _n-s_. it is clear, therefore, that tuns are recorded in b . the uinal and its coefficient in a are equally clear. the period glyph here appears as a frog (maya, _uo_), which, as we have seen { } elsewhere, may have been chosen to represent the -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 . note the clasped hand across the lower part of the face, and compare this form with figure , _s-w_. the whole glyph, therefore, stands for uinals. in b 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 b records kins. the whole number expressed by b -b is . . . . ; reducing this by means of table xiii to units of the first order, we have: b = × , = , , a = × , = , b = × = , a = × = b = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and respectively), to the remainder, the terminal date reached will be ahau chen. the day part of this terminal date is recorded in a . 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 , _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 . note the fleshless lower jaw of this head and compare it with the same element in figure , _m-r_. this glyph a records, therefore, the day reached by the initial series, ahau. the position of the month glyph in this text is most unusual. passing over b , the first glyph of the supplementary series, the month glyph follows it immediately in a . 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 . compare this head with the heads for , in figure , _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 , _o, p_. [illustration: initial series on stela j, copan] { } the superfix of figure , _o, p_, has been retained unchanged as the superfix in a b. 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 . . . . ahau chen. the student will note that this initial series records a date just tuns later than the initial series on stela b at copan (pl. , _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 , _a_,[ ] 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 (pl. , _b_), and the student will readily recognize it in the same position in _a_ of the same plate. the initial series number follows in , , , , and (pl. , _b_). referring to these corresponding positions in _a_, we find that cycles are recorded in , and katuns in . at this point the diagonal glyph- band passes under another band, emerging at , where the tun sign with a coefficient of is recorded. here the band turns again and, crossing backward diagonally, shows uinals in . at this point the band passes under three diagonals running in the opposite direction, emerging at position , the glyph in which are recorded kins. this number . . . . reduces by means of table xiii to units of the first order, as follows: = × , = , , = × , = , = × = , = × = = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau cumhu. referring again to plate , _b_, for the sequence of the glyphs in this text, it is clear that the day of this terminal date should be recorded in , immediately after the kins of the initial-series number in . it will be seen, however, in plate , _a_, that { } glyph is effaced, and consequently the day is missing. passing over , , , , and , in _a_ and _b_ of the plate named, we reach in the lower half of the closing glyph of the supplementary series here shown with a coefficient of . compare this form with figure . the month glyph, therefore, should follow in the upper half of .[ ] this glyph is very clearly the form for the month cumhu (see fig. , _g', h'_), and it seems to have attached to it the bar and dot coefficient . a comparison of this with the month coefficient , 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 , or in maya notation, bar. since the initial-series number is very clearly . . . . , and since this number leads to the terminal date ahau cumhu, it would seem that the ancient scribes had made an error in this text, recording bar and dots instead of 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 . . . . ahau 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 .[ ] 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 and is followed by the initial series in - . the student will have little difficulty in identifying , , and as cycles, katuns, and tuns, respectively. the uinal and kin glyphs in and , 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 for their uinal and kin coefficients.[ ] this { } 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 uinals and kins were originally recorded in glyphs and , respectively. furthermore, an inspection of the coefficients of these two glyphs in figure , _a_, shows that both of them are of the same general size and shape as the tun coefficient in , which, as we have seen, is very clearly . it is more than probable that the uinal and kin coefficients in this text were originally , like the tun coefficient, and that through weathering they have been eroded down to their present shape. in figure , _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 . it seems more than likely from the foregoing that the uinal and kin coefficients in this number were originally , and proceeding on this assumption, we have recorded in glyphs - , figure , _a_, the number . . . . . [illustration: fig. . 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: = × , = , , = × , = , = × = = × = = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date ahau tzec will be reached. [illustration: fig. . 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 immediately after the kin glyph in . the coefficient, though somewhat eroded, appears quite clearly as ( dots separated by an ornamental crescent). the day sign itself is the profile variant for ahau shown in figure , _h', i'_. the agreement of { } the day recorded with the day determined by calculations based on the assumption that the kin and uinal coefficients are both , of itself tends to establish the accuracy of these assumptions. passing over , , , , , , and , we reach in the closing glyph of the supplementary series, and in 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 tzec. the coefficient is just wide enough for three vertical divisions ( bars and 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 , _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, . . . . ahau tzec. if this is so, stela h is the earliest hotun-marker at quirigua.[ ] the student will have noticed from the foregoing texts, and it has also been stated several times, that the cycle coefficient is almost invariably . 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. , _a_ and _b_, respectively), in which the cycle coefficient in each case was . as explained on page , footnote , 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 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 , footnote , 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 . 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. { } [illustration: fig. . the initial series on the tuxtla statuette, the oldest initial series known (in the early part of cycle ).] [illustration: fig. . 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 ; in other words, both record dates which fell in the cycle immediately preceding that of the historic period, or cycle . 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 . . . . ahau 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. { } the initial series on the first of these minor antiquities, the tuxtla statuette, is shown in figure .[ ] 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. ), that is, numeration by position, as in the codices. see the discussion of initial series in the codices in chapter vi (pp. - ), and plates and . 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 . 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 cycles, katuns, tuns, uinals, and kins, that is, . . . . ; reducing this to units of the first order by means of table xiii, we have: × , = , , × , = , × = × = × = --------- , , solving this initial-series number for its terminal date, it will be found to be caban kankin. returning once more to our text (see fig. ), we find the day coefficient above reached, , is recorded just below the kins and appears to be attached to some character the details of which are, unfortunately, effaced. the month coefficient and the month sign kankin do not appear in the accompanying text, at least in recognizable form. this initial series would seem to be, therefore, . . . . caban kankin, of which the day sign, month coefficient, and month sign are effaced or unrecognizable. in spite of its unusual form and the absence of the day sign, and the month coefficient and sign the writer is inclined to accept the above date as a contemporaneous initial series.[ ] [illustration: fig. . drawings of the initial series: _a_, on the leyden plate. this records a cycle- 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- date, and is one of the latest initial series known.] the other initial series showing a cycle coefficient is on the leyden plate, a drawing of which is reproduced in figure , _a._ this initial series is far more satisfactory than the one just described, and { } its authenticity, generally speaking, is unquestioned. the student will easily identify a -b 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 . the initial-series number, expressed by normal-form numerals and head-variant period glyphs, follows in a -a . 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 a has the clasped hand, which is the distinguishing characteristic of the cycle head, and as such should have appeared in the head in a . neither the tun head in a nor the kin head in a 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 a , where the large mouth curl appears very clearly. however, the number recorded here may be read as . . . . 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. { } reducing this number to units of the first order by means of table xiii, we have: a = × , = , , a = × , = , a = × = , a = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be eb yaxkin. the day part of this date is very clearly recorded in a , the coefficient 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 , _s-u_. the month glyph appears in a a, the lower half of which unmistakably records the month yaxkin. (see fig. , _k, l_.) note the _yax_ and _kin_ elements in each. the only difficulty here seems to be the fact that a bar ( ) 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 . he would explain the bar as being merely ornamental. the whole initial series reads: . . . . eb yaxkin. the fact that there are some few irregularities in this text confirms rather than invalidates the antiquity which has been ascribed to it by the writer. dating from the period when the maya were just emerging from savagery to the arts and practices of a semicivilized state, it is not at all surprising that this inscription should reflect the crudities and uncertainties of its time. indeed, it is quite possible that at the very early period from which it probably dates ( . . . . eb yaxkin) the period glyphs had not yet become sufficiently conventionalized to show individual peculiarities, and their identity may have been determined solely by their position with reference to the introducing glyph, as seemingly is the case in some of the period glyphs of this text. the initial series on the leyden plate precedes the initial series on stela at tikal, the earliest contemporaneous date from the monuments, by more than 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- initial series are occasionally found in the dresden codex, though none are quite so early as the initial series from the tuxtla statuette. { } passing over the initial series whose cycle coefficient is , many of which have already been described, we come next to the consideration of initial series whose cycle coefficient is , a very limited number indeed. as explained in chapter i, the southern cities did not long survive the opening of cycle , and since initial-series dating did not prevail extensively in the later cities of the north, initial series showing cycles are very unusual. in figure , _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 a -b and is followed by the initial-series number in a -a . the student will have little difficulty in deciphering all of the coefficients except that belonging to the kin in a , which is a head-variant numeral, and the whole number will be found to read . . . .?. the coefficient of the day of the terminal date is very clearly (see b ) and the month part, zac (see a ). we may now read this initial series as . . . .? ? zac; in other words, the kin coefficient and the day sign are still indeterminate. first substituting as the missing value of the kin coefficient, the terminal date reached will be . . . . ahau yax. but according to table xv, position yax is just days earlier than position zac, the month part recorded in a . consequently, in order to reach zac from . . . . ahau yax, more days are necessary. counting these forward from . . . . ahau yax, the date reached will be . . . . muluc zac, which is the date recorded on this lintel. compare the day sign with figure , _m, n_, and the month sign with figure , _s, t_. { } [illustration: fig. . the cycle- initial series from quen santo (from drawings): _a_, stela ; _b_, stela . 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 yet remain to be considered, namely, stelæ and at quen santo.[ ] the first of these is shown in figure , a, but unfortunately only a fragment of this monument has been recovered. in a -b appears a perfectly regular form of the introducing glyph (see fig. ), and this is followed in a -b 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 a as cycles, noting the clasped hand on the head-variant period glyph, and b as katuns. the glyph in a has very clearly the coefficient , 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 b we are perfectly justified in assuming that tuns are recorded here. both the coefficient and the glyph in b are unfamiliar. however, as the former must be one of the numerals to , inclusive, since it is not one of the numerals to , inclusive, it is clear that it must be a new form for . 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 th position after the introducing glyph, b , we are justified in assuming that uinals are recorded here. beyond this we can not proceed with certainty, though the values for the missing parts suggested below are probably those recorded on the lost fragments of the monument. as recorded in a -b this number reads . . . .?. now, if we assume that the missing term is filled with , 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 from quen santo very clearly records the close of the hotun next after . . . . , which the writer believes this monument marks. for { } this reason it seems probable that the glyph which stood in a recorded kins. reducing this number to units of the first order by means of table xiii, we obtain: a = × , = , , b = × , = , a = × = , b = × = a [ ] = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau yax, and the whole initial series originally recorded on this monument was probably . . . . ahau yax. in figure , _b_, is shown stela from quen santo. the workmanship on this monument is somewhat better than on stela and, moreover, its initial series is complete. the introducing glyph appears in a -b and is followed by the initial-series number in a -a . again, cycles are very clearly recorded in a , the clasped hand of the cycle head still appearing in spite of the weathering of this glyph. the katun sign in b is almost entirely effaced, though sufficient traces of its coefficient remain to enable us to identify it as . 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 had been recorded here the uneffaced dot would have been nearer the bottom. it is clear that and are quite out of the question and that remains the only possible value of the numeral here. we are justified in assuming that the effaced period glyph was the katun sign. in a tuns are very clearly recorded; note the fleshless lower jaw of the tun head. the uinal head with its characteristic mouth curl appears in b . the coefficient of this latter glyph is identical with the uinal coefficient in the preceding text (see fig. , _a_) in b , which we there identified as a form for . therefore we must make the same identification here, and b then becomes uinals. from its position, if not from its appearance, we are justified in designating the glyph in a the head for the kin period; since the coefficient attached to this head is the same as the one in the preceding glyph (b ), we may therefore conclude that kins are recorded here. the whole number expressed in a -a is { } therefore . . . . . reducing this to units of the first order by means of table xiii, we have: a = × , = , , b = × , = , a = × = , b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be ahau chen. although the day sign in b is effaced, the coefficient appears quite clearly. the month glyph is recorded in a . the student will have little difficulty in restoring the coefficient as , and the month glyph is certainly either chen, yax, zac, or ceh (compare fig. , _o_ and _p_, _q_ and _r_, _s_ and _t_, and _u_ and _v_, respectively). moreover, since the month coefficient is , the day sign in b can have been only chicchan, oc, men, or ahau (see table vii); since the kin coefficient in a is , the effaced day sign must have been ahau. therefore the initial series on stela at quen santo reads . . . . ahau chen and marked the hotun immediately following the hotun commemorated by stela at the same site. the student will note also that the date on stela 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. , _b_). and a glance at the map in plate will show, further, that chichen itza and quen santo are separated from each other by almost the entire length (north and south) of the maya territory, the former being in the extreme northern part of yucatan and the latter considerably to the south of the central maya cities. the presence of two monuments so close together chronologically and yet so far apart geographically is difficult to explain. moreover, the problem is further complicated by the fact that not one of the many cities lying between has yielded thus far a date as late as either of these.[ ] the most logical explanation of this interesting phenomenon seems to be that while the main body of the maya moved northward into yucatan after the collapse of the southern cities others retreated southward into the highlands of guatemala; that while the northern emigrants { } 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- 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,[ ] are the only ones which are not counted from the starting point of maya chronology, the date ahau cumhu. in figure , _a_, is shown the initial series on the east side of stela c at quirigua.[ ] the introducing glyph appears in a -b , and is followed by the initial-series number in a -a . the student will easily read this as . . . . . reducing this number to units of the first order by means of table xiii, we have: a = × , = , , b = × , = a = × = b = × = a = × = --------- , , deducting from this number all the calendar rounds possible, [ ] (see table xvi), and applying rules , , and (pp. , , and ), respectively, to the remainder, the terminal date reached should be, under ordinary circumstances, ahau kankin. an inspection of our text, however, will show that the terminal date recorded in b -a is unmistakably ahau cumhu, and not ahau kankin. the month part in a is unusually clear, and there can be no doubt { } that it is cumhu. compare a with figure , _g', h'_. if we have made no mistake in calculations, then it is evident that . . . . counted forward from the starting point of maya chronology, ahau cumhu, will not reach the terminal date recorded. further, since the count in initial series has never been known to be backward,[ ] we are forced to accept one of two conclusions: either the starting point is not ahau 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 . . . . is counted. the terminal date reached by the count is recorded very clearly as ahau cumhu. now, if we reverse our operation and count the given number, . . . . , _backward_ from the known terminal date, ahau cumhu, we reach the starting point from which the count proceeds. [illustration: fig. . initial series which proceed from a date prior to ahau 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, (see p. , footnote ), and applying rules , , and (pp. , , , 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 ahau zotz. this is the first initial series yet encountered which has not proceeded from the date ahau 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 a -a , . . . . , be counted forward from ahau zotz as a starting point, the terminal date reached by calculation will agree with the terminal date as recorded in b -a , ahau cumhu. { } let us next examine the initial series on the tablet from the temple of the cross at palenque, which is shown in figure , _b_.[ ] the introducing glyph appears in a -b , and is followed by the initial-series number in a -b . the period glyphs in b , b , b , b , and b are all expressed by their corresponding normal forms, which will be readily recognized. passing over the cycle coefficient in a for the present, it is clear that the katun coefficient in a is . note the dots around the mouth, characteristic of the head for (fig. , _g-l_), and the fleshless lower jaw, the essential element of the head for (fig. , _m-r_). the combination of the two gives the head in a the value of . the tun coefficient in a is equally clear as . note the banded headdress, characteristic of the head for (fig. , _h, i_), and the fleshless lower jaw of the head, the combination of the two giving the head for (fig. , _w_).[ ] the head for and the hand zero sign appear as the coefficient of the uinal and kin signs in a and a , respectively. the number will read, therefore, ?. . . . . let us examine the cycle coefficient in a again. the natural assumption, of course, is that it is . but the dots characteristic of the head for are not to be found here. as this head has no fleshless lower jaw, it can not be or any number above , and as there is no clasped hand associated with it, it can not signify , so we are limited to the numbers, , , , , ,[ ] , , , , , and , as the numeral here recorded. comparing this form with these numerals in figures and , it is evident that it can not be , , , , , , , or , and that it must therefore be , , or . substituting these three values in turn, we have . . . . , . . . . , and . . . . as the possible numbers recorded in a -b , and reducing these numbers to units of the first order and deducting the highest number of calendar rounds possible from each, and applying rules , , and (pp. , , and , respectively) to their remainders, the terminal dates reached will be: . . . . ahau pax . . . . ahau yax . . . . ahau 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 a can be determined. the terminal date of this initial series is recorded in a -b and the student will easily read it as ahau tzec. the only difference { } between the day coefficient and the month coefficient is that the latter has a fleshless lower jaw, increasing its value by . moreover, comparison of the month sign in b with _g_ and _h_, figure , 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. , a): either the starting point of this initial series is not the date ahau cumhu, or there is some error in the original text.[ ] assuming that the ancient scribes made no mistakes in this inscription, let us count backward from the recorded terminal date, ahau tzec, each of the three numbers . . . . , . . . . , and . . . . , one of which, we have seen, is recorded in a -b . 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 , , and (pp. , , and , respectively), to the remainders, the starting points will be found to be: ahau mol for . . . . ahau mac for . . . . ahau zotz for . . . . 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 , , or . most maya students have accepted as the starting point of this initial-series number the last of the three dates above given, ahau zotz, which involves also the identification of the cycle coefficient in a as . the writer has reached the same conclusion from the following points: . the cycle coefficient in a , except for its very unusual headdress, is almost identical with the other two head-variant numerals, whose values are known to be . these three head numerals are shown side by side in figure , _t-v, t_ being the form in a 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. ), 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 a represents the numeral , and if this is so the starting point of the initial series under discussion is ahau zotz. . aside from the fact that seems to be the best reading of the head in a , and consequently that the starting point of this number is ahau zotz, the writer believes that ahau 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 ahau mol or ahau mac. [illustration: initial series and secondary series on lintel , yaxchilan] { } as we have seen in discussing the preceding text, from the east side of stela c at quirigua (fig. , _a_), the initial series there recorded was counted from the same starting point, ahau zotz, as the initial series from the temple of the cross at palenque, if we read the latter as . . . . . this coincidence, the writer believes, is sufficient to warrant the identification of the head in a (fig. , _b_) as the head numeral and the acceptance of this initial series as proceeding from the same starting point as the quirigua text just described, namely, the date ahau 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. - ) 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 at yaxchilan, which is figured in plate .[ ] as usual, when an initial series is recorded, the introducing glyph opens the text and this sign appears in a , being followed by the initial-series number itself in b -b . this the student will readily decipher as . . . . , recording apparently a very early date in maya history, within years of . . . . ahau ceh, the date arbitrarily fixed by the writer as the opening of the first great period. reducing this number by means of table xiii to units of the first order[ ] and deducting all the calendar rounds possible, (see table xvi), and applying rules , , and (pp. , , and , respectively) to the remainder, the terminal date reached will be kan yax. this date the student will find recorded in a and a a, glyph b b being the month-sign "indicator," or the closing glyph of the { } supplementary series, here shown with the coefficient . compare the day sign in a a with the sign for kan in figure , _f_, and the month sign in a a with the sign for yax in figure , _q, r_. we have then recorded in a -a [ ], and a a the initial-series date . . . . kan 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 c -c 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: . there is no introducing glyph, a fact which at once eliminates the possibility that it might be an initial series. . there is no kin period glyph, the uinal sign in c having two coefficients instead of one. . 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. ) 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. ) 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 and , above) are characteristic of the number in c -c , it is probable that a secondary series is recorded here, and that it expresses kins, uinals, tun, and katuns. reversing this, and writing it according to the notation followed by most maya students (see p. , footnote ), we have as the number recorded by c -c , . . . . reducing this number to units of the first order by means of table xiii, we have: c = × , = , d = × = c = × = c = × = ------- , since all the calendar rounds which this number contains, (see { } table xvi) may be deducted from it without affecting its value, we can further reduce it to , ( , - , ), and this will be the number used in the following calculations. it was stated (on p. ) 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 . . . , which we have reduced to , units of the first order, is counted _forward_ from the date kan yax, the one next preceding it in our text, a date, moreover, the initial-series value of which is known. remembering that this date kan yax is our new starting point, and that the count is forward, by applying rules , , and (pp. , , and , respectively), to , , the new terminal date reached will be muluc tzec; and this date is recorded in c -d . compare c with the sign for the day muluc in figure , _m, n_, and d with the sign for the month tzec in figure , _g, h_. furthermore, by adding the secondary-series number . . . to . . . . (the initial-series number which fixes the position of the date kan yax in the long count), the initial-series value of the terminal date of the secondary series (calculated and identified above as muluc tzec) can also be determined as follows: . . . . kan yax initial series . . . secondary-series number . . . . muluc tzec initial series of the secondary-series terminal date muluc tzec the student may verify the above calculations by treating . . . . as a new initial-series number, and counting it forward from ahau cumhu, the starting point of maya chronology. the terminal date reached will be found to be the same date as the one recorded in c -d , namely, muluc tzec. what is the meaning then of this text, which records two dates nearly years apart?[ ] 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, . . . . muluc 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 . . . . muluc tzec in point { } of time than to . . . . kan yax, the initial-series date recorded on this lintel. indeed, while they range from days[ ] to years from the former, the one nearest the latter is more than years later. this practically proves that . . . . muluc tzec indicates the "contemporaneous time" of this lintel and that . . . . kan 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 . . . . muluc 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 muluc tzec, the initial-series value of which was found to be . . . . , 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 at piedras negras, figured in plate .[ ] 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 a and is followed by the initial-series number . . . . in a -a . 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 a , c , namely, cib yaxkin.[ ] compare a with the sign for cib in figure , _z_, and c with the sign for yaxkin in figure , _k, l_. the initial series recorded in a -a , c is . . . . cib yaxkin. [illustration: initial series and secondary series on stela , piedras negras] { } passing over the glyphs in b -e , the meanings of which are unknown, we reach in d e 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 d e 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: . . . reducing this to units of the first order, we have: e = × = , d = × = d = × = ----- , remembering that secondary-series numbers are usually counted from the dates next preceding them in the texts, in this case cib yaxkin, and proceeding according to rules , , and (pp. , , and , respectively), the terminal date of the secondary series reached will be chuen kankin, which is recorded in f g , though unfortunately these glyphs are somewhat effaced. moreover, since the position of cib 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, chuen kankin: . . . . cib yaxkin . . . . . . chuen kankin but the end of this text has not been reached with the date chuen kankin in f g . passing over f g , the meanings of which are unknown, we reach in f an inverted ahau with the coefficient above it. as explained on page , this probably signifies 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. , _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 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 chuen kankin is our new starting point. counting forward from this date, according to rules , , and (pp. , , and , respectively), the terminal date reached will be cib kankin, and this latter date is recorded in g -g . compare g with the sign for cib in a and in figure , _z_, and g with the sign for kankin in figure , _y, z_. moreover, since the initial-series value of chuen kankin was calculated above as . . . . , { } the initial-series value of this new date, cib kankin, also can be calculated from it: . . . . chuen kankin . . . . cib kankin passing over g as unknown, we reach in g -g another secondary-series number. the student will have little difficulty in identifying g as uinals, kins, and g as katun. it will be noted that no tun sign appears in this number, which is a very unusual condition. by far the commoner practice in such cases in which units of some period are involved is to record the period with a coefficient . however, this was not done in the present case, and since no tuns are recorded, we may conclude that none were involved, and g -g may be written .( ). . . reducing this number to units of the first order, we have: g = × , = , ([ ]) × = g = × = g = × = ----- , remembering that the starting point from which this number is counted is the date next preceding it, cib kankin, and applying rules , , and (pp. , , and , respectively), the terminal date reached will be imix zac; this latter date is recorded in g -g . compare g with the sign for imix in figure , _a, b_, and g with the sign for zac in figure , _s, t_. moreover, since the initial series of cib kankin was obtained by calculation from the date next preceding it, the initial series of imix zac may be determined in the same way. . . . . cib kankin . .[ ] . . . . . imix zac with the above date closes the known part of this text, the remaining glyphs, g -g , being of unknown meaning. assembling all the glyphs deciphered above, the known part of this text reads as follows: . . . . a -a , c cib yaxkin . . d e . . . . f g chuen kankin f . . . . g g cib kankin . .[ ] . g g . . . . g g imix zac [illustration: initial series (_a_) and secondary series (_b_) on stela k, quirigua] { } we have recorded here four different dates, of which the last, . . . . imix zac, probably represents the actual date, or very near thereto, of this monument.[ ] the period covered between the first and last of these dates is about 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 is figured the initial series from stela k at quirigua.[ ] the text opens on the north side of this monument (see pl. , _a_) with the introducing glyph in a -b . this is followed by the initial-series number . . . . in a -b , which leads to the terminal date ahau yax. the day part of this date the student will find recorded in its regular position, a a. passing over a b and b , the meanings of which are unknown, we reach in a a secondary-series number composed very clearly of uinals and kins ( . ), which reduces to the following number of units of the first order: a = × = a = × = --- the first assumption is that this number is counted forward from the terminal date of the initial series, ahau yax, and performing the operations indicated in rules , , and (pp. , , and , respectively) the terminal date reached will be oc uo. now, although the day sign in b b is clearly oc (see fig. , _o-q_), its coefficient is very clearly , not , and, moreover, the month in a a is unmistakably kayab (see fig. , _d'-f'_). here then instead of finding the date determined by calculation, oc uo, the date recorded is oc kayab, and consequently there is some departure from the practices heretofore encountered. since the association of the number . is so close with ( ) the terminal date of the initial series, ahau yax, and ( ) the date oc 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 { } number backward and see whether we can reach the date recorded in b b-a a ( oc kayab) in this way. counting _backward_ from ahau yax, according to rules , , and (pp. , , and , respectively), the terminal date reached will be oc kayab, as recorded in b b-a . 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 oc kayab, which may be determined by calculation: . . . . ahau yax . . . . . oc kayab this text closes on the south side of the monument in a very unusual manner (see pl. , _b_). in b a appears the month-sign indicator, here recorded as a head variant with a coefficient , and following immediately in b b a secondary-series number composed of uinals and kins, or, in other words, nothing. it is obvious that in counting this number . , or nothing, either backward or forward from the date next preceding it in the text, oc kayab in b b-a a on the north side of the stela, the same date oc kayab will remain. but this date is not repeated in a , where the terminal date of this secondary series, . , seems to be recorded. however, if we count . from the terminal date of the initial series, ahau yax, we reach the date recorded in a , ahau yax,[ ] and this whole text so far as deciphered will read: . . . . ahau yax . backward . . . . oc kayab . forward from initial series . . . . ahau yax the reason for recording a secondary-series number equal to zero, the writer believes, was because the first secondary-series date oc 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 . . . . ahau zac (see pl. , _c_). mr. bowditch ( : p. ) has advanced a very plausible explanation to account for the presence of the date . . . . oc kayab { } on this monument. he shows that at the time when stela k was erected, namely, . . . . ahau yax, the official calendar had outrun the seasons by just days, or exactly the number of days recorded in a , plate , a (north side); and further, that instead of being the day yax, which occurred at quirigua about the beginning of the dry season,[ ] in reality the season was days behind, or at 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 days recorded in a may well represent the days actually needed on the date . . . . ahau yax to bring the calendar into harmony with the current season. if this be true, then the date . . . . oc kayab represented the day indicated by the sun when the calendar showed that the d hotun in katun of cycle had been completed. mr. bowditch suggests the following free interpretation of this passage: "the sun has just set at its northern point[ ] and we are counting the day yax-- days from 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 days on this monument. [illustration: fig. . the initial series on stela j, quirigua.] in figures and are illustrated the initial series and secondary series from stela j at quirigua.[ ] for lack of space the introducing glyph in this text has been omitted; it occupies the position of six glyph-blocks, however, a -b , after which the initial-series number . . . . follows in a -b . this leads to the terminal date ahau zotz, which is recorded in a , b , b , the glyph in a being the month-sign indicator here shown with the coefficient . compare b with the second variant for ahau in figure _h', i'_, and b with the sign for zotz in figure , _e, f_. the { } initial-series part of this text therefore in a -b , b , is perfectly regular and reads as follows: . . . . ahau zotz. the secondary series, however, are unusual and differ in several respects from the ones heretofore presented. [illustration: fig. . the secondary series on stela j, quirigua.] the first secondary series inscribed on this monument (see fig. , _a_) is at b -b . this series the student should readily decipher as kins, uinals, tuns, and katuns, which we may write . . . . 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, b , which, however, he proceeded to nullify at once by attaching to it the coefficient . for in so far as the numerical value is concerned, . . and . . . are equal. the next peculiarity is that the date which follows this number in b -a 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 caban kayab; compare b with the sign for caban in figure , _a', b'_, and a with the sign for kayab in figure , _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, . . . . . we may safely conclude, therefore, that the date in a -b is . . . . caban kayab, and use it in our calculations as such. reducing . . . to units of the first order, we have: b = × , = a = × = , b = × = b = × = ----- , { } applying rules , , and (pp. , , and , respectively) to this number, the terminal date reached will be ahau chen, which is nowhere recorded in the text (see fig. , a). the initial series corresponding to this date, however, may be calculated from the initial series which we have assigned to the date caban kayab: . . . . caban kayab . . . . . . . ahau chen although the date . . . . ahau 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. ), . . . . ahau zotz. the other secondary series on this monument (see fig. , _b_) appears at b -a , and records tuns, uinals, and kins, which we may write thus: . . . as in the preceding case, the date following this number in b -a is its starting point, not its terminal date, a very unusual feature, as has been explained. this date is cimi tzec--compare b with the sign for cimi in figure , _h, i_, and a with the sign for tzec in figure , _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 . . . . cimi tzec. reducing the number recorded in b -a , . . , to units of the first order, we have: a = × = , b = × = b = × = ----- , applying rules , , and (pp. , , and , respectively) to the number, the terminal date reached will be ahau zotz, which does not appear in figure , _b_. the initial series corresponding to this date may be calculated as follows: . . . . cimi tzec . . . . . . ahau zotz but this was the initial series recorded on the reverse of this monument, consequently the secondary-series dates, both of which have { } preceded the initial-series date in point of time, bring this count up to the contemporaneous time of this monument, which was . . . . ahau 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: . . . . caban kayab figure , _a_, b -a . . . b -b [ . . . . ] [ ahau chen][ ] [ . . ][ ] . . . . cimi tzec figure , _b_, b -a . . b -a . . . . ahau zotz figure , a -b , b by the above arrangement all the dates present in the text lead up to . . . . ahau 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: ( ) the starting points of secondary-series numbers do not always precede the numbers counted from them, and ( ) the terminal dates and starting points are not always both recorded. the former point will be illustrated in the following example: in plate , _a_, is figured the initial series from the west side of stela f at quirigua.[ ] the introducing glyph appears in a -b and is followed by the initial-series number in a -a . this is expressed by head variants and reads as follows: . . . . . the terminal date reached by this number is caban kayab, which is recorded in b -a . the student will readily identify the numerals as above by comparing them with the forms in figures - , and the day and month signs by comparing them with figures , _a', b'_, and , _d'-f'_, respectively. the initial series therefore reads . . . . caban kayab.[ ] [illustration: initial series (_a_) and secondary series (_b_) on stela f (west side), quirigua] { } passing over b -a , the meanings of which are unknown, we reach in b the secondary-series number . . . reducing this to units of the first order, we have: b b = × = , b a = × = b a = × = ----- , assuming that our starting point is the date next preceding this number in the text, that is, the initial-series terminal date caban kayab in b -a , and applying rules , , and (pp. , , and , respectively), the terminal day reached will be cimi tzec. this date the student will find recorded in plate , _b_, b b-a a. compare b b with the sign for cimi in figure , _h, i_, and a a with the sign for tzec in figure , _g, h_. moreover, since the initial-series value of the starting point caban kayab is known, the initial-series value of the terminal date cimi tzec may be calculated from it: . . . . caban kayab . . . . . . cimi tzec[ ] in a is recorded the date ahau mol (compare a a with fig. , _k', i'_, and a b with fig. , _m, n_) and in a the date ahau yax (compare a a with fig. , _e'-g'_ and a b with fig. , _q, r_). this latter date, ahau yax, is recorded elsewhere at quirigua in a secondary series attached to an initial series, where it has the initial-series value . . . . . this value we may assume, therefore, belongs to it in the present case, giving us the full date . . . . ahau yax. for the present let us pass over the first of these two dates, namely, ahau mol, the initial series of which as well as the reason for its record here will better appear later. in b -a a is recorded another secondary-series number composed of kins, uinals, tuns, and katun, which we may write thus: . . . . the student will note that the katun coefficient in a a is expressed by an unusual form, the thumb. as explained on page , this has a numerical value of . 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, ahau yax in a , 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 a b b a is caban kayab, which, as we have seen, is also the date recorded by the initial series in plate , _a_, a -a . we are perfectly justified in { } assuming, therefore, that the caban kayab in a b-b a had the same initial-series value as the caban kayab in plate , _a_, b -a , namely, . . . . . reducing the number in b -a a, namely, . . . , to units of the first order, we have: a a = × , = , b b = × = , b a = × = b a = × = ------ , remembering that this number is to be counted forward from the date caban kayab, and applying rules , , and (pp. , , and , respectively), the terminal date reached will be ahau zip, which is recorded in a . compare the coefficient of the day sign in a a with the coefficient of the katun sign in a a, and the day sign itself with the profile variant for ahau in figure , _h', i'_. for the month sign, compare a b with figure , 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: . . . . caban kayab . . . . . . . ahau zip passing over to the east side of this monument, the student will find recorded there the continuation of this inscription (see pl. ).[ ] this side, like the other, opens with an introducing glyph a -b , which is followed by an initial series in a -a . although this number is expressed by head variants, the forms are all familiar, and the student will have little difficulty in reading it as . . . . . the terminal date which this number reaches is recorded in b -b ; that is, [ ] ahau zip, the "month indicator" appearing as a head variant in a with the head-variant coefficient . 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 . . . . ahau 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] { } [illustration: fig. . glyphs which may disclose the nature of the events that happened at quirigua on the dates: _a_, . . . . caban kayab; _b_, . . . . cimi tzec.] we have explained all the dates figured except ahau mol in plate , _b_, a , 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. , ) that one of the dates reached in the course of the calculations was just 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 ahau mol here under discussion is . . . . , exactly katun earlier than the initial-series date on stela f. in other words, if we give to the date ahau mol in a the value . . . . , 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 ahau 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: . . . . caban kayab plate , _a_, a -a . . plate , _a_, a . . . . cimi tzec plate , _b_, b b-a a [ . . . . ] ahau mol plate , _b_, a [ . . . . ] ahau yax plate , _b_, a . . . . caban kayab plate , _b_, a b b a . . . plate , _b_, b a a . . . . ahau zip plate , _b_, a (repeated as initial series on east side of monument) . . . . ahau zip plate , a -b -b the student will note the close similarity between this inscription and that on stela j (figured in figs. and ), a summary of which appears on page . both commence with the same date, . . . . caban kayab; both show the date . . . . cimi tzec; both have dates which are just katun in advance of the hotuns which they mark; and finally, both are hotun-markers, stela j preceding stela f by just hotun. the date from which both proceed, . . . . caban 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 , _a_, tells the meaning of the event which happened on this date, which is, moreover, the earliest date at quirigua which { } 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 . . . . caban 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. ) 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 , 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 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 . . . . ahau ceh had ushered in a new cycle there could be no change in the cycle coefficient until after a lapse of very nearly ( . +) years. consequently, after cycle 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 ." indeed, in period-ending dating the cycle 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 , ' , december , ' , being frequently seen in place of the full forms july , , a. d., december , , a. d.; or again, even more briefly, / / and / / 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 (exactly, . +) 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 ] { } in plate 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 , _a_, is figured a period-ending date from stela at copan.[ ] the date ahau ceh appears very clearly in glyphs and . compare the month sign with figure , _u, v_. there follows in 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 its resemblance to figure , _o_, will be evident. indeed, figure , _o_, has precisely the same lower element as glyph . in glyph follows the particular katun, , whose end fell on the date recorded in glyphs and . 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, ahau cumhu, as follows: since the cycle glyph is not expressed, we may fill this omission as the maya themselves filled it, by supplying cycle . 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 , 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 , as . . . . . 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 , , and (pp. , , and , respectively) to the remainder, the student will find that the terminal date reached will be the same as the date recorded in glyphs and , namely, ahau ceh. in other words, the katun , which ended on the date ahau ceh, was . . . . ahau ceh, and both indicate exactly the same position in the long count. the next example (pl. , _b_) is taken from the tablet in the temple of the foliated cross at palenque.[ ] in glyph appears the date ahau uo (compare the month form with fig. , _b, c_) and in glyph the "ending" of katun . the ending sign here is the variant shown in figure , _a-h_, and it occurs just above the coefficient . these two glyphs therefore record the fact that katun ended with the day ahau uo. the student may again test the accuracy of the record by changing this period-ending date to its { } corresponding initial-series number, . . . . , 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 and , ahau uo. in plate , _c_, is figured a period-ending date taken from stela at naranjo.[ ] the date ahau muan appears very clearly in glyphs and (compare the month form with fig. , _a', b'_). glyph is the ending sign, here showing three common "ending elements," ( ) the clasped hand; ( ) the element with the curl infix; ( ) the tassel-like postfix. compare this form with the ending signs in figure , _l-q_, and with the zero signs in figure . in glyph is recorded the particular katun, , which came to its end on the date recorded in and . the element prefixed to the katun in glyph 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 , _a-h_, with which the ending element in glyph should be compared. the glyphs to in plate , _c_, therefore record that katun came to an end on the date ahau muan. as we have seen above, this could be shown to correspond with the initial series . . . . ahau muan. this same date, ahau muan ending katun , is also recorded on stela at tikal (see pl. , _d_).[ ] the date itself appears in glyphs and and is followed in by a sign which is almost exactly like the ending sign in glyph just discussed (see pl. , _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 . compare glyph with the ending signs in figure , _l-q_, and with the zero signs in figure . as in the preceding example, glyph shows the particular katun whose end is recorded here--katun . 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 , _a-h_. as above stated, the initial series corresponding to this date is . . . . ahau muan. one more example will suffice to illustrate the use of katun period-ending dates. in plate , _e_, is figured a period-ending date from stela at copan.[ ] in glyphs and appears the date ahau yax (compare the month in glyph with fig. , _q, r_), which is followed by the ending sign in . this is composed of the hand, a very common "ending" element (see fig. , _j, k_) with a grotesque head superfix, also another "ending sign" (see _i, r, u, v_ of the plate just named). in glyph follows the particular katun (katun ) whose { } end is here recorded. this date corresponds to the initial series . . . . ahau yax. cases where tun endings are recorded are exceedingly rare. the bare statement that a certain tun, as tun , for example, had come to its end left much to be desired in the way of accuracy, since there was a tun in every katun, and consequently any given tun recurred after an interval of years; in other words, there were three or four different tun '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 or 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 , _f_, is figured a tun-ending date from the tablet in the temple of the inscription at palenque.[ ] in glyph appears an ending sign showing the hand element and the grotesque flattened head (for the latter see fig. , _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. , _h_). the presence of the tun sign with these two ending signs indicates probably that some tun ending follows. glyphs and record the date ahau tzec, and glyph records tun . we have here then the record of a tun , which ended on the date ahau tzec. but which of the many tun s 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 , but this assumption does not aid us greatly, since there were twenty different tun s in cycle , one for each of the twenty katuns. however, in the full text of the inscription from which this example is taken, ahau chen is the date next preceding, and although the fact is not recorded, this latter date closed katun of cycle . moreover, shortly after the tun-ending date here under discussion, the date " ahau zotz, end of katun ," is recorded. it seems likely, therefore, that this particular tun , which ended on the date ahau tzec, was . . . . of the long count, after . . . . but before . . . . . reducing this number to units of the first order, and applying the several rules given for solving initial series, the terminal date of . . . . will be found to agree with the terminal date recorded in glyphs and , namely, ahau tzec, { } and this tun ending corresponded, therefore, to the initial series . . . . ahau tzec. another tun-ending date from stela at tikal is figured in plate , _g_.[ ] in glyphs and the date ahau yaxkin appears, the month sign being represented as a head variant, which has the essential elements of the sign for yaxkin (see fig. , _k, l_). following this in glyph is tun , to which is prefixed the same ending-sign variant as the prefixial or superfixial elements in figure , _i, r, u, v_. we have recorded here then "tun ending on ahau 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 of goodman's tables (goodman, ), however, it appears that tun of katun of cycle closed with this date ahau 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 . . . . ahau yaxkin. there is a very unusual period-ending date on the west side of stela c at quirigua[ ] (see pl. , _h_). in glyphs and appears the number kins, uinals, tuns, and katuns, which we may write . . . and following this in glyphs and is the date ahau kayab. at first sight this would appear to be a secondary series, the number . . . being counted forward from some preceding date to reach the date ahau 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 ahau yaxkin, illustrated together with its corresponding initial-series number in figure , _a_. however, all attempts to reach the date ahau kayab by counting either forward or backward the number . . . from the date ahau 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 of katun came to an end on the date ahau kayab. let us see whether this is true. assuming that our cycle coefficient is , as we have done in all the other period-ending dates presented, we may express glyphs and as the following initial-series number, provided they represent a period ending, not a secondary-series number: . . . . . reducing this number to units of the st order, and applying the rules previously given for solving initial series, the terminal date reached will be ahau kayab, identical with the date recorded in glyphs and . we may conclude, therefore, that this example records the fact that "tun of katun ended on the date ahau kayab," this being identical with the initial series . . . . ahau kayab. [illustration: examples of period-ending dates in cycles other than cycle ] { } the foregoing period-ending dates have all been in cycle , 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 . in plate , _a_, is figured a period-ending date from the tablet in the temple of the cross at palenque.[ ] in glyphs and appears the date ahau cumhu (compare the month form in glyph with fig. , _g', h'_), and in glyph an ending sign (compare glyph with the ending signs in fig. , _l-q_, and with the zero signs in fig. ). there follows in glyph , cycle . these four glyphs record the fact, therefore, that cycle closed on the date ahau cumhu, the starting point of maya chronology. this same date is again recorded on a round altar at piedras negras (see pl. , _b_).[ ] in glyphs and appears the date ahau cumhu, and in glyph a 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 , _l-q_, and figure . glyph b clearly records cycle . the dates in plate , _a, b_, are therefore identical. in both cases the cycle is expressed by its normal form. in plate , _c_, is figured a period-ending date from the tablet in the temple of the foliated cross at palenque.[ ] in glyph appears an ending sign in which the hand element and tassel-like postfix show clearly. this is followed in glyph by cycle , the clasped hand on the head variant unmistakably indicating the cycle head. finally, in glyphs and appears the date ahau uayeb (compare the month form with fig. , _i'_).[ ] the glyphs in plate , _c_, record, therefore, the fact that cycle closed on the date ahau 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 , and our initial-series number will be, therefore, . . . . . reducing this to units of the st order and proceeding as in the case of initial series, the terminal date reached will be ahau uayeb, just as recorded in glyphs and . the initial series corresponding to this period-ending date will be . . . . ahau uayeb. these three period-ending dates (pl. , _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 { } precede the opening of cycle , the first historic epoch of the maya civilization, by periods ranging from , to , 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 , being fixed therein by an adjoining period-ending date that may have been historical. this case is figured in plate , _g_.[ ] in glyphs and appears the date ahau ceh (compare the month form in glyph with fig. , _u, v_). this is followed in glyph by a sign which shows the same ending element as the forms in figure , _i, r, u, v_, and this in turn is followed by cycle in glyph . the date recorded in this case is cycle ending on the date ahau ceh, which corresponds to the initial series . . . . ahau ceh. now, in glyphs and is recorded the date caban xul (compare the day sign with fig. , _a', b'_, and the month sign with fig. , _i, j_), and following this date in glyph is the number kins, uinals, or . . 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 . in glyph forward from the date caban xul in glyphs and , the terminal date reached will be the date recorded in glyphs and ; that is, the next date following the number. reducing . to units of the first order, we have: glyph = × = glyph = × = --- counting this number forward from caban xul according to the rules which apply in such cases, the terminal day reached will be ahau ceh, exactly the date which is recorded in glyphs and . but this latter date, we have just seen, is declared by the text to have closed cycle , and therefore corresponded with the initial series . . . . ahau ceh. hence, from this known initial series we may calculate the initial series of the date caban xul by subtracting from . . . . the number . , by which the date caban xul precedes the date . . . . ahau ceh: . . . . ahau ceh . . . . . caban xul this latter date fell in cycle , 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 { } the southern maya, though the monument upon which it is recorded probably dates from an epoch at least years later. in a few cases cycle- ending dates have been found. some of these are surely "contemporaneous," that is, the monuments upon which they appear really date from cycle , while others are as surely "prophetic," that is, the monuments upon which they are found antedate cycle . examples of both kinds follow. in plate , _e_, is figured a period-ending date from stela at copan.[ ] glyphs and declare the date ahau ?, the month sign in glyph being effaced. in glyph is recorded cycle , 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 , _a-h_, and it would seem probable, therefore, that these three glyphs record the end of cycle . let us test this by changing the period-ending date in glyph 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 and the initial-series number will be, therefore, . . . . . 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 ahau zip. but this agrees exactly with the date recorded in glyphs and so far as the latter go, and since the two agree so far as they go, we may conclude that glyphs - in plate , _e_, express "cycle ending on the date ahau 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- ending date on zoömorph g at quirigua (see pl. , _f_). indeed, this date, as will appear below, is almost surely "prophetic" in character. glyphs and record the date ahau zip (compare the month form in glyph with fig. , _d_) and glyph shows very clearly "the end of cycle ." compare the ending prefix in glyph with the same element in fig. , _a-h_. hence we have recorded here the fact that "cycle ended on the date ahau 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 , and, according to page , it records the date . . . . ahau muan. on the grounds of antecedent probability, we are justified in assuming at the outset that this date { } 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,[ ] 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 . . . . ahau muan was the contemporaneous date of zoömorph g, not . . . . ahau zip, that is, the initial series corresponding to the period-ending date here under discussion (see pl. , _f_).[ ] 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 . . . . ahau 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 . . . . ahau muan rather than from . . . . ahau zip. if assigned to the former date, every hotun from . . . . ahau xul to . . . . ahau 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 . . . . ahau zip is assigned to this monument, the hotun ending . . . . ahau muan is left without its corresponding monument at this city, as are also all the hotuns after . . . . ahau mol up to . . . . ahau zip, a total of four in all. the perfect sequence of the monuments at quirigua developed by regarding zoömorph g as dating from . . . . ahau muan, and the very fragmentary sequence which arises if it is regarded as dating from . . . . ahau 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 ending on ahau zip" on zoömorph g is "prophetic" in character, since it did not occur until nearly 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- ending date, which differs from the preceding in that it is almost surely contemporaneous, is that on stela at seibal, { } the latest of the great southern sites.[ ] this is figured in plate , _d_. glyphs and show very clearly the date ahau zip, and glyph declares this to be "at the end of cycle ."[ ] compare the ending-sign superfix in glyph with figure , _a-h_. this glyph is followed by katun in , which in turn is followed by the date ahau kayab in and . finally, glyph declares "the end of katun ." counting forward katun from . . . . ahau zip, the date reached will be ahau kayab, as recorded by and , and the initial series corresponding to this date will be . . . . ahau kayab, as declared by glyph . see below: . . . . ahau zip . . . . . . . ahau kayab end of katun . this latter date is found also on stelæ , , and , at the same city. another cycle- ending date which was probably "prophetic", like the one on zoömorph g at quirigua, is figured on altar s at copan (see fig. ). in the first glyph on the left appears an initial-series introducing glyph; this is followed in glyphs - by the initial-series number . . . . , which the student will find leads to the terminal date ahau yax recorded in glyph . this whole initial series reads, therefore, . . . . ahau yax. in glyph a is recorded katuns and in glyph the date ahau zip, in other words, a secondary series.[ ] reducing the number in glyph a to units of the first order, we have: a = × , = , { × = not recorded { × = { × = ------ , { } [illustration: fig. . the initial series, secondary series, and period-ending date on altar s, copan.] counting this number forward from the date ahau yax, the terminal date reached will be found to agree with the date recorded in glyph , ahau zip. but turning to our text again, we find that this date is declared by glyph a to be at the end of cycle . compare the ending sign, which appears as the superfix in glyph a, with figure , _a-h_. therefore the secondary-series date ahau zip, there recorded, closed cycle . the same fact could have been determined by adding the secondary-series number in glyph a to the initial-series number of the starting point ahau yax in glyphs - : . . . . ahau yax .( . . ) . . . . ahau zip [illustration: initial series, secondary series, and period-ending dates on stela , piedras negras] { } the "end of cycle " in glyph a is merely redundancy. the writer believes that . . . . ahau yax indicates the present time of altar s rather than . . . . ahau 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 . . . . ahau yax. a possible explanation of the record of cycle on this monument is the following: on the date of this monument, . . . . ahau yax, just three-fourths of cycle 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, katuns, was left in cycle . this concludes the discussion of cycle- period-ending dates. the student will note in the preceding example (fig. ) that initial-series, secondary-series, and period-ending dating have all been used together in the same text, glyphs - recording an initial-series date, glyphs a and , a secondary-series date, and glyphs and a, 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 is shown the inscription on stela at piedras negras. the introducing glyph appears in a and is followed by the initial-series number . . . . in b -b . this number reduced to units of the first order and counted forward from its starting point will be found to reach the terminal date cib yaxkin, which the student will readily recognize in a -b ; the "month-sign indicator" appearing very clearly in a , with the coefficient affixed to it. compare the day sign in a with figure , _z_, and the month sign in b with figure , _k, l_. the initial series recorded in a -a , b reads, therefore, . . . . cib yaxkin. in c d is recorded the number kins, uinals, and tuns; that is, . . , 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, cib yaxkin, the terminal date of the secondary series will be found to be cib kankin, which the student will find recorded in c b d a. the initial-series value of this latter date may be calculated as follows: . . . . cib yaxkin . . . . . . cib kankin following along the text, the next secondary-series number appears in d -c a and consists of kins,[ ] uinals, tun, and katun; that { } is, . . . . reducing this number to units of the first order and counting it forward from the date next preceding it in the text, that is, cib kankin in c b d a, the new terminal date reached will be cimi uo, which the student will find recorded in d -c . compare the day sign in d with figure , _h, i_, and the month sign in c with figure , _b, c_. the initial-series value of this new date may be calculated from the known initial-series value of the preceding date: . . . . cib kankin . . . . . . . cimi uo the third secondary series appears in e and consists of kins,[ ] uinals, and tuns, or . . . reducing this number to units of the first order and counting it forward from the date next preceding it in the text, cimi uo, in d -c , the new terminal date reached will be imix yax, which the student will find recorded in e f . the day sign in e 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 e with figure , _a, b_, also the month sign in f with figure , _q, r_. the initial series of this new terminal date may be calculated as above: . . . . cimi uo . . . . . . imix yax the fourth and last secondary series in this text follows in f and consists of kins and uinals, that is, . . reducing this number to units of the first order and counting it forward from the date next preceding it in the text, imix yax in e f , the new terminal date reached will be ahau muan, which the student will find recorded in f -f . compare the month sign in f with figure , _a' b'_. but the glyph following this date in f 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. , _l-q_, and ). moreover, in f is recorded "the end of katun ." compare the ending prefix in this glyph with figure , _a-h_. this would seem to indicate that the date in f -f , ahau muan, closed katun of cycle of the long count. whether this be true or not may be tested by finding the initial-series value corresponding to ahau muan, as above: . . . . imix yax . . . . . ahau muan [illustration: initial series, secondary series, and period-ending dates on stela e (west side), quirigua] { } this shows that the date ahau muan closed katun , as glyphs f -f declare. this may also be verified by changing "the end of katun " recorded in f -f into its corresponding initial-series value, . . . . , and solving for the terminal date. the day reached by these calculations will be ahau muan, as above. this text, in so far as it has been deciphered, therefore reads: . . . . cib yaxkin a -a , b . . c d . . . . cib kankin c b d a . . . d -c a . . . . cimi uo d -c . . e . . . . imix yax e f . f . . . . ahau muan f -f end of katun f -f 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 at piedras negras, namely, . . . . cib yaxkin. compare plate with plate . indeed, these two monuments, stelæ and , stand in front of the same building. all things considered, the inscription on stela 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 and figure .[ ] this text begins with the initial series on the west side. the introducing glyph appears in a -b and is followed by the initial-series number . . [ ]. . in a -a . reducing this number to units of the first order, remembering the correction in the tun coefficient in a noted below, and applying the rules previously given for solving initial series, the terminal date { } reached will be caban kayab. this the student will readily recognize in b -b b, the form in b a being the "month sign indicator," here shown with a head-variant coefficient . compare b with figure , _a', b'_, and b b with figure , _d'-f'_. this initial series therefore should read as follows: . . . . caban kayab. following down the text, there is reached in b b-a a, a secondary-series number consisting of kins, uinals, and tuns, that is, . . . counting this number forward from the date next preceding it in the text, caban kayab, the date reached will be ahau yax, which the student will find recorded in b . compare the month form in b b with figure , _q, r_. but since the initial-series value of caban kayab is known, the initial-series value of ahau yax may be calculated from it as follows: . . . . caban kayab . . . . . . ahau yax [illustration: fig. . the initial series on stela e (east side), quirigua.] the next secondary-series number appears in b , plate , _b_, and consists of kins, uinals, and tun, that is, . . .[ ] the student will find that all efforts to reach the next date recorded in the text, cimi tzec in a b b a, by counting forward . . from ahau yax in b , the date next preceding this number, will prove unsuccessful. however, by counting _backward_ . . from cimi tzec, he will find the date from which the count proceeds is ahau chen, though this latter date is nowhere recorded in this text. we have seen elsewhere, on stela f for example (pl. , _a, b_), that the date cimi tzec corresponded to the initial-series number . . . . ; consequently, we may calculate the position of the unrecorded { } date ahau chen in the long count from this known initial series, by subtracting[ ] . . from it: . . . . cimi tzec . . . . . . ahau chen we now see that there are tuns, that is, hotun, not recorded here, namely, the hotun from . . . . ahau yax, to . . . . ahau chen, and further, that the secondary-series number . . in b is counted from the unexpressed date ahau chen to reach the terminal date cimi tzec recorded in a b b a. the next secondary-series number appears in a b b and consists of kins, uinals, tun, and katun, that is, . . . . as in the preceding case, however, all efforts to reach the date following this number, imix muan in a b b a, by counting it forward from cimi tzec, the date next preceding it in the text, will prove unavailing. as before, it is necessary to count it _backward_ from imix muan to determine the starting point. performing this operation, the starting point will be found to be the date cimi zotz. since neither of these two dates, imix muan and cimi 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 a b b a and consists of kins,[ ] uinals, and tuns. reducing this number to units of the first order and counting it forward from the date next preceding it in the text, imix muan in a b b a, the terminal date reached will be ahau cumhu, which the student will find recorded in a . compare the month sign with figure , _g', h'_. but immediately following this date in b a is katun and in the upper part of b b the hand-denoting ending. these glyphs a and b would seem to indicate, therefore, that katun came to an end on the date ahau cumhu. that they do, may be proved beyond all doubt by changing this period ending into its corresponding initial-series number . . . . and solving for the terminal date. this will be found to be ahau cumhu, which is recorded in a . this latter date, therefore, had the following position in the long count: . . . . ahau 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 imix muan and cimi zotz, which we were obliged to leave indeterminate above. since the date ahau cumhu was derived { } by counting forward . . from imix muan, the initial-series value of the latter may be calculated by subtracting . . from the initial-series value of the former: . . . . ahau cumhu . . . . . . imix muan and since the date imix muan was reached by counting forward . . . from cimi zotz, the initial-series value of the latter may be calculated by subtracting . . . from the now known initial-series value of the former: . . . . imix muan . . . . . . . cimi zotz although this latter date is not recorded in the text, the date next preceding the number . . . is cimi tzec, which corresponded to the initial series . . . . cimi tzec, as we have seen, a date which was exactly tuns earlier than cimi zotz, . . . . - . . . . = . . . the inscription on the west side closes then in a b with the record that katun ended on the date ahau cumhu. the inscription on the east side of this same monument opens with this same date expressed as an initial series, . . . . ahau cumhu. see figure , a -a , a ,[ ] and a . 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: . . .[ ] . caban kayab plate , _a_, a -b , b b . . plate , _a_, b b-a a . . . . ahau yax plate , _a_, b [ . . ] undeclared . . . . ahau chen " . . plate , _b_, b . . . . cimi tzec plate , _b_, a b, b a [ . . ] undeclared { } . . . . cimi zotz " . . . plate , _b_, a b b . . . . imix muan plate , _b_, a b b a . . plate , _b_, a b b a . . . . ahau cumhu plate , _b_, a end of katun plate , _b_, b east side: . . . . ahau cumhu figure , a -a , a , a 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,[ ] 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 . . . . caban kayab x x x x . . . . ahau yax - x x - . . . . ahau chen x - x - . . . . cimi tzec x x x x . . . . cimi zotz - - x - . . . . ahau mol - x - - . . . . ahau zotz x - - - . . . . ahau zip - x - - . . . . imix muan - - x - . . . . ahau cumhu - - x - . . . . ahau 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, . . . . caban kayab, as their original starting point (see above). this date would almost certainly seem, therefore, to indicate some very important event in the annals of quirigua. moreover, since it is the earliest date found at this city which can reasonably be regarded as having occurred during the actual occupancy of the site, it is not improbable that it may represent, as explained elsewhere, the time at which quirigua was founded.[ ] it is necessary, however, to { } caution the student that the above explanation of the date . . . . caban 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 . . . . ahau yax, and two others, stelæ e and j, the date . . . . ahau chen, one hotun later. all four come together again, however, with the date . . . . cimi tzec, which is recorded on each. this date, like . . . . caban kayab, designates probably another important event in quirigua history, the nature of which, however, again escapes us. after the date . . . . cimi 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, . . . . ahau 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. ) 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 , dates of the calendar round and could be fixed only within a period of years. a few examples of calendar-round dating are given in figure and plate . in figure , a, is shown a part of the inscription on altar m at quirigua.[ ] in a b appears a number consisting of kins, uinals, and tuns, that is, . . , and following this in a b b , the date ahau yax, and in a b b the date ahau zac. compare the month glyphs in b and b with _q_ and _r_, and _s_ and _t_, respectively, of figure . this has every appearance of being a secondary series, one of the two dates being the starting point of the number . . , and the other its terminal date. reducing . . to units of the first order, we have: b = × = , a = × = a = × = ----- , [illustration: calendar-round dates on altar , tikal] { } counting this number forward from ahau yax, the nearest date to it in the text, the terminal date reached will be found to be ahau zac, the date which, we have seen, was recorded in a b b . it is clear, therefore, that this text records the fact that . . has been counted forward from the date ahau yax and the date ahau 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 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 of the long count. the reasons for this assumption are quite obvious. [illustration: fig. . calendar-round dates: _a_, altar m, quirigua; _b_, altar z, copan.] the overwhelming majority of maya dates fall in cycle , 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 are given, the student will find that the date ahau yax occurred as a tun ending in cycle , at . . . . ahau 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 ahau yax in this text is . . . . ahau yax, and if this is so the initial-series value of the date ahau zac will be: . . . . ahau yax . . . . . . ahau zac { } in the case of this particular text the initial-series value . . . . might have been assigned to the date ahau 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 , _b_, is shown a part of the inscription from altar z at copan.[ ] in a b appears a number consisting of kin, uinals, and tun, that is, . . , and following this in b -a is the date ahau cumhu, but no record of its position in the long count. if ahau cumhu is the terminal date of the number . . , the starting point can be calculated by counting this number backward, giving the date cauac zac. on the other hand, if ahau cumhu is the starting point, the terminal date reached by counting . . forward will be imix mol. however, since an ending prefix appears just before the date ahau cumhu in a (compare fig. , _a-h_), and since another, though it must be admitted a very unusual ending sign, appears just after this date in a (compare the prefix of b with the prefix of fig. , _o_, and the subfix with the subfixes of _l-n_ and _q_ of the same figure), it seems probable that ahau 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 which ended with the date ahau cumhu was . . . . ahau cumhu, which not only ended a hotun but a katun as well.[ ] if this is true, the unrecorded starting point cauac zac can be shown to have the following initial-series value: . . . . ahau cumhu . . backward . . . . cauac zac in each of the above examples, as we have seen, there was a date which ended one of the katuns of cycle , 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 , 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 at tikal figured in plate is a case in point. this text opens with the date muluc muan in glyphs and (the first glyph or starting point is indicated by the star). { } compare glyph with figure , _m_, _n_, and glyph with figure , _a', b'_. in glyphs and appears a secondary-series number consisting of kins, uinals, and tuns ( . . ). reducing this number to units of the first order and counting it forward from the date next preceding it in the text, muluc muan in glyphs and , the terminal date reached will be manik xul, which the student will find recorded in glyphs and . compare glyph with figure , _j_, and glyph with figure , _i, j_. the next secondary-series number appears in glyphs and , and consists of kins, uinals, and tuns ( . . ). reducing this to units of the first order and counting forward from the date next preceding it in the text, manik xul in glyphs and , the terminal date reached will be cimi mac, which the student will find recorded in glyphs and . compare glyph with figure , _h, i_, and glyph with figure , _w_, _x_. although no number appears in glyph , there follows in glyphs and the date muluc kankin, which the student will find is just three days later than cimi mac, that is, one day manik kankin, two days lamat kankin, and three days muluc 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 , _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 in plate , as the last, muluc kankin, for example, the positions at which this date occurred in cycle may be determined from goodman's tables to be as follows: . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin . . . . muluc kankin { } next let us ascertain whether or not altar 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:[ ] "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 in all its glory, still unharmed, _and in front of it, deeply buried in the earth, we found circular altar _, 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 ," was found in connection with another monument at tikal, namely, stela . but the date on this latter monument has already been deciphered as " ahau muan ending katun " (see pl. , _d_; also p. ), and this date, as we have seen, corresponded to the initial series . . . . ahau muan. our next step is to ascertain whether or not any of the initial-series values determined above as belonging to the date muluc kankin on altar are near the initial series . . . . ahau muan, which is the initial-series date corresponding to the period-ending date on stela . by comparing . . . . with the initial-series values of muluc kankin given above the student will find that the fifth value, . . . . , corresponds with a date muluc kankin, which was only days ( uinal and kins) earlier than . . . . ahau muan. consequently it may be concluded that . . . . was the particular day muluc 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 may be obtained by calculation. the texts on altar and stela are given below to show their close connection: _altar _ . . . . muluc muan glyphs and . . glyphs and . . . . manik xul glyphs and . . glyphs and . . . . cimi mac glyphs and ( ) undeclared . . . . muluc kankin glyphs and ( . ) (time between the two monuments, days.) _stela _ . . . . ahau muan a -a sometimes, however, monuments showing calendar-round dates stand { } 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. . texts showing actual errors in the originals: _a_, lintel, yaxchilan; _b_, altar q, copan; _c_, stela , naranjo.] errors in the original texts may be divided into two general classes: ( ) those which are revealed by inspection, and ( ) 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 , _a_. a very cursory inspection of this text--an initial series from a lintel at yaxchilan--will show that the uinal coefficient in c represents an impossible condition from the maya point of view. this glyph as it stands { } unmistakably records uinals, a number which had no existence in the maya system of numeration, since uinals are always recorded as tun and uinal.[ ] therefore the coefficient in c is incorrect on its face, a fact we have been able to determine before proceeding with the calculation indicated. if not , 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 . . .?. appearing in b -d , and the terminal date which it reaches, imix zip, appearing in c d . compare c with figure , _a, b_, and d with figure , d. we know to begin with that the uinal coefficient must be one of the eighteen numerals to , inclusive. trying first, the number will be . . . . , which the student will find leads to the date imix chen. our first trial, therefore, has proved unsuccessful, since the date recorded is imix zip. the day parts agree, but the month parts are not the same. this month part chen is useful, however, for one thing, it shows us how far distant we are from the month part zip, which is recorded. it appears from table xv that in counting forward from position chen just days are required to reach position zip. consequently, our first trial number . . . . falls short of the number necessary by just days. but days are equal to uinals; therefore we must increase . . . . by uinals. this gives us the number . . . . . reducing this to units of the first order and solving for the terminal date, the date reached will be imix zip, which agrees with the date recorded, in c d . we may conclude, therefore, that the uinal coefficient in c should have been , instead of as recorded. another error of the same kind--that is, one which may be detected by inspection--is shown in figure , _b_. passing over glyphs , , and , we reach in glyph the date kan uo. compare the upper half of with figure , _f_, and the lower half with figure , _b, c_. the coefficient of the month sign is very clearly , 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 , , , and . 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 instead of the actually recorded. these glyphs present seemingly a regular secondary series, the starting point being given in and , the number in , and the terminal date in . counting this number . forward from the starting point, ahau kayab, the terminal date reached will be kan 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 { } have shown, we are justified in assuming that the month coefficient which should have been used in glyph was , instead of . in other words, the craftsman to whom the sculpturing of this inscription was intrusted engraved here dots instead of dots, and ornamental crescent, which, together with the bars present, would have given the month coefficient determined by calculation, . 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 , _a_. in this text the initial-series number recorded in a -a is very clearly . . . . , and the terminal date in b -b b is equally clearly caban kayab. now, if this number . . . . 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 caban kayab, not caban kayab, as recorded. moreover, if the same number is counted forward from the date ahau zotz, which may have been another starting point for initial series, as we have seen, the terminal date reached will be caban zip, not caban 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 caban kayab occurred at the following positions in cycle of the long count: . . . . caban kayab . . . . caban kayab . . . . caban kayab . . . . caban kayab . . . . caban kayab . . . . caban kayab . . . . caban kayab . . . . caban kayab an examination of these values will show that the sixth in the list, . . . . , is very close to the number recorded in our text, . . . . . indeed, the only difference between the two is that the former has tuns while the latter has only . the similarity between these two numbers is otherwise so close and the error in this { } event would be so slight--the record of dots and ornamental crescent instead of dots--that the conclusion is almost inevitable that the error here is in the tun coefficient, having been recorded instead of . in this particular case the secondary series and the period-ending date, which follow the initial-series number . . . . , prove that the above reading of tuns for the 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 , _c_. in glyphs and appears the date eznab uo (compare glyph with fig. , _c'_, and glyph with fig. , _b, c_). in glyph follows a number consisting of kins and uinals ( . ). finally, in glyphs and is recorded the date men yaxkin (compare glyph with fig. , _y_, and glyph with fig. , _k, l_). this has every appearance of being a secondary series, of which eznab uo is the starting point, . , the number to be counted, and men yaxkin the terminal date. reducing . to units of the first order and counting it forward from the starting point indicated, the terminal date reached will be men yaxkin. this differs from the terminal date recorded in glyphs and in having a day coefficient of instead of . since this involves but a very slight change in the original text, we are probably justified in assuming; that the day coefficient in glyph should have been instead of as recorded. one more example will suffice to show the kind of errors usually encountered in the inscriptions. in plate is figured the initial series from stela n at copan. the introducing glyph appears in a and is followed by the initial-series number . . . . in a -a , 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 ahau zip. this agrees with the terminal date recorded in a -a except for the month coefficient, which is in the text instead of , 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 at which the date ahau zip occurred. referring to goodman's tables, these will be found to be: . . . . ahau zip . . . . ahau zip . . . . ahau zip . . . . ahau zip . . . . ahau zip . . . . ahau zip . . . . ahau zip . . . . ahau zip [illustration: initial series on stela n, copan, showing error in month coefficient] { } the number in the above list coming nearest to the number recorded in this text ( . . . . ) is the next to the last, . . . . . but in order to reach this value of the date ahau zip ( . . . . ) with the number actually recorded, two considerable changes in it are first necessary, ( ) replacing the tuns in a by tuns, that is, changing bars to dots, and ( ) replacing uinals in a by uinals, that is, changing the sign to bars and dots. but these changes involve a very considerable alteration of the original, and it seems highly improbable, therefore, that the date here _intended_ was . . . . ahau zip. moreover, as any other number in the above list involves at least three changes of the number recorded in order to reach ahau 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 . . . . forward in the long count will be ahau zip, as we have seen on the preceding page, and this date differs from the terminal date recorded by -- bar in the month coefficient. it would seem probable, therefore, that the bar to the left of the month sign in a should have been omitted, in which case the text would correctly record the date . . . . ahau 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[ ] 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, { } 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[ ] 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. { } 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 days, as we have seen (p. ), this subject will be taken up first. texts recording tonalamatls the _tonalamatl_, or -day period, as represented in the codices is usually divided into five parts of days each, although tonalamatls of four parts, each containing days, and tonalamatls of ten parts, each containing days, are not at all uncommon. these divisions are further subdivided, usually into unequal parts, all the divisions in one tonalamatl, however, having subdivisions of the same length. so far as its calendric side is concerned,[ ] the tonalamatl may be considered as having three essential parts, as follows: . a column of day signs. . red numbers, which are the coefficients of the day signs. . black numbers, which show the distances between the days designated by ( ) and ( ). the number of the day signs in ( ), usually , , or , shows the number of parts into which the tonalamatl is divided. every red number in ( ) is used _once_ with every day sign in ( ) to designate a day which is reached in counting one of the black numbers in ( ) forward from another of the days recorded by ( ) and ( ). 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. { } most of the numbers, that is ( ) and ( ), in the tonalamatl are presented in a horizontal row across the page or pages[ ] 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 days, or, in other words, any tonalamatl with the divisions peculiar to it could be used in endless repetition throughout time, commencing anew every 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 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 ( ), 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 ._ 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[ ] 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 { } 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 th 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 . if any tonalamatl fails to give as the result of this test, it may be regarded as incorrect or irregular. the foregoing material may be reduced to the following: _rule ._ 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 possible, the resulting number will be the coefficient of the beginning day desired. _rule ._ 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 ._ the sum of all the black numbers multiplied by the number of day signs in the column of day signs will equal exactly if the tonalamatl is perfectly regular and correct. { } in plate is figured page 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 b" designates the middle part of page of the dresden codex, and "dresden c" the lower part of page 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 b (see the middle division in pl. ). the student will readily recognize the three essential parts mentioned on page : ( ) the column of day signs, ( ) the red numbers, and ( ) 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 (p. ) this will be found by prefixing the first red number to the topmost day sign in the column. the first red number in dresden b stands in the regular position (above the column of day signs), and is very clearly , that is, one red dot. a comparison of the topmost day sign in this column with the forms of the day signs in figure will show that the day sign here recorded is ix (see fig. , _t_), and the opening day of this tonalamatl will be, therefore, 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 ix. according to rule (p. ), the first black number--in this case , 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 --in order to give the coefficient of the day beginning the next subdivision, all s 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: (first red number) + (next black number) = . deducting all the s possible, we have left ( - ) as the coefficient of the day beginning the next subdivision of the tonalamatl. this number will be found as the red number immediately following the first black number, . to find the corresponding day sign, we must turn to rule (p. ) and count forward in table i this same black number, , 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 manik, of which the is expressed by the second red number and the name part manik only indicated by the calculations. [illustration: page of the dresden codex, showing tonalamatls in all three divisions] { } the beginning day of the next subdivision of the tonalamatl may now be calculated from the day manik by means of rules and (p. ). 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 ( bar and dot) has been affixed. it was explained on page that in representing tonalamatls the maya had to have a sign which by itself would signify the number , since numeration by position was impossible. this special character for the number was given in figure , 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 is attached to this sign thus: (), and the whole number is to be read + = . this number, as we have seen in chapter iv, would ordinarily have been written thus (): unit of the second order ( units of the first order) + units of the first order = . as explained on page , 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 . returning to our text, we find that the "next black number" is ( + ), and this is to be added to the red number next preceding it, which, as we have seen, is an abbreviation for the day manik (see rule , p. ). adding to gives , and deducting all the s possible, namely, two, we have left ( - ); this number , which is the coefficient of the beginning day of the next _subdivision_, will be found recorded just to the right of the black . the day sign corresponding to this coefficient will be found by counting forward in table i from the day name manik. this will give the day name ben, and 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 , and proceeding as before, this is to be added to the red number next preceding it, , the abbreviation for ben. adding to we have , and deducting all the s possible, we obtain again ( - ), which is recorded just to the right of the black (rule , p. ).[ ] counting forward in table i from the day name ben, the day name reached will be cimi, and the day cimi will be the beginning day of the next part of the tonalamatl. but since is the last black number, we should have reached in cimi the beginning day of the _second main division_ of { } the tonalamatl (see p. ), 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 , _i, j_. the day recorded is therefore cimi. the first division of the tonalamatl under discussion is subdivided, therefore, into three parts, the first part commencing with the day ix, containing days; the second commencing with the day manik, containing days; and the third commencing with the day ben, containing days. the second division of the tonalamatl commences with the day cimi, as we have seen above, and adding to this the first black number, , as before, according to rules and (p. ), the beginning day of the next subdivision will be found to be cauac. of this, however, only the is declared (see to the right of the black ). adding the next black number, , to this day, according to the above rules the beginning day of the next subdivision will be found to be chicchan. of this, however, the again is the only part declared. adding the next and last black number, , to this day, chicchan, according to the rules just mentioned the beginning day of the next, or third, main division will be found to be eznab. compare the third day sign in the column of day signs with the form for eznab in figure , _z, a'_. the second division of this tonalamatl contains, therefore, three parts: the first, commencing with the day cimi, containing days; the second, commencing with the day cauac, containing days; and the third, commencing with the day chicchan, containing days. similarly the third division, commencing with the day eznab, could be shown to have three parts, of , , and days each, commencing with the day eznab, chuen, and caban, respectively. it could be shown, also, that the fourth division commenced with the day oc (compare the fourth sign in the column of day signs with figure , _o_), and, further, that it had three subdivisions containing , , and days each, commencing with the days oc, akbal, and muluc, respectively. finally, the fifth and last division of the tonalamatl will commence with the day ik. compare the last day sign in the column of day signs with figure , _c, d_; and its three subdivisions of , , and days each with the days ik, men, and imix, respectively. the student will note also that when the last black number, , has been added to the beginning day of the _last subdivision_ of the _last division_, the day reached will be ix, the day with which the tonalamatl commenced. this period is continuous, therefore, reentering itself immediately on its conclusion and commencing anew. { } there follows below an outline[ ] of this particular tonalamatl: ---------------------+---------+-----------+---------+---------+--------- | st | d | d | th | th |division |division |division |division |division ---------------------+---------+-----------+---------+---------+--------- st part, days, | | | | | beginning with day | ix | cimi | eznab | oc | ik | | | | | d part, days, | | | | | beginning with day | manik | cauac | chuen | akbal | men | | | | | d part, days, | | | | | beginning with day | ben | chicchan | caban | muluc | imix | | | | | total number of days | | | | | ---------------------+---------+-----------+---------+---------+--------- next tonalamatl: st division, st part, days, beginning with the day ix, etc. we may now apply rule (p. ) as a test to this tonalamatl. multiplying the sum of all the black numbers, + + = , by the number of day signs in the column of day signs, , we obtain ( × ), which proves that this tonalamatl is regular and correct. the student will note in the middle division of plate 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. ). 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[ ] 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 { } 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 , dresden c. 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 th day the tonalamatl reenters itself and commences anew. prefixing the first red number, , to the first day sign, chuen (see fig. , _p, q_), according to rule (p. ), the beginning day of the tonalamatl will be found to be chuen. adding to this the first black number, , according to rules and (p. ), the beginning day of the next subdivision will be found to be caban. since this day begins only a subdivision of the tonalamatl, however, its name part caban is omitted, and merely the coefficient recorded. commencing with the day caban and adding to it the next black number in the text, again , according to rules and (p. ), the beginning day of the next subdivision will be found to be akbal, represented by its coefficient only. adding the last black number in the text, , to akbal, according to the rules just mentioned, the beginning day of the next part of the tonalamatl will be found to be cib. and since the black which gave this new day is the last black number in the text, the new day 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 , _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, , to the beginning day of the last subdivision of the last division, eznab, will bring the count back to the day chuen with which the tonalamatl began: { } ---------------------+----------+---------+----------+---------- | st | d | d | th |division |division |division |division ---------------------+----------+---------+----------+---------- st part, days, | | | | beginning with day | chuen | cib | imix | cimi | | | | d part, days, | | | | beginning with day | caban | ik | manik | eb | | | | d part, days, | | | | beginning with day | akbal | lamat | ben | eznab | | | | total number of days | | | | ---------------------+----------+---------+----------+---------- next tonalamatl: st division, st part, days, beginning with the day chuen, etc. applying the test rule to this tonalamatl (see rule , p. ), we have: + + = , the sum of the black numbers, and the number of the day signs in the column of day signs,[ ] × = , the exact number of days in a tonalamatl. the next tonalamatl (see the upper part of pl. , that is, dresden a) occupies only the latter two-thirds of the upper division, the black and red being the last black and red numbers, respectively, of another tonalamatl. the presence of day signs arranged in two parallel columns of five each would seem at first to indicate that this is a tonalamatl of 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 ahau. adding to this the first black number, , the beginning day of the next subdivision will be found to be 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, (also out of place), to this day, manik, the beginning day of the next part will be eb. but since is the last black number, 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 , _r_, will show that eb is recorded in this place. { } in this manner all of the beginning days could be worked out as below: ---------------------+----------+---------+----------+----------+-------- | st | d | d | th | th |division |division |division |division |division ---------------------+----------+---------+----------+----------+-------- st part, days, | | | | | beginning with day | ahau | eb | kan | cib | lamat | | | | | d part, days, | | | | | beginning with day | manik | cauac | chuen | akbal | men | | | | | total number of days | | | | | ---------------------+----------+---------+----------+----------+-------- the application of rule (p. ) to this tonalamatl gives: × = , 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 as the first and the same black and as the first. the outline of this tonalamatl, which began with the day oc, follows: ---------------------+----------+---------+---------+---------+---------- | st | d | d | th | th |division |division |division |division |division ---------------------+----------+---------+---------+---------+---------- st part, days, | | | | | beginning with day | oc | ik | ix | cimi | eznab | | | | | d part, days, | | | | | beginning with day | caban | muluc | imix | ben | chicchan | | | | | total number of days | | | | | ---------------------+----------+---------+---------+---------+---------- the application of rule (p. ) to this tonalamatl gives: × = , the exact number of days in a tonalamatl. it is interesting to note that the above tonalamatl, beginning with the day oc, commenced just days later than the first tonalamatl, which began with the day ahau. in other words, the first of the two tonalamatls in dresden a 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 , upper division, is from dresden a, 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, , to this day ? ahau, the day reached will be ix, of which only is recorded. since ix was reached by counting forward from the day with which the count must have started, by counting back from ix the starting point will be found to be ahau, and we may supply a red bar above the column of the day signs. adding the next black number, , to this day ix, the beginning day of the next _division_ will be found to be eb, which appears as the second day sign in the column of day signs. [illustration: page of the dresden codex, showing tonalamatls in all three divisions] { } the last red number is , thus establishing as correct our restoration of a red above the column of day signs. from here this tonalamatl presents no unusual features and it may be worked as follows: ---------------------+----------+---------+----------+----------+-------- | st | d | d | th | th |division |division |division |division |division ---------------------+----------+---------+----------+----------+-------- st part, days, | | | | | beginning with day | ahau | eb | kan | cib | lamat | | | | | d part, days, | | | | | beginning with day | ix | cimi | eznab | oc | ik | | | | | total number of days | | | | | ---------------------+----------+---------+----------+----------+-------- applying rule (p. ), we have: × = , the exact number of days in a tonalamatl. the next tonalamatl (see lower part of pl. , that is, dresden c) has day signs arranged in two parallel columns of each. this, at its face value, would seem to be divided into divisions, and the calculations confirm the results of the preliminary inspection. the tonalamatl opens with the day lamat. adding to this the first black number, , the day reached will be ahau, of which only the is recorded here. adding to ahau the next black number, , the day reached will be ix. and since 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.[ ] commencing with ix and adding to it the first black number , the day reached will be cimi, and adding to this the next black number, , the day reached will be 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: ---------------------+----------+---------+----------+----------+-------- | st | d | d | th | th |division |division |division |division |division ---------------------+----------+---------+----------+----------+-------- st part, days, | | | | | beginning with day | lamat | ix | ahau | cimi | eb | | | | | d part, days, | | | | | beginning with day | ahau | cimi | eb | eznab | kan | | | | | total number of days | | | | | ---------------------+----------+---------+----------+----------+-------- { } (concluded) ---------------------+----------+---------+----------+----------+-------- | th | th | th | th | th |division |division |division |division |division ---------------------+----------+---------+----------+----------+-------- st part, days, | | | | | beginning with day | eznab | kan | oc | cib | ik | | | | | d part, days, | | | | | beginning with day | oc | cib | ik | lamat | ix | | | | | total number of days | | | | | ---------------------+----------+---------+----------+----------+-------- applying rule (p. ) to this tonalamatl, we have: × = , the exact number of days in a tonalamatl. the tonalamatl which appears in the middle part on plate --that is, dresden b--extends over on page b, where there is a black and a red . 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: ---------------------+----------+---------+----------+---------- | st | d | d | th |division |division |division |division ---------------------+----------+---------+----------+---------- st part, days, | | | | beginning with day | ik | manik | eb | caban | | | | d part, days, | | | | beginning with day | men | ahau | chicchan| oc | | | | d part, days, | | | | beginning with day | cimi | chuen | cib | imix | | | | th part, days, | | | | beginning with day | ix | cauac | kan | muluc | | | | total number of days | | | | ---------------------+----------+---------+----------+---------- applying rule (p. ) to this tonalamatl, we have: × = , 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. ) extends across the middle part of two pages (tro-cor. b, b). the four day signs at the left indicate that it is divided into four divisions, of which the first begins with the day ik.[ ] adding to this the first black number , the day chuen is reached, and proceeding in this manner the tonalamatl may be outlined as follows: [illustration: middle divisions of pages and of the codex tro-cortesiano, showing one tonalamatl extending across the two pages] [illustration: page of the codex tro-cortesiano, showing tonalamatls in the lower three sections] { } ---------------------+----------+----------+----------+---------- | st | d | d | th |division |division |division |division ---------------------+----------+------- --+----------+---------- st part, days, | | | | beginning with day | ik | manik | eb | caban | | | | d part, days, | | | | beginning with day | chuen | cib | imix | cimi | | | | d part, days, | | | | beginning with day | ahau | chicchan| oc | men | | | | th part, days, | | | | beginning with day | oc | men | ahau | chicchan | | | | th part, days, | | | | beginning with day | cib | imix | cimi | chuen | | | | th part, days, | | | | beginning with day | eznab | akbal | lamat | ben | | | | th part, days, | | | | beginning with day | lamat | ben | eznab | akbal | | | | th part, days, | | | | beginning with day | ben | eznab | akbal | lamat | | | | th part, days, | ahau | chicchan| oc | men beginning with day |[ ] |[ ] |[ ] |[ ] | | | | total number of days | | | | ---------------------+----------+----------+----------+---------- applying rule (p. ) to this tonalamatl, we have: × = , the exact number of days in a tonalamatl. another set of interesting tonalamatls is figured in plate , tro-cor., .[ ] the first one on this page appears in the second division, b, 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: ---------------------+---------+---------+---------+----------+-------- | st | d | d | th | th |division |division |division |division |division ---------------------+---------+---------+---------+----------+-------- st part, days, | | | | | beginning with day | manik | cauac | chuen | akbal | men | | | | | d part, days, | | | | | beginning with day | muluc | imix | ben | chicchan| caban | | | | | d part, days, | | | | | beginning with day | cib | lamat | ahau | eb | kan | | | | | th part, days, | | | | | beginning with day | eznab | oc | ik | ix | cimi | | | | | th part, days, | | | | | beginning with day | lamat | ahau | eb | kan | cib | | | | | th part, days, | | | | | beginning with day | caban | muluc | imix | ben | chicchan | | | | | total number of days | | | | | ---------------------+---------+---------+---------+----------+-------- applying rule (p. ) to this tonalamatl, we have: × = , { } the exact number of days in a tonalamatl. the next tonalamatl on this page (see third division in pl. , that is, tro-cor., c) 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: ---------------------+----------+---------+---------+---------+-------- | st | d | d | th | th |division |division |division |division |division ---------------------+----------+---------+---------+---------+-------- st part, days, | | | | | beginning with day | ahau | eb | kan | cib | lamat | | | | | d part, days, | | | | | beginning with day | caban | muluc | imix | ben | chicchan | | | | | d part, days, | | | | | beginning with day | oc | ik | ix | cimi | eznab | | | | | th part, days, | | | | | beginning with day | ahau | eb | kan | cib | lamat | | | | | total number of | | | | | days | | | | | ---------------------+----------+---------+---------+---------+-------- applying rule (p. ) to this tonalamatl, we have: × = , the exact number of days in a tonalamatl. the last tonalamatl in plate , tro-cor., d, commences with the same day, 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, ahau, eb, kan, cib, and lamat. tro-cor. d differs from tro-cor. c in the number and length of the parts into which its divisions are divided. adding the first black number, , to the beginning day, ahau, the day reached will be muluc, of which only the appears in the text. adding to this the next black number, , the day reached will be ben. an examination of the text shows, however, that the day actually recorded is eb, the last red number with the second day sign. this latter day is just the day before ben, and since the sum of the black numbers in this case does not equal any factor of ( + = ), and since changing the last black number from to would make the sum of the black numbers equal to a factor of ( + = ), and would bring the count to eb, the day actually recorded, we are justified in assuming that there is an error in our original text, and that should have been written here instead of . the outline of this tonalamatl, corrected as suggested, follows: { } ----------------------+----------+---------+---------+----------+-------- | st | d | d | th | th |division |division |division |division |division ----------------------+----------+---------+---------+----------+-------- st part, days, | | | | | beginning with day | ahau | eb | kan | cib | lamat | | | | | d part, [ ] days,| | | | | beginning with day | muluc | imix | ben | chicchan| caban | | | | | total number of days | | | | | ----------------------+----------+---------+---------+----------+-------- applying rule (p. ) to this tonalamatl, we have: × = , 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: . the calendric parts, made up, as we have seen on page , of (_a_) the column of day signs; (_b_) the red numbers; (_c_) the black numbers. . the pictures of anthropomorphic figures and animals engaged in a variety of pursuits, and . 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 ( ) and ( ), above. as pointed out at the beginning of this chapter, the most promising { } 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 , 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 . 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 ahau 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 (dresden ), in the lower left-hand corner, in the second column to the right. the initial-series number here recorded is . . . . , of which the zero in the d place (uinals) and the zero in the st 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 of the dresden codex, showing initial series] { } 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 st order, as follows: × , = , , × , = , × = , × = × = ---------- , , deducting from this number all the calendar rounds possible, (see table xvi), it may be reduced to zero, since calendar rounds contain exactly , , units of the first order. see the preliminary rule on page . applying rules , , and (pp. , , and ) to the remainder, that is, , the terminal date of the initial series will be found to be ahau cumhu, exactly the same as the starting point of maya chronology. this must be true, since counting forward from the date ahau cumhu, the date ahau cumhu will be reached. instead of recording this date immediately below the last period of its initial-series number, that is, the kins, it was written below the number just to the left. the terminal date of the initial series we are discussing, therefore, is ahau cumhu, and it is recorded just to the left of its usual position in the lower left-hand corner of plate . the coefficient of the day sign, , is effaced but the remaining parts of the date are perfectly clear. compare the day sign ahau with the corresponding form in figure , _c', d'_, and the month sign cumhu with the corresponding form in figure , _z-b'_. the initial series here recorded is therefore . . . . ahau cumhu. just to the right of this initial series is another, the number part of which the student will readily read as follows: . . . . . treating this in the usual way, it may be reduced thus: × , = , , × , = , × = , × = × = ---------- , , deducting from this number all the calendar rounds possible, (see table xvi), it may be reduced to , . applying to this number rules , , and (pp. , , and , respectively), its terminal date will be found to be ahau kayab; this date is recorded just to the left below the kin place of the _preceding_ initial { } series. compare the day sign and month sign of this date with figures , _c', d'_, and , _x, y_, respectively. this second initial series in plate therefore reads . . . . ahau kayab. in connection with the first of these two initial series, . . . . ahau cumhu, there is recorded a secondary series. this consists of tuns, uinals, and kins ( . . ) 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 - 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 , and, as explained on page , it usually is attached only to the lowest period. returning once more to our text, in plate we see this "backward" sign--a red circle surmounted by a knot--surrounding the kins of this secondary-series number . . , 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, ahau cumhu, the date reached will be ahau kayab. but since the date ahau cumhu is stated in the text to have corresponded with the initial-series value . . . . , by deducting . . from this number we may work out the initial-series value for this date as follows: . . . . ahau cumhu . . backward . . . . ahau kayab the accuracy of this last calculation is established by the fact that the initial-series value . . . . is recorded as the second initial series on the page above described, and corresponds to the date ahau 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, ahau 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, ahau kayab, which was written under the initial series . . . . ; and since the initial-series value of ahau kayab also appears to the right of . . . . as . . . . , this causes a displacement in its terminal date likewise. { } two other initial series will suffice to exemplify this kind of count in the codices. in plate is figured page from the dresden codex. in the two right-hand columns appear two black numbers. the first of these reads quite clearly . . . . , which the student is perfectly justified in assuming is an initial-series number consisting of cycles, katuns, tuns, uinals, and kin. moreover, above the cycles is a glyph which bears considerable resemblance to the initial-series introducing glyph (see fig. , _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: × , = , , × , = , × = , × = × = ---------- , , deducting from this number all the calendar rounds possible, (see table xvi), it may be reduced to , . applying rules , , and (pp. , , and , respectively) to this remainder, the terminal date reached will be imix 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, . . . . . 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, . . . . , is another number consisting of tun, uinals, and kins ( . . ). 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 kins of this secondary-series number ( . . ) 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 imix mol in this case. assuming that this is the case here, we might count . . _backward_ from the date imix mol. performing all the operations indicated in such cases, the terminal date reached will be found to be chicchan 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 chicchan zip, and it is not improbable that the { } ancient scribe intended to write instead chicchan zip, the date indicated by the calculations. we probably have here: . . . . ( imix mol) . . backward . . . . chicchan [ ] zip in these calculations the terminal date of the initial series, imix mol, is suppressed, and the only date given is chicchan 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 . the initial-series number . . . . there recorded reduces to units of the first order as follows: × , = , , × , = , × = , × = × = ---------- , , deducting from this number all the calendar rounds possible, (see table xvi), it will be reduced to , and applying rules , , and (pp. , , and , respectively) to this remainder, the terminal date reached will be kan yaxkin. this date is not recorded. there follows below, however, a secondary-series number consisting of uinals and kin ( . ). the red circle around the lower term of this (the kin) indicates that the whole number, . , 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 . backward from . . . . kan yaxkin, the terminal date reached will be akbal pop, again very close to the date recorded immediately above, akbal pop. indeed, the date as recorded, akbal 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 instead of the 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 { } in making the correction here suggested. we have recorded here therefore: . . . . ( kan yaxkin) . backward . . . . akbal [ ] pop in these calculations the terminal date of the initial series, kan yaxkin, is suppressed and the only date given is akbal 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[ ] there are of these altogether, distributed as follows: page : . . . . [ ]| page : . . . . page : . . . . | page : . . . . page : . . . . | page : . . . . page : . . . . | page : . . . . page : . . . . [ ]| page : . . . . page : . . . . | page : . . . . [ ] page : . . . . | page : . . . . page : . . . . [ ]| page : . . . . page : . . . . [ ]| page : . . . . page : . . . . [ ]| page : . . . . page : . . . . [ ]| page : . . . . page : . . . . | page : . . . . page : . . . . | page : . . . . page : . . . . | there is a wide range of time covered by these initial series; indeed, from the earliest . . . . (on p. ) to the latest, . . . . (on p. ) 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 . . . . represents the time at which the manuscript was made, then the preceding dates reach back { } for more than a thousand years. on the other hand, if . . . . 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 . says professor förstemann (_bulletin _, p. ) 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 , , in the second column of page [ . . . . ahau cumhu, the first initial series figured in plate ], has the greatest claim to be interpreted as the present point of time. in a later article (_bulletin _, p. ) professor förstemann says: "but i think it is more probable that the date farthest to the right ( ahau, zip ...) denotes the present, the other two [namely, . . . . ahau cumhu and . . . . ahau kayab] alluding to remarkable days in the future." he assigns to this date ahau zip the position of . . . . 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 ahau zip actually reads ahau 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 , _b, c_. the date ahau uo occurs at . . . . , 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 , that is, . . . . ahau kayab: "my opinion is that the date . . . . ahau kayab is the present time with reference to the time of writing the codex and is the date from which the whole calculation starts."[ ] 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 . . . . or . . . . 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 of the dresden codex, showing the serpent numbers] { } 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 . 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 , reads as follows: . . . . . , which, reduced to units of the first order, reads: × , , = , , × , = , × , = , × = , × = × = ---------- , , 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 ix 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 , , _backward_ from ix tzec. performing this operation according to the rules laid down in such cases, the starting point reached will be kan xul, but this date is not found in the text. the red number in the first serpent is . . . . . , which reduces to-- × , , = , , × , = , × , = , × = , × = × = ---------- , , { } assuming that the date below this number, cimi kayab, was its terminal date, the starting point can be reached by counting backward. this will be found to be kan kayab, a date actually found on this page (see pl. ), just above the animal figure emerging from the second serpent's mouth. the black number in the second serpent reads . . . . . , which reduces as follows: × , , = , , × , = , × , = , × = , × = × = ---------- , , assuming that the date below this number, akbal 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 kan 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 , the red number in the second serpent, reads, . . . . . and reduces as follows: × , , = , , × , = , × , = , × = , × = × = ---------- , , assuming that the date below this number, kan uo,[ ] 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 kan kayab, which appears above this last serpent. [illustration: fig. . example of first method of numeration in the codices (part of page 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 kan kayab, a date actually recorded in the text just above them. the all-important question of course is, what position did the date kan kayab occupy in the long count? the page ( ) of the dresden codex we { } are discussing sheds no light on this question. there are, however, two other pages in this codex ( and ) on which serpent numbers appear presenting this date, kan kayab, under conditions which may shed light on the position it held in the long count. on page there are recorded katuns, tuns, uinals, and kins (see fig. ); these are immediately followed by the date kan 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 ahau cumhu appears just above in the text, the first supposition is that . . . is a secondary-series number which, if counted forward from ahau cumhu, the starting point of maya chronology, will reach kan kayab, the date recorded immediately after it. proceeding on this assumption and performing the operations indicated, the terminal date reached will be kan cumhu, not kan 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 , is a period-ending date almost exactly like this (see pl. , _h_). on this monument . . . ahau kayab is recorded, and it was proved by calculation that . . . . would lead to this date if counted forward from the starting point of maya chronology. in effect, then, this . . . ahau kayab was a period-ending date, declaring that tun of katun (of cycle , unexpressed) ended on the date ahau kayab. interpreting in the same way the glyphs in figure , we have the record that kin of uinal of tun of katun (of cycle , unexpressed) fell (or ended) on the date kan 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 kan ceh, instead of kan 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 kan ceh is just uinals earlier than kan 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 . . . . reaches the date kan kayab. on the above grounds the writer is inclined to believe that the last three serpent numbers on plate , which were shown to have proceeded from a date kan kayab, were counted from the date . . . . kan kayab. { } 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 a series of this kind commences with the day ahau.[ ] of this series the number . . just above the ahau is the first term, and the day 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 ahau[ ] in this particular case. counting forward then . . from ahau, the unexpressed starting point, the first terminal date, 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: , [ ] , [ ] , [ ] , [ ] ahau ahau ahau ahau , , , , ahau ahau ahau ahau , , , , ahau ahau ahau ahau , , , , ahau ahau ahau ahau , [ ] , , , ahau ahau ahau ahau (unexpressed starting point, ahau.) in the above outline each number represents the total distance of the day just below it from the unexpressed starting point, ahau, _not_ the distance from the date immediately preceding it in the series. for example, the second number, , ( . . ), is not to be counted forward from ahau in order to reach its terminal date, ahau, but from the unexpressed starting point of the whole series, the day ahau. similarly the third number, , ( . . . ), is not to be counted forward from ahau in order to reach ahau, but from ahau instead, and so on throughout the series. { } beginning with the number , and the starting point ahau, the first twelve terms, that is, the numbers in the three lowest rows, are the first multiples of , . , = × , , = × , , = × , , = × , , = × , , = × , , = × , , = × , , = × , , = × , , = × , , = × , the days recorded under each of these numbers, as mentioned above, are the terminal dates of these distances from the starting point, 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 , . but , is × , , 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 ahau; in other words, not until the thirteenth multiple of , is reached is the terminal day the same as the starting point. with this thirteenth term , ceases to be the unit of increase, and the thirteenth term itself ( , ) is used as a difference to reach the remaining three terms on this top line, all of which are multiples of , . , = × , or × , , = × , or × , , = × , or × , , = × , or × , counting forward each one of these from the starting point of this entire series, ahau, each will be found to reach as its terminal day 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 , , admit of an easy explanation. in the first place, the opening term , , which serves as the unit of increase for the entire series up to and including the th term, is the so-called venus-solar period, containing solar years of days each and venus years of days each. this important period is the subject of extended treatment elsewhere in the dresden codex (pp. - ), in which it is repeated times in all, divided into three equal divisions of periods each. the th term of our series , is, as we have seen, × , , the exact number of { } days treated of in the upper divisions of pages - of the dresden codex. the th term ( , ) is the exact number of days treated of in the first two divisions, and finally, the th, or next to the last term ( , ), is the exact number of days treated of in all three divisions of these pages. this th term ( , ) is the first in which the tonalamatl of 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 ( , ) the mars year of days is brought into harmony with all the other periods named. this number, as just mentioned, represents the sum of all the venus-solar periods on pages - of the dresden codex. this next to the last number seems to possess more remarkable properties than the last number ( , ), 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: tonalamatls of days each solar years of days each venus years of days each mars years of days each venus-solar periods of , days each calendar rounds of , days each it will be noted in plate that the concealed starting point of this series is the day ahau, and that just to the left on the same plate are two dates, ahau kayab and ahau uo, both of which show this same day, and one of which, ahau kayab, is accompanied by its corresponding initial series . . . . . it seems not unlikely, therefore, that the day ahau with which this series commences was ahau kayab, which in turn was . . . . ahau kayab of the long count. this is rendered somewhat probable by the fact that the second division of venus-solar periods on pages - of the dresden codex also has the same date, ahau 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 . . . . . ahau 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. * * * * * { } index abbreviation in dating, use, , addition, method, adultery, punishment, - aguilar, s. de, on maya records, ahholpop (official), duties, ahkulel (deputy-chief), powers, ahpuch (god), nature, alphabet, nonexistence, amusements, nature, arabic system of numbers, maya parallel, , architecture, development, arithmetic, system, - ascending series, texts recording - astronomical computations-- accuracy, in codices, - , - aztec-- calendar, - ikomomatic hieroglyphics, rulership succession, backward sign-- glyph, use, , bakhalal (city), founding, bar, numerical value, - bar and dot numerals-- antiquity, - examples, plates showing, , , , , , form and nature, - batab (chief), powers, bibliography, xv-xvi bowditch, c. p.-- cited, , , , , , on dating system, - , - , on hieroglyphics, , , on supplementary series, works, vii-viii brinton, _dr._ d. g.-- error by, on hieroglyphics, , , - , , on numerical system, calendar-- harmonization, , starting point, - , - , - subdivisions, - _see also_ calendar round; chronology; dating; long count. calendar round-- explanation, - glyph, calendar-round dating-- examples, - limitations, chakanputan (city), founding and destruction chichen itza (city)-- history, , , , - temple of the initial series, lintel, interpretation, chilan balam-- books of, chronology based on, chronology-- basis, correlation, duration, starting point, - , - , - , - _see also_ calendar. cities, southern-- occupancy of, diagram showing, rise and fall of, - civilization, rise and fall, - closing sign of supplementary series, glyph, - , closing signs. _see_ ending signs. clothing, character, - cocom family, tyranny, - , codex peresianus, tonalamatls named in, codex tro-cortesianus, texts, - codices-- astronomical character, - , - character in general, , colored glyphs used in, , dates of, day signs in, errors, - , examples from, interpretation, - glyphs for twenty ( ) used in, , historical nature, - , - initial-series dating in, examples, - interpretation, - , - numeration glyphs used in, - , - order of reading, , , , , - tonalamatls in, - zero glyph used in, coefficients, numerical. _see_ numerical coefficients. cogolludo, c. l., on dating system, , colored glyphs, use of, in codices, , commerce, customs, computation, possibility of errors in, - confederation, formation and disruption, - { } copan (city)-- altar q, error on , altar s, interpretation - altar z, interpretation history stela a, interpretation - stela b, interpretation - stela d, interpretation - stela j, interpretation - stela m, interpretation - stela n, error on - interpretation - , - stela p, interpretation stela , interpretation stela , interpretation - stela , interpretation - stela , interpretation stela , antiquity interpretation - stela , interpretation - cresson, h. t., cited customs. _see_ manners and customs. cycle-- glyphs length , number of, in great cycle - numbering of, in inscriptions , - cycle , dates - , - cycle -- dates , , , , , prevalence in maya dating cycle , dates - , - cycle, great-- length , number of cycles in - cycles, great, great, and higher-- discussion - glyphs omitted in dating dates-- abbreviation , errors in computing - errors in originals - , - , interpretation, in initial series - , - in period endings - in secondary series - , - monuments erected to mark - , - of same name, distinction between - repetition shown by red glyphs in codices dates, initial. _see_ initial-series dating. dates, initial and secondary, interpretation - dates, initial, secondary, and period-ending, interpretation - dates, period-ending. _see_ period-ending dates. dates, prophetic-- examples - use - dates, secondary. _see_ secondary-series dating. dates, terminal-- absence finding - importance - position - dating-- methods - , - change _see also_ calendar-round dating; initial-series; period-ending; secondary-series. starting point - , - , - determination - day-- first of year - glyphs , , , coefficients - , - position - omission - , identification - , - names - , numbers - position in solar year - round of - days, intercalary, lack of days, unlucky, dates - death, fear of , death god-- glyph , nature decimal system, parallel _see also_ vigesimal system. destruction of the world, description divination, codices used for divorce, practice dot, numerical value - dot and bar numbers. _see_ bar and dot numbers. dresden codex-- date - publication iii texts - , - plates showing , , , , drunkenness, prevalence ek ahau (god), nature - ending signs-- in period-ending dates in "zero" - enumeration-- systems - comparison _see also_ numerals. errors in texts-- examples - , - , plate showing feathered serpent (god), nature - fiber-paper books. _see_ codices. fish, used in introducing glyph - , five-tun period. see hotun. fÖrstemann, _prof._ ernst-- cited , investigations iii, , methods of solving numerals on hieroglyphics on prophetic dates full-figure glyphs-- nature - , - plate showing _see also_ time periods. funeral customs, description - future life, belief as to { } glyph block, definition, glyphs. _see_ hieroglyphs. gods, nature, - goodman, j. t.-- chronologic tables of, cited, , , - , investigation, iii-iv on introducing glyph, on length of great cycle, on supplementary series, government, nature, - great cycle-- length, number of cycles in, - haab (solar year)-- first day, - glyph, nature, - position of days in, , - subdivisions, habitat of the maya, - map, hair, method of dressing, halach uinic (chief), powers, - hand, used as ending sign, - head-variant numerals-- antiquity, , - characteristics, - derivation, discovery, iii explanation, - , , - forms, - value, identification, - parallel to arabic numerals, plates showing, , , , , , use of, in time-period glyphs, - , _see also_ full-figure glyphs. hewett, _dr._ e. l., cited , hieroglyphs-- antiquity, iii, proofs, , character, iv, - classification, decipherment, - , , - errors in interpretation, - errors in original text, - methods, - inversion of significance, mat pattern, - materials inscribed upon, modifications, - order of reading, , , , , - , , , original errors, - progress, iv, symmetry, - , - , textbooks, vii _see also_ numerals. hieroglyphs, closing, use, - , - , hieroglyphs, introducing, use in dating, - history-- codices containing, - dates, , - , - , - decipherment, iv-v, , dates only, - outline, - recording, methods, - hodge, f. w., letter of transmittal, iii-v holmes, w. h., cited, hospitality, customs, hotun period, hunting, division of spoils, ideographic writing, argument for - ikonomatic writing, nature - initial-series dating-- bar and dot numbers in, examples, - , - plates showing, , , , , , disuse, - , examples, interpretation, - , - plates showing, , , , , , , , , , , , , , , , , , explanation, - , - head-variant numbers, examples, - , - plates showing, , , , , , introducing glyph, identification by, irregular forms of, examples, - , - order of reading, , - , , position of month signs in, - reference to long count, - regular forms of, interpretation, - replacement by u kahlay katunob dating, - starting point, , , - , - , , , , - used in codices, examples, - plate showing, used on monuments, inscriptions on monuments-- cycles in, numbering, - date of, contemporaneous, , , , - , , - date of carving, usual, day signs in, errors, - historical dates, interpretation, - examples, - method, - length of great cycle used in, - numeration glyphs. _see_ numerals. _see also_ monuments; stelÆ. introducing glyph-- lack, nature, - , - , , - inverted glyph, meaning, itzamna (god), nature, justice, rules of, katun (time period)-- glyph, - identification in u kahlay katunob, - length, , monument erected to mark end, naming, - series of, - use of, in period-ending dates, - { } kin. _see_ day. kukulcan (god), nature, - labor, customs, landa, bishop diego de-- biography, on maya alphabet, on maya calendar, , , , on maya customs, , - , on maya records, , landry, m. d., investigations, leyden plate, interpretation, , - literature, list, xv-xvi see also bibliography. long count-- date fixing in, - , - nature, - see also chronology. maize god, nature, maler, teobert-- cited, , , , , , , , , , , , on altar at tikal, manners and customs, description, - marriage customs, - mars-solar period, relation to tonalamatl, mat pattern of glyphs, - maudslay, a. p.-- cited , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , on zero glyph, maya, surviving tribes, - maya, southern-- cities, - occupancy of, diagram showing, government, - rise and fall, - mayapan (city)-- history, - mortuary customs, time records, - military customs, nature - minus sign. _see_ backward sign. month. see uinal. monuments-- age, - date of erection, , , , - , , - historical dates on, period-marking function, - , - texts. _see_ inscriptions. _see also_ stelÆ. moon, computation of revolutions, morley, s. g., on books of chilan balam, mythology, dates, , , , nacon (official), duties, nahua, influence on maya, - naranjo (city)-- antiquity, stela , interpretation, - stela , error in, interpretation, stela , interpretation, - supplementary series, absence, - normal date, fixing, of normal forms of time-period glyphs. _see_ time periods. north star, deification, numbers, expression-- high, - thirteen to nineteen, , , - numerals-- bar and dot system, - examples, plates showing, , , , , , colors, , combinations of, for higher numbers, - forms, - head-variant forms, - , , - plates showing, , , , , , one to nineteen, bar and dot forms, - head-variant forms, - order of reading, , , , - , , ornamental variants, - parallels to roman and arabic systems, solution, - systems, - comparison, _see also_ vigesimal system. transcribing, mode _see also_ hieroglyphs; thirteen; twenty; zero. numerical coefficients - palenque (city)-- history, palace stairway inscription, interpretation, - temple of the cross, tablet, interpretation, - , temple of the foliated cross, tablet, interpretation, - , - , temple of the inscriptions, tablet, interpretation, , - temple of the sun, tablet, interpretation, - period-ending dates-- ending glyph, examples, interpretation, - plates showing, , , , glyphs, - , katun used in, - nature, tun used in, - period-marking stones. _see_ monuments. phonetic writing-- argument for, - traces discovered, iv, - piedras negras (city)-- altar inscription, interpretation, antiquity, stela , interpretation, - stela , interpretation, - plongeon, f. le, cited, ponce, alonzo, on maya records, priesthood, organization, - prophesying, codices used for, prophetic dates-- examples, - use, - { } quen santo (city)-- history, stela , interpretation, - stela , interpretation, - quirigua (city)-- altar m, interpretation, - five-tun period used at, - founding of, possible date, - monuments, stela a, interpretation, - stela c, interpretation, - , , - , supplementary series, absence, stela d, interpretation, stela e, error in, - interpretation, - stela f, interpretation, - , - plates showing, , stela h, interpretation, - stela i, interpretation, - stela j, interpretation, - , - stela k, interpretation, - zoömorph g, interpretation, - , - , - zoömorph p, interpretation - reading, order of, , , , , , , , religion, nature, - renaissance, commencement, rochefoucauld, f. a. de la, alphabet devised by, roman system of numbers, parallel, rosny, leon de, cited, rulership-- nature, - succession, - scarification, practice, schellhas, _dr._ paul, investigations, sculpture, development - secondary-series dating-- examples, interpretation, - , - plates showing, , , , , , , explanation, - , irregular forms, order of reading, , - , reference to initial series, - , - starting point, , - , - , , - determination, - seibal (city)-- antiquity, stela , interpretation, - seler, _dr._ eduard-- cited, , , on aztec calendar, on hieroglyphics, serpent numbers-- interpretation, - nature, range, , slaves, barter in, southern maya. _see_ maya, southern. spanish conquest, influence, - spectacle glyph, function, spinden, _dr._ h. j.-- cited, works, stelÆ-- character, dates, , - inscriptions on, , - see also monuments, and names of cities. stones, inscriptions on superfix, effect - supplementary series-- closing-sign, - , explanation, , lack of, examples, - , position, , symmetry in glyphs, modifications due to, - , - , terminal dates-- determination, - importance as check on calculations, - position, - textbooks, need for, vii thirteen-- glyphs, , numbers above, expression, , , - thomas, _dr._ cyrus-- cited, on maya alphabet, thompson, e. h., investigations tikal (city)-- altar , interpretation, - antiquity, history, stela , importance, interpretation, - stela , interpretation, stela , interpretation, - stela , association with altar , interpretation, , time-- counting backward, - counting forward, - glyphs for, only ones deciphered, , lapse of, determination, - expression, - , - indicated by black glyphs, marked by monuments, - , - method of describing, - recording, - use of numbers, starting point, - , - , - _see also_ chronology. time-marking stones. _see_ monuments. time periods-- full-figure glyphs, - , - plate showing, head-variant glyphs, - plates showing, , , , , , length, normal glyphs, - plate showing, omission of, reduction to days, - _see also_ cycle; great cycle; haab; katun; tonalamatl; tun; uinal. tonalamatl (time period)-- graphic representation, interpretation, - { } nature, - , relation to zero sign, - starting point, - subdivisions, texts recording, - essential parts of, use of glyph for " " with, , , , , used in codices, - plates showing, , , , used in divination, wheel of days, _see also_ year, sacred. translation of glyphs-- errors, - methods, - progress, tun (time period)-- glyph, length, , use of, in period-ending dates, - tuxtla statuette, interpretation, , - twenty-- glyphs, - , need for, in codices, , needlessness of, in inscriptions, use of in, , , uinal-- days, first day, glyph, glyph, - length, , , list, names and glyphs for, - u kahlay katunob dating-- accuracy, antiquity, - explanation, - katun sequence, - order of reading, replacement of initial-series dating by, - uxmal (city), founding, venus-solar period-- divisions, - relation to tonalamatl, , - vigesimal numeration-- discovery, iii explanation, - , - possible origin, used in codices, - villagutiere, s. j., on maya records, war god, nature, weapons, character, - world, destruction, prophecy, world epoch, glyph, - worship, practices, - writing. _see_ hieroglyphics; numerals; reading. xaman ek (god), nature yaxchilan (city)-- lintel, error in, - lintel , interpretation, - stela , interpretation, - structure , interpretation, - year, sacred, use in divination, _see also_ tonalamatl. year, solar. _see_ haab. yucatan-- colonization, - spanish conquest, - water supply, yum kaax (god), nature. zero-- glyphs, - , - origin, - variants, * * * * * notes [ ] 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. [ ] 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. ). see morley, 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. , footnote ). 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: . that of mr. c. p. bowditch ( a), found in his pamphlet entitled "memoranda on the maya calendars used in the books of chilan balam." . that of prof. eduard seler ( - : i, pp. - ). see also _bulletin _, p. . . that of mr. j. t. goodman ( ). . that of pio perez, in stephen's incidents of travel in yucatan ( : i, pp. - ; ii, pp. - ) and in landa, : pp. - . 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 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. [ ] it is probable that at this early date yucatan had not been discovered, or at least not colonized. [ ] 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 [ b] under the title of "the maya chronicles." this translation with a few corrections has been freely consulted in the following discussion."--morley, b: p. . 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. [ ] 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" ( ), to which students are referred for further information, dr. h. j. spinden has treated this subject extensively. [ ] 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. [ ] by nahua is here meant the peoples who inhabited the valley of mexico and adjacent territory at this time. [ ] the ball court, a characteristically nahua development. [ ] one authority (landa, : p. ) 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." [ ] the first appearance of the spaniards in yucatan was six years earlier (in ), when the caravel of valdivia, returning from the isthmus of darien to hispaniola, foundered near jamaica. about 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. [ ] 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 . at the age of he joined the franciscan order. he came to yucatan during the decade following the close of the conquest, in , where he was one of the most zealous of the early missionaries. in he was appointed bishop of merida, which position he held until his death in . his priceless _relacion_, written about , 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 . 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. [ ] 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. [ ] 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. [ ] landa, : p. . [ ] as the result of a trip to the maya field in the winter of , 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 . . . . ; of piedras negras to . . . . ; of naranjo to . . . . ; and of altar de sacrificios to . . . . . (this new material is not embodied in pl. .) [ ] as will be explained in chapter v, the writer has suggested the name _hotun_ for the tun, or , day, period. [ ] 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. [ ] there can be no doubt that förstemann has identified the sign for the planet venus and possibly a few others. (see förstemann, : p. .) [ ] 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 letters with numerous variants. later dr. f. le plongeon defined 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. [ ] thus the whole rebus in figure 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. [ ] the period of the synodical revolution of venus as computed to-day is . days. [ ] according to modern calculations, the period of the lunar revolution is . , or approximately ½ days. for revolutions the accumulated error would be . × = . days. this error the maya obviated by using . in some calculations and . in others, the latter offsetting the former. thus the first revolutions of the sequence are divided into three groups; the first revolutions being computed at . , each giving a total of days; and the second revolutions also being computed at . each, giving a total of another days. the third group of revolutions, however, was computed at . each, giving a total of days. the total number of days in the first revolutions was thus computed to be + + = , which is very close to the time computed by modern calculations, . . [ ] this is the tropical year or the time from one equinox to its return. [ ] landa, : p. . [ ] cogolludo, : i, lib. iv, v, p. . [ ] for example, if the revolution of venus had been the governing phenomenon, each monument would be distant from some other by days; if that of mars, days; if that of mercury, or 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, and , rest on no known astronomical phenomena but are the direct result of the maya vigesimal system of numeration. [ ] it is possible that the codex peresianus may treat of historical matter, as already explained. [ ] 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. ) 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. imix]". again, "here commences the count of the calendar of the indians, saying in their language hun imix (*) [i. e. imix]." (ibid., p. .) [ ] 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 _, p. .) [ ] as bishop landa wrote not later than , this is old style. the corresponding day in the gregorian calendar would be july . [ ] this is probably to be accounted for by the fact that in the maya system of chronology, as we shall see later, the -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. [ ] later researches of the writer ( ) have convinced him that figure , _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. [ ] the writer was able to prove during his last trip to the maya field that figure , _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. [ ] the meanings of these words in nahuatl, the language spoken by the aztec, are "year bundle" and "our years will be bound," respectively. these doubtless refer to the fact that at the expiration of this period the aztec calendar had made one complete round; that is, the years were bound up and commenced anew. [ ] _bulletin _, p. . [ ] all initial series now known, with the exception of two, have the date ahau 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 ahau zotz--more than , 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 ahau zotz, and , years later approximately on ahau cumhu the world, including mankind, may have been created. [ ] some writers have called the date ahau 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. [ ] that is, dates which signified present time when they were recorded. [ ] 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. [ ] for the discussion of the number of cycles in a great cycle, a question concerning which there are two different opinions, see pp. et seq. [ ] 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. [ ] mr. bowditch ( : app. viii, - ) discusses the possible meanings of this element. [ ] for explanation of the term "full-figure glyphs," see p. . [ ] see the discussion of serpent numbers in chapter vi. [ ] these three inscriptions are found on stela n, west side, at copan, the tablet of the temple of the inscriptions at palenque, and stela at tikal. for the discussion of these inscriptions, see pp. - . [ ] the discussion of glyphs which may represent the great cycle or period of the th order will be presented on pp. - in connection with the discussion of numbers having six or more orders of units. [ ] the figure on zoömorph b at quirigua, however, has a normal human head without grotesque characteristics. [ ] the full-figure glyphs are included with the head variants in this proportion. [ ] any system of counting time which describes a date in such a manner that it can not recur, satisfying all the necessary conditions, for , years, must be regarded as absolutely accurate in so far as the range of human life on this planet is concerned. [ ] 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 at tikal, and stela at yaxchilan. [ ] refer to p. and figure . it will be noted that the third tooth (i. e. day) after the one named akbal cumhu is cimi cumhu. [ ] 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. [ ] in chapter iv it will be shown that two bars stand for the number . it will be necessary to anticipate the discussion of maya numerals there presented to the extent of stating that a bar represented and a dot or ball, . the varying combinations of these two elements gave the values up to . [ ] 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 , years. see brinton ( b: pp. - ). it is necessary to note here a correction on p. of that work. doctor brinton has omitted a katun 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 ahau, whereas the berendt copy shows this event took place during the katun omitted, katun ahau. [ ] there are, of course, a few exceptions to this rule--that is, there are some monuments which indicate an interval of more than , 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 , p. . [ ] 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. [ ] the word "numeral," as used here, has been restricted to the first twenty numbers, to , inclusive. [ ] see p. , footnote . [ ] in one case, on the west side of stela e at quirigua, the number 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 , , , and never appear thus separated in any other text known. [ ] 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. [ ] care should be taken to distinguish the number or figure from any period which contained periods of the order next below it; otherwise the uinal, katun, and cycle glyphs could all be construed as signs for , since each of these periods contains units of the period next lower. [ ] the maya numbered by relative position from bottom to top, as will be presently explained. [ ] this form of zero is always red and is used with black bar and dot numerals as well as with red in the codices. [ ] it is interesting to note in this connection that the zapotec made use of the same outline in graphic representations of the tonalamatl. on page of the zapotec codex féjerváry-mayer an outline formed by the days of the tonalamatl exactly like the one in fig. , _a_, is shown. [ ] 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. [ ] the forms shown attached to these numerals are those of the day and month signs (see figs. , , and , , respectively), and of the period glyphs (see figs. - , inclusive). reference to these figures will explain the english translation in the case of any form which the student may not remember. [ ] 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 , the hatchet eye denoting and the fleshless lower jaw . compare (+) with fig. , _f-i_, where the head for is shown. the glyph () here shown is the normal form for the kin sign. compare fig. , b. the meaning of these two forms would thus seem to be kins. in the passage in which these glyphs occur the glyph next preceding the head for is " tuns," the numerical coefficient 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. [ ] it will appear presently that the number could be expressed in two different ways: ( ) by a special head meaning , and ( ) by the essential characteristic of the head for applied to the head for (i. e., + = ). [ ] for the discussion of initial series in cycles other than cycle , see pp. - . [ ] the subfixial element in the first three forms of fig. does not seem to be essential, since it is wanting in the last. [ ] as previously explained, the number is used only in the codices and there only in connection with tonalamatls. [ ] 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. [ ] the numerals and periods given in fig. 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. could be expressed equally well by its corresponding head form without affecting in the least the values of the resulting numbers. [ ] there may be three other numbers in the inscriptions which are considerably higher (see pp. - ). [ ] these are: ( ) the tablet from the temple of the cross at palenque; ( ) altar at piedras negras; and ( ) the east side of stela c at quirigua. [ ] this case occurs on the tablet from the temple of the foliated cross at palenque. [ ] it seems probable that the number on the north side of stela c at copan was not counted from the date ahau cumhu. the writer has not been able to satisfy himself, however, that this number is an initial series. [ ] mr. bowditch ( : pp. - ) 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. - , the number is written uinals and kins, instead of tun, uinal, and kins. [ ] that it was a cycle is shown from the fact that it was just cycles in advance of cycle ending on the date ahau cumhu. [ ] see p. and fig. for method of designating the individual glyphs in a text. [ ] the kins are missing from this number (see a , fig. ). at the maximum, however, they could increase this large number only by . they have been used here as at . [ ] as will be explained presently, the kin sign is frequently omitted and its coefficient attached to the uinal glyph. see p. . [ ] glyph a is missing but undoubtedly was the kin sign and coefficient. [ ] the lowest period, the kin, is missing. see a , fig. . [ ] 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. [ ] a few exceptions to this have been noted on pp. , . [ ] the books of chilan balam have been included here as they are also expressions of the native maya mind. [ ] this excludes, of course, the use of the numerals to , inclusive, in the day names, and in the numeration of the cycles; also the numerals to , 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. [ ] 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 ( : pp. - ) is probably the most serviceable. of the tables mr. goodman's archæic annual calendar and archæic chronological calendar ( ) 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. [ ] this number is formed on the basis of cycles to a great cycle ( × , = , , ). the writer assumes that he has established the fact that cycles were required to make great cycle, in the inscriptions as well as in the codices. [ ] 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. [ ] these intervening glyphs the writer believes, as stated in chapter ii, are those which tell the real story of the inscriptions. [ ] only two exceptions to this rule have been noted throughout the maya territory: ( ) the initial series on the east side of stela c at quirigua, and ( ) 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 ahau zotz. [ ] in the inscriptions an initial series may always be identified by the so-called introducing glyph (see fig. ) which invariably precedes it. [ ] 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. ). (see _bulletin_ , p. .) [ ] there are a few cases in which the "backward sign" includes also the numeral in the second position. [ ] in the text wherein this number is found the date ahau camhu stands below the lowest term. [ ] it should be noted here that in the _u kahlay katunob_ also, from the books of chilan balam, the count is always forward. [ ] 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, katuns, tuns, uinals, and kin are written . . . ; and cycles, katuns, tun, uinal, and kins are written . . . . . 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. [ ] 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. [ ] the student can prove this point for himself by turning to the tonalamatl wheel in pl. ; after selecting any particular day, as ik for example, proceed to count 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 imix or akbal, the th day will be ik again. [ ] the student may prove this for himself by reducing . . . . to days ( , , ), and counting forward this number from the date ahau cumhu, as described in the rules on pages - . the terminal date reached will be ahau ceh, as given above. [ ] 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. [ ] in adding two maya numbers, for example . . . . and . . , care should be taken first to arrange like units under like, as: . . . . . . ------------- . . . . next, beginning at the right, the kins or units of the st place are added together, and after all the s (here ) have been deducted from this sum, place the remainder (here ) in the kin place. next add the uinals, or units of the d place, adding to them for each which was carried forward from the st place. after all the s possible have been deducted from this sum (here ) place the remainder (here ) in the uinal place. next add the tuns, or units of the d place, adding to them for each which was carried forward from the d place, and after deducting all the s possible (here ) place the remainder (here ) 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: . . . . . . ------------ . . . . kins from = ; uinals from uinals ( tun has to be borrowed) = ; tuns from tuns ( katun has to be borrowed, which, added to the tun left in the minuend, makes tuns) = tuns; katuns from katuns ( katun having been borrowed) = katuns; and cycles from cycles = cycles. [ ] 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 ( : p. ) 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 ( : p. ) 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. ). [ ] 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. 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. [ ] in a few cases the sign shown in fig. occurs elsewhere in the supplementary series than as its "closing" glyph. in such cases its coefficient is not restricted to the number or . [ ] in the codices frequently the month parts of dates are omitted and starting points and terminal dates alike are expressed as days only; thus, ahau, imix, kan, etc. this is nearly always the case in tonalamatls and in certain series of numbers in the dresden codex. [ ] 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. b), in which the date ahau cumhu is recorded thus (). compare the month form in this date with fig. , _z-b'_. mr. gates ( : p. ) finds three month signs in the codex peresianus, on pp. , , and at c , c , and b , respectively. the first of these is zac (). compare this form with fig. , _o_. the second is yaxkin (+). compare this form with fig. , _i-j_. the third is cumhu (++); see fig. , _z-b'_. [ ] as used throughout this work, the word "inscriptions" is applied only to texts from the monuments. [ ] 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. [ ] initial series which have all their period glyphs expressed by normal forms are comparatively rare; consequently the four examples presented in pl. , although they are the best of their kind, leave something to be desired in other ways. in pl. , _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. [ ] 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, - : ii, pls. , , , , , , , . [ ] all glyphs expressed in this way are to be understood as inclusive. thus a -b signifies glyphs, namely, a , b , a , b , [ ] 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. [ ] the initial series on stela at tikal is the only exception known. see pp. - . [ ] as will appear in the following examples, nearly all initial series have as their cycle coefficient. [ ] in the present case therefore so far as these calculations are concerned, , is the equivalent of , , . [ ] it should be remembered in this connection, as explained on pp. , , that the positions in the divisions of the year which the maya called , , , and correspond in our method of naming the positions of the days in the months to the th, th, th, and th positions, respectively. [ ] as stated in footnote , p. , the meaning of the supplementary series has not yet been worked out. [ ] the reasons which have led the writer to this conclusion are given at some length on pp. - . [ ] for the full text of this inscription see maler, b: pl. . [ ] 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 (p. ) and step (p. ), 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 ahau cumhu and that the direction of the count will always be forward. [ ] 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. [ ] for the full text of this inscription see hewett, : pl. xxxv _c_. [ ] so far as the writer knows, the existence of a period containing tuns has not been suggested heretofore. the very general practice of closing inscriptions with the end of some particular -tun period in the long count, as . . . . , or . . . . , or . . . . , or . . . . , 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. [ ] for the full text of this inscription see maler, b: pl. . [ ] the student should note that from this point steps (p. ) and (p. ) have been omitted in discussing each text (see p. , footnote ). [ ] 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. [ ] the student may apply a check at this point to his identification of the day sign in a as being that for the day eb. since the month coefficient in a is surely ( 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 a with the signs for ik, manik, and caban, _c, j_, and _a', b'_, respectively, of fig. , it is very evident that a bears no resemblance to any of them; hence, since eb is the only one left which can occupy a position , the day sign in a must be eb, a fact supported by the comparison of a with fig. , _s-u_, above. [ ] the full text of this inscription will be found in maudslay, - : i, pls. - . [ ] the full text of this inscription is given in maudslay, - : i, pls. - . [ ] note the decoration on the numerical bar. [ ] 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. , glyph a , and inscription of the hieroglyphic stairway at naranjo, glyph a (?). (maler, b: pl. .) [ ] for the full text of this inscription see maudslay, - : i, pls. - . [ ] in this glyph-block, a , the order of reading is irregular; instead of passing over to b a after reading a a (the tuns), the next glyph to be read is the sign below a a, a b, which records uinals, and only after this has been read does b a follow. [ ] texts illustrating the head-variant numerals in full will be presented later. [ ] the preceding hotun ended with the day . . . . ahau xul and therefore the opening day of the next hotun, day later, will be . . . . imix xul. [ ] for the full text of this inscription, see maudslay, - : i, pls. , . [ ] the oldest initial series at copan is recorded on stela , which is years older than stela . for a discussion of this text see pp. , . [ ] an exception to this statement should be noted in an initial series on the hieroglyphic stairway, which records the date . . . . ahau zotz. the above remark applies only to the large monuments, which, the writer believes, were period-markers. stela 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. [ ] for the full text of this inscription, see maudslay, - : ii, pls. - . [ ] although this date is considerably older than that on stela at copan, its several glyphs present none of the marks of antiquity noted in connection with the preceding example (pl. , _b_). for example, the ends of the bars denoting 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, . . . . ahau kayab, more than three hundred years later than the initial series . . . . ahau 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 . . . . ahau yaxkin does not represent the period which stela c was erected to mark, but some far earlier date in maya history. [ ] for the full text of this inscription see maudslay, - : i, pl. . [ ] for the full text of this inscription see maler, : ii, no. , pls. , . [ ] for the full text of this inscription see maler, : ii, no. , pl. , . [ ] for the full text of this inscription see maler, : v, no. , pl. . [ ] 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 . . . . kan yax on lintel at yaxchilan, . . . . ahau yazkin on the west side of stela c at quirigua, and . . . . ahau 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 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. [ ] 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. - . [ ] for the full text of this inscription see maudslay, - : ii, pls. - . [ ] for the full text of this inscription see maudslay, - : iv, pls. - . [ ] as explained on p. , footnote , 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 , years. [ ] for the full text of this inscription see maudslay, - ; iv, pls. - . [ ] for the full text of this inscription, see maudslay, - : iv, pl. . [ ] 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 the date reached will be within days of the date originally recorded. even though its maximum value ( ) had originally been recorded here, it could have carried the count only days further. by using as the kin coefficient, therefore, we can not be more than days from the original date. [ ] for the full text of this inscription see maudslay, - : i, pls. , . [ ] 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. [ ] for the full text of this inscription see maudslay, - : ii, pls. - . [ ] for the text of this monument see spinden, : vi, pl. , . [ ] for the discussion of full-figure glyphs, see pp. - . [ ] the characteristics of the heads for , , , and will be found in the heads for , , , and , respectively. [ ] for the full text of this inscription see maudslay, - : i, pls. , . [ ] 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. - , 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. [ ] for the full text of this inscription, see maudslay, - : i, pls. - . [ ] the student should remember that in this diagonal the direction of reading is from bottom to top. see pl. , _b_, glyphs , , , , , , etc. consequently the upper half of follows the lower half in this particular glyph. [ ] for the full text of this inscription see hewett, : pl. xxii _b_. [ ] 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 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 for its uinal and kin coefficients. [ ] in 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., . . . . ahau xul. [ ] for the full text of this inscription see holmes, : pp. et seq., and pls. - . [ ] for a full discussion of the tuxtla statuette, including the opinions of several writers as to its inscription, see holmes, : pp. et seq. the present writer gives therein at some length the reasons which have led him to accept this inscription as genuine and contemporaneous. [ ] for the full text of these inscriptions, see seler, - : ii, , and c: i, , fig. . during his last visit to the maya territory the writer discovered that stela at tikal has a cycle- initial series, namely, . . . . . ahau ceh. [ ] missing. [ ] at seibal a period-ending date . . . . ahau kayab is clearly recorded, but this is some 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 . . . . ahau ceh, and seibal with the same date (not as an initial series, however) are the nearest, though even these fall years short of the quen santo and chichen itza initial series. [ ] 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 . . . . is recorded in connection with the date ahau 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 ( : pp. - ) 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, - : i, pls. - . [ ] for the full text of this inscription, see ibid.: ii, pls. , , . [ ] table xvi contains only calendar rounds ( , , ), but by adding calendar rounds ( , ) the number to be subtracted, calendar rounds ( , , ), will be reached. [ ] counting . . . . backward from the starting point of maya chronology, ahau cumhu, gives the date ahau zotz, which is no nearer the terminal date recorded in b -a than the date ahau kankin reached by counting forward. [ ] for the full text of this inscription, see maudslay, - : iv, pls. - . [ ] as noted in chapter iv, this is one of the only two heads for found in the inscriptions which is composed of the essential element of the head applied to the head, the combination of the two giving . usually the head for 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. [ ] although at first sight the headdress resembles the tun sign, a closer examination shows that it is not this element. [ ] 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. [ ] for the full text of this inscription see maler, : ii, no. , pl. . [ ] 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. [ ] 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. [ ] the number . . . is equal to , days, or ½ years. [ ] it is interesting to note in this connection that the date . . . . ahau tzec, which is within days of . . . . muluc tzec, is recorded in four different inscriptions at yaxchilan, one of which (see pl. , _a_) has already been figured. [ ] for the full text of this inscription see maler, : ii, no. , pl. . [ ] the month-sign indicator appears in b with a coefficient . [ ] not expressed. [ ] the writer has recently established the date of this monument as . . . . ahau pax, or days later than the above date. [ ] for the full text of this inscription, see maudslay, - : ii, pls. - . [ ] although the details of the day and month signs are somewhat effaced, the coefficient in each case is , 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. , _q, r_. [ ] since the maya new year's day, pop, always fell on the th of july, the day yax always fell on jan. th, at the commencement of the dry season. [ ] since pop fell on july th (old style), kayab fell on june th, 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. [ ] for the full text of this inscription, see maudslay, - : ii, pl. . [ ] bracketed dates are those which are not actually recorded but which are reached by numbers appearing in the text. [ ] although not recorded, the number . . is the distance from the date . . . . reached by the secondary series on one side to the starting point of the secondary series on the other side, that is, . . . . cimi tzec. [ ] for the full text of this inscription see maudslay, - : ii, pls. , , . for convenience in figuring, the lower parts of columns a and b are shown in _b_ instead of below the upper part. the numeration of the glyph-blocks, however, follows the arrangement in the original. [ ] this is one of the two initial series which justified the assumptions made in the previous text that the date caban kayab, which was recorded there, had the initial-series value . . . . , as here. [ ] this is the text in which the initial-series value . . . . was found attached to the date cimi tzec. [ ] for the full text of this inscription see maudslay, - : ii, pls. , . [ ] the frontlet seems to be composed of but one element, indicating for this head the value instead of . however, as the calculations point to , it is probable there was originally another element to the frontlet. [ ] see maudslay, - : i, pl. , west side, glyphs a b-a a. [ ] see ibid.: iv, pl. , glyphs n o . [ ] see maler, b: iv, no. , pl. , east side, glyphs a -b . [ ] see ibid., : v, pl. , glyphs a -a . [ ] see maudslay, - : i, pl. , glyphs a , b . [ ] see maudslay, - : iv, pl. , glyphs m -n . [ ] maler, : v, pl. , east side, glyphs a -a . [ ] see maudslay, - : ii, pl. , west side, glyphs b -a . [ ] see maudslay, - : iv, pl. , glyphs d -c . [ ] see maler, : ii, no. , pl. , glyphs a -a . [ ] see maudslay, op. cit., pl. , glyphs c -d . [ ] it will be remembered that uayeb was the name for the _xma kaba kin_, the 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. [ ] see maudslay, - : iv, pl. , glyphs p -r . glyphs q -p are omitted from pl. , _g_, as they appear to be uncalendrical. [ ] see maudslay, - : i, pl. , glyphs c d , a . [ ] this excludes stela c, which has two initial series (see figs. and ), though neither of them, as explained on p. , footnote , records the date of this monument. the true date of this monument is declared by the period-ending date figured in pl. , _h_, which is . . . . ahau kayab. (see p. .) [ ] see maudslay, - : ii, pl. , west side, glyphs g h , f . [ ] the dates . . . . ahau yax and . . . . ahau chen on stelæ and , respectively, at quen santo, are purposely excluded from this statement. quen santo is in the highlands of guatemala (see pl. ) 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. [ ] see maler, a: iv, no. , pl. , glyphs e , f , a , and a . [ ] 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 . [ ] the usual positions of the uinal and kin coefficients in d a are reversed, the kin coefficient standing above the uinal sign instead of at the left of it. the calculations show, however, that , not , is the kin coefficient. [ ] in this number also the positions of the uinal and kin coefficients are reversed. [ ] for the full text of this inscription, see maudslay, - : ii, pls. - . [ ] the student will note that , not , tuns are recorded in a . as explained elsewhere (see pp. , ), this is an error on the part of the ancient scribe who engraved this inscription. the correct tun coefficient is , as used above. [ ] 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 , has an ornamental dot between the two middle dots. [ ] since we counted _backward_ . . from cimi tzec to reach ahau chen, we must _subtract_ . . from the initial-series value of cimi tzec to reach the initial-series value of ahau chen. [ ] it is obvious that the kin and uinal coefficients are reversed in a b since the coefficient above the uinal sign is very clearly , an impossible value for the uinal coefficient in the inscriptions, uinals _always_ being written tun, uinal. therefore the must be the kin coefficient. see also p. , footnote . [ ] the first glyph of the supplementary series, b a, very irregularly stands between the kin period glyph and the day part of the terminal date. [ ] incorrectly recorded as . see pp. , . [ ] 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. [ ] the initial series on the west side of stela d at quirigua is . . . . caban yaxkin, which was just katuns later than . . . . caban kayab, or, in other words, the second katun anniversary, if the term anniversary may be thus used, of the latter date. [ ] for the full text of this inscription, see maudslay, - : ii, pl. . [ ] for the full text of this inscription, see maudslay, - : i, pl. . [ ] every fourth hotun ending in the long count was a katun ending at the same time, namely: . . . . ahau tzec . . . . ahau zotz . . . . ahau zip . . . . ahau pop . . . . ahau cumhu etc. [ ] maler, : no. , p. . [ ] for a seeming exception to this statement, in the codices, see p. , footnote . [ ] 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. [ ] 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. [ ] as explained on p. , 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. [ ] 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. [ ] if there should be two or more columns of day signs the topmost sign of the left-hand column is to be read first. [ ] 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. [ ] this and similar outlines which follow are to be read down in columns. [ ] the fifth sign in the lower row is also a sign of the death god (see fig. ). note the eyelashes, suggesting the closed eyes of the dead. [ ] the last sign chuen, as mentioned above, is only a repetition of the first sign, indicating that the tonalamatl has re-entered itself. [ ] as previously stated, the order of reading the glyphs in columns is from left to right and top to bottom. [ ] the right-hand dot of the is effaced. [ ] the manuscript has incorrectly . [ ] in the title of plate the page number should read instead of . [ ] the manuscript incorrectly has . [ ] incorrectly recorded as in the text. [ ] incorrectly recorded as in the text. [ ] _bull. , bur. amer. ethn._, p. . [ ] 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. [ ] the manuscript incorrectly reads . . . . ; that is, reversing the position of the tun and uinal coefficients. [ ] the manuscript incorrectly reads . . . . . the katun coefficient is changed to , above. these corrections are all suggested by professor förstemann and are necessary if the calculations he suggests are correct, as seems probable. [ ] the manuscript incorrectly reads . . . . . the uinal coefficient is changed to an , above. [ ] the manuscript incorrectly reads . . . . . the uinal coefficient is changed to , above. [ ] the manuscript incorrectly reads . . . . . the uinal coefficient is changed to , above. [ ] the manuscript incorrectly reads . . . . . the tun coefficient is changed to , above. [ ] bowditch, : p. . [ ] the manuscript has incorrectly uo. it is obvious this can not be correct, since from table vii kan can occupy only the d, th, th, or th position in the months. the correct reading here, as we shall see, is probably uo. this reading requires only the addition of a single dot. [ ] in the text the coefficient appears to be , but in reality it is , the lower dot having been covered by the marginal line at the bottom. [ ] counting backward . . ( , ) from ahau, ahau is reached. [ ] professor förstemann restored the top terms of the four numbers in this row, so as to make them read as given above. [ ] the manuscript reads . . . , which professor förstemann corrects to . . . ; in other words, changing the uinal from to . this correction is fully justified in the above calculations.