Chapter 4

Plate 3PAGE 74 OF THE DRESDEN CODEX, SHOWING THE END OF THE WORLD (ACCORDING TO FÖRSTEMANN)

PAGE 74 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 (1894 b: p.32) states:

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

Mr. Bowditch (1910: p. 199) has also brought forward very cogent points tending to show that in part at least the inscriptions treat of the intercalation of days necessary to bring the dated monuments, based on a 365-day year, into harmony with the true solar year of 365.2421 days.[23]

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

The reasons which have led him to this conclusion follow:

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

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

The Maya of Yucatan had a similar method of marking time, though their unit of enumeration was 7,200 days, or four times thelength of the one used for the same purpose in the older cities. The following quotations from early Spanish chroniclers explain this practice and indicate that the inscriptions presented on these time-markers were of an historical nature:

There were discovered in the plaza of that city [Mayapan] seven or eight stones each ten feet in length, round at the end, and well worked. These had some writings in the characters which they use, but were so worn by water that they could not be read. Moreover, they think them to be in memory of the foundation and destruction of that city. There are other similar ones, although higher, at Zilan, one of the coast towns. The natives when asked what these things were, replied that they were accustomed to erect one of these stones every twenty years, which is the number they use for counting their ages.[24]

The other is even more explicit:

Their lustras having reached five in number, which made twenty years, which they call a katun, they place a graven stone on another of the same kind laid in lime and sand in the walls of their temples and the houses of the priests, as one still sees to-day in the edifices in question, and in some ancient walls of our own convent at Merida, about which there are some cells. In a city named Tixhualatun, which signifies "place where one graven stone is placed upon another," they say are their archives, where everybody had recourse for events of all kinds, as we do to Simancas.[25]

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

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

Third.The dates on the monuments are such as to constitute a strong antecedent probability of their historical character. Like the records of most ancient peoples, the Maya monuments, judging from their dates, were at first scattered and few. Later, as new cities were founded and the nation waxed stronger and stronger, the number of monuments increased, until at the flood tide of Maya prosperity they were, comparatively speaking, common. Finally, as decline set in, fewer and fewer monuments were erected, and eventually effort in this field ceased altogether. The increasing number of the monuments by ten-year periods is shown in plate4, 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:

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 4

Plate 4DIAGRAM SHOWING OCCURRENCE OF DATES RECORDED IN CYCLE 9

DIAGRAM SHOWING OCCURRENCE OF DATES RECORDED IN CYCLE 9

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

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

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

The consideration of these indisputable facts tends to establish the historical rather than the astronomical character of the monuments. For had the erection of the monuments depended on the successive recurrences of some astronomical phenomenon, there would be corresponding intervals between the dates of such monuments[26]the length of which would indicate the identity of the determining phenomenon; and they would hardly have presented the same logical increase due to the natural growth of a nation, which the accompanying diagram clearly sets forth.

Fourth.Although no historical codices[27]are known to have survived, history was undoubtedly recorded in these ancient Maya books. The statements of the early Spanish writers are very explicit on this point, as the following quotations from their works will show. Bishop Landa (here, as always, one of the most reliable authorities) says: "And the sciences which they [the priests] taught were the count of the years, months and days, the feasts and ceremonies, the administration of their sacraments, days, and fatal times, their methods of divination and prophecy, and foretelling events, and the remedies for the sick, andtheir antiquities" [p. 44]. And again, "they [the priests] attended the service of the temples and to the teaching of their sciences andhow to write them in their books." And again, [p. 316], "This people also used certain characters or letters with whichthey wrote in their books their ancient mattersand sciences."

Father Lizana says (see Landa, 1864: p. 352): "Thehistory and authorities we can citeare certain ancient characters, scarcely understood by many and explained by some old Indians, sons of the priestsof 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 (tomeLVIII, p. 392) who visited Yucatan as early as 1588, is equally clear: "The natives of Yucatan are among all the inhabitants of New Spain especially deserving of praise for three things. First that before the Spaniards came they made use of characters and letters with whichthey wrote out their histories, their ceremonies, the order of sacrifices to their idols and their calendars in books made of the bark of a certain tree."

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

Finally, as late as 1697, some of these historical codices were in the possession of the last great independent Maya ruler, one Canek. Says Villagutierre (1701: lib.VI, cap.IV) in this connection: "Because their king [Canek] had read it in hisanaltehes[fiber-books or codices] they had knowledge of the provinces of Yucatan, and of the fact that their ancestors had formerly come from them;analtehesor 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.

ChapterIII. HOW THE MAYA RECKONED TIME

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

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

Table I.THE TWENTY MAYA DAY NAMES

In conformity with the universal practice just mentioned the Maya made the day, which they calledkin, the primary unit of their calendar. There were twenty such units, named as in TableI; these followed each other in the order there shown. WhenAhau, the last day in the list, had been reached, the count began anew withImix, and thus repeated itself again and again without interruption, throughout time. It is important that the student should fix thisMaya 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.

Fig. 16Fig. 16. The day signs in the inscriptions.

Fig. 16. The day signs in the inscriptions.

Fig. 17Fig. 17. The day signs in the codices.

Fig. 17. The day signs in the codices.

The glyphs for these twenty days are shown in figures16and17. The forms in figure16are from the inscriptions and those in figure17from 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 sameday in each. The sign for the first day,Imix, is practically identical in both. Compare figure16,aandb, with figure17,aandb. The usual form for the dayIkin the inscriptions (see fig.16,c), however, is unlike the glyph for the same day in the codices (fig.17,c,d). The forms forAkbalandKanare practically the same in each (see fig.16,d,e, andf, and fig.17,eandf, respectively). The dayChicchan, figure16,g, occurs rarely in the inscriptions; when present, it takes theform of a grotesque head. In the codices the common form for this day is very different (fig.17,g). The head variant, however (fig.17,h), shows a slightly closer similarity to the form from the inscriptions. The forms in both figure16,h,i, and figure17,i,j, for the dayCimishow little resemblance to each other. Although figure17,i, represents the common form in the codices, the variant injmore closely resembles the form in figure16,h,i. The dayManikis practically the same in both (see figs.16,j, and17,k), as is alsoLamat(figs.16,k,l, and17,l,m). The dayMulucoccurs rarely in the inscriptions (fig.16,m,n). Of these two variantsmmore closely resembles the form from the codices (fig.17,n). The glyph for the dayOc(fig.16,o,p,q) is not often found in the inscriptions. In the codices, on the other hand, this day is frequently represented as shown in figure17,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 dayChuenoccurs but once in the inscriptions where the form is clear enough to distinguish its characteristic (see fig.16,r). This form bears a general resemblance to the glyph for this day in the codices (fig.17,p,q). The forms for the dayEbin both figures16,s,t,u, and17,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 dayBenoccurs but rarely in the inscriptions, its form (fig.16,v) is practically identical with that in the codices (see fig.17,s). The dayIxin the inscriptions appears as in figure16,w,x. The form in the codices is shown in figure17,t. The essential element in each seems to be the three prominent dots or circles. The dayMenoccurs very rarely on the monuments. The form shown in figure16,y, is a grotesque head not unlike the sign for this day in the codices (fig.17,u). The signs for the dayCibin the inscriptions and the codices (figs.16,z, and17,v,w), respectively, are very dissimilar. Indeed, the form forCib(fig.17,v) in the codices resembles more closely the sign for the dayCaban(fig.16,a',b') than it does the form forCibin the inscriptions (see fig.16,z). The only element common to both is the line paralleling the upper part of the glyph (*) and the short vertical lines connecting it with the outline at the top. The glyphs for the dayCabanin both figures16,a',b', and17,x,y, show a satisfactory resemblance to each other. The forms for the dayEznabare also practically identical (see figs.16,c', and17,z,a'). The forms for the dayCauac, on the other hand, are very dissimilar; compare figures16,d', and17,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 byfar the most important, since it is found in both the codices and the inscriptions more frequently than all of the others combined, isAhau(see figs.16,e'-k', and17,c',d'). The latter form is the only one found in the codices, and is identical withe',f', figure16, the usual sign for this day in the inscriptions. The variants in figure16,g'-k', appear on some of the monuments, and because of the great importance of this dayAhauit 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 figures16and17will 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 anessential elementpeculiar 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 isuinal, while the word for 'man' isuinik. The parallel is interesting and may possibly explain why the number twenty was selected as the basis of the Maya system of numeration, which, as we shall see later, was vigesimal, that is, increasing by twenties or multiples thereof.

The Tonalamatl, or 260-day Period

Merely calling a day by one of the twenty names given in TableI, however, did not sufficiently describe it according to the Maya notion. For instance, there was no day in the Maya calendar called merelyImix,Ik, orAkbal, or, in fact, by any of the other names given in TableI. Before the name of a day was complete it was necessary to prefix to it a number ranging from 1 to 13, inclusive, as6 Imixor13 Akbal. Then and only then did a Maya day receive its complete designation and find its proper place in the calendar.

The manner in which these thirteen numbers, 1 to 13, inclusive, were joined to the twenty names of TableIwas as follows: Selectingany one of the twenty names[28]as a starting point,Kanfor example, the number 1 was prefixed to it. See TableII, 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 nameKanindicates the starting point above chosen. The nameChicchanimmediately followingKanin TableIIwas given the next number in order (2), namely,2 Chicchan. The next name,Cimi, was given the next number (3), namely,3 Cimi, and so on as follows:4 Manik,5 Lamat,6 Muluc,7 Oc,8 Chuen,9 Eb,10 Ben,11 Ix,12 Men,13 Cib.

Table II.SEQUENCE OF MAYA DAYS

Instead of giving to the next name in TableII(Caban) the number 14, the number 1 was prefixed; for, as previously stated, the numerical coefficients of the days did not rise above the number 13. Following the day1 Caban,the sequence continued as before:2 Eznab,3 Cauac,4 Ahau. After the day4 Ahau, the last in TableII, the next number in order, in this case 5, was prefixed to the next name in order—that is,Imix, the first name in TableII—and the count continued without interruption:5 Imix,6 Ik,7 Akbal, or back to the nameKanwith 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 TableII,Kan, selected for the starting point, was given the number next in order, i. e., 8, and the day following7 Akbalin TableIIwould be, therefore,8 Kan, and the sequence would continue to be formed in the same way:8 Kan,9 Chicchan,10 Cimi,11 Manik,12 Lamat,13 Muluc,1 Oc,2 Chuen,3 Eb, and so on. So far as the Maya conception of time was concerned, this sequence of days went on without interruption, forever.

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

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

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 5

Plate 5TONALAMATL WHEEL, SHOWING SEQUENCE OF THE 260 DIFFERENTLY NAMED DAYS

TONALAMATL WHEEL, SHOWING SEQUENCE OF THE 260 DIFFERENTLY NAMED DAYS

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

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

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

This is graphically shown in the wheel figured in plate5, where the sequence of the days, commencing with1 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 point1 Imix, is shown in parenthesis. Now, if the star opposite the day1 Imixbe conceived to be stationary and the wheel to revolve in a sinistral circuit, that is contra-clockwise, the days will pass the star in the order which they occupy in the 260-day sequence. It appears from this diagram also that the day1 Imixcan not recur until after 260 days shall have passed, and that it always follows the day13 Ahau. This must be true sinceAhauis the name immediately precedingImixin the sequence of the day names and 13 is the number immediately preceding 1. After the day13 Ahau(the 260th from the starting point) is reached, the day1 Imix, the 261st, recurs and the sequence, having entered into itself again, begins anew as before.

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

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

This round of the 260 differently named days was called by the Aztec thetonalamatl, or "book of days." The Maya name for this period is unknown[29]and students have accepted the Aztec name for it. The tonalamatl is frequently represented in the Maya codices, there being more than 200 examples in the Codex Tro-Cortesiano alone. It was a very useful period for the calculations of the priests because of the different sets of factors into which it can be resolved,namely, 4×65, 5×52, 10×26, 13×20, and 2×130. Tonalamatls divided into 4, 5, and 10 equal parts of 65, 52, and 26 days, respectively, occur repeatedly throughout the codices.

It is all the more curious, therefore, that this period is rarely represented in the inscriptions. The writer recalls but one city (Copan) in which this period is recorded to any considerable extent. It might almost be inferred from this fact alone that the inscriptions do not treat of prophecy, divinations, or ritualistic and ceremonial matters, since these subjects in the codices are always found in connection with tonalamatls. If true this considerably restricts the field of which the inscriptions may treat.

Mr. Goodman has identified the glyph shown in figure18as the sign for the 260-day period, but on wholly insufficient evidence the writer believes. On the other hand, so important a period as the tonalamatl undoubtedly had its own particular glyph, but up to the present time all efforts to identify this sign have proved unsuccessful.

The Haab, or Year of 365 Days

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

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

If the student can be made to realize that all Maya periods, from the lowest to the highest known, are always in a continuous sequence,each returning into itself and beginning anew after completion, he will have grasped the most fundamental principle of Maya chronology—its absolute continuity throughout.

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

So far as the calendar is concerned, then, the year consisted of but 365 days. It was divided into 18 periods of 20 days each, designated in Mayauinal, and a closing period of 5 days known as thexma kaba kin, or "days without name." The sum of these (18×20+5) exactly made up the calendar year.

Table III.THE DIVISIONS OP THE MAYA YEAR

The names of these 19 divisions of the year are given in TableIIIin 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 monthPop, which, according to the early Spanish authorities, Bishop Landa (1864: p. 276) included, always fell on the 16th of July.[30]Uayeb, the last division of the year, contained only 5 days, the last day ofUayebbeing at the same time the 365th day of the year. Consequently, when this day was completed, the next in order was the Maya New Year's Day, the first day of the monthPop, after which the sequence repeated itself as before.

The xma kaba kin, or "days without name," were regarded as especially unlucky and ill-omened. Says Pio Perez (see Landa, 1864: p. 384) in speaking of these closing days of the year: "Some call themu yail kinoru 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 1 o'clock, in reality the first hour after noon, that is, the hour between 12 noon and 1 p. m., has passed and the second hour after noon is about to commence. When we say it is 2 o'clock, in reality the second hour after noon is finished and the third hour about to commence. In other words, we count the time of day by referring to passed periods and not current periods. This is the method used in reckoning astronomical time. During the passage of the first hour after midnight the hours are said to be zero, the time being counted by the number of minutes and seconds elapsed. Thus, half past 12 is written: 0hr.30min.0sec., and quarter of 1, 0hr.45min.0sec.. Indeed one hour can not be written until the first hour after midnight is completed, or until it is 1 o'clock, namely, 1hr.0min.0sec..

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

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

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

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

This is well illustrated by the Maya method of numbering the positions of the days in the months, which, as we shall see, was identical with our own method of counting astronomical time. For example, the first day of the Maya monthPopwas writtenZero Pop, (0 Pop) for not until one whole day ofPophad passed could the day1 Popbe written; by that time, however, the first day of the month had passed and the second day commenced. In other words, the second day ofPopwas written1 Pop; the third day,2 Pop; the fourth day,3 Pop; and so on through the 20 days of the Maya month. This method of numbering the positions of the days in the month led to calling the last day of a month 19 instead of 20. This appears in TableIV, in which the last 6 days of one year and the first 22 of the next year are referred to their corresponding positions in the divisions of the Maya year. It must be remembered in using this Table that the closing period of the Maya year, the xma kaba kin, orUayeb, contained only 5 days, whereas all the other periods (the 18 uinals) had 20 days each.

Curiously enough no glyph for thehaab, or year, has been identified as yet, in spite of the apparent importance of this period.[31]Theglyphs which represent the 18 different uinals and the xma kaba kin, however, are shown in figures19and20. The forms in figure19are taken from the inscriptions and those in figure20from the codices.

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

The signs for the first four months,Pop,Uo,Zip, andZotz, show a convincing similarity in both the inscriptions and the codices. The essential elements ofPop(figs.19,a, and20,a) are the crossed bands and thekinsign. The latter is found in both the forms figured, though only a part of the former appears in figure20,a.Uohas two forms in the inscriptions (see fig.19,b,c),[32]which are, however, very similar to each other as well as to the corresponding forms in the codices (fig.20,b,c). The glyphs for the monthZipare identical in both figures19,d, and20,d. The grotesque heads forZotzin figures19,e,f,[33]and20,e, are also similar to each other. The essentialcharacteristic seems to be the prominent upturned and flaring nose. The forms forTzec(figs.19,g,h, and20,f) show only a very general similarity, and those forXul, the next month, are even more unlike. The only sign forXulin the inscriptions (fig.19,i,j) bears very little resemblance to the common form for this month in the codices (fig.20,g), though it is not unlike the variant inh, figure20. 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.

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