An Introduction to the Study of the Maya Hieroglyphs by Sylvanus Griswold Morley

Chapter 3 HOW THE MAYA RECKONED TIME

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rkness 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 w

ttle 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 fractio

E TWENTY MA

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

ay signs in th

day signs i

s (fig. 16, m, n). Of these two variants m more closely resembles the form from the codices (fig. 17, n). The glyph for the day Oc (fig. 16, o, p, q) is not often found in the inscriptions. In the codices, on the other hand, this day is frequently represented as shown in figure 17, o. This form bears no resemblance to the forms in the inscriptions. There is, however, a head-variant form found very rarely in the codices that bears a slight resemblance to the forms in the inscriptions. The day Chuen occurs but once in the inscriptions where the form is clear enough to distinguish its characteristic (see fig. 16, r). This form bears a general resemblance to the glyph for this day in the codices (fig. 17, p, q). The forms for the day Eb in both figures 16, s, t, u, and 17, r, are grotesque heads showing but remote resemblance to one another. The essential element in both, however, is the same, that is, the element occupying the position of the ear. Although the day Ben occurs but rarely in the inscriptions, its form (fig. 16, v) is practically identical with that in the codices (see fig. 17, s). The day Ix in the inscriptions appears as in figure 16, w, x. The form in the codices is shown in figure 17, t. The essential element in each seems to be the three prominent dots or circles. The day Men occurs very rarely on the monuments. The form shown in figure 16, y, is a grotesque head not unlike the sign for this day in the codices (fig. 17, u). The si

rities 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 figur

an'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

atl, or 260

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 i

le 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

SEQUENCE O

hic

8 C

as prefixed to the next name in order-that is, Imix, the first name in Table II-and the count continued without interruption: 5 Imix, 6 Ik, 7 Akbal, or back to the name Kan with which it started. There was no break in the sequence, however, even at this point (or at any other, for that matter). The next name in Table II, Kan, selected for the starting point, was given

equence is in reality exceedingly simple, bei

day names repeats itself again

CAN ETHNOLOGYBU

ING SEQUENCE OF THE 26

1 to 13, inclusive, repeats itself again and agai

een made by prefixing any one of the 13 numbers to any one of the 20 names, the number next in

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

posite the day 1 Imix be conceived to be stationary and the wheel to revolve in a sinistral circuit, that is contra-clockwise, the days will pass the star in the order which they occupy in the 260-day sequence. It appears from this diagram also that the day 1 Imix can not recur until after 260 days shall have passed, and that it always follo

the tonalamatl (ac

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 o

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 matt

icient evidence the writer believes. On the other hand, so important a period as the tonalamatl undoubtedly had

or Year

or so-called Sacred Year, let us turn to the consideration of

atements, 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 inte

always in a continuous sequence, each returning into itself and beginning anew after completion, he w

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

18 periods of 20 days each, designated in Maya uinal, and a closing period of 5 days known as the

E DIVISIONS O

II in the order in which they follow one another; the twentieth

l on the 16th of July.[30] Uayeb, the last division of the year, contained only 5 days, the last day of Uayeb being at the same time the 365th day of the year. Conseq

eved 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 th

ext 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

e 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 fi

eventh 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, sin

ay 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 se

than the day, as hours, minutes, and seconds, are referred to in terms of past tim

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 p

ever, the first day of the month had passed and the second day commenced. In other words, the second day of Pop was written 1 Pop; the third day, 2 Pop; the fourth day, 3 Pop; and so on through the 20 days of the Maya month. This method of numbering the positions of the days in the month led to calling the last day of a month 19 instead of 20. This appears in

f this period.[31] The glyphs which represent the 18 different uinals and the xma kaba kin, however, are shown in

ONS OF DAYS AT T

ar 19 Cumhu last da

year 0 Uayeb fi

of the ye

of the y

4 Uayeb last day of

p first day of the month

f next y

of next

of next y

ear 19 Pop last da

year 0 Uo first d

of next

. e

r to each other as well as to the corresponding forms in the codices (fig. 20, b, c). The glyphs for the month Zip are identical in both figures 19, d, and 20, d. The grotesque heads for Zotz in figures 19, e, f,[33] and 20, e, are also similar to each other. The essential characteristic seems to be the prominent upturned and flaring nose. The forms for Tzec (figs. 19, g, h, and 20, f) show only a very general similarity,

nth signs in th

month signs i

ions (fig. 19, w) bearing absolutely no resemblance to that shown in figure 20, q, r, the only form for this month in the codices. The very unusual variant (fig. 19, x), from Stela 25 at Piedras Negras is perhaps a trifle nearer the form found in the codices. The flattened oval in the main part of the variant is somewhat like the upper part of the glyph in figure 20, q. The essential element of the glyph for the month Mac, so far as the inscriptions are concerned, is the element (*) found as the superfix in both w and x, figure 19. The sign for the month Kankin (figs.

corresponding forms in the codices, and that such variations as are found may readily be accounted for by the fact that the codic

for the days and months given in figures 16, 17, 19, and 20, since his progress will dep

Round, or 189

ings: (1) The number of differently named days; (2) the names of these days; (3) the order in which they invariably followed one another. And in the second place we learned in the discussion of the Maya year, or haab, just concluded, four ot

l 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, a

essential parts: (1) The name glyph, and (2) the numerical coefficient. Disregarding the latter for the present, let us firs

re are only three possibilities concerning the names or num

nces contain no common factor, each one of the units i

a multiple of the sum of the units in the other, only the

(except in those cases which fall under (2), that is, in which one is a mul

r, and since neither is a multiple of the other, it is clear that only the last of the three contingenci

s in Table I, and the next task is to find out which of these

Following out this same idea, it appears that the 361st day of the second year will have the same name as that with which it began, that is, the 6th name in the sequence, the 362d day the 7th name, the 363d the 8th, the 364th the 9th, and the 365th, or last day of the second year, the 10th name. Therefore the 1st day of the third year (the 731st from the beginning) will have the 11th name in the sequence. Similarly it could be shown th

his equation indicates that the beginning day of the fifth year has been reached; and the 1 in the third term indicates that the name-part of this day is the 1st name in the sequence of twen

four names are shown in their relation to the sequence of twenty). Beginning with any one of these, Ik for example, the next in order, Manik, is 5 d

POSITIONS OF DAYS

essarily true because these 19 divisions of the year, with the exception of the last, each contained 20 days, and consequently the name of the first day of the first division determined the names of the first days of all the succeeding divisions of that particular year.

succeeding in the sequence of twenty. The third days in each division of that year must have had the same name, the fourth days the same name, and so on, throughout the 20 days of the month. For example, if a year began with the day-name Ik, all

ccupy the same positions in all

s also must be filled with one of another group of four names, and the third positions with one of another g

ames can ever occupy any given posi

he years when Caban is the 1st, Ik will be the 6th, Manik the 11th, and Eb the 16th, it is clear that any one of this group which begins the year may occupy also three other positions in the divisions of the year, these positions being 5 days distant from each other. Consequently, it follows that A

es 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

NS OF DAYS IN DIV

held by da

16th 2

17th 3

18th 4

9th 5th

ays in eac

c Ch

u C

itten not 2 Pop, but 1 Pop, and the last day, not 20 Pop, but 19 Pop. Consequently, before we can use the names in Table VI as the Maya used them, we must make this shift, keeping in mind, however, that Ik, Manik, Eb, and Caban (the only four of the twenty names which could

rding to the Maya conception, that is, with the shift in the month coeffici

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 posit

S IN DIVISIONS OF MAYA YEAR

ns held

5, 10, 15 1, 6, 11, 16 2, 7,

ays in eac

c Ch

u C

b, remembering always that as yet we have been dealing only with the name parts of the days and not their complete designations. B

ons could begin only with one of these

n in the divisions of the year could be

articular day-name returned to the same

our positions in the divisions of the year, each of which it held i

ps of four day-names each, any day-name of any group being five d

ar day-name occupied the same relative pos

mplete designations of the Maya days, but only their name parts or name glyphs,

way that any one of the days whose name-part is Ik, Manik, Eb, or Caban shall occupy the first position of the first division of the year; that is, 0 Pop, or, as we should write it, t

nd follows the sequence shown in plate 5. The second wheel, B (fig. 21), is somewhat larger, having 365 cogs. Each of the spaces or sockets between these represents one of the 365 positions of the days in the divisions of the year, beginning with 0 Pop and ending with 4 Uayeb. See Table IV for the positions of the days

60 days (A), and haab wheel of 365 positions (B); the combin

As the wheels revolve in the directions indicated, the days of the tonalamatl successively fall into their appropriate positions in the divisions of the year. Since the number of cogs in A is smaller than the number in B, it is clear that the former will have returned to its starting point, 2 Ik (that is, made one complete r

cupy the position 0 Pop, or, in other words, cog 2 Ik in A will return to the position 0 Pop in B in fewer than 260 revolutions of A. The actual solution of the problem is a simple question of arithmetic. Since the day 2 Ik can not return to its original position in A until after 260 days shall have passed, and since the day 0 Pop can not return to its original position in B until after 365 days shall have passed, it is clear that the day 2 Ik 0 Pop can not recur until after a number of days shall have passed equal to the least common multiple of these numbe

though the Maya developed a much more elaborate system of counting time, wherein any date of the Calendar Round could be fixed with absolute certainty within a period of 374,

elop 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

r says in this

ry 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

rrence 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 la

point of departure, and measuring time by an accurate system, the Maya were able to secure p

r Round: a, According to Goodm

r F?rstemann 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 doub

a distinctive glyph which should represent this period was not acute. The contribution of the Calendar Round to Maya chronology was its 18,980 dates, and the glyphs which composed these are found repeatedly in both the codices and the i

d another without interruption or the interpolation of a single day; and further, that the Calendar Round may be likened to a large cogwheel having 18,980 t

Long

ave

ished 1 day from the 259

tion of 1 day from the 364 others

hey distinguished 1 day from the

in fixing a day within a period of 374,400 years, as stated a

quently, in order to prevent confusion of days of the same name in successive Calendar Rounds or, in other words, t

76 B. C., which were won by a certain Coroebus. The Romans took as their starting point the supposed date of the foundation of Rome, 753 B. C. The Babylonians counted time as beginning with the Era of Nabonassar, 747 B. C. The death of Alexander the Great, in 325 B. C., ushered in the Era of Alexander. With the occupation of Babylon in 311 B. C. by Seleucus Nicator began the so-called Era of Seleucid?. The conquest of Spain by Au

ry 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 5509 B. C.

ting 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 da

ng to approximate its real character, however, we are not without some assistance from the codices and the inscriptions. For instance, it is clear that all Maya dates which it is possible to regard as contemporaneous[38] refer to a time fully 3,00

ist, 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 dat

chronology there is a silence of more than 3,000 ye

the dated monuments[39] had their origin in t

ok place on this date 4 Ahau 8 Cumhu, in reality when this day was present time they h

s primary unit immediately gives rise to exceedingly awkward numbers for its higher terms; that is, 52, 104, 156, 208, 260, 312, etc. Indeed, the expression of really large numbers in terms of 52 involves the use of comparatively large multipliers and hence of more or less intricate multiplications, since the unit of progres

its, 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

THE MAYA T

n =

1 uinal

= 1 tun

1 katun =

1 cycle =

1 great cycle

3d place was due probably to the desire to bring the unit of this order (the tun) into agreement with the solar year of 365 days, the number 360 being much closer to 365 than 400, the third term of a constant vigesimal progression. We have seen on page 45 that the 18 uinals of the haab were equivalent to 360 days or kins, precisely the number contained

(except the 2d) always appearing as 1 unit of the order next higher. For

rent factors which the Maya utilized in r

h there could be only 18,980 (the nu

point, 4 Ahau 8 Cumhu, fr

the units, used in measu

ctors were combined to express the

ial

1,300,000 and 1,500,000 days; and this number is followed by one of the 18,980 dates of the Calendar Round. As we shall see in the next chapter, if this large number of days expressed as above be counted forward from the fixed starting point of Maya chronology,

18,980 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 t

owing section of Ca

ter three, 56,940, and so on. Indeed, it is only a question of the number of revolutions of A until as many as 1,500,000, or any number of days in fact, will have passed t

will use up 1,461,460 of the 1,461,463 days, since 77×18,980 = 1,461,460. Consequently, when 77 Calendar Rounds shall have passed we shall still have left 3 days (1,461,463 - 1,461,460 = 3), which must be carried forward into the next Calendar Round. The 1,461,461st day will be 5 Imix 9 Cumhu, that is, the day follo

RODUCIN

introducing glyph," the Maya name for which is unknown. Several examples of thi

trinal

comblike late

ign (see fig

trinal

al-series "int

alized fish fins or tails; in other words, that they are a kind of glyphic synecdoche in which a part (the fin) stands for the whole (the fish). That the original form of this element was the fish and not its conventionalized fin (*) seems to be indicated by several facts: (1) On Stela D at Copan, where only full-figure glyphs are presented,[43] the two comblike appendages of the "introducing glyph" appear unmistakably as two fishes. (2) In some of the earliest stel? at Copan, as Stel? 15 and P, while these elements are not fish forms, a head (fish?) appears with the conventionalized comb element in each case. The writer believes the interpretation of this phenomenon to be, that at the early epoch in which Stel? 15 and P were erected the conventionalization of the element in question had not been entirely accomplished, and that the head was added to indicate the form from which the element was derived.

the comblike elements in the katun glyph, as well as in the "i

yet been positively identified. It is possible, however, that the sign shown in figure 24, f, may be a form of the "introducing glyph"; at least it

g that the analogy here is close, the writer nevertheless is inclined to reject Mr. Goodman's identification on the following grounds: (1) This glyph never occurs with a numerical coefficient, while units of all the other orders-that is, cycles, katuns, tuns, uinals, and kins are never without them. (2) Units of the 6th order in the codices invariably have a numerical coefficient, as do all the other orders. (3) In the only

be found to be quite apart from the numerical side of the Initial Series, at least in so far

hs" 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

examine the signs for the remaining orders or periods of the chronological system (cycles, katuns, tuns, uinals, an

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 codic

-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 on

YCLE

cycle: a-c, Normal fo

figure variant

in the signs for the months Chen, Yax, Zac, and Ceh (see figs. 19, o-v, 20, l-p). This has been called the Cauac element because it is similar to the sign for the day Cauac in the codices (fig. 17, b'), though on rather inadequate grounds the writer is inclined to believe. The head variant of the cycle glyph is shown in figure 25, d-f. The essential characteristic of this grotesq

ATUN

katun: a-d, Normal fo

figure variant

fig. 27, c, d) is identical with the normal form in the inscriptions (fig. 27, a, b). Several head variants are found. The most easily recognized, though not the most common, is shown in figure 27, e, in which the superfix is the same as in the normal form; that is, the element (?), which probably signifies 20 in this connection. To be logical, therefore, the head element should be the same as the head variant of the tun glyph, but this is not the case (see fig. 29, e-h). When this superfix is present, the identification of the head variant of the katun glyph is an easy matter, but when it is absen

TUN

tun: a-d, Normal form

-figure varia

ariant, which bears a general resemblance to the head variant for the cycle and katun, has several forms. The one most readily recognized, because it has the normal sign for its superfix, is shown in figure 29, d, e. The determining characteristic of the head variant of the tun glyph, however, is the fleshless lower jaw (?), as shown in figure 29 f, g, though even this is lacking i

INAL

uinal: a-c, Normal fo

ariant of uinal sign o

variant of uinal si

uch cases the glyph seems to be without determining characteristics. The animal represented in the full-figure variants of the uinal is that of a frog (fig. 32,) the head of which presents precisely the same characteristics as the head variants of the uinal, just described. That the head variant of the uinal-period glyph was originally derived from the representation of a frog can hardly be denied in the face of such striking confirmatory evidence as that afforded by the full-figure form of the uinal in figure 33. Here the spotted body, flattened head, prominent mouth, and bulging eyes of the frog are so realistically portrayed that there is no doubt as to the identity of the figure intended. Mr. Bowditch (1910: p. 257) has pointed out in this connection an interesting phonetic coincidence, which can hardly be other than intentional.

KIN

, b, Normal forms; c, d, misc

that they were derived from two entirely distinct glyphs. Still another and very unusual sign for the kin is shown in figure 34, d; indeed, the writer recalls but two places where it occurs: Stela 1 at Piedras Negras, and Stela C (north side) at Quirigua. It is composed of the normal form of the sign for the day Ahau (fig. 16, e') inverted and a subfixial element which varies in each of the two cases. These variants (fig. 34, c, d) are found only in the inscriptions. The head variants of the kin period differ from each other as much as the various normal forms above given. The form shown in figure 34, e, may be readily recognized by its subfixial element (*) and the element (?), both of which appear in the normal form, figure 34, a. In some cases, as in figure 34, f-h, this variant also has the square irid and the crooked, snag-like teeth projecting from the front of the mouth. Again, any one of these features, or even all,

-figure varia

ral periods of Table VIII. After an exhaustive study of these as found in May

atter in all Initial Series known is in the proportion of about 80 per cent of the total[48] against 12 per cent, the periods in the remaining 8 per cent being

use of the former preceded the first use of the latter by about 300 years, while in Initial Series normal-form period gly

un sign in figure 36, c, is practically identical with the form in figure 36, d. Instances of this kind could be multiplied indefinitely, but the foregoing are sufficient to demonstrate that in so far as the normal-form period glyphs are concerned but little variation occurred from first to last. Similarly, it may be said, the head variants for any given period, while differing greatly in appearance at different epochs, retained, never

arated sites and of different epochs, s

gure 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 t

dary

; (7) the Day glyph; (8) the Month glyph. Moreover, its use in any inscription which contained more than one date would have resulted in needless repetition. For example, if all the dates on any given monument were expressed by Initial Series, every one would show the long distance (more than 3,000 years) which separated it from the common

s 7 Akbal 11 Cumhu, and its position in the Long Count is fixed by the statement in cycles, katuns, tuns, etc., that 1,461,463 days separate it from the starting point, 4 Ahau 8 Cumhu. Now let us suppose we have the date 10 Cimi 14 Cumhu, which is recorded as being 3 days later than the day 7 Akbal 11 Cumhu,[51] the Initial Series of which is known to be 1,461,463. It is clear that the Initial Series corresponding to the date 10 Cimi 14 Cumhu, although not actually expressed, will also be known since it must equal 1,461,463 (Initial Series of 7 Akbal 11 Cumh

f 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

hem 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 Second

ar-rou

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

-endin

ar round dating. In this method a date was described as being at the end of some particular period in the Long Count; that is, closing a certain cycle, katun, or tun.[52] It is clea

katun, and cycle are exactly divisible b

onsequently, all the periods of the Long Count, except the kin or pr

lways involves the use of at lea

of the Long Count, as C

as 8 Ahau 13 Ceh, or 6 Ahau 13 Muan, the closing date

ended," or which indicates at least that the per

t 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 "endi

ich appears as the main element in the forms shown in figure 37, j-q. The two first of these never stand by themselves but always modify some other sign. The first (fig. 37, a-h, t) is always attached to the sign of the period whose end is recorded either as a superfix (see fig. 37, a, whe

ding signs

separate glyph, which precedes the sign of the period whose end is recorded (see fig. 37, l-q). In these cases the subordinate elements differ somewhat, although the element (*) appears as the

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 expr

as occurring at the end of a certain katun could recur after an interval of about 18,000 years in round numbers, as against 374,400 years in the other 2 methods. For all p

ods-most frequently with the katun, next with the cycle, and but very rarely with the tun. Mr. Bowditch (1910: pp. 176 et seq

lay K

is has been designated the Sequence of the Katuns, because in this method the katun, or 7,200-day period, was the unit used for measuring the passage of time. The Maya themselves called the Sequence of the Katuns u tzolan katun, "the series of the katuns"; or u kahlay uxoc

for the katun of which it was the close. The katun, as we have seen on page 77, always ended with some day Ahau, consequently this day-name is the only one of the twenty which appears in the u kahlay katunob. In this method the

CE OF KATUNS IN

Ahau Kat

Ahau Ka

Ahau Kat

Ahau Ka

hau Katun

anging its value. This truth enables us to formulate the following rule for finding numerical coefficients: Deduct all the multiples of 13 possible from the number to be counted forward, and then count forward the remainder from the known coefficient, subtracting 13 if the resulting number is above 13, since 13 is the highest possible number which can be attached to a day sign. If we apply this rule to the sequence of the numerical coefficients in Table IX, we shall find that it accounts for the retrograding sequence there observed. The first katun in Table IX, Katun 2 Ahau, is named after its ending day, 2 Ahau. Now let us see whether the application of this rule will give us 13 Ahau as the ending day of the next katun. The number to be counted forward from 2 Ahau is 7,200, the number of days in one katun; therefore we must first deduct from 7,200 all the 13s possible. 7,200 ÷ 13 = 55311?13. In other words, after we have deducted all the 13's possible, that is, 553 of them, there is a remainder of 11. This the rule says is to be added (or counted forward) from the known coefficient (in this case 2) in

has to be added to the known coefficient to find the unknown. But since 13 has to be deducted from the resulting number when it is above 13, subtracting 2 will always give us exactly the same coefficient as adding 11; consequently we may formulate

ccur anywhere within a period of 7,200 days, or nearly 20 years, and yet fulfill the given conditions. In other words, no matter how accurately this Katun 2 Ahau itself might be fixed in a long stretch of time, there was always the possibility of a maximum error of about 20 years in such dating, since the statement of the katun did not fix a date any closer than as occurring somewhere within a certain 20-year period. When greater accuracy was desired the particular tun in which the date occurred was also given, as Tun 13 of Katun 2 Ahau. This fixed a date as falling somewhere within a certain 360 days, which was accurately fixed in a much longer perio

mitting 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 dat

e south or the north; on the other hand, it is so closely connected with the Long Count and Period-ending dating, which occurs repeatedl

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

th day sign Ahau, possibly indicating presenc

ya history, and from their very nature they have to do with long periods. This is not true of the monuments,[55] which, as we have seen, were probably set up to mark the passage of certain periods, not exceeding a katun in length in any case. Consequently, each monument would have inscribed upon it only one or two katun ending days and the events which were connected more or less closely with it. In other words, the monuments were erected at short intervals[56] and probably recorded events contemporaneous with their erection, while the u kahlay katunob, on the other hand, were historical summaries reaching back to a remote time. The former were the periodicals of current events

s kind. It has been stated (p. 33) that the Codex Peresianus probably treats in part at least of historical matter. The basis for this assertion is that in this particular manuscrip

e southern and older cities. While the Spanish authorities do not mention the u kahlay katunob as do the native writers, they state very clearly that this was the system used in counting time. Says Bishop Landa (1864: p. 312) in this connection: "The Indians not only had a count by years and days ... but they had a certain method of counting time and their affairs by ages, which they made from twenty to twenty years ... these they call katunes." Cogolludo (1688: lib. iv, cap. v, p. 186) makes

e 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 p

was far less exact than Initial-series dating; not only could dates satisfying all given conditions recur much more frequently in th

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 aft

g; (4) Period-ending dating; (5) Katun-ending dating, or the u kahlay katunob. While apparently differing considerably from one another, in reality all are expressions of the same fundamental

same dates, the 18,980 d

to the same fundamen

time counters, thos

urged constantly to bear in mind two vi

lamatl, the 365 positions of the haab, the 18,980 dates of the Calendar Round, and the kins, uinals, tuns, katuns, and cycles of the vigesimal system of numeration. When the con

ent time, but passed time, as in the c

rests the whole May