Another example showing the use of these_An Introduction to the Study of the Maya Hieroglyphs

the same text is the inscription on Stela E at Quirigua, illustrated in

plate 24 and figure 82.[224] This text begins with the Initial Series on

the west side. The introducing glyph appears in A1-B3 and is followed by

the Initial-series number 9.14.13[225].4.17 in A4-A6. Reducing this number

to units of the first order, remembering the correction in the tun

coefficient in A5 noted below, and applying the rules previously given for

solving Initial Series, the terminal date {236} reached will be 12 Caban 5

Kayab. This the student will readily recognize in B6-B8b, the form in B8a

being the "month sign indicator," here shown with a head-variant

coefficient 10. Compare B6 with figure 16, _a', b'_, and B8b with figure

19, _d'-f'_. This Initial Series therefore should read as follows:

9.14.13.4.17 12 Caban 5 Kayab. Following down the text, there is reached in

B10b-A11a, a Secondary-series number consisting of 3 kins, 13 uinals, and 6

tuns, that is, 6.13.3. Counting this number forward from the date next

preceding it in the text, 12 Caban 5 Kayab, the date reached will be 4 Ahau

13 Yax, which the student will find recorded in B11. Compare the month form

in B11b with figure 19, _q, r_. But since the Initial-series value of 12

Caban 5 Kayab is known, the Initial-series value of 4 Ahau 13 Yax may be

calculated from it as follows:

9.14.13. 4.17 12 Caban 5 Kayab

6.13. 3

9.15. 0. 0. 0 4 Ahau 13 Yax

[Illustration: FIG. 82. The Initial Series on Stela E (east side),

Quirigua.]

The next Secondary-series number appears in B12, plate 24, _B_, and

consists of 6 kins, 14 uinals, and 1 tun, that is, 1.14.6.[226] The student

will find that all efforts to reach the next date recorded in the text, 6

Cimi 4 Tzec in A13b B13a, by counting forward 1.14.6 from 4 Ahau 13 Yax in

B11, the date next preceding this number, will prove unsuccessful. However,

by counting _backward_ 1.14.6 from 6 Cimi 4 Tzec, he will find the date

from which the count proceeds is 10 Ahau 8 Chen, though this latter date is

nowhere recorded in this text. We have seen elsewhere, on Stela F for

example (pl. 19, _A, B_), that the date 6 Cimi 4 Tzec corresponded to the

Initial-series number 9.15.6.14.6; consequently, we may calculate the

position of the unrecorded {237} date 10 Ahau 8 Chen in the Long Count from

this known Initial Series, by subtracting[227] 1.14.6 from it:

9.15.6.14.6 6 Cimi 4 Tzec

1.14.6

9.15.5. 0.0 10 Ahau 8 Chen

We now see that there are 5 tuns, that is, 1 hotun, not recorded here,

namely, the hotun from 9.15.0.0.0 4 Ahau 13 Yax, to 9.15.5.0.0 10 Ahau 8

Chen, and further, that the Secondary-series number 1.14.6 in B12 is

counted from the unexpressed date 10 Ahau 8 Chen to reach the terminal date

6 Cimi 4 Tzec recorded in A13b B13a.

The next Secondary-series number appears in A14b B14 and consists of 15

kins, 16 uinals, 1 tun, and 1 katun, that is, 1.1.16.15. As in the

preceding case, however, all efforts to reach the date following this

number, 11 Imix 19 Muan in A15b B15a, by counting it forward from 6 Cimi 4

Tzec, the date next preceding it in the text, will prove unavailing. As

before, it is necessary to count it _backward_ from 11 Imix 19 Muan to

determine the starting point. Performing this operation, the starting point

will be found to be the date 7 Cimi 9 Zotz. Since neither of these two

dates, 11 Imix 19 Muan and 7 Cimi 9 Zotz, occurs elsewhere at Quirigua, we

must leave their corresponding Initial-series values indeterminate for the

present.

The last Secondary Series in this text is recorded in A17b B17a and

consists of 19 kins,[228] 4 uinals, and 8 tuns. Reducing this number to

units of the first order and counting it forward from the date next

preceding it in the text, 11 Imix 19 Muan in A15b B15a, the terminal date

reached will be 13 Ahau 18 Cumhu, which the student will find recorded in

A18. Compare the month sign with figure 19, _g', h'_. But immediately

following this date in B18a is Katun 17 and in the upper part of B18b the

hand-denoting ending. These glyphs A18 and B18 would seem to indicate,

therefore, that Katun 17 came to an end on the date 13 Ahau 18 Cumhu. That

they do, may be proved beyond all doubt by changing this period ending into

its corresponding Initial-series number 9.17.0.0.0 and solving for the

terminal date. This will be found to be 13 Ahau 18 Cumhu, which is recorded

in A18. This latter date, therefore, had the following position in the Long

Count: 9.17.0.0.0 13 Ahau 18 Cumhu. But having determined the position of

this latter date in the Long Count, that is, its Initial-series value, it

is now possible to fix the positions of the two dates 11 Imix 19 Muan and 7

Cimi 9 Zotz, which we were obliged to leave indeterminate above. Since the

date 13 Ahau 18 Cumhu was derived {238} by counting forward 8.4.19 from 11

Imix 19 Muan, the Initial-series value of the latter may be calculated by

subtracting 8.4.19 from the Initial-series value of the former:

9.17. 0. 0. 0 13 Ahau 18 Cumhu

8. 4.19

9.16.11.13. 1 11 Imix 19 Muan

And since the date 11 Imix 19 Muan was reached by counting forward

1.1.16.15 from 7 Cimi 9 Zotz, the Initial-series value of the latter may be

calculated by subtracting 1.1.16.15 from the now known Initial-series value

of the former:

9.16.11.13. 1 11 Imix 19 Muan

1. 1.16.15

9.15. 9.14. 6 7 Cimi 9 Zotz

Although this latter date is not recorded in the text, the date next

preceding the number 1.1.16.15 is 6 Cimi 4 Tzec, which corresponded to the

Initial Series 9.15.6.14.6 6 Cimi 4 Tzec, as we have seen, a date which was

exactly 3 tuns earlier than 7 Cimi 9 Zotz, 9.15.9.14.6 - 9.15.6.14.6 =

3.0.0.

The inscription on the west side closes then in A18 B18 with the record

that Katun 17 ended on the date 13 Ahau 18 Cumhu. The inscription on the

east side of this same monument opens with this same date expressed as an

Initial Series, 9.17.0.0.0 13 Ahau 18 Cumhu. See figure 82, A1-A6, A7,[229]

and A10.

The reiteration of this date as an Initial Series, when its position in the

Long Count had been fixed unmistakably on the other side of the same

monument by its record as a Period-ending date, together with the fact that

it is the latest date recorded in this inscription, very clearly indicates

that it alone designated the contemporaneous time of Stela E, and hence

determines the fact that Stela E was a hotun-marker. This whole text, in so

far as deciphered, reads as follows:

West side: 9.14.13.[230]4.17 12 Caban 5 Kayab Plate 24, _A_, A1-B5, B8b

6. 13. 3 Plate 24, _A_, B10b-A11a

9.15. 0. 0. 0 4 Ahau 13 Yax Plate 25, _A_, B11

[5. 0. 0] Undeclared

9.15. 5. 0. 0 10 Ahau 8 Chen "

1. 14. 6 Plate 24, _B_, B12

9.15. 6. 14. 6 6 Cimi 4 Tzec Plate 24, _B_, A13b, B13a

[3. 0. 0] Undeclared

{239}

9.15. 9. 14. 6 7 Cimi 9 Zotz "

1. 1. 16.15 Plate 24, _B_, A14b B14

9.16.11. 13. 1 11 Imix 19 Muan Plate 24, _B_, A15b B15a

8. 4.19 Plate 24, _B_, A17b B17a

9.17. 0. 0. 0 13 Ahau 18 Cumhu Plate 24, _B_, A18

End of Katun 17 Plate 24, _B_, B18

East side: 9.17. 0. 0. 0 13 Ahau 18 Cumhu Figure 82, A1-A6, A7, A10

Comparing the summary of the inscription on Stela E at Quirigua, just

given, with the summaries of the inscriptions on Stelæ J and F, and

Zoömorph G, at the same city, all four of which are shown side by side in

Table XVII,[231] the interrelationship of these four monuments appears very

clearly.

TABLE XVII. INTERRELATIONSHIP OF DATES ON STELÆ E, F, AND J AND ZOÖMORPH G,

QUIRIGUA

Date Stela J Stela F Stela E Zoömorph G

9.14.13. 4.17 12 Caban 5 Kayab X X X X

9.15. 0. 0. 0 4 Ahau 13 Yax - X X -

9.15. 5. 0. 0 10 Ahau 8 Chen X - X -

9.15. 6.14. 6 6 Cimi 4 Tzec X X X X

9.15. 9.14. 6 7 Cimi 9 Zotz - - X -

9.15.10. 0. 0 3 Ahau 3 Mol - X - -

9.16. 5. 0. 0 8 AHAU 8 ZOTZ X - - -

9.16.10. 0. 0 1 AHAU 8 ZIP - X - -

9.16.11.13. 1 11 Imix 19 Muan - - X -

9.17. 0. 0. 0 13 AHAU 18 CUMHU - - X -

9.17.15. 0. 0 5 AHAU 3 MUAN - - - X

In spite of the fact that each one of these four monuments marks a

different hotun in the Long Count, and consequently dates from a different

period, all of them go back to the same date, 9.14.13.4.17 12 Caban 5

Kayab, as their original starting point (see above). This date would almost

certainly seem, therefore, to indicate some very important event in the

annals of Quirigua. Moreover, since it is the earliest date found at this

city which can reasonably be regarded as having occurred during the actual

occupancy of the site, it is not improbable that it may represent, as

explained elsewhere, the time at which Quirigua was founded.[232] It is

necessary, however, to {240} caution the student that the above explanation

of the date 9.14.13.4.17 12 Caban 5 Kayab, or indeed any other for that

matter, is in the present state of our knowledge entirely a matter of

conjecture.

Passing on, it will be seen from Table XVII that two of the monuments,

namely, Stelæ E and F, bear the date 9.15.0.0.0 4 Ahau 3 Yax, and two

others, Stelæ E and J, the date 9.15.5.0.0 10 Ahau 8 Chen, one hotun later.

All four come together again, however, with the date 9.15.6.14.6 6 Cimi 4

Tzec, which is recorded on each. This date, like 9.14.13.4.17 12 Caban 5

Kayab, designates probably another important event in Quirigua history, the

nature of which, however, again escapes us. After the date 9.15.6.14.6 6

Cimi 4 Tzec, these monuments show no further correspondences, and we may

pass over the intervening time to their respective closing dates with but

scant notice, with the exception of Zoömorph G, which records a half dozen

dates in the hotun that it marks, 9.17.15.0.0 5 Ahau 3 Muan. (These latter

are omitted from Table XVII.)

This concludes the presentation of Initial-series, Secondary-series, and

Period-ending, dating, with which the student should be sufficiently

familiar by this time to continue his researches independently.

It was explained (see p. 76) that, when a Secondary-series date could not

be referred ultimately to either an Initial-series date or a Period-ending

date, its position in the Long Count could not be determined with

certainty, and furthermore that such a date became merely one of the 18,980

dates of the Calendar Round and could be fixed only within a period of 52

years. A few examples of Calendar-round dating are given in figure 83 and

plate 25. In figure 83, A, is shown a part of the inscription on Altar M at

Quirigua.[233] In A1 B1 appears a number consisting of 0 kins, 2 uinals,

and 3 tuns, that is, 3.2.0, and following this in A2b B2, the date 4 Ahau

13 Yax, and in A3b B3 the date 6 Ahau 18 Zac. Compare the month glyphs in

B2 and B3 with _q_ and _r_, and _s_ and _t_, respectively, of figure 19.

This has every appearance of being a Secondary Series, one of the two dates

being the starting point of the number 3.2.0, and the other its terminal

date. Reducing 3.2.0 to units of the first order, we have:

B1 = 3 × 360 = 1,080

A1 = 2 × 20 = 40

A1 = 0 × 1 = 0

-----

1,120

[Illustration: CALENDAR-ROUND DATES ON ALTAR 5, TIKAL]

{241}

Counting this number forward from 4 Ahau 13 Yax, the nearest date to it in

the text, the terminal date reached will be found to be 6 Ahau 18 Zac, the

date which, we have seen, was recorded in A3b B3. It is clear, therefore,

that this text records the fact that 3.2.0 has been counted forward from

the date 4 Ahau 13 Yax and the date 6 Ahau 18 Zac has been reached, but

there is nothing given by means of which the position of either of these

dates in the Long Count can be determined; consequently either of these

dates will be found recurring like any other Calendar-round date, at

intervals of every 52 years. In such cases the first assumption to be made

is that one of the dates recorded the close of a hotun, or at least of a

tun, in Cycle 9 of the Long Count. The reasons for this assumption are

quite obvious.

[Illustration: FIG. 83. Calendar-round dates: _A_, Altar M, Quirigua; _B_,

Altar Z, Copan.]

The overwhelming majority of Maya dates fall in Cycle 9, and nearly all

inscriptions have at least one date which closed some hotun or tun of that

cycle. Referring to Goodman's Tables, in which the tun endings of Cycle 9

are given, the student will find that the date 4 Ahau 13 Yax occurred as a

tun ending in Cycle 9, at 9.15.0.0.0 4 Ahau 13 Yax, in which position it

closed not only a hotun but also a katun. Hence, it is probable, although

the fact is not actually recorded, that the Initial-series value of the

date 4 Ahau 13 Yax in this text is 9.15.0.0.0 4 Ahau 13 Yax, and if this is

so the Initial-series value of the date 6 Ahau 18 Zac will be:

9.15.0.0.0 4 Ahau 13 Yax

3.2.0

9.15.3.2.0 6 Ahau 18 Zac

{242} In the case of this particular text the Initial-series value

9.15.0.0.0 might have been assigned to the date 4 Ahau 13 Yax on the ground

that this Initial-series value appears on two other monuments at Quirigua,

namely, Stelæ E and F, with this same date.

In figure 83, _B_, is shown a part of the inscription from Altar Z at

Copan.[234] In A1 B1 appears a number consisting of 1 kin, 8 uinals, and 1

tun, that is, 1.8.1, and following this in B2-A3 is the date 13 Ahau 18

Cumhu, but no record of its position in the Long Count. If 13 Ahau 18 Cumhu

is the terminal date of the number 1.8.1, the starting point can be

calculated by counting this number backward, giving the date 12 Cauac 2

Zac. On the other hand, if 13 Ahau 18 Cumhu is the starting point, the

terminal date reached by counting 1.8.1 forward will be 1 Imix 9 Mol.

However, since an ending prefix appears just before the date 13 Ahau 18

Cumhu in A2 (compare fig. 37, _a-h_), and since another, though it must be

admitted a very unusual ending sign, appears just after this date in A3

(compare the prefix of B3 with the prefix of fig. 37, _o_, and the subfix

with the subfixes of _l-n_ and _q_ of the same figure), it seems probable

that 13 Ahau 18 Cumhu is the terminal date and also a Period-ending date.

Referring to Goodman's Tables, it will be found that the only tun in Cycle

9 which ended with the date 13 Ahau 18 Cumhu was 9.17.0.0.0 13 Ahau 18

Cumhu, which not only ended a hotun but a katun as well.[235] If this is

true, the unrecorded starting point 12 Cauac 2 Zac can be shown to have the

following Initial-series value:

9.17. 0.0. 0 13 Ahau 18 Cumhu

1.8. 1 Backward

9.16.18.9.19 12 Cauac 2 Zac

In each of the above examples, as we have seen, there was a date which

ended one of the katuns of Cycle 9, although this fact was not recorded in

connection with either. Because of this fact, however, we were able to date

both of these monuments with a degree of probability amounting almost to

certainty. In some texts the student will find that the dates recorded did

not end any katun, hotun, or even tun, in Cycle 9, or in any other cycle,

and consequently such dates can not be assigned to their proper positions

in the Long Count by the above method.

The inscription from Altar 5 at Tikal figured in plate 25 is a case in

point. This text opens with the date 1 Muluc 2 Muan in glyphs 1 and 2 (the

first glyph or starting point is indicated by the star). {243} Compare

glyph 1 with figure 16, _m_, _n_, and glyph 2 with figure 19, _a', b'_. In

glyphs 8 and 9 appears a Secondary-series number consisting of 18 kins, 11

uinals, and 11 tuns (11.11.18). Reducing this number to units of the first

order and counting it forward from the date next preceding it in the text,

1 Muluc 2 Muan in glyphs 1 and 2, the terminal date reached will be 13

Manik 0 Xul, which the student will find recorded in glyphs 10 and 11.

Compare glyph 10 with figure 16, _j_, and glyph 11 with figure 19, _i, j_.

The next Secondary-series number appears in glyphs 22 and 23, and consists

of 19 kins, 9 uinals, and 8 tuns (8.9.19). Reducing this to units of the

first order and counting forward from the date next preceding it in the

text, 13 Manik 0 Xul in glyphs 10 and 11, the terminal date reached will be

11 Cimi 19 Mac, which the student will find recorded in glyphs 24 and 25.

Compare glyph 24 with figure 16, _h, i_, and glyph 25 with figure 19, _w_,

_x_. Although no number appears in glyph 26, there follows in glyphs 27 and

28 the date 1 Muluc 2 Kankin, which the student will find is just three

days later than 11 Cimi 19 Mac, that is, one day 12 Manik 0 Kankin, two

days 13 Lamat 1 Kankin, and three days 1 Muluc 2 Kankin.

In spite of the fact that all these numbers are counted regularly from the

dates next preceding them to reach the dates next following them, there is

apparently no glyph in this text which will fix the position of any one of

the above dates in the Long Count. Moreover, since none of the day parts

show the day sign Ahau, it is evident that none of these dates can end any

uinal, tun, katun, or cycle in the Long Count, hence their positions can

not be determined by the method used in fixing the dates in figure 83, _A_

and _B_.

There is, however, another method by means of which Calendar-round dates

may sometimes be referred to their proper positions in the Long Count. A

monument which shows only Calendar-round dates may be associated with

another monument or a building, the dates of which are fixed in the Long

Count. In such cases the fixed dates usually will show the positions to

which the Calendar-round dates are to be referred.

Taking any one of the dates given on Altar 5 in plate 25, as the last, 1

Muluc 2 Kankin, for example, the positions at which this date occurred in

Cycle 9 may be determined from Goodman's Tables to be as follows:

9. 0.16. 5.9 1 Muluc 2 Kankin

9. 3. 9. 0.9 1 Muluc 2 Kankin

9. 6. 1.13.9 1 Muluc 2 Kankin

9. 8.14. 8.9 1 Muluc 2 Kankin

9.11. 7. 3.9 1 Muluc 2 Kankin

9.13.19.16.9 1 Muluc 2 Kankin

9.16.12.11.9 1 Muluc 2 Kankin

9.19. 5. 6.9 1 Muluc 2 Kankin

{244} Next let us ascertain whether or not Altar 5 was associated with any

other monument or building at Tikal, the date of which is fixed

unmistakably in the Long Count. Says Mr. Teobert Maler, the discoverer of

this monument:[236] "A little to the north, fronting the north side of this

second temple and very near it, is a masonry quadrangle once, no doubt,

containing small chambers and having an entrance to the south. In the

middle of this quadrangle stands Stela 16 in all its glory, still unharmed,

_and in front of it, deeply buried in the earth, we found Circular Altar

5_, which was destined to become so widely renowned." It is evident from

the foregoing that the altar we are considering here, called by Mr. Maler

"Circular Altar 5," was found in connection with another monument at Tikal,

namely, Stela 16. But the date on this latter monument has already been

deciphered as "6 Ahau 13 Muan ending Katun 14" (see pl. 21, _D_; also p.

224), and this date, as we have seen, corresponded to the Initial Series

9.14.0.0.0 6 Ahau 13 Muan.

Our next step is to ascertain whether or not any of the Initial-series

values determined above as belonging to the date 1 Muluc 2 Kankin on Altar

5 are near the Initial Series 9.14.0.0.0 6 Ahau 13 Muan, which is the

Initial-series date corresponding to the Period-ending date on Stela 16. By

comparing 9.14.0.0.0 with the Initial-series values of 1 Muluc 2 Kankin

given above the student will find that the fifth value, 9.13.19.16.9,

corresponds with a date 1 Muluc 2 Kankin, which was only 31 days (1 uinal

and 11 kins) earlier than 9.14.0.0.0 6 Ahau 13 Muan. Consequently it may be

concluded that 9.13.19.16.9 was the particular day 1 Muluc 2 Kankin which

the ancient scribes had in mind when they engraved this text. From this

known Initial-series value the Initial-series values of the other dates on

Altar 5 may be obtained by calculation. The texts on Altar 5 and Stela 16

are given below to show their close connection:

_Altar 5_

9.12.19.12. 9 1 Muluc 2 Muan glyphs 1 and 2

11.11.18 glyphs 8 and 9

9.13.11. 6. 7 13 Manik 0 Xul glyphs 10 and 11

8. 9.19 glyphs 22 and 23

9.13.19.16. 6 11 Cimi 19 Mac glyphs 24 and 25

(3) undeclared

9.13.19.16. 9 1 Muluc 2 Kankin glyphs 27 and 28

(1.11) (Time between the two monuments, 31 days.)

_Stela 16_

9.14.0.0.0 6 Ahau 13 Muan A1-A4

Sometimes, however, monuments showing Calendar-round dates stand {245}

alone, and in such cases it is almost impossible to fix their dates in the

Long Count. At Yaxchilan in particular Calendar-round dating seems to have

been extensively employed, and for this reason less progress has been made

there than elsewhere in deciphering the inscriptions.

ERRORS IN THE ORIGINALS

Before closing the presentation of the subject of the Maya inscriptions the

writer has thought it best to insert a few texts which show actual errors

in the originals, mistakes due to the carelessness or oversight of the

ancient scribes.

[Illustration: FIG. 84. Texts showing actual errors in the originals: _A_,

Lintel, Yaxchilan; _B_, Altar Q, Copan; _C_, Stela 23, Naranjo.]

Errors in the original texts may be divided into two general classes: (1)

Those which are revealed by inspection, and (2) those which do not appear

until after the indicated calculations have been made and the results fail

to agree with the glyphs recorded.

An example of the first class is illustrated in figure 84, _A_. A very

cursory inspection of this text--an Initial Series from a lintel at

Yaxchilan--will show that the uinal coefficient in C1 represents an

impossible condition from the Maya point of view. This glyph as it stands

{246} unmistakably records 19 uinals, a number which had no existence in

the Maya system of numeration, since 19 uinals are always recorded as 1 tun

and 1 uinal.[237] Therefore the coefficient in C1 is incorrect on its face,

a fact we have been able to determine before proceeding with the

calculation indicated. If not 19, what then was the coefficient the ancient

scribe should have engraved in its place? Fortunately the rest of this text

is unusually clear, the Initial-series number 9.15.6.?.1 appearing in

B1-D1, and the terminal date which it reaches, 7 Imix 19 Zip, appearing in

C2 D2. Compare C2 with figure 16, _a, b_, and D2 with figure 19, d. We know

to begin with that the uinal coefficient must be one of the eighteen

numerals 0 to 17, inclusive. Trying 0 first, the number will be 9.15.6.0.1,

which the student will find leads to the date 7 Imix 4 Chen. Our first

trial, therefore, has proved unsuccessful, since the date recorded is 7

Imix 19 Zip. The day parts agree, but the month parts are not the same.

This month part 4 Chen is useful, however, for one thing, it shows us how

far distant we are from the month part 19 Zip, which is recorded. It

appears from Table XV that in counting forward from position 4 Chen just

260 days are required to reach position 19 Zip. Consequently, our first

trial number 9.15.6.0.1 falls short of the number necessary by just 260

days. But 260 days are equal to 13 uinals; therefore we must increase

9.15.6.0.1 by 13 uinals. This gives us the number 9.15.6.13.1. Reducing

this to units of the first order and solving for the terminal date, the

date reached will be 7 Imix 19 Zip, which agrees with the date recorded, in

C2 D2. We may conclude, therefore, that the uinal coefficient in C1 should

have been 13, instead of 19 as recorded.

Another error of the same kind--that is, one which may be detected by

inspection--is shown in figure 84, _B_. Passing over glyphs 1, 2, and 3, we

reach in glyph 4 the date 5 Kan 13 Uo. Compare the upper half of 4 with

figure 16, _f_, and the lower half with figure 19, _b, c_. The coefficient

of the month sign is very clearly 13, which represents an impossible

condition when used to indicate the position of a day whose name is Kan;

for, according to Table VII, the only positions which the day Kan can ever

occupy in any division of the year are 2, 7, 12, and 17. Hence, it is

evident that we have detected an error in this text before proceeding with

the calculations indicated. Let us endeavor to ascertain the coefficient

which should have been used with the month sign in glyph 4 instead of the

13 actually recorded. These glyphs present seemingly a regular Secondary

Series, the starting point being given in 1 and 2, the number in 3, and the

terminal date in 4. Counting this number 3.4 forward from the starting

point, 6 Ahau 13 Kayab, the terminal date reached will be 5 Kan 12 Uo.

Comparing this with the terminal date actually recorded, we find that the

two agree except for the month coefficient. But since the date recorded

represents an impossible condition, as we {247} have shown, we are

justified in assuming that the month coefficient which should have been

used in glyph 4 was 12, instead of 13. In other words, the craftsman to

whom the sculpturing of this inscription was intrusted engraved here 3 dots

instead of 2 dots, and 1 ornamental crescent, which, together with the 2

bars present, would have given the month coefficient determined by

calculation, 12. An error of this kind might occur very easily and indeed

in many cases may be apparent rather than real, being due to weathering

rather than to a mistake in the original text.

Some errors in the inscriptions, however, can not be detected by

inspection, and develop only after the calculations indicated have been

performed, and the results are found to disagree with the glyphs recorded.

Errors of this kind constitute the second class mentioned above. A case in

point is the Initial Series on the west side of Stela E at Quirigua,

figured in plate 24, _A_. In this text the Initial-series number recorded

in A4-A6 is very clearly 9.14.12.4.17, and the terminal date in B6-B8b is

equally clearly 12 Caban 5 Kayab. Now, if this number 9.14.12.4.17 is

reduced to units of the first order and is counted forward from the same

starting point as practically all other Initial Series, the terminal date

reached will be 3 Caban 10 Kayab, not 12 Caban 5 Kayab, as recorded.

Moreover, if the same number is counted forward from the date 4 Ahau 8

Zotz, which may have been another starting point for Initial Series, as we

have seen, the terminal date reached will be 3 Caban 10 Zip, not 12 Caban 5

Kayab, as recorded. The inference is obvious, therefore, that there is some

error in this text, since the number recorded can not be made to reach the

date recorded. An error of this kind is difficult to detect, because there

is no indication in the text as to which glyph is the one at fault. The

first assumption the writer makes in such cases is that the date is correct

and that the error is in one of the period-glyph coefficients. Referring to

Goodman's Table, it will be found that the date 12 Caban 5 Kayab occurred

at the following positions in Cycle 9 of the Long Count:

9. 1. 9.11.17 12 Caban 5 Kayab

9. 4. 2. 6.17 12 Caban 5 Kayab

9. 6.15. 1.17 12 Caban 5 Kayab

9. 9. 7.14.17 12 Caban 5 Kayab

9.12. 0. 9.17 12 Caban 5 Kayab

9.14.13. 4.17 12 Caban 5 Kayab

9.17. 5.17.17 12 Caban 5 Kayab

9.19.18.12.17 12 Caban 5 Kayab

An examination of these values will show that the sixth in the list,

9.14.13.4.17, is very close to the number recorded in our text,

9.14.12.4.17. Indeed, the only difference between the two is that the

former has 13 tuns while the latter has only 12. The similarity between

these two numbers is otherwise so close and the error in this {248} event

would be so slight--the record of 2 dots and 1 ornamental crescent instead

of 3 dots--that the conclusion is almost inevitable that the error here is

in the tun coefficient, 12 having been recorded instead of 13. In this

particular case the Secondary Series and the Period-ending date, which

follow the Initial-series number 9.14.12.4.17, prove that the above reading

of 13 tuns for the 12 actually recorded is the one correction needed to

rectify the error in this text.

Another example indicating an error which can not be detected by inspection

is shown in figure 84, _C_. In glyphs 1 and 2 appears the date 8 Eznab 16

Uo (compare glyph 1 with fig. 16, _c'_, and glyph 2 with fig. 19, _b, c_).

In glyph 3 follows a number consisting of 17 kins and 4 uinals (4.17).

Finally, in glyphs 4 and 5 is recorded the date 2 Men 13 Yaxkin (compare

glyph 4 with fig. 16, _y_, and glyph 5 with fig. 19, _k, l_). This has

every appearance of being a Secondary Series, of which 8 Eznab 16 Uo is the

starting point, 4.17, the number to be counted, and 2 Men 13 Yaxkin the

terminal date. Reducing 4.17 to units of the first order and counting it

forward from the starting point indicated, the terminal date reached will

be 1 Men 13 Yaxkin. This differs from the terminal date recorded in glyphs

4 and 5 in having a day coefficient of 1 instead of 2. Since this involves

but a very slight change in the original text, we are probably justified in

assuming; that the day coefficient in glyph 4 should have been 1 instead of

2 as recorded.

One more example will suffice to show the kind of errors usually

encountered in the inscriptions. In plate 26 is figured the Initial Series

from Stela N at Copan. The introducing glyph appears in A1 and is followed

by the Initial-series number 9.16.10.0.0 in A2-A6, all the coefficients of

which are unusually clear. Reducing this to units of the first order and

solving for the terminal date, the date reached will be 1 Ahau 3 Zip. This

agrees with the terminal date recorded in A7-A15 except for the month

coefficient, which is 8 in the text instead of 3, as determined by

calculation. Assuming that the date recorded is correct and that the error

is in the coefficient of the period glyphs the next step is to find the

positions in Cycle 9 at which the date 1 Ahau 8 Zip occurred. Referring to

Goodman's Tables, these will be found to be:

9. 0. 8.11.0 1 Ahau 8 Zip

9. 3. 1. 6.0 1 Ahau 8 Zip

9. 5.14. 1.0 1 Ahau 8 Zip

9. 8. 6.14.0 1 Ahau 8 Zip

9.10.19. 9.0 1 Ahau 8 Zip

9.13.12. 4.0 1 Ahau 8 Zip

9.16. 4.17.0 1 Ahau 8 Zip

9.18.17.12.0 1 Ahau 8 Zip

[Illustration: INITIAL SERIES ON STELA N, COPAN, SHOWING ERROR

IN MONTH COEFFICIENT]

{249} The number in the above list coming nearest to the number recorded in

this text (9.16.10.0.0) is the next to the last, 9.16.4.17.0. But in order

to reach this value of the date 1 Ahau 8 Zip (9.16.4.17.0) with the number

actually recorded, two considerable changes in it are first necessary, (1)

replacing the 10 tuns in A4 by 4 tuns, that is, changing 2 bars to 4 dots,

and (2) replacing 0 uinals in A5 by 17 uinals, that is, changing the 0 sign

to 3 bars and 2 dots. But these changes involve a very considerable

alteration of the original, and it seems highly improbable, therefore, that

the date here _intended_ was 9.16.4.17.0 1 Ahau 8 Zip. Moreover, as any

other number in the above list involves at least three changes of the

number recorded in order to reach 1 Ahau 8 Zip, we are forced to the

conclusion that the error must be in the terminal date, not in one of the

coefficients of the period glyphs. Let us therefore assume in our next

trial that the Initial-series number is correct as it stands, and that the

error lies somewhere in the terminal date. But the terminal date reached in

counting 9.16.10.0.0 forward in the Long Count will be 1 Ahau 3 Zip, as we

have seen on the preceding page, and this date differs from the terminal

date recorded by 5--1 bar in the month coefficient. It would seem probable,

therefore, that the bar to the left of the month sign in A15 should have

been omitted, in which case the text would correctly record the date

9.16.10.0.0 1 Ahau 3 Zip.

The student will note that in all the examples above given the errors have

been in the numerical coefficients, and not in the signs to which they are

attached; in other words, that although the numerals are sometimes

incorrectly recorded, the period, day, and month glyphs never are.

Throughout the inscriptions, the exceptions to this rule are so very rare

that the beginner is strongly advised to disregard them altogether, and to

assume when he finds an incorrect text that the error is in one of the

numerical coefficients. It should be remembered also in this connection

that errors in the inscriptions are exceedingly rare, and a glyph must not

be condemned as incorrect until every effort has been made to explain it in

some other way.

This concludes the presentation of texts from the inscriptions. The student

will have noted in the foregoing examples, as was stated in Chapter II,

that practically the only advances made looking toward the decipherment of

the glyphs have been on the chronological side. It is now generally

admitted that the relative ages[238] of most Maya monuments can be

determined from the dates recorded upon them, and that the final date in

almost every inscription indicates the time at or near which the monument

bearing it was erected, or at least formally dedicated. The writer has

endeavored to show, moreover, {250} that many, if indeed not most, of the

monuments, were "time markers" or "period stones," in every way similar to

the "period stones" which the northern Maya are known to[239] have erected

at regularly recurring periods. That the period which was used as this

chronological unit may have varied in different localities and at different

epochs is not at all improbable. The northern Maya at the time of the

Spanish Conquest erected a "period stone" every katun, while the evidence

presented in the foregoing texts, particularly those from Quirigua and

Copan, indicates that the chronological unit in these two cities at least

was the hotun, or quarter-katun period. Whatever may have been the

chronological unit used, the writer believes that the best explanation for

the monuments found so abundantly in the Maya area is that they were

"period stones," erected to commemorate or mark the close of successive

periods.

That we have succeeded in deciphering, up to the present time, only the

calendric parts of the inscriptions, the chronological skeleton of Maya

history as it were, stripped of the events which would vitalize it, should

not discourage the student nor lead him to minimize the importance of that

which is already gained. Thirty years ago the Maya inscriptions were a

sealed book, yet to-day we read in the glyphic writing the rise and fall of

the several cities in relation to one another, and follow the course of

Maya development even though we can not yet fill in the accompanying

background. Future researches, we may hope, will reconstruct this

background from the undeciphered glyphs, and will reveal the events of Maya

history which alone can give the corresponding chronology a human interest.

{251}

CHAPTER VI

THE CODICES

The present chapter will treat of the application of the material presented

in Chapters III and IV to texts drawn from the codices, or hieroglyphic

manuscripts; and since these deal in great part with the tonalamatl, or

sacred year of 260 days, as we have seen (p. 31), this subject will be

taken up first.

TEXTS RECORDING TONALAMATLS

The _tonalamatl_, or 260-day period, as represented in the codices is

usually divided into five parts of 52 days each, although tonalamatls of

four parts, each containing 65 days, and tonalamatls of ten parts, each

containing 26 days, are not at all uncommon. These divisions are further

subdivided, usually into unequal parts, all the divisions in one

tonalamatl, however, having subdivisions of the same length.

So far as its calendric side is concerned,[240] the tonalamatl may be

considered as having three essential parts, as follows:

1. A column of day signs.

2. Red numbers, which are the coefficients of the day signs.

3. Black numbers, which show the distances between the days designated by

(1) and (2).

The number of the day signs in (1), usually 4, 5, or 10, shows the number

of parts into which the tonalamatl is divided. Every red number in (2) is

used _once_ with every day sign in (1) to designate a day which is reached

in counting one of the black numbers in (3) forward from another of the

days recorded by (1) and (2). The most important point for the student to

grasp in studying the Maya tonalamatl is the fundamental difference between

the use of the red numbers and the black numbers. The former are used only

as day coefficients, and together with the day signs show the days which

begin the divisions and subdivisions of the tonalamatl. The black numbers,

on the other hand, are exclusively _time counters_, which show only the

distances between the dates indicated by the day signs and their

corresponding coefficients among the red numbers. They show in effect the

lengths of the periods and subperiods into which the tonalamatl is divided.

{252}

Most of the numbers, that is (2) and (3), in the tonalamatl are presented

in a horizontal row across the page or pages[241] of the manuscript, the

red alternating with the black. In some instances, however, the numbers

appear in a vertical column or pair of columns, though in this case also

the same alternation in color is to be observed. More rarely the numbers

are scattered over the page indiscriminately, seemingly without fixed order

or arrangement.

It will be noticed in each of the tonalamatls given in the following

examples that the record is greatly abbreviated or skeletonized. In the

first place, we see no month signs, and consequently the days recorded are

not shown to have had any fixed positions in the year. Furthermore, since

the year positions of the days are not fixed, any day could recur at

intervals of every 260 days, or, in other words, any tonalamatl with the

divisions peculiar to it could be used in endless repetition throughout

time, commencing anew every 260 days, regardless of the positions of these

days in succeeding years. Nor is this omission the only abbreviation

noticed in the presentation of the tonalamatl. Although every tonalamatl

contained 260 days, only the days commencing its divisions and subdivisions

appear in the record; and even these are represented in an abbreviated

form. For example, instead of repeating the numerical coefficients with

each of the day signs in (1), the coefficient was written once above the

column of day signs, and in this position was regarded as belonging to each

of the different day signs in turn. It follows from this fact that all the

main divisions of the tonalamatl begin with days the coefficients of which

are the same. Concerning the beginning days of the subdivisions, a still

greater abbreviation is to be noted. The day signs are not shown at all,

and only their numerical coefficients appear in the record. The economy of

space resulting from the above abbreviations in writing the days will

appear very clearly in the texts to follow.

In reading tonalamatls the first point to be determined is the name of the

day with which the tonalamatl began. This will be found thus:

_Rule 1._ To find the beginning day of a tonalamatl, prefix the first red

number, which will usually be found immediately above the column of the day

signs, to the uppermost[242] day sign in the column.

From this day as a starting point, the first black number in the text is to

be counted forward; and _the coefficient_ of the day reached will be the

second red number in the text. As stated above, the _day signs_ of the

beginning days of the subdivisions are always omitted. From the second red

number, which, as we have seen, is the {253} coefficient of the beginning

day of the second _subdivision_ of the first division, the _second black

number_ is to be counted forward in order to reach the third red number,

which is the coefficient of the day beginning the _third subdivision_ of

the first division. This operation is continued until the last black number

has been counted forward from the red number just preceding it and the last

red number has been reached.

This last red number will be found to be the same as the first red number,

and the day which the count will have reached will be shown by the first

red number (or the last, since the two are identical) used with the _second

day sign_ in the column. And this latter day will be the beginning day of

the _second division_ of the tonalamatl. From this day the count proceeds

as before. The black numbers are added to the red numbers immediately

preceding them in each case, until the last red number is reached, which,

together with _the third day sign_ in the column, forms the beginning day

of _the third division_ of the tonalamatl. After this operation has been

repeated until the last red number in the last division of the tonalamatl

has been reached--that is, the 260th day--the count will be found to have

reentered itself, or in other words, the day reached by counting forward

the last black number of the last division will be the same as the

beginning day of the tonalamatl.

It follows from the foregoing that the sum of all the black numbers

multiplied by the number of day signs in the column--the number of main

divisions in the tonalamatl--will equal exactly 260. If any tonalamatl

fails to give 260 as the result of this test, it may be regarded as

incorrect or irregular.

The foregoing material may be reduced to the following:

_Rule 2._ To find the coefficients of the beginning days of succeeding

divisions and subdivisions of the tonalamatl, add the black numbers to the

red numbers immediately preceding them in each case, and, after subtracting

all the multiples of 13 possible, the resulting number will be the

coefficient of the beginning day desired.

_Rule 3._ To find the day signs of the beginning days of the succeeding

divisions and subdivisions of the tonalamatl, count forward in Table I the

black number from the day sign of the beginning day of the preceding

division or subdivision, and the day name reached in Table I will be the

day sign desired. If it is at the beginning of one of the _main divisions_

of the tonalamatl, the day sign reached will be found to be recorded in the

column of day signs, but if at the beginning of a _subdivision_ it will be

unexpressed.

To these the test rule above given may be added:

_Rule 4._ The sum of all the black numbers multiplied by the number of day

signs in the column of day signs will equal exactly 260 if the tonalamatl

is perfectly regular and correct. {254}

In plate 27 is figured page 12 of the Dresden Codex. It will be noted that

this page is divided into three parts by red division lines; after the

general practice these have been designated _a, b_, and _c, a_ being

applied to the upper part, _b_ to the middle part, and _c_ to the lower

part. Thus "Dresden 12b" designates the middle part of page 12 of the

Dresden Codex, and "Dresden 15c" the lower part of page 15 of the same

manuscript. Some of the pages of the codices are divided into four parts,

or again, into two, and some are not divided at all. The same description

applies in all cases, the parts being lettered from top to bottom in the

same manner throughout.

The first tonalamatl presented will be that shown in Dresden 12b (see the

middle division in pl. 27). The student will readily recognize the three

essential parts mentioned on page 251: (1) The column of day signs, (2) the

red numbers, and (3) the black numbers. Since there are five day signs in

the column at the left of the page, it is evident that this tonalamatl has

five main divisions. The first point to establish is the day with which

this tonalamatl commenced. According to rule 1 (p. 252) this will be found

by prefixing the first red number to the topmost day sign in the column.

The first red number in Dresden 12b stands in the regular position (above

the column of day signs), and is very clearly 1, that is, one red dot. A

comparison of the topmost day sign in this column with the forms of the day

signs in figure 17 will show that the day sign here recorded is Ix (see

fig. 17, _t_), and the opening day of this tonalamatl will be, therefore, 1

Ix. The next step is to find the beginning days of the succeeding

subdivisions of the first main division of the tonalamatl, which, as we

have just seen, commenced with the day 1 Ix. According to rule 2 (p. 253),

the first black number--in this case 13, just to the right of and slightly

below the day sign Ix--is to be added to the red number immediately

preceding it--in this case 1--in order to give the coefficient of the day

beginning the next subdivision, all 13s possible being first deducted from

the resulting number. Furthermore, this coefficient will be the red number

next following the black number.

Applying this rule to the present case, we have:

1 (first red number) + 13 (next black number) = 14. Deducting all the 13s

possible, we have left 1 (14 - 13) as the coefficient of the day beginning

the next subdivision of the tonalamatl. This number 1 will be found as the

red number immediately following the first black number, 13. To find the

corresponding day sign, we must turn to rule 3 (p. 253) and count forward

in Table I this same black number, 13, from the preceding day sign, in this

case Ix. The day sign reached will be Manik. But since this day begins only

a _subdivision_ in this tonalamatl, not one of the _main divisions_, its

day sign will not be recorded, and we have, therefore, the day 1 Manik, of

which the 1 is expressed by the second red number and the name part Manik

only indicated by the calculations.

[Illustration: PAGE 12 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN

ALL THREE DIVISIONS]

{255}

The beginning day of the next subdivision of the tonalamatl may now be

calculated from the day 1 Manik by means of rules 2 and 3 (p. 253). Before

proceeding with the calculation incident to this step it will be necessary

first to examine the next black number in our tonalamatl. This will be

found to be composed of this sign () to which 6 (1 bar and 1 dot) has been

affixed. It was explained on page 92 that in representing tonalamatls the

Maya had to have a sign which by itself would signify the number 20, since

numeration by position was impossible. This special character for the

number 20 was given in figure 45, and a comparison of it with the sign here

under discussion will show that the two are identical. But in the present

example the number 6 is attached to this sign thus: (), and the whole

number is to be read 20 + 6 = 26. This number, as we have seen in Chapter

IV, would ordinarily have been written thus (): 1 unit of the second order

(20 units of the first order) + 6 units of the first order = 26. As

explained on page 92, however, numeration by position--that is, columns of

units--was impossible in the tonalamatls, in which many of the numbers

appear in a horizontal row, consequently some character had to be devised

which by itself would stand for the number 20.

Returning to our text, we find that the "next black number" is 26 (20 + 6),

and this is to be added to the red number 1 next preceding it, which, as we

have seen, is an abbreviation for the day 1 Manik (see rule 2, p. 253).

Adding 26 to 1 gives 27, and deducting all the 13s possible, namely, two,

we have left 1 (27 - 26); this number 1, which is the coefficient of the

beginning day of the next _subdivision_, will be found recorded just to the

right of the black 26.

The day sign corresponding to this coefficient 1 will be found by counting

forward 26 in Table I from the day name Manik. This will give the day name

Ben, and 1 Ben will be, therefore, the beginning day of the next

subdivision (the third subdivision of the first main division).

The next black number in our text is 13, and proceeding as before, this is

to be added to the red number next preceding it, 1, the abbreviation for 1

Ben. Adding 13 to 1 we have 14, and deducting all the 23s possible, we

obtain 1 again (14 - 13), which is recorded just to the right of the black

13 (rule 2, p. 253).[243] Counting forward 13 in Table I from the day name

Ben, the day name reached will be Cimi, and the day 1 Cimi will be the

beginning day of the next part of the tonalamatl. But since 13 is the last

black number, we should have reached in 1 Cimi the beginning day of the

_second main division_ of {256} the tonalamatl (see p. 253), and this is

found to be the case, since the day sign Cimi is _the second_ in the column

of day signs to the left. Compare this form with figure 17, _i, j_. The day

recorded is therefore 1 Cimi.

The first division of the tonalamatl under discussion is subdivided,

therefore, into three parts, the first part commencing with the day 1 Ix,

containing 13 days; the second commencing with the day 1 Manik, containing

26 days; and the third commencing with the day 1 Ben, containing 13 days.

The second division of the tonalamatl commences with the day 1 Cimi, as we

have seen above, and adding to this the first black number, 13, as before,

according to rules 2 and 3 (p. 253), the beginning day of the next

subdivision will be found to be 1 Cauac. Of this, however, only the 1 is

declared (see to the right of the black 13). Adding the next black number,

26, to this day, according to the above rules the beginning day of the next

subdivision will be found to be 1 Chicchan. Of this, however, the 1 again

is the only part declared. Adding the next and last black number, 13, to

this day, 1 Chicchan, according to the rules just mentioned the beginning

day of the next, or third, main division will be found to be 1 Eznab.

Compare the third day sign in the column of day signs with the form for

Eznab in figure 17, _z, a'_. The second division of this tonalamatl

contains, therefore, three parts: The first, commencing with the day 1

Cimi, containing 13 days; the second, commencing with the day 1 Cauac,

containing 26 days; and the third, commencing with the day 1 Chicchan,

containing 13 days.

Similarly the third division, commencing with the day 1 Eznab, could be

shown to have three parts, of 13, 26, and 13 days each, commencing with the

day 1 Eznab, 1 Chuen, and 1 Caban, respectively. It could be shown, also,

that the fourth division commenced with the day 1 Oc (compare the fourth

had three subdivisions containing 13, 26, and 13 days each, commencing with

the days 1 Oc, 1 Akbal, and 1 Muluc, respectively. Finally, the fifth and

last division of the tonalamatl will commence with the day 1 Ik. Compare

the last day sign in the column of day signs with figure 17, _c, d_; and

its three subdivisions of 13, 26, and 13 days each with the days 1 Ik, 1

Men, and 1 Imix, respectively. The student will note also that when the

last black number, 13, has been added to the beginning day of the _last

subdivision_ of the _last division_, the day reached will be 1 Ix, the day

with which the tonalamatl commenced. This period is continuous, therefore,

reentering itself immediately on its conclusion and commencing anew. {257}

There follows below an outline[244] of this particular tonalamatl:

---------------------+---------+-----------+---------+---------+---------

|1st |2d |3d |4th |5th

---------------------+---------+-----------+---------+---------+---------

beginning with day |1 Ix |1 Cimi |1 Eznab |1 Oc |1 Ik

| | | | |

| | | | |

| | | | |

Total number of days |52 |52 |52 |52 |52

---------------------+---------+-----------+---------+---------+---------

Next tonalamatl: 1st Division, 1st part, 13 days, beginning with the day 1

Ix, etc.

We may now apply rule 4 (p. 253) as a test to this tonalamatl. Multiplying

the sum of all the black numbers, 13 + 26 + 13 = 52, by the number of day

signs in the column of day signs, 5, we obtain 260 (52 × 5), which proves

that this tonalamatl is regular and correct.

The student will note in the middle division of plate 27 that the pictures

are so arranged that one picture stands under the first subdivisions of all

the divisions, the second picture under the second subdivisions, and the

third under the third subdivisions. It has been conjectured that these

pictures represent the gods who were the patrons or guardians of the

subdivisions of the tonalamatls, under which each appears. In the present

case the first god pictured is the Death Deity, God A (see fig. 3). Note

the fleshless lower jaw, the truncated nose, and the vertebræ. The second

deity is unknown, but the third is again the Death God, having the same

characteristics as the god in the first picture. The cloak worn by this

deity in the third picture shows the crossbones, which would seem to have

been an emblem of death among the Maya as among us. The glyphs above these

pictures probably explain the nature of the periods to which they refer, or

perhaps the ceremonies peculiar or appropriate to them. In many cases the

name glyphs of the deities who appear below them are given; for example, in

the present text, the second and sixth glyphs in the upper row[245] record

in each case the fact that the Death God is figured below.

The glyphs above the pictures offer one of the most promising problems in

the Maya field. It seems probable, as just explained, that the four or six

glyphs which stand above each of the pictures in a tonalamatl tell the

meaning of the picture to which they are appended, and any advances made,

looking toward their deciphering, will lead to far-reaching results in the

meaning of the {258} nonnumerical and noncalendric signs. In part at least

they show the name glyphs of the gods above which they occur, and it seems

not unlikely that the remaining glyphs may refer to the actions of the

deities who are portrayed; that is, to the ceremonies in which they are

engaged. More extended researches along this line, however, must be made

before this question can be answered.

The next tonalamatl to be examined is that shown in the lower division of

plate 27, Dresden 12c. At first sight this would appear to be another

tonalamatl of five divisions, like the preceding one, but a closer

examination reveals the fact that the last day sign in the column of day

signs is like the first, and that consequently there are only four

different signs denoting four divisions. The last, or fifth sign, like the

last red number to which it corresponds, merely indicates that after the

260th day the tonalamatl reenters itself and commences anew.

Prefixing the first red number, 13, to the first day sign, Chuen (see fig.

17, _p, q_), according to rule 1 (p. 252), the beginning day of the

tonalamatl will be found to be 13 Chuen. Adding to this the first black

number, 26, according to rules 2 and 3 (p. 253), the beginning day of the

next subdivision will be found to be 13 Caban. Since this day begins only a

subdivision of the tonalamatl, however, its name part Caban is omitted, and

merely the coefficient 13 recorded. Commencing with the day 13 Caban and

adding to it the next black number in the text, again 26, according to

rules 2 and 3 (p. 253), the beginning day of the next subdivision will be

found to be 13 Akbal, represented by its coefficient 13 only. Adding the

last black number in the text, 13, to 13 Akbal, according to the rules just

mentioned, the beginning day of the next part of the tonalamatl will be

found to be 13 Cib. And since the black 13 which gave this new day is the

last black number in the text, the new day 13 Cib will be the beginning day

of the next or _second division_ of the tonalamatl, and it will be recorded

as the second sign in the column of day signs. Compare the second day sign

in the column of day signs with figure 17, _v, w_.

Following the above rules, the student will have no difficulty in working

out the beginning days of the remaining divisions and subdivisions of this

tonalamatl. These are given below, though the student is urged to work them

out independently, using the following outline simply as a check on his

work. Adding the last black number, 13, to the beginning day of the last

subdivision of the last division, 13 Eznab, will bring the count back to

the day 13 Chuen with which the tonalamatl began: {259}

---------------------+----------+---------+----------+----------

|1st |2d |3d |4th

|Division |Division |Division |Division

---------------------+----------+---------+----------+----------

1st part, 26 days, | | | |

beginning with day |13 Chuen |13 Cib |13 Imix |13 Cimi

| | | |

2d part, 26 days, | | | |

beginning with day |13 Caban |13 Ik |13 Manik |13 Eb

| | | |

3d part, 13 days, | | | |

beginning with day |13 Akbal |13 Lamat |13 Ben |13 Eznab

| | | |

Total number of days |65 |65 |65 |65

---------------------+----------+---------+----------+----------

Next tonalamatl: 1st division, 1st part, 26 days, beginning with the day 13

Chuen, etc.

Applying the test rule to this tonalamatl (see rule 4, p. 253), we have: 26

+ 26 + 13 = 65, the sum of the black numbers, and 4 the number of the day

signs in the column of day signs,[246] 65 × 4 = 260, the exact number of

days in a tonalamatl.

The next tonalamatl (see the upper part of pl. 27, that is, Dresden 12a)

occupies only the latter two-thirds of the upper division, the black 12 and

red 11 being the last black and red numbers, respectively, of another

tonalamatl.

The presence of 10 day signs arranged in two parallel columns of five each

would seem at first to indicate that this is a tonalamatl of 10 divisions,

but it develops from the calculations that instead there are recorded here

two tonalamatls of five divisions each, the first column of day signs

designating one tonalamatl and the second another quite distinct therefrom.

The first red numeral is somewhat effaced, indeed all the red has

disappeared and only the black outline of the glyph remains. Its position,

however, above the column of day signs, seems to indicate its color and

use, and we are reasonably safe in stating that the first of the two

tonalamatls here recorded began with the day 8 Ahau. Adding to this the

first black number, 27, the beginning day of the next subdivision will be

found to be 9 Manik, neither the coefficient nor day sign of which appears

in the text. Assuming that the calculation is correct, however, and adding

the next black number, 25 (also out of place), to this day, 9 Manik, the

beginning day of the next part will be 8 Eb. But since 25 is the last black

number, 8 Eb will be the beginning day of the next main division and should

appear as the second sign in the first column of day signs. Comparison of

this form with figure 17, _r_, will show that Eb is recorded in this place.

{260} In this manner all of the beginning days could be worked out as

below:

---------------------+----------+---------+----------+----------+--------

|1st |2d |3d |4th |5th

---------------------+----------+---------+----------+----------+--------

beginning with day |8 Ahau |8 Eb |8 Kan |8 Cib |8 Lamat

| | | | |

| | | | |

Total number of days |52 |52 |52 |52 |52

---------------------+----------+---------+----------+----------+--------

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260,

the exact number of days in a tonalamatl. As previously explained, the

second column of day signs belongs to another tonalamatl, which, however,

utilized the same red 8 as the first and the same black 27 and 25 as the

first. The outline of this tonalamatl, which began with the day 8 Oc,

follows:

---------------------+----------+---------+---------+---------+----------

|1st |2d |3d |4th |5th

---------------------+----------+---------+---------+---------+----------

beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab

| | | | |

| | | | |

Total number of days |52 |52 |52 |52 |52

---------------------+----------+---------+---------+---------+----------

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260,

the exact number of days in a tonalamatl. It is interesting to note that

the above tonalamatl, beginning with the day 8 Oc, commenced just 130 days

later than the first tonalamatl, which began with the day 8 Ahau. In other

words, the first of the two tonalamatls in Dresden 12a was just half

completed when the second one commenced, and the second half of the first

tonalamatl began with the same day as the first half of the second

tonalamatl, and vice versa.

The tonalamatl in plate 28, upper division, is from Dresden 15a, and is

interesting because it illustrates how certain missing parts may be filled

in. The first red number is missing and we can only say that this

tonalamatl began with some day Ahau. However, adding the first black

number, 34, to this day ? Ahau, the day reached will be 13 Ix, of which

only 13 is recorded. Since 13 Ix was reached by counting 34 forward from

the day with which the count must have started, by counting back 34 from 13

Ix the starting point will be found to be 5 Ahau, and we may supply a red

bar above the column of the day signs. Adding the next black number, 18, to

this day 13 Ix, the beginning day of the next _division_ will be found to

be 5 Eb, which appears as the second day sign in the column of day signs.

[Illustration: PAGE 15 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN

ALL THREE DIVISIONS]

{261}

The last red number is 5, thus establishing as correct our restoration of a

red 5 above the column of day signs. From here this tonalamatl presents no

unusual features and it may be worked as follows:

---------------------+----------+---------+----------+----------+--------

|1st |2d |3d |4th |5th

---------------------+----------+---------+----------+----------+--------

beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat

| | | | |

beginning with day |13 Ix |13 Cimi |13 Eznab |13 Oc |13 Ik

| | | | |

Total number of days |52 |52 |52 |52 |52

---------------------+----------+---------+----------+----------+--------

Applying rule 4 (p. 253), we have: 5 × 52 = 260, the exact number of days

in a tonalamatl. The next tonalamatl (see lower part of pl. 28, that is,

Dresden 15c) has 10 day signs arranged in two parallel columns of 5 each.

This, at its face value, would seem to be divided into 10 divisions, and

the calculations confirm the results of the preliminary inspection.

The tonalamatl opens with the day 3 Lamat. Adding to this the first black

number, 12, the day reached will be 2 Ahau, of which only the 2 is recorded

here. Adding to 2 Ahau the next black number, 14, the day reached will be 3

Ix. And since 14 is the last black number, this new day will be the

beginning of the next division in the tonalamatl and will appear as the

upper day sign in the second column.[247] Commencing with 3 Ix and adding

to it the first black number 12, the day reached will be 2 Cimi, and adding

to this the next black number, 14, the day reached will be 3 Ahau, which

appears as the second glyph in the first column. This same operation if

carried throughout will give the following outline of this tonalamatl:

---------------------+----------+---------+----------+----------+--------

|1st |2d |3d |4th |5th

---------------------+----------+---------+----------+----------+--------

| | | | |

| | | | |

Total number of days |26 |26 |26 |26 |26

---------------------+----------+---------+----------+----------+--------

{262} (Concluded)

---------------------+----------+---------+----------+----------+--------

|6th |7th |8th |9th |10th

---------------------+----------+---------+----------+----------+--------

beginning with day |3 Eznab |3 Kan |3 Oc |3 Cib |3 Ik

| | | | |

beginning with day |2 Oc |2 Cib |2 Ik |2 Lamat |2 Ix

| | | | |

Total number of days |26 |26 |26 |26 |26

---------------------+----------+---------+----------+----------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 10 × 26 = 260, the

exact number of days in a tonalamatl.

The tonalamatl which appears in the middle part on plate 28--that is,

Dresden 15b--extends over on page 16b, where there is a black 13 and a red

1. The student will have little difficulty in reaching the result which

follows: The last day sign is the same as the first, and consequently this

tonalamatl is divided into four, instead of five, divisions:

---------------------+----------+---------+----------+----------

|1st |2d |3d |4th

|Division |Division |Division |Division

---------------------+----------+---------+----------+----------

1st part, 13 days, | | | |

beginning with day |1 Ik |1 Manik |1 Eb |1 Caban

| | | |

2d part, 31 days, | | | |

beginning with day |1 Men |1 Ahau |1 Chicchan|1 Oc

| | | |

3d part, 8 days, | | | |

beginning with day |6 Cimi |6 Chuen |6 Cib |6 Imix

| | | |

4th part, 13 days, | | | |

beginning with day |1 Ix |1 Cauac |1 Kan |1 Muluc

| | | |

Total number of days |65 |65 |65 |65

---------------------+----------+---------+----------+----------

Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the

exact number of days in a tonalamatl. The tonalamatls heretofore presented

have all been taken from the Dresden Codex. The following examples,

however, have been selected from tonalamatls in the Codex Tro-Cortesianus.

The student will note that the workmanship in the latter manuscript is far

inferior to that in the Dresden Codex. This is particularly true with

respect to the execution of the glyphs.

The first tonalamatl figured from the Codex Tro-Cortesianus (see pl. 29)

extends across the middle part of two pages (Tro-Cor. 10b, 11b). The four

day signs at the left indicate that it is divided into four divisions, of

which the first begins with the day 13 Ik.[248] Adding to this the first

black number 9, the day 9 Chuen is reached, and proceeding in this manner

the tonalamatl may be outlined as follows:

[Illustration: MIDDLE DIVISIONS OF PAGES 10 AND 11 OF THE CODEX

TRO-CORTESIANO, SHOWING ONE TONALAMATL EXTENDING ACROSS THE TWO

PAGES]

[Illustration: PAGE 102 OF THE CODEX TRO-CORTESIANO, SHOWING

TONALAMATLS IN THE LOWER THREE SECTIONS]

{263}

---------------------+----------+----------+----------+----------

|1st |2d |3d |4th

|Division |Division |Division |Division

---------------------+----------+------- --+----------+----------

1st part, 9 days, | | | |

beginning with day |13 Ik |13 Manik |13 Eb |13 Caban

| | | |

2d part, 9 days, | | | |

beginning with day |9 Chuen |9 Cib |9 Imix |9 Cimi

| | | |

3d part, 10 days, | | | |

beginning with day |5 Ahau |5 Chicchan|5 Oc |5 Men

| | | |

4th part, 6 days, | | | |

beginning with day |2 Oc |2 Men |2 Ahau |2 Chicchan

| | | |

5th part, 2 days, | | | |

beginning with day |8 Cib |8 Imix |8 Cimi |8 Chuen

| | | |

6th part, 10 days, | | | |

beginning with day |10 Eznab |10 Akbal |10 Lamat |10 Ben

| | | |

7th part, 5 days, | | | |

beginning with day |7 Lamat |7 Ben |7 Eznab |7 Akbal

| | | |

8th part, 7 days, | | | |

beginning with day |12 Ben |12 Eznab |12 Akbal |12 Lamat

| | | |

9th part, 7 days, |6 Ahau |6 Chicchan|6 Oc |6 Men

beginning with day |[249] |[249] |[249] |[249]

| | | |

Total number of days |65 |65 |65 |65

---------------------+----------+----------+----------+----------

Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the

exact number of days in a tonalamatl.

Another set of interesting tonalamatls is figured in plate 30, Tro-Cor.,

102.[250] The first one on this page appears in the second division, 102b,

and is divided into five parts, as the column of five day signs shows. The

order of reading is from left to right in the pair of number columns, as

will appear in the following outline of this tonalamatl:

---------------------+---------+---------+---------+----------+--------

|1st |2d |3d |4th |5th

---------------------+---------+---------+---------+----------+--------

| | | | |

| | | | |

beginning with day |13 Cib |13 Lamat |13 Ahau |13 Eb |13 Kan

| | | | |

beginning with day |2 Eznab |2 Oc |2 Ik |2 Ix |2 Cimi

| | | | |

beginning with day |12 Lamat |12 Ahau |12 Eb |12 Kan |12 Cib

| | | | |

| | | | |

Total number of days |52 |52 |52 |52 |52

---------------------+---------+---------+---------+----------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, {264}

the exact number of days in a tonalamatl. The next tonalamatl on this page

(see third division in pl. 29, that is, Tro-Cor., 102c) is interesting

chiefly because of the fact that the pictures which went with the third and

fourth parts of the five divisions are omitted for want of space. The

outline of this tonalamatl follows:

---------------------+----------+---------+---------+---------+--------

|1st |2d |3d |4th |5th

---------------------+----------+---------+---------+---------+--------

beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat

| | | | |

| | | | |

beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab

| | | | |

beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat

| | | | |

days |52 |52 |52 |52 |52

---------------------+----------+---------+---------+---------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, the

exact number of days in a tonalamatl. The last tonalamatl in plate 29,

Tro-Cor., 102d, commences with the same day, 4 Ahau, as the preceding

tonalamatl and, like it, has five divisions, each of which begins with the

same day as the corresponding division in the tonalamatl just given, 4

Ahau, 4 Eb, 4 Kan, 4 Cib, and 4 Lamat. Tro-Cor. 102d differs from Tro-Cor.

102c in the number and length of the parts into which its divisions are

divided.

Adding the first black number, 29, to the beginning day, 4 Ahau, the day

reached will be 7 Muluc, of which only the 7 appears in the text. Adding to

this the next black number, 24, the day reached will be 5 Ben. An

examination of the text shows, however, that the day actually recorded is 4

Eb, the last red number with the second day sign. This latter day is just

the day before 5 Ben, and since the sum of the black numbers in this case

does not equal any factor of 260 (29 + 24 = 53), and since changing the

last black number from 24 to 23 would make the sum of the black numbers

equal to a factor of 260 (29 + 23 = 52), and would bring the count to 4 Eb,

the day actually recorded, we are justified in assuming that there is an

error in our original text, and that 23 should have been written here

instead of 24. The outline of this tonalamatl, corrected as suggested,

follows: {265}

----------------------+----------+---------+---------+----------+--------

|1st |2d |3d |4th |5th

----------------------+----------+---------+---------+----------+--------

beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat

| | | | |

| | | | |

Total number of days |52 |52 |52 |52 |52

----------------------+----------+---------+---------+----------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 52 × 5 = 260, the

exact number of days in a tonalamatl.

The foregoing tonalamatls have been taken from the pages of the Dresden

Codex or those of the Codex Tro-Cortesiano. Unfortunately, in the Codex

Peresianus no complete tonalamatls remain, though one or two fragmentary

ones have been noted.

No matter how they are divided or with what days they begin, all

tonalamatls seem to be composed of the same essentials:

1. The calendric parts, made up, as we have seen on page 251, of (_a_) the

column of day signs; (_b_) the red numbers; (_c_) the black numbers.

2. The pictures of anthropomorphic figures and animals engaged in a variety

of pursuits, and

3. The groups of four or six glyphs above each of the pictures.

The relation of these parts to the tonalamatl as a whole is practically

determined. The first is the calendric background, the chronological

framework, as it were, of the period. The second and third parts amplify

this and give the special meaning and significance to the subdivisions. The

pictures represent in all probability the deities who presided over the

several subdivisions of the tonalamatls in which they appear, and the

glyphs above them probably set forth their names, as well as the ceremonies

connected with, or the prognostications for, the corresponding periods.

It will be seen, therefore, that in its larger sense the meaning of the

tonalamatl is no longer a sealed book, and while there remains a vast

amount of detail yet to be worked out the foundation has been laid upon

which future investigators may build with confidence.

In closing this discussion of the tonalamatl it may not be out of place to

mention here those whose names stand as pioneers in this particular field

of glyphic research. To the investigations of Prof. Ernst Förstemann we owe

the elucidation of the calendric part of the tonalamatl, and to Dr. Paul

Schellhas the identification of the gods and their corresponding name

glyphs in parts (2) and (3), above. As pointed out at the beginning of this

chapter, the most promising {266} line of research in the codices is the

groups of glyphs above the pictures, and from their decipherment will

probably come the determination of the meaning of this interesting and

unusual period.

TEXTS RECORDING INITIAL SERIES

Initial Series in the codices are unusual and indeed have been found, up to

the present time, in only one of the three known Maya manuscripts, namely,

the Dresden Codex. As represented in this manuscript, they differ

considerably from the Initial Series heretofore described, all of which

have been drawn from the inscriptions. This difference, however, is

confined to unessentials, and the system of counting and measuring time in

the Initial Series from the inscriptions is identical with that in the

Initial Series from the codices.

The most conspicuous difference between the two is that in the codices the

Initial Series are expressed by the second method, given on page 129, that

is, numeration by position, while in the inscriptions, as we have seen, the

period glyphs are used, that is, the first method, on page 105. Although

this causes the two kinds of texts to appear very dissimilar, the

difference is only superficial.

Another difference the student will note is the absence from the codices of

the so-called Initial-series "introducing glyph." In a few cases there

seems to be a sign occupying the position of the introducing glyph, but its

identification as the Initial-series "introducing glyph" is by no means

sure, and, moreover, as stated above, it does not occur in all cases in

which there are Initial Series.

Another difference is the entire absence from the codices of Supplementary

Series; this count seems to be confined exclusively to the monuments. Aside

from these points the Initial Series from the two sources differ but

little. All proceed from identically the same starting point, the date 4

Ahau 8 Cumhu, and all have their terminal dates or related Secondary-series

dates recorded immediately after them.

The first example of an Initial Series from the codices will be found in

plate 31 (Dresden 24), in the lower left-hand corner, in the second column

to the right. The Initial-series number here recorded is 9.9.16.0.0, of

which the zero in the 2d place (uinals) and the zero in the 1st place

(kins) are expressed by red numbers. This use of red numbers in the last

two places is due to the fact that the zero sign in the codices is _always

red_.

[Illustration: PAGE 24 OF THE DRESDEN CODEX, SHOWING INITIAL SERIES]

{267} The student will note the absence of all period glyphs from this

Initial Series and will observe that the multiplicands of the cycle, katun,

tun, uinal, and kin are fixed by the positions of each of the corresponding

multipliers. By referring to Table XIV the values of the several positions

in the second method of writing the numbers will be found, and using these

with their corresponding coefficients in each case the Initial-series

number here recorded may be reduced to units of the 1st order, as follows:

9 × 144,000 = 1,296,000

9 × 7,200 = 64,800

16 × 360 = 5,760

0 × 20 = 0

0 × 1 = 0

----------

1,366,560

Deducting from this number all the Calendar Rounds possible, 72 (see Table

XVI), it may be reduced to zero, since 72 Calendar Rounds contain exactly

1,366,560 units of the first order. See the preliminary rule on page 143.

Applying rules 1, 2, and 3 (pp. 139, 140, and 141) to the remainder, that

is, 0, the terminal date of the Initial Series will be found to be 4 Ahau 8

Cumhu, exactly the same as the starting point of Maya chronology. This must

be true, since counting forward 0 from the date 4 Ahau 8 Cumhu, the date 4

Ahau 8 Cumhu will be reached. Instead of recording this date immediately

below the last period of its Initial-series number, that is, the 0 kins, it

was written below the number just to the left. The terminal date of the

Initial Series we are discussing, therefore, is 4 Ahau 8 Cumhu, and it is

recorded just to the left of its usual position in the lower left-hand

corner of plate 31. The coefficient of the day sign, 4, is effaced but the

remaining parts of the date are perfectly clear. Compare the day sign Ahau

with the corresponding form in figure 17, _c', d'_, and the month sign

Cumhu with the corresponding form in figure 20, _z-b'_. The Initial Series

here recorded is therefore 9.9.16.0.0 4 Ahau 8 Cumhu. Just to the right of

this Initial Series is another, the number part of which the student will

readily read as follows: 9.9.9.16.0. Treating this in the usual way, it may

be reduced thus:

9 × 144,000 = 1,296,000

9 × 7,200 = 64,800

9 × 360 = 3,240

16 × 20 = 320

0 × 1 = 0

----------

1,364,360

Deducting from this number all the Calendar Rounds possible, 71 (see Table

XVI), it may be reduced to 16,780. Applying to this number rules 1, 2, and

3 (pp. 139, 140, and 141, respectively), its terminal date will be found to

be 1 Ahau 18 Kayab; this date is recorded just to the left below the kin

place of the _preceding_ Initial {268} Series. Compare the day sign and

month sign of this date with figures 17, _c', d'_, and 20, _x, y_,

respectively. This second Initial Series in plate 31 therefore reads

9.9.9.16.0 1 Ahau 18 Kayab. In connection with the first of these two

Initial Series, 9.9.16.0.0 4 Ahau 8 Cumhu, there is recorded a Secondary

Series. This consists of 6 tuns, 2 uinals, and 0 kins (6.2.0) and is

recorded just to the left of the first Initial Series from which it is

counted, that is, in the left-hand column.

It was explained on pages 136-137 that the almost universal direction of

counting was forward, but that when the count was backward in the codices,

this fact was indicated by a special sign or symbol, which gave to the

number it modified the significance of "backward" or "minus." This sign is

shown in figure 64, and, as explained on page 137, it usually is attached

only to the lowest period. Returning once more to our text, in plate 31 we

see this "backward" sign--a red circle surmounted by a knot--surrounding

the 0 kins of this Secondary-series number 6.2.0, and we are to conclude,

therefore, that this number is to be counted backward from some date.

Counting it backward from the date which stands nearest it in our text, 4

Ahau 8 Cumhu, the date reached will be 1 Ahau 18 Kayab. But since the date

4 Ahau 8 Cumhu is stated in the text to have corresponded with the

Initial-series value 9.9.16.0.0, by deducting 6.2.0 from this number we may

work out the Initial-series value for this date as follows:

9.9.16. 0.0 4 Ahau 8 Cumhu

6. 2.0 Backward

9.9. 9.16.0 1 Ahau 18 Kayab

The accuracy of this last calculation is established by the fact that the

Initial-series value 9.9.9.16.0 is recorded as the second Initial Series on

the page above described, and corresponds to the date 1 Ahau 18 Kayab as

here.

It is difficult to say why the terminal dates of these two Initial Series

and this Secondary Series should have been recorded to the _left_ of the

numbers leading to them, and not just _below_ the numbers in each case. The

only explanation the writer can offer is that the ancient scribe wished to

have the starting point of his Secondary-series number, 4 Ahau 8 Cumhu,

recorded as near that number as possible, that is, just below it, and

consequently the Initial Series leading to this date had to stand to the

right. This caused a displacement of the corresponding terminal date of his

Secondary Series, 1 Ahau 18 Kayab, which was written under the Initial

Series 9.9.16.0.0; and since the Initial-series value of 1 Ahau 18 Kayab

also appears to the right of 9.9.16.0.0 as 9.9.9.16.0, this causes a

displacement in its terminal date likewise. {269}

Two other Initial Series will suffice to exemplify this kind of count in

the codices. In plate 32 is figured page 62 from the Dresden Codex. In the

two right-hand columns appear two black numbers. The first of these reads

quite clearly 8.16.15.16.1, which the student is perfectly justified in

assuming is an Initial-series number consisting of 8 cycles, 16 katuns, 15

tuns, 16 uinals, and 1 kin. Moreover, above the 8 cycles is a glyph which

bears considerable resemblance to the Initial-series introducing glyph (see

fig. 24, _f_). Note in particular the trinal superfix. At all events,

whether it is an Initial Series or not, the first step in deciphering it

will be to reduce this number to units of the first order:

8 × 144,000 = 1,152,000

16 × 7,200 = 115,200

15 × 360 = 5,400

16 × 20 = 320

1 × 1 = 1

----------

1,272,921

Deducting from this number all the Calendar Rounds possible, 67 (see Table

XVI), it may be reduced to 1,261. Applying rules 1, 2, and 3 (pp. 139, 140,

and 141, respectively) to this remainder, the terminal date reached will be

4 Imix 9 Mol. This is not the terminal date recorded, however, nor is it

the terminal date standing below the next Initial-series number to the

right, 8.16.14.15.4. It would seem then that there must be some mistake or

unusual feature about this Initial Series.

Immediately below the date which stands under the Initial-series number we

are considering, 8.16.15.16.1, is another number consisting of 1 tun, 4

uinals, and 16 kins (1.4.16). It is not improbable that this is a

Secondary-series number connected in some way with our Initial Series. The

red circle surmounted by a knot which surrounds the 16 kins of this

Secondary-series number (1.4.16) indicates that the whole number is to be

counted _backward_ from some date. Ordinarily, the first Secondary Series

in a text is to be counted from the terminal date of the Initial Series,

which we have found by calculation (if not by record) to be 4 Imix 9 Mol in

this case. Assuming that this is the case here, we might count 1.4.16

_backward_ from the date 4 Imix 9 Mol.

Performing all the operations indicated in such cases, the terminal date

reached will be found to be 3 Chicchan 18 Zip; this is very close to the

date which is actually recorded just above the Secondary-series number and

just below the Initial-series number. The date here recorded is 3 Chicchan

13 Zip, and it is not improbable that the {270} ancient scribe intended to

write instead 3 Chicchan 18 Zip, the date indicated by the calculations. We

probably have here:

8.16.15.16. 1 (4 Imix 9 Mol)

1. 4.16 Backward

8.16.14.11. 5 3 Chicchan 18[252] Zip

In these calculations the terminal date of the Initial Series, 4 Imix 9

Mol, is suppressed, and the only date given is 3 Chicchan 18 Zip, the

terminal date of the Secondary Series.

Another Initial Series of this same kind, one in which the terminal date is

not recorded, is shown just to the right of the preceding in plate 32. The

Initial-series number 8.16.14.15.4 there recorded reduces to units of the

first order as follows:

8 × 144,000 = 1,152,000

16 × 7,200 = 115,200

14 × 360 = 5,040

15 × 20 = 300

4 × 1 = 4

----------

1,272,544

Deducting from this number all the Calendar Rounds possible, 67 (see Table

XVI), it will be reduced to 884, and applying rules 1, 2, and 3 (pp. 139,

140, and 141, respectively) to this remainder, the terminal date reached

will be 4 Kan 17 Yaxkin. This date is not recorded. There follows below,

however, a Secondary-series number consisting of 6 uinals and 1 kin (6.1).

The red circle around the lower term of this (the 1 kin) indicates that the

whole number, 6.1, is to be counted _backward_ from some date, probably, as

in the preceding case, from the terminal date of the Initial Series above

it. Assuming that this is the case, and counting 6.1 backward from

8.16.14.15.4 4 Kan 17 Yaxkin, the terminal date reached will be 13 Akbal 16

Pop, again very close to the date recorded immediately above, 13 Akbal 15

Pop. Indeed, the date as recorded, 13 Akbal 15 Pop, represents an

impossible condition from the Maya point of view, since the day name Akbal

could occupy only the first, sixth, eleventh, and sixteenth positions of a

month. See Table VII. Consequently, through lack of space or carelessness

the ancient scribe who painted this book failed to add one dot to the three

bars of the month sign's coefficient, thus making it 16 instead of the 15

actually recorded. We are obliged to make some correction in this

coefficient, since, as explained above, it is obviously incorrect as it

stands. Since the addition of a single dot brings the whole date into

harmony with the date determined by calculation, we are probably justified

{271} in making the correction here suggested. We have recorded here

therefore:

8.16.14.15.4 (4 Kan 17 Yaxkin)

6.1 Backward

8.16.14. 9.3 13 Akbal 16[253] Pop

In these calculations the terminal date of the Initial Series, 4 Kan 17

Yaxkin, is suppressed and the only date given is 13 Akbal 16 Pop, the

terminal date of the Secondary Series.

The above will suffice to show the use of Initial Series in the codices,

but before leaving this subject it seems best to discuss briefly the dates

recorded by these Initial Series in relation to the Initial Series on the

monuments. According to Professor Förstemann[254] there are 27 of these

altogether, distributed as follows:

Page 24: 9. 9.16. 0. 0[255]| Page 58: 9.12.11.11. 0

Page 24: 9. 9. 9.16. 0 | Page 62: 8.16.15.16. 1

Page 31: 8.16.14.15. 4 | Page 62: 8.16.14.15. 4

Page 31: 8.16. 3.13. 0 | Page 63: 8.11. 8. 7. 0

Page 31: 10.13.13. 3. 2[256]| Page 63: 8.16. 3.13. 0

Page 43: 9.19. 8.15. 0 | Page 63: 10.13. 3.16. 4[257]

Page 45: 8.17.11. 3. 0 | Page 63: 10.13.13. 3. 2

Page 51: 8.16. 4. 8. 0[258]| Page 70: 9.13.12.10. 0

Page 51: 10.19. 6. 1. 8[259]| Page 70: 9.19.11.13. 0

Page 52: 9.16. 4.11.18[260]| Page 70: 10.17.13.12.12

Page 52: 9.19. 5. 7. 8[261]| Page 70: 10.11. 3.18.14

Page 52: 9.16. 4.10. 8 | Page 70: 8. 6.16.12. 0

Page 52: 9.16. 4.11. 3 | Page 70: 8.16.19.10. 0

Page 58: 9.18. 2. 2. 0 |

There is a wide range of time covered by these Initial Series; indeed, from

the earliest 8.6.16.12.0 (on p. 70) to the latest, 10.19.6.1.8 (on p. 51)

there elapsed more than a thousand years. Where the difference between the

earliest and the latest dates is so great, it is a matter of vital

importance to determine the contemporaneous date of the manuscript. If the

closing date 10.19.6.1.8 represents the time at which the manuscript was

made, then the preceding dates reach back {272} for more than a thousand

years. On the other hand, if 8.6.16.12.0 records the present time of the

manuscript, then all the following dates are prophetic. It is a difficult

question to answer, and the best authorities have seemed disposed to take a

middle course, assigning as the contemporaneous date of the codex a date

about the middle of Cycle 9. Says Professor Förstemann (_Bulletin 28_, p.

402) on the subject:

In my opinion my demonstration also definitely proves that these large

numbers [the Initial Series] do not proceed from the future to the

past, but from the past, through the present, to the future. Unless I

am quite mistaken, the highest numbers among them seem actually to

reach into the future, and thus to have a prophetic meaning. Here the

question arises, At what point in this series of numbers does the

present lie? or, Has the writer in different portions of his work

adopted different points of time as the present? If I may venture to

express my conjecture, it seems to me that the first large number in

the whole manuscript, the 1,366,560 in the second column of page 24

[9.9.16.0.0 4 Ahau 8 Cumhu, the first Initial Series figured in plate

31], has the greatest claim to be interpreted as the present point of

time.

In a later article (_Bulletin 28_, p. 437) Professor Förstemann says: "But

I think it is more probable that the date farthest to the right (1 Ahau, 18

Zip ...) denotes the present, the other two [namely, 9.9.16.0.0 4 Ahau 8

Cumhu and 9.9.9.16.0 1 Ahau 18 Kayab] alluding to remarkable days in the

future." He assigns to this date 1 Ahau 18 Zip the position of 9.7.16.12.0

in the Long Count.

The writer believes this theory to be untenable because it involves a

correction in the original text. The date which Professor Förstemann calls

1 Ahau 18 Zip actually reads 1 Ahau 18 Uo, as he himself admits. The month

sign he corrects to Zip in spite of the fact that it is very clearly Uo.

Compare this form with figure 20, _b, c_. The date 1 Ahau 18 Uo occurs at

9.8.16.16.0, but the writer sees no reason for believing that this date or

the reading suggested by Professor Förstemann indicates the contemporaneous

time of this manuscript.

Mr. Bowditch assigns the manuscript to approximately the same period,

selecting the second Initial Series in plate 31, that is, 9.9.9.16.0 1 Ahau

18 Kayab: "My opinion is that the date 9.9.9.16.0 1 Ahau 18 Kayab is the

present time with reference to the time of writing the codex and is the

date from which the whole calculation starts."[262] The reasons which have

led Mr. Bowditch to this conclusion are very convincing and will make for

the general acceptance of his hypothesis.

Although the writer has no better suggestion to offer at the present time,

he is inclined to believe that both of these dates are far too early for

this manuscript and that it is to be ascribed to a very much later period,

perhaps to the centuries following immediately the colonization of Yucatan.

There can be no doubt that very early dates appear in the Dresden Codex,

but rather than accept one so early as 9.9.9.16.0 or 9.9.16.0.0 as the

contemporaneous date of the manuscript the writer would prefer to believe,

on historical grounds, that the manuscript now known as the Dresden Codex

is a copy of an earlier manuscript and that the present copy dates from the

later Maya period in Yucatan, though sometime before either Nahuatl or

Castilian acculturation had begun.

[Illustration: PAGE 62 OF THE DRESDEN CODEX, SHOWING THE SERPENT

NUMBERS]

{273}

TEXTS RECORDING SERPENT NUMBERS

The Dresden Codex contains another class of numbers which, so far as known,

occur nowhere else. These have been called the Serpent numbers because

their various orders of units are depicted between the coils of serpents.

Two of these serpents appear in plate 32. The coils of each serpent inclose

two different numbers, one in red and the other in black. Every one of the

Serpent numbers has six terms, and they represent by far the highest

numbers to be found in the codices. The black number in the first, or

left-hand serpent in plate 32, reads as follows: 4.6.7.12.4.10, which,

reduced to units of the first order, reads:

4 × 2,880,000 = 11,520,000

6 × 144,000 = 864,000

7 × 7,200 = 50,400

12 × 360 = 4,320

4 × 20 = 80

10 × 1 = 10

----------

12,438,810

The next question which arises is, What is the starting point from which

this number is counted? Just below it the student will note the date 3 Ix 7

Tzec, which from its position would seem almost surely to be either the

starting point or the terminal date, more probably the latter. Assuming

that this date is the terminal date, the starting point may be calculated

by counting 12,438,810 _backward_ from 3 Ix 7 Tzec. Performing this

operation according to the rules laid down in such cases, the starting

point reached will be 9 Kan 12 Xul, but this date is not found in the text.

The red number in the first serpent is 4.6.11.10.7.2, which reduces to--

4 × 2,880,000 = 11,520,000

6 × 144,000 = 864,000

11 × 7,200 = 79,200

10 × 360 = 3,600

7 × 20 = 140

2 × 1 = 2

----------

12,466,942

{274} Assuming that the date below this number, 3 Cimi 14 Kayab, was its

terminal date, the starting point can be reached by counting backward. This

will be found to be 9 Kan 12 Kayab, a date actually found on this page (see

pl. 32), just above the animal figure emerging from the second serpent's

mouth.

The black number in the second serpent reads 4.6.9.15.12.19, which reduces

as follows:

4 × 2,880,000 = 11,520,000

6 × 144,000 = 864,000

9 × 7,200 = 64,800

15 × 360 = 5,400

12 × 20 = 240

19 × 1 = 19

----------

12,454,459

Assuming that the date below this number, 13 Akbal 1 Kankin, was the

terminal date, its starting point can be shown by calculation to be just

the same as the starting point for the previous number, that is, the date 9

Kan 12 Kayab, and as mentioned above, this date appears above the animal

figure emerging from the mouth of this serpent.

The last Serpent number in plate 32, the red number in the second serpent,

reads, 4.6.1.9.15.0 and reduces as follows:

4 × 2,880,000 = 11,520,000

6 × 144,000 = 864,000

1 × 7,200 = 7,200

9 × 360 = 3,240

15 × 20 = 300

0 × 1 = 0

----------

12,394,740

Assuming that the date below this number, 3 Kan 17 Uo,[263] was its

terminal date, its starting point can be shown by calculation to be just

the same as the starting point of the two preceding numbers, namely, the

date 9 Kan 12 Kayab, which appears above this last serpent.

[Illustration: FIG. 85. Example of first method of numeration in the

codices (part of page 69 of the Dresden Codex).]

It will be seen from the foregoing that three of the four Serpent dates

above described are counted from the date 9 Kan 12 Kayab, a date actually

recorded in the text just above them. The all-important question of course

is, What position did the date 9 Kan 12 Kayab occupy in the Long Count? The

page (62) of the Dresden Codex we {275} are discussing sheds no light on

this question. There are, however, two other pages in this Codex (61 and

69) on which Serpent numbers appear presenting this date, 9 Kan 12 Kayab,

under conditions which may shed light on the position it held in the Long

Count. On page 69 there are recorded 15 katuns, 9 tuns, 4 uinals, and 4

kins (see fig. 85); these are immediately followed by the date 9 Kan 12

Kayab. It is important to note in this connection that, unlike almost every

other number in this codex, this number is expressed by the first method,

the one in which the period glyphs are used. As the date 4 Ahau 8 Cumhu

appears just above in the text, the first supposition is that 15.9.4.4 is a

Secondary-series number which, if counted forward from 4 Ahau 8 Cumhu, the

starting point of Maya chronology, will reach 9 Kan 12 Kayab, the date

recorded immediately after it. Proceeding on this assumption and performing

the operations indicated, the terminal date reached will be 9 Kan 7 Cumhu,

not 9 Kan 12 Kayab, as recorded. The most plausible explanation for this

number and date the writer can offer is that the whole constitutes a

Period-ending date. On the west side of Stela C at Quirigua, as explained

on page 226, is a Period-ending date almost exactly like this (see pl. 21,

_H_). On this monument 17.5.0.0 6 Ahau 13 Kayab is recorded, and it was

proved by calculation that 9.17.5.0.0 would lead to this date if counted

forward from the starting point of Maya chronology. In effect, then, this

17.5.0.0 6 Ahau 13 Kayab was a Period-ending date, declaring that Tun 5 of

Katun 17 (of Cycle 9, unexpressed) ended on the date 6 Ahau 13 Kayab.

Interpreting in the same way the glyphs in figure 85, we have the record

that Kin 4 of Uinal 4 of Tun 9 of Katun 15 (of Cycle 9, unexpressed) fell

(or ended) on the date 9 Kan 12 Kayab. Changing this Period-ending date

into its corresponding Initial Series and solving for its terminal date,

the latter date will be found to be 13 Kan 12 Ceh, instead of 9 Kan 12

Kayab. At first this would appear to be even farther from the mark than our

preceding attempt, but if the reader will admit a slight correction, the

above number can be made to reach the date recorded. The date 13 Kan 12 Ceh

is just 5 uinals earlier than 9 Kan 12 Kayab, and if we add one bar to the

four dots of the uinal coefficient, this passage can be explained in the

above manner, and yet agree in all particulars. This is true since

9.15.9.9.4 reaches the date 9 Kan 12 Kayab. On the above grounds the writer

is inclined to believe that the last three Serpent numbers on plate 32,

which were shown to have proceeded from a date 9 Kan 12 Kayab, were counted

from the date 9.15.9.9.4 9 Kan 12 Kayab. {276}

TEXTS RECORDING ASCENDING SERIES

There remains one other class of numbers which should be described before

closing this chapter on the codices. The writer refers to the series of

related numbers which cover so many pages of the Dresden Codex. These

commence at the bottom of the page and increase toward the top, every other

number in the series being a multiple of the first, or beginning number.

One example of this class will suffice to illustrate all the others.

In the lower right-hand corner of plate 31 a series of this kind commences

with the day 9 Ahau.[264] Of this series the number 8.2.0 just above the 9

Ahau is the first term, and the day 9 Ahau the first terminal date. As

usual in Maya texts, the starting point is not expressed; by calculation,

however, it can be shown to be 1 Ahau[265] in this particular case.

Counting forward then 8.2.0 from 1 Ahau, the unexpressed starting point,

the first terminal date, 9 Ahau, will be reached. See the lower right-hand

corner in the following outline, in which the Maya numbers have all been

reduced to units of the first order:

151,840[266] 113,880[266] 75,920[266] 37,960[266]

1 Ahau 1 Ahau 1 Ahau 1 Ahau

185,120 68,900 33,280 9,100

1 Ahau 1 Ahau 1 Ahau 1 Ahau

35,040 32,120 29,200 26,280

6 Ahau 11 Ahau 3 Ahau 8 Ahau

23,360 20,440 17,520 14,600

13 Ahau 5 Ahau 10 Ahau 2 Ahau

11,680[267] 8,760 5,840 2,920

7 Ahau 12 Ahau 4 Ahau 9 Ahau

(Unexpressed starting point, 1 Ahau.)

In the above outline each number represents the total distance of the day

just below it from the unexpressed starting point, 1 Ahau, _not_ the

distance from the date immediately preceding it in the series. For example,

the second number, 5,840 (16.4.0), is not to be counted forward from 9 Ahau

in order to reach its terminal date, 4 Ahau, but from the unexpressed

starting point of the whole series, the day 1 Ahau. Similarly the third

number, 8,760 (1.4.6.0), is not to be counted forward from 4 Ahau in order

to reach 12 Ahau, but from 1 Ahau instead, and so on throughout the series.

{277}

Beginning with the number 2,920 and the starting point 1 Ahau, the first

twelve terms, that is, the numbers in the three lowest rows, are the first

12 multiples of 2,920.

2,920 = 1 × 2,920 20,440 = 7 × 2,920

5,840 = 2 × 2,920 23,360 = 8 × 2,920

8,760 = 3 × 2,920 26,280 = 9 × 2,920

11,680 = 4 × 2,920 29,200 = 10 × 2,920

14,600 = 5 × 2,920 32,120 = 11 × 2,920

17,520 = 6 × 2,920 35,040 = 12 × 2,920

The days recorded under each of these numbers, as mentioned above, are the

terminal dates of these distances from the starting point, 1 Ahau. Passing

over the fourth row from the bottom, which, as will appear presently, is

probably an interpolation of some kind, the thirteenth number--that is, the

right-hand one in the top row--is 37,960. But 37,960 is 13 × 2,920, a

continuation of our series the twelfth term of which appeared in the

left-hand number of the third row. Under the thirteenth number is set down

the day 1 Ahau; in other words, not until the thirteenth multiple of 2,920

is reached is the terminal day the same as the starting point.

With this thirteenth term 2,920 ceases to be the unit of increase, and the

thirteenth term itself (37,960) is used as a difference to reach the

remaining three terms on this top line, all of which are multiples of

37,960.

37,960 = 1 × 37,960 or 13 × 2,920

75,920 = 2 × 37,960 or 26 × 2,920

113,880 = 3 × 37,960 or 39 × 2,920

151,840 = 4 × 37,960 or 52 × 2,920

Counting forward each one of these from the starting point of this entire

series, 1 Ahau, each will be found to reach as its terminal day 1 Ahau, as

recorded under each. The fourth line from the bottom is more difficult to

understand, and the explanation offered by Professor Förstemann, that the

first and third terms and the second and fourth are to be combined by

addition or subtraction, leaves much to be desired. Omitting this row,

however, the remaining numbers, those which are multiples of 2,920, admit

of an easy explanation.

In the first place, the opening term 2,920, which serves as the unit of

increase for the entire series up to and including the 13th term, is the

so-called Venus-Solar period, containing 8 Solar years of 365 days each and

5 Venus years of 584 days each. This important period is the subject of

extended treatment elsewhere in the Dresden Codex (pp. 46-50), in which it

is repeated 39 times in all, divided into three equal divisions of 13

periods each. The 13th term of our series 37,960 is, as we have seen, 13 ×

2,920, the exact number of {278} days treated of in the upper divisions of

pages 46-50 of the Dresden Codex. The 14th term (75,920) is the exact

number of days treated of in the first two divisions, and finally, the

15th, or next to the last term (113,880), is the exact number of days

treated of in all three divisions of these pages.

This 13th term (37,960) is the first in which the tonalamatl of 260 days

comes into harmony with the Venus and Solar years, and as such must have

been of very great importance to the Maya. At the same time it represents

two Calendar Rounds, another important chronological count. With the next

to the last term (113,880) the Mars year of 780 days is brought into

harmony with all the other periods named. This number, as just mentioned,

represents the sum of all the 39 Venus-Solar periods on pages 46-50 of the

Dresden Codex. This next to the last number seems to possess more

remarkable properties than the last number (151,840), in which the Mars

year is not contained without a remainder, and the reason for its record

does not appear.

The next to the last term contains:

438 Tonalamatls of 260 days each

312 Solar years of 365 days each

195 Venus years of 584 days each

146 Mars years of 780 days each

39 Venus-Solar periods of 2,920 days each

6 Calendar Rounds of 18,980 days each

It will be noted in plate 31 that the concealed starting point of this

series is the day 1 Ahau, and that just to the left on the same plate are

two dates, 1 Ahau 18 Kayab and 1 Ahau 18 Uo, both of which show this same

day, and one of which, 1 Ahau 18 Kayab, is accompanied by its corresponding

Initial Series 9.9.9.16.0. It seems not unlikely, therefore, that the day 1

Ahau with which this series commences was 1 Ahau 18 Kayab, which in turn

was 9.9.9.16.0 1 Ahau 18 Kayab of the Long Count. This is rendered somewhat

probable by the fact that the second division of 13 Venus-Solar periods on

pages 46-50 of the Dresden Codex also has the same date, 1 Ahau 18 Kayab,

as its terminal date. Hence, it is not improbable (more it would be unwise

to say) that the series of numbers which we have been discussing was

counted from the date 9.9.9.16.0. 1 Ahau 18 Kayab.

The foregoing examples cover, in a general way, the material presented in

the codices; there is, however, much other matter which has not been

explained here, as unfitted to the needs of the beginner. To the student

who wishes to specialize in this field of the glyphic writing the writer

recommends the treatises of Prof. Ernst Förstemann as the most valuable

contribution to this subject.

* * * * *

{279}

INDEX

ABBREVIATION IN DATING, use, 222, 252

ADDITION, method, 149

ADULTERY, punishment, 9-10

AGUILAR, S. DE, on Maya records, 36

AHHOLPOP (official), duties, 13

AHKULEL (deputy-chief), powers, 13

AHPUCH (god), nature, 17

ALPHABET, nonexistence, 27

AMUSEMENTS, nature, 10

ARABIC SYSTEM OF NUMBERS, Maya parallel, 87, 96

ARCHITECTURE, development, 5

ARITHMETIC, system, 87-155

ASCENDING SERIES, texts recording 276-278

ASTRONOMICAL COMPUTATIONS--

accuracy, 32

in codices, 31-32, 276-278

AZTEC--

calendar, 58-59

ikomomatic hieroglyphics, 29

rulership succession, 16

Another example showing the use of these three methods of dating in one and