Chapter 24 of 31 · 14664 words · ~73 min read

Chapter IV

, would ordinarily have been written thus (): 1 unit of the second order (20 units of the first order) + 6 units of the first order = 26. As explained on page 92, however, numeration by position--that is, columns of units--was impossible in the tonalamatls, in which many of the numbers appear in a horizontal row, consequently some character had to be devised which by itself would stand for the number 20.

Returning to our text, we find that the "next black number" is 26 (20 + 6), and this is to be added to the red number 1 next preceding it, which, as we have seen, is an abbreviation for the day 1 Manik (see rule 2, p. 253). Adding 26 to 1 gives 27, and deducting all the 13s possible, namely, two, we have left 1 (27 - 26); this number 1, which is the coefficient of the beginning day of the next _subdivision_, will be found recorded just to the right of the black 26.

The day sign corresponding to this coefficient 1 will be found by counting forward 26 in Table I from the day name Manik. This will give the day name Ben, and 1 Ben will be, therefore, the beginning day of the next subdivision (the third subdivision of the first main division).

The next black number in our text is 13, and proceeding as before, this is to be added to the red number next preceding it, 1, the abbreviation for 1 Ben. Adding 13 to 1 we have 14, and deducting all the 23s possible, we obtain 1 again (14 - 13), which is recorded just to the right of the black 13 (rule 2, p. 253).[243] Counting forward 13 in Table I from the day name Ben, the day name reached will be Cimi, and the day 1 Cimi will be the beginning day of the next part of the tonalamatl. But since 13 is the last black number, we should have reached in 1 Cimi the beginning day of the _second main division_ of {256} the tonalamatl (see p. 253), and this is found to be the case, since the day sign Cimi is _the second_ in the column of day signs to the left. Compare this form with figure 17, _i, j_. The day recorded is therefore 1 Cimi.

The first division of the tonalamatl under discussion is subdivided, therefore, into three parts, the first part commencing with the day 1 Ix, containing 13 days; the second commencing with the day 1 Manik, containing 26 days; and the third commencing with the day 1 Ben, containing 13 days.

The second division of the tonalamatl commences with the day 1 Cimi, as we have seen above, and adding to this the first black number, 13, as before, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 1 Cauac. Of this, however, only the 1 is declared (see to the right of the black 13). Adding the next black number, 26, to this day, according to the above rules the beginning day of the next subdivision will be found to be 1 Chicchan. Of this, however, the 1 again is the only part declared. Adding the next and last black number, 13, to this day, 1 Chicchan, according to the rules just mentioned the beginning day of the next, or third, main division will be found to be 1 Eznab. Compare the third day sign in the column of day signs with the form for Eznab in figure 17, _z, a'_. The second division of this tonalamatl contains, therefore, three parts: The first, commencing with the day 1 Cimi, containing 13 days; the second, commencing with the day 1 Cauac, containing 26 days; and the third, commencing with the day 1 Chicchan, containing 13 days.

Similarly the third division, commencing with the day 1 Eznab, could be shown to have three parts, of 13, 26, and 13 days each, commencing with the day 1 Eznab, 1 Chuen, and 1 Caban, respectively. It could be shown, also, that the fourth division commenced with the day 1 Oc (compare the fourth sign in the column of day signs with figure 17, _o_), and, further, that it had three subdivisions containing 13, 26, and 13 days each, commencing with the days 1 Oc, 1 Akbal, and 1 Muluc, respectively. Finally, the fifth and last division of the tonalamatl will commence with the day 1 Ik. Compare the last day sign in the column of day signs with figure 17, _c, d_; and its three subdivisions of 13, 26, and 13 days each with the days 1 Ik, 1 Men, and 1 Imix, respectively. The student will note also that when the last black number, 13, has been added to the beginning day of the _last subdivision_ of the _last division_, the day reached will be 1 Ix, the day with which the tonalamatl commenced. This period is continuous, therefore, reentering itself immediately on its conclusion and commencing anew. {257}

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

---------------------+---------+-----------+---------+---------+--------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+---------+-----------+---------+---------+--------- 1st part, 13 days, | | | | | beginning with day |1 Ix |1 Cimi |1 Eznab |1 Oc |1 Ik | | | | | 2d part, 26 days, | | | | | beginning with day |1 Manik |1 Cauac |1 Chuen |1 Akbal |1 Men | | | | | 3d part, 13 days, | | | | | beginning with day |1 Ben |1 Chicchan |1 Caban |1 Muluc |1 Imix | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+---------+-----------+---------+---------+---------

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

We may now apply rule 4 (p. 253) as a test to this tonalamatl. Multiplying the sum of all the black numbers, 13 + 26 + 13 = 52, by the number of day signs in the column of day signs, 5, we obtain 260 (52 × 5), which proves that this tonalamatl is regular and correct.

The student will note in the middle division of plate 27 that the pictures are so arranged that one picture stands under the first subdivisions of all the divisions, the second picture under the second subdivisions, and the third under the third subdivisions. It has been conjectured that these pictures represent the gods who were the patrons or guardians of the subdivisions of the tonalamatls, under which each appears. In the present case the first god pictured is the Death Deity, God A (see fig. 3). Note the fleshless lower jaw, the truncated nose, and the vertebræ. The second deity is unknown, but the third is again the Death God, having the same characteristics as the god in the first picture. The cloak worn by this deity in the third picture shows the crossbones, which would seem to have been an emblem of death among the Maya as among us. The glyphs above these pictures probably explain the nature of the periods to which they refer, or perhaps the ceremonies peculiar or appropriate to them. In many cases the name glyphs of the deities who appear below them are given; for example, in the present text, the second and sixth glyphs in the upper row[245] record in each case the fact that the Death God is figured below.

The glyphs above the pictures offer one of the most promising problems in the Maya field. It seems probable, as just explained, that the four or six glyphs which stand above each of the pictures in a tonalamatl tell the meaning of the picture to which they are appended, and any advances made, looking toward their deciphering, will lead to far-reaching results in the meaning of the {258} nonnumerical and noncalendric signs. In part at least they show the name glyphs of the gods above which they occur, and it seems not unlikely that the remaining glyphs may refer to the actions of the deities who are portrayed; that is, to the ceremonies in which they are engaged. More extended researches along this line, however, must be made before this question can be answered.

The next tonalamatl to be examined is that shown in the lower division of plate 27, Dresden 12c. At first sight this would appear to be another tonalamatl of five divisions, like the preceding one, but a closer examination reveals the fact that the last day sign in the column of day signs is like the first, and that consequently there are only four different signs denoting four divisions. The last, or fifth sign, like the last red number to which it corresponds, merely indicates that after the 260th day the tonalamatl reenters itself and commences anew.

Prefixing the first red number, 13, to the first day sign, Chuen (see fig. 17, _p, q_), according to rule 1 (p. 252), the beginning day of the tonalamatl will be found to be 13 Chuen. Adding to this the first black number, 26, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 13 Caban. Since this day begins only a subdivision of the tonalamatl, however, its name part Caban is omitted, and merely the coefficient 13 recorded. Commencing with the day 13 Caban and adding to it the next black number in the text, again 26, according to rules 2 and 3 (p. 253), the beginning day of the next subdivision will be found to be 13 Akbal, represented by its coefficient 13 only. Adding the last black number in the text, 13, to 13 Akbal, according to the rules just mentioned, the beginning day of the next part of the tonalamatl will be found to be 13 Cib. And since the black 13 which gave this new day is the last black number in the text, the new day 13 Cib will be the beginning day of the next or _second division_ of the tonalamatl, and it will be recorded as the second sign in the column of day signs. Compare the second day sign in the column of day signs with figure 17, _v, w_.

Following the above rules, the student will have no difficulty in working out the beginning days of the remaining divisions and subdivisions of this tonalamatl. These are given below, though the student is urged to work them out independently, using the following outline simply as a check on his work. Adding the last black number, 13, to the beginning day of the last subdivision of the last division, 13 Eznab, will bring the count back to the day 13 Chuen with which the tonalamatl began: {259}

---------------------+----------+---------+----------+---------- |1st |2d |3d |4th |Division |Division |Division |Division ---------------------+----------+---------+----------+---------- 1st part, 26 days, | | | | beginning with day |13 Chuen |13 Cib |13 Imix |13 Cimi | | | | 2d part, 26 days, | | | | beginning with day |13 Caban |13 Ik |13 Manik |13 Eb | | | | 3d part, 13 days, | | | | beginning with day |13 Akbal |13 Lamat |13 Ben |13 Eznab | | | | Total number of days |65 |65 |65 |65 ---------------------+----------+---------+----------+----------

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

Applying the test rule to this tonalamatl (see rule 4, p. 253), we have: 26 + 26 + 13 = 65, the sum of the black numbers, and 4 the number of the day signs in the column of day signs,[246] 65 × 4 = 260, the exact number of days in a tonalamatl.

The next tonalamatl (see the upper part of pl. 27, that is, Dresden 12a) occupies only the latter two-thirds of the upper division, the black 12 and red 11 being the last black and red numbers, respectively, of another tonalamatl.

The presence of 10 day signs arranged in two parallel columns of five each would seem at first to indicate that this is a tonalamatl of 10 divisions, but it develops from the calculations that instead there are recorded here two tonalamatls of five divisions each, the first column of day signs designating one tonalamatl and the second another quite distinct therefrom.

The first red numeral is somewhat effaced, indeed all the red has disappeared and only the black outline of the glyph remains. Its position, however, above the column of day signs, seems to indicate its color and use, and we are reasonably safe in stating that the first of the two tonalamatls here recorded began with the day 8 Ahau. Adding to this the first black number, 27, the beginning day of the next subdivision will be found to be 9 Manik, neither the coefficient nor day sign of which appears in the text. Assuming that the calculation is correct, however, and adding the next black number, 25 (also out of place), to this day, 9 Manik, the beginning day of the next part will be 8 Eb. But since 25 is the last black number, 8 Eb will be the beginning day of the next main division and should appear as the second sign in the first column of day signs. Comparison of this form with figure 17, _r_, will show that Eb is recorded in this place. {260} In this manner all of the beginning days could be worked out as below:

---------------------+----------+---------+----------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 27 days, | | | | | beginning with day |8 Ahau |8 Eb |8 Kan |8 Cib |8 Lamat | | | | | 2d part, 25 days, | | | | | beginning with day |9 Manik |9 Cauac |9 Chuen |9 Akbal |9 Men | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+----------+----------+--------

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. As previously explained, the second column of day signs belongs to another tonalamatl, which, however, utilized the same red 8 as the first and the same black 27 and 25 as the first. The outline of this tonalamatl, which began with the day 8 Oc, follows:

---------------------+----------+---------+---------+---------+---------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+---------+---------+---------- 1st part, 27 days, | | | | | beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab | | | | | 2d part, 25 days, | | | | | beginning with day |9 Caban |9 Muluc |9 Imix |9 Ben |9 Chicchan | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+---------+---------+----------

The application of rule 4 (p. 253) to this tonalamatl gives: 5 × 52 = 260, the exact number of days in a tonalamatl. It is interesting to note that the above tonalamatl, beginning with the day 8 Oc, commenced just 130 days later than the first tonalamatl, which began with the day 8 Ahau. In other words, the first of the two tonalamatls in Dresden 12a was just half completed when the second one commenced, and the second half of the first tonalamatl began with the same day as the first half of the second tonalamatl, and vice versa.

The tonalamatl in plate 28, upper division, is from Dresden 15a, and is interesting because it illustrates how certain missing parts may be filled in. The first red number is missing and we can only say that this tonalamatl began with some day Ahau. However, adding the first black number, 34, to this day ? Ahau, the day reached will be 13 Ix, of which only 13 is recorded. Since 13 Ix was reached by counting 34 forward from the day with which the count must have started, by counting back 34 from 13 Ix the starting point will be found to be 5 Ahau, and we may supply a red bar above the column of the day signs. Adding the next black number, 18, to this day 13 Ix, the beginning day of the next _division_ will be found to be 5 Eb, which appears as the second day sign in the column of day signs.

[Illustration: PAGE 15 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN ALL THREE DIVISIONS]

{261}

The last red number is 5, thus establishing as correct our restoration of a red 5 above the column of day signs. From here this tonalamatl presents no unusual features and it may be worked as follows:

---------------------+----------+---------+----------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 34 days, | | | | | beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat | | | | | 2d part, 18 days, | | | | | beginning with day |13 Ix |13 Cimi |13 Eznab |13 Oc |13 Ik | | | | | Total number of days |52 |52 |52 |52 |52 ---------------------+----------+---------+----------+----------+--------

Applying rule 4 (p. 253), we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The next tonalamatl (see lower part of pl. 28, that is, Dresden 15c) has 10 day signs arranged in two parallel columns of 5 each. This, at its face value, would seem to be divided into 10 divisions, and the calculations confirm the results of the preliminary inspection.

The tonalamatl opens with the day 3 Lamat. Adding to this the first black number, 12, the day reached will be 2 Ahau, of which only the 2 is recorded here. Adding to 2 Ahau the next black number, 14, the day reached will be 3 Ix. And since 14 is the last black number, this new day will be the beginning of the next division in the tonalamatl and will appear as the upper day sign in the second column.[247] Commencing with 3 Ix and adding to it the first black number 12, the day reached will be 2 Cimi, and adding to this the next black number, 14, the day reached will be 3 Ahau, which appears as the second glyph in the first column. This same operation if carried throughout will give the following outline of this tonalamatl:

---------------------+----------+---------+----------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 12 days, | | | | | beginning with day |3 Lamat |3 Ix |3 Ahau |3 Cimi |3 Eb | | | | | 2d part, 14 days, | | | | | beginning with day |2 Ahau |2 Cimi |2 Eb |2 Eznab |2 Kan | | | | | Total number of days |26 |26 |26 |26 |26 ---------------------+----------+---------+----------+----------+--------

{262} (Concluded)

---------------------+----------+---------+----------+----------+-------- |6th |7th |8th |9th |10th |Division |Division |Division |Division |Division ---------------------+----------+---------+----------+----------+-------- 1st part, 12 days, | | | | | beginning with day |3 Eznab |3 Kan |3 Oc |3 Cib |3 Ik | | | | | 2d part, 14 days, | | | | | beginning with day |2 Oc |2 Cib |2 Ik |2 Lamat |2 Ix | | | | | Total number of days |26 |26 |26 |26 |26 ---------------------+----------+---------+----------+----------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 10 × 26 = 260, the exact number of days in a tonalamatl.

The tonalamatl which appears in the middle part on plate 28--that is, Dresden 15b--extends over on page 16b, where there is a black 13 and a red 1. The student will have little difficulty in reaching the result which follows: The last day sign is the same as the first, and consequently this tonalamatl is divided into four, instead of five, divisions:

---------------------+----------+---------+----------+---------- |1st |2d |3d |4th |Division |Division |Division |Division ---------------------+----------+---------+----------+---------- 1st part, 13 days, | | | | beginning with day |1 Ik |1 Manik |1 Eb |1 Caban | | | | 2d part, 31 days, | | | | beginning with day |1 Men |1 Ahau |1 Chicchan|1 Oc | | | | 3d part, 8 days, | | | | beginning with day |6 Cimi |6 Chuen |6 Cib |6 Imix | | | | 4th part, 13 days, | | | | beginning with day |1 Ix |1 Cauac |1 Kan |1 Muluc | | | | Total number of days |65 |65 |65 |65 ---------------------+----------+---------+----------+----------

Applying rule 4 (p. 253) to this tonalamatl, we have: 4 × 65 = 260, the exact number of days in a tonalamatl. The tonalamatls heretofore presented have all been taken from the Dresden Codex. The following examples, however, have been selected from tonalamatls in the Codex Tro-Cortesianus. The student will note that the workmanship in the latter manuscript is far inferior to that in the Dresden Codex. This is particularly true with respect to the execution of the glyphs.

The first tonalamatl figured from the Codex Tro-Cortesianus (see pl. 29) extends across the middle part of two pages (Tro-Cor. 10b, 11b). The four day signs at the left indicate that it is divided into four divisions, of which the first begins with the day 13 Ik.[248] Adding to this the first black number 9, the day 9 Chuen is reached, and proceeding in this manner the tonalamatl may be outlined as follows:

[Illustration: MIDDLE DIVISIONS OF PAGES 10 AND 11 OF THE CODEX TRO-CORTESIANO, SHOWING ONE TONALAMATL EXTENDING ACROSS THE TWO PAGES]

[Illustration: PAGE 102 OF THE CODEX TRO-CORTESIANO, SHOWING TONALAMATLS IN THE LOWER THREE SECTIONS]

{263}

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:

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, {264} the exact number of days in a tonalamatl. The next tonalamatl on this page (see third division in pl. 29, that is, Tro-Cor., 102c) is interesting chiefly because of the fact that the pictures which went with the third and fourth parts of the five divisions are omitted for want of space. The outline of this tonalamatl follows:

---------------------+----------+---------+---------+---------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ---------------------+----------+---------+---------+---------+-------- 1st part, 17 days, | | | | | beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat | | | | | 2d part, 13 days, | | | | | beginning with day |8 Caban |8 Muluc |8 Imix |8 Ben |8 Chicchan | | | | | 3d part, 10 days, | | | | | beginning with day |8 Oc |8 Ik |8 Ix |8 Cimi |8 Eznab | | | | | 4th part, 12 days, | | | | | beginning with day |5 Ahau |5 Eb |5 Kan |5 Cib |5 Lamat | | | | | Total number of | | | | | days |52 |52 |52 |52 |52 ---------------------+----------+---------+---------+---------+--------

Applying rule 4 (p. 253) to this tonalamatl, we have: 5 × 52 = 260, the exact number of days in a tonalamatl. The last tonalamatl in plate 29, Tro-Cor., 102d, commences with the same day, 4 Ahau, as the preceding tonalamatl and, like it, has five divisions, each of which begins with the same day as the corresponding division in the tonalamatl just given, 4 Ahau, 4 Eb, 4 Kan, 4 Cib, and 4 Lamat. Tro-Cor. 102d differs from Tro-Cor. 102c in the number and length of the parts into which its divisions are divided.

Adding the first black number, 29, to the beginning day, 4 Ahau, the day reached will be 7 Muluc, of which only the 7 appears in the text. Adding to this the next black number, 24, the day reached will be 5 Ben. An examination of the text shows, however, that the day actually recorded is 4 Eb, the last red number with the second day sign. This latter day is just the day before 5 Ben, and since the sum of the black numbers in this case does not equal any factor of 260 (29 + 24 = 53), and since changing the last black number from 24 to 23 would make the sum of the black numbers equal to a factor of 260 (29 + 23 = 52), and would bring the count to 4 Eb, the day actually recorded, we are justified in assuming that there is an error in our original text, and that 23 should have been written here instead of 24. The outline of this tonalamatl, corrected as suggested, follows: {265}

----------------------+----------+---------+---------+----------+-------- |1st |2d |3d |4th |5th |Division |Division |Division |Division |Division ----------------------+----------+---------+---------+----------+-------- 1st part, 29 days, | | | | | beginning with day |4 Ahau |4 Eb |4 Kan |4 Cib |4 Lamat | | | | | 2d part, 23[251] days,| | | | | beginning with day |7 Muluc |7 Imix |7 Ben |7 Chicchan|7 Caban | | | | | Total number of days |52 |52 |52 |52 |52 ----------------------+----------+---------+---------+----------+--------

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

The foregoing tonalamatls have been taken from the pages of the Dresden Codex or those of the Codex Tro-Cortesiano. Unfortunately, in the Codex Peresianus no complete tonalamatls remain, though one or two fragmentary ones have been noted.

No matter how they are divided or with what days they begin, all tonalamatls seem to be composed of the same essentials:

1. The calendric parts, made up, as we have seen on page 251, of (_a_) the column of day signs; (_b_) the red numbers; (_c_) the black numbers.

2. The pictures of anthropomorphic figures and animals engaged in a variety of pursuits, and

3. The groups of four or six glyphs above each of the pictures.

The relation of these parts to the tonalamatl as a whole is practically determined. The first is the calendric background, the chronological framework, as it were, of the period. The second and third parts amplify this and give the special meaning and significance to the subdivisions. The pictures represent in all probability the deities who presided over the several subdivisions of the tonalamatls in which they appear, and the glyphs above them probably set forth their names, as well as the ceremonies connected with, or the prognostications for, the corresponding periods.

It will be seen, therefore, that in its larger sense the meaning of the tonalamatl is no longer a sealed book, and while there remains a vast amount of detail yet to be worked out the foundation has been laid upon which future investigators may build with confidence.

In closing this discussion of the tonalamatl it may not be out of place to mention here those whose names stand as pioneers in this particular field of glyphic research. To the investigations of Prof. Ernst Förstemann we owe the elucidation of the calendric part of the tonalamatl, and to Dr. Paul Schellhas the identification of the gods and their corresponding name glyphs in parts (2) and (3), above. As pointed out at the beginning of this chapter, the most promising {266} line of research in the codices is the groups of glyphs above the pictures, and from their decipherment will probably come the determination of the meaning of this interesting and unusual period.

TEXTS RECORDING INITIAL SERIES

Initial Series in the codices are unusual and indeed have been found, up to the present time, in only one of the three known Maya manuscripts, namely, the Dresden Codex. As represented in this manuscript, they differ considerably from the Initial Series heretofore described, all of which have been drawn from the inscriptions. This difference, however, is confined to unessentials, and the system of counting and measuring time in the Initial Series from the inscriptions is identical with that in the Initial Series from the codices.

The most conspicuous difference between the two is that in the codices the Initial Series are expressed by the second method, given on page 129, that is, numeration by position, while in the inscriptions, as we have seen, the period glyphs are used, that is, the first method, on page 105. Although this causes the two kinds of texts to appear very dissimilar, the difference is only superficial.

Another difference the student will note is the absence from the codices of the so-called Initial-series "introducing glyph." In a few cases there seems to be a sign occupying the position of the introducing glyph, but its identification as the Initial-series "introducing glyph" is by no means sure, and, moreover, as stated above, it does not occur in all cases in which there are Initial Series.

Another difference is the entire absence from the codices of Supplementary Series; this count seems to be confined exclusively to the monuments. Aside from these points the Initial Series from the two sources differ but little. All proceed from identically the same starting point, the date 4 Ahau 8 Cumhu, and all have their terminal dates or related Secondary-series dates recorded immediately after them.

The first example of an Initial Series from the codices will be found in plate 31 (Dresden 24), in the lower left-hand corner, in the second column to the right. The Initial-series number here recorded is 9.9.16.0.0, of which the zero in the 2d place (uinals) and the zero in the 1st place (kins) are expressed by red numbers. This use of red numbers in the last two places is due to the fact that the zero sign in the codices is _always red_.

[Illustration: PAGE 24 OF THE DRESDEN CODEX, SHOWING INITIAL SERIES]

{267} The student will note the absence of all period glyphs from this Initial Series and will observe that the multiplicands of the cycle, katun, tun, uinal, and kin are fixed by the positions of each of the corresponding multipliers. By referring to Table XIV the values of the several positions in the second method of writing the numbers will be found, and using these with their corresponding coefficients in each case the Initial-series number here recorded may be reduced to units of the 1st order, as follows:

9 × 144,000 = 1,296,000 9 × 7,200 = 64,800 16 × 360 = 5,760 0 × 20 = 0 0 × 1 = 0 ---------- 1,366,560

Deducting from this number all the Calendar Rounds possible, 72 (see Table XVI), it may be reduced to zero, since 72 Calendar Rounds contain exactly 1,366,560 units of the first order. See the preliminary rule on page 143.

Applying rules 1, 2, and 3 (pp. 139, 140, and 141) to the remainder, that is, 0, the terminal date of the Initial Series will be found to be 4 Ahau 8 Cumhu, exactly the same as the starting point of Maya chronology. This must be true, since counting forward 0 from the date 4 Ahau 8 Cumhu, the date 4 Ahau 8 Cumhu will be reached. Instead of recording this date immediately below the last period of its Initial-series number, that is, the 0 kins, it was written below the number just to the left. The terminal date of the Initial Series we are discussing, therefore, is 4 Ahau 8 Cumhu, and it is recorded just to the left of its usual position in the lower left-hand corner of plate 31. The coefficient of the day sign, 4, is effaced but the remaining parts of the date are perfectly clear. Compare the day sign Ahau with the corresponding form in figure 17, _c', d'_, and the month sign Cumhu with the corresponding form in figure 20, _z-b'_. The Initial Series here recorded is therefore 9.9.16.0.0 4 Ahau 8 Cumhu. Just to the right of this Initial Series is another, the number part of which the student will readily read as follows: 9.9.9.16.0. Treating this in the usual way, it may be reduced thus:

9 × 144,000 = 1,296,000 9 × 7,200 = 64,800 9 × 360 = 3,240 16 × 20 = 320 0 × 1 = 0 ---------- 1,364,360

Deducting from this number all the Calendar Rounds possible, 71 (see Table XVI), it may be reduced to 16,780. Applying to this number rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), its terminal date will be found to be 1 Ahau 18 Kayab; this date is recorded just to the left below the kin place of the _preceding_ Initial {268} Series. Compare the day sign and month sign of this date with figures 17, _c', d'_, and 20, _x, y_, respectively. This second Initial Series in plate 31 therefore reads 9.9.9.16.0 1 Ahau 18 Kayab. In connection with the first of these two Initial Series, 9.9.16.0.0 4 Ahau 8 Cumhu, there is recorded a Secondary Series. This consists of 6 tuns, 2 uinals, and 0 kins (6.2.0) and is recorded just to the left of the first Initial Series from which it is counted, that is, in the left-hand column.

It was explained on pages 136-137 that the almost universal direction of counting was forward, but that when the count was backward in the codices, this fact was indicated by a special sign or symbol, which gave to the number it modified the significance of "backward" or "minus." This sign is shown in figure 64, and, as explained on page 137, it usually is attached only to the lowest period. Returning once more to our text, in plate 31 we see this "backward" sign--a red circle surmounted by a knot--surrounding the 0 kins of this Secondary-series number 6.2.0, and we are to conclude, therefore, that this number is to be counted backward from some date.

Counting it backward from the date which stands nearest it in our text, 4 Ahau 8 Cumhu, the date reached will be 1 Ahau 18 Kayab. But since the date 4 Ahau 8 Cumhu is stated in the text to have corresponded with the Initial-series value 9.9.16.0.0, by deducting 6.2.0 from this number we may work out the Initial-series value for this date as follows:

9.9.16. 0.0 4 Ahau 8 Cumhu 6. 2.0 Backward 9.9. 9.16.0 1 Ahau 18 Kayab

The accuracy of this last calculation is established by the fact that the Initial-series value 9.9.9.16.0 is recorded as the second Initial Series on the page above described, and corresponds to the date 1 Ahau 18 Kayab as here.

It is difficult to say why the terminal dates of these two Initial Series and this Secondary Series should have been recorded to the _left_ of the numbers leading to them, and not just _below_ the numbers in each case. The only explanation the writer can offer is that the ancient scribe wished to have the starting point of his Secondary-series number, 4 Ahau 8 Cumhu, recorded as near that number as possible, that is, just below it, and consequently the Initial Series leading to this date had to stand to the right. This caused a displacement of the corresponding terminal date of his Secondary Series, 1 Ahau 18 Kayab, which was written under the Initial Series 9.9.16.0.0; and since the Initial-series value of 1 Ahau 18 Kayab also appears to the right of 9.9.16.0.0 as 9.9.9.16.0, this causes a displacement in its terminal date likewise. {269}

Two other Initial Series will suffice to exemplify this kind of count in the codices. In plate 32 is figured page 62 from the Dresden Codex. In the two right-hand columns appear two black numbers. The first of these reads quite clearly 8.16.15.16.1, which the student is perfectly justified in assuming is an Initial-series number consisting of 8 cycles, 16 katuns, 15 tuns, 16 uinals, and 1 kin. Moreover, above the 8 cycles is a glyph which bears considerable resemblance to the Initial-series introducing glyph (see fig. 24, _f_). Note in particular the trinal superfix. At all events, whether it is an Initial Series or not, the first step in deciphering it will be to reduce this number to units of the first order:

8 × 144,000 = 1,152,000 16 × 7,200 = 115,200 15 × 360 = 5,400 16 × 20 = 320 1 × 1 = 1 ---------- 1,272,921

Deducting from this number all the Calendar Rounds possible, 67 (see Table XVI), it may be reduced to 1,261. Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to this remainder, the terminal date reached will be 4 Imix 9 Mol. This is not the terminal date recorded, however, nor is it the terminal date standing below the next Initial-series number to the right, 8.16.14.15.4. It would seem then that there must be some mistake or unusual feature about this Initial Series.

Immediately below the date which stands under the Initial-series number we are considering, 8.16.15.16.1, is another number consisting of 1 tun, 4 uinals, and 16 kins (1.4.16). It is not improbable that this is a Secondary-series number connected in some way with our Initial Series. The red circle surmounted by a knot which surrounds the 16 kins of this Secondary-series number (1.4.16) indicates that the whole number is to be counted _backward_ from some date. Ordinarily, the first Secondary Series in a text is to be counted from the terminal date of the Initial Series, which we have found by calculation (if not by record) to be 4 Imix 9 Mol in this case. Assuming that this is the case here, we might count 1.4.16 _backward_ from the date 4 Imix 9 Mol.

Performing all the operations indicated in such cases, the terminal date reached will be found to be 3 Chicchan 18 Zip; this is very close to the date which is actually recorded just above the Secondary-series number and just below the Initial-series number. The date here recorded is 3 Chicchan 13 Zip, and it is not improbable that the {270} ancient scribe intended to write instead 3 Chicchan 18 Zip, the date indicated by the calculations. We probably have here:

8.16.15.16. 1 (4 Imix 9 Mol) 1. 4.16 Backward 8.16.14.11. 5 3 Chicchan 18[252] Zip

In these calculations the terminal date of the Initial Series, 4 Imix 9 Mol, is suppressed, and the only date given is 3 Chicchan 18 Zip, the terminal date of the Secondary Series.

Another Initial Series of this same kind, one in which the terminal date is not recorded, is shown just to the right of the preceding in plate 32. The Initial-series number 8.16.14.15.4 there recorded reduces to units of the first order as follows:

8 × 144,000 = 1,152,000 16 × 7,200 = 115,200 14 × 360 = 5,040 15 × 20 = 300 4 × 1 = 4 ---------- 1,272,544

Deducting from this number all the Calendar Rounds possible, 67 (see Table XVI), it will be reduced to 884, and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to this remainder, the terminal date reached will be 4 Kan 17 Yaxkin. This date is not recorded. There follows below, however, a Secondary-series number consisting of 6 uinals and 1 kin (6.1). The red circle around the lower term of this (the 1 kin) indicates that the whole number, 6.1, is to be counted _backward_ from some date, probably, as in the preceding case, from the terminal date of the Initial Series above it. Assuming that this is the case, and counting 6.1 backward from 8.16.14.15.4 4 Kan 17 Yaxkin, the terminal date reached will be 13 Akbal 16 Pop, again very close to the date recorded immediately above, 13 Akbal 15 Pop. Indeed, the date as recorded, 13 Akbal 15 Pop, represents an impossible condition from the Maya point of view, since the day name Akbal could occupy only the first, sixth, eleventh, and sixteenth positions of a month. See Table VII. Consequently, through lack of space or carelessness the ancient scribe who painted this book failed to add one dot to the three bars of the month sign's coefficient, thus making it 16 instead of the 15 actually recorded. We are obliged to make some correction in this coefficient, since, as explained above, it is obviously incorrect as it stands. Since the addition of a single dot brings the whole date into harmony with the date determined by calculation, we are probably justified {271} in making the correction here suggested. We have recorded here therefore:

8.16.14.15.4 (4 Kan 17 Yaxkin) 6.1 Backward 8.16.14. 9.3 13 Akbal 16[253] Pop

In these calculations the terminal date of the Initial Series, 4 Kan 17 Yaxkin, is suppressed and the only date given is 13 Akbal 16 Pop, the terminal date of the Secondary Series.

The above will suffice to show the use of Initial Series in the codices, but before leaving this subject it seems best to discuss briefly the dates recorded by these Initial Series in relation to the Initial Series on the monuments. According to Professor Förstemann[254] there are 27 of these altogether, distributed as follows:

Page 24: 9. 9.16. 0. 0[255]| Page 58: 9.12.11.11. 0 Page 24: 9. 9. 9.16. 0 | Page 62: 8.16.15.16. 1 Page 31: 8.16.14.15. 4 | Page 62: 8.16.14.15. 4 Page 31: 8.16. 3.13. 0 | Page 63: 8.11. 8. 7. 0 Page 31: 10.13.13. 3. 2[256]| Page 63: 8.16. 3.13. 0 Page 43: 9.19. 8.15. 0 | Page 63: 10.13. 3.16. 4[257] Page 45: 8.17.11. 3. 0 | Page 63: 10.13.13. 3. 2 Page 51: 8.16. 4. 8. 0[258]| Page 70: 9.13.12.10. 0 Page 51: 10.19. 6. 1. 8[259]| Page 70: 9.19.11.13. 0 Page 52: 9.16. 4.11.18[260]| Page 70: 10.17.13.12.12 Page 52: 9.19. 5. 7. 8[261]| Page 70: 10.11. 3.18.14 Page 52: 9.16. 4.10. 8 | Page 70: 8. 6.16.12. 0 Page 52: 9.16. 4.11. 3 | Page 70: 8.16.19.10. 0 Page 58: 9.18. 2. 2. 0 |

There is a wide range of time covered by these Initial Series; indeed, from the earliest 8.6.16.12.0 (on p. 70) to the latest, 10.19.6.1.8 (on p. 51) there elapsed more than a thousand years. Where the difference between the earliest and the latest dates is so great, it is a matter of vital importance to determine the contemporaneous date of the manuscript. If the closing date 10.19.6.1.8 represents the time at which the manuscript was made, then the preceding dates reach back {272} for more than a thousand years. On the other hand, if 8.6.16.12.0 records the present time of the manuscript, then all the following dates are prophetic. It is a difficult question to answer, and the best authorities have seemed disposed to take a middle course, assigning as the contemporaneous date of the codex a date about the middle of Cycle 9. Says Professor Förstemann (_Bulletin 28_, p. 402) on the subject:

In my opinion my demonstration also definitely proves that these large numbers [the Initial Series] do not proceed from the future to the past, but from the past, through the present, to the future. Unless I am quite mistaken, the highest numbers among them seem actually to reach into the future, and thus to have a prophetic meaning. Here the question arises, At what point in this series of numbers does the present lie? or, Has the writer in different portions of his work adopted different points of time as the present? If I may venture to express my conjecture, it seems to me that the first large number in the whole manuscript, the 1,366,560 in the second column of page 24 [9.9.16.0.0 4 Ahau 8 Cumhu, the first Initial Series figured in plate 31], has the greatest claim to be interpreted as the present point of time.

In a later article (_Bulletin 28_, p. 437) Professor Förstemann says: "But I think it is more probable that the date farthest to the right (1 Ahau, 18 Zip ...) denotes the present, the other two [namely, 9.9.16.0.0 4 Ahau 8 Cumhu and 9.9.9.16.0 1 Ahau 18 Kayab] alluding to remarkable days in the future." He assigns to this date 1 Ahau 18 Zip the position of 9.7.16.12.0 in the Long Count.

The writer believes this theory to be untenable because it involves a correction in the original text. The date which Professor Förstemann calls 1 Ahau 18 Zip actually reads 1 Ahau 18 Uo, as he himself admits. The month sign he corrects to Zip in spite of the fact that it is very clearly Uo. Compare this form with figure 20, _b, c_. The date 1 Ahau 18 Uo occurs at 9.8.16.16.0, but the writer sees no reason for believing that this date or the reading suggested by Professor Förstemann indicates the contemporaneous time of this manuscript.

Mr. Bowditch assigns the manuscript to approximately the same period, selecting the second Initial Series in plate 31, that is, 9.9.9.16.0 1 Ahau 18 Kayab: "My opinion is that the date 9.9.9.16.0 1 Ahau 18 Kayab is the present time with reference to the time of writing the codex and is the date from which the whole calculation starts."[262] The reasons which have led Mr. Bowditch to this conclusion are very convincing and will make for the general acceptance of his hypothesis.

Although the writer has no better suggestion to offer at the present time, he is inclined to believe that both of these dates are far too early for this manuscript and that it is to be ascribed to a very much later period, perhaps to the centuries following immediately the colonization of Yucatan. There can be no doubt that very early dates appear in the Dresden Codex, but rather than accept one so early as 9.9.9.16.0 or 9.9.16.0.0 as the contemporaneous date of the manuscript the writer would prefer to believe, on historical grounds, that the manuscript now known as the Dresden Codex is a copy of an earlier manuscript and that the present copy dates from the later Maya period in Yucatan, though sometime before either Nahuatl or Castilian acculturation had begun.

[Illustration: PAGE 62 OF THE DRESDEN CODEX, SHOWING THE SERPENT NUMBERS]

{273}

TEXTS RECORDING SERPENT NUMBERS

The Dresden Codex contains another class of numbers which, so far as known, occur nowhere else. These have been called the Serpent numbers because their various orders of units are depicted between the coils of serpents. Two of these serpents appear in plate 32. The coils of each serpent inclose two different numbers, one in red and the other in black. Every one of the Serpent numbers has six terms, and they represent by far the highest numbers to be found in the codices. The black number in the first, or left-hand serpent in plate 32, reads as follows: 4.6.7.12.4.10, which, reduced to units of the first order, reads:

4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 7 × 7,200 = 50,400 12 × 360 = 4,320 4 × 20 = 80 10 × 1 = 10 ---------- 12,438,810

The next question which arises is, What is the starting point from which this number is counted? Just below it the student will note the date 3 Ix 7 Tzec, which from its position would seem almost surely to be either the starting point or the terminal date, more probably the latter. Assuming that this date is the terminal date, the starting point may be calculated by counting 12,438,810 _backward_ from 3 Ix 7 Tzec. Performing this operation according to the rules laid down in such cases, the starting point reached will be 9 Kan 12 Xul, but this date is not found in the text.

The red number in the first serpent is 4.6.11.10.7.2, which reduces to--

4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 11 × 7,200 = 79,200 10 × 360 = 3,600 7 × 20 = 140 2 × 1 = 2 ---------- 12,466,942

{274} Assuming that the date below this number, 3 Cimi 14 Kayab, was its terminal date, the starting point can be reached by counting backward. This will be found to be 9 Kan 12 Kayab, a date actually found on this page (see pl. 32), just above the animal figure emerging from the second serpent's mouth.

The black number in the second serpent reads 4.6.9.15.12.19, which reduces as follows:

4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 9 × 7,200 = 64,800 15 × 360 = 5,400 12 × 20 = 240 19 × 1 = 19 ---------- 12,454,459

Assuming that the date below this number, 13 Akbal 1 Kankin, was the terminal date, its starting point can be shown by calculation to be just the same as the starting point for the previous number, that is, the date 9 Kan 12 Kayab, and as mentioned above, this date appears above the animal figure emerging from the mouth of this serpent.

The last Serpent number in plate 32, the red number in the second serpent, reads, 4.6.1.9.15.0 and reduces as follows:

4 × 2,880,000 = 11,520,000 6 × 144,000 = 864,000 1 × 7,200 = 7,200 9 × 360 = 3,240 15 × 20 = 300 0 × 1 = 0 ---------- 12,394,740

Assuming that the date below this number, 3 Kan 17 Uo,[263] was its terminal date, its starting point can be shown by calculation to be just the same as the starting point of the two preceding numbers, namely, the date 9 Kan 12 Kayab, which appears above this last serpent.

[Illustration: FIG. 85. Example of first method of numeration in the codices (part of page 69 of the Dresden Codex).]

It will be seen from the foregoing that three of the four Serpent dates above described are counted from the date 9 Kan 12 Kayab, a date actually recorded in the text just above them. The all-important question of course is, What position did the date 9 Kan 12 Kayab occupy in the Long Count? The page (62) of the Dresden Codex we {275} are discussing sheds no light on this question. There are, however, two other pages in this Codex (61 and 69) on which Serpent numbers appear presenting this date, 9 Kan 12 Kayab, under conditions which may shed light on the position it held in the Long Count. On page 69 there are recorded 15 katuns, 9 tuns, 4 uinals, and 4 kins (see fig. 85); these are immediately followed by the date 9 Kan 12 Kayab. It is important to note in this connection that, unlike almost every other number in this codex, this number is expressed by the first method, the one in which the period glyphs are used. As the date 4 Ahau 8 Cumhu appears just above in the text, the first supposition is that 15.9.4.4 is a Secondary-series number which, if counted forward from 4 Ahau 8 Cumhu, the starting point of Maya chronology, will reach 9 Kan 12 Kayab, the date recorded immediately after it. Proceeding on this assumption and performing the operations indicated, the terminal date reached will be 9 Kan 7 Cumhu, not 9 Kan 12 Kayab, as recorded. The most plausible explanation for this number and date the writer can offer is that the whole constitutes a Period-ending date. On the west side of Stela C at Quirigua, as explained on page 226, is a Period-ending date almost exactly like this (see pl. 21, _H_). On this monument 17.5.0.0 6 Ahau 13 Kayab is recorded, and it was proved by calculation that 9.17.5.0.0 would lead to this date if counted forward from the starting point of Maya chronology. In effect, then, this 17.5.0.0 6 Ahau 13 Kayab was a Period-ending date, declaring that Tun 5 of Katun 17 (of Cycle 9, unexpressed) ended on the date 6 Ahau 13 Kayab.

Interpreting in the same way the glyphs in figure 85, we have the record that Kin 4 of Uinal 4 of Tun 9 of Katun 15 (of Cycle 9, unexpressed) fell (or ended) on the date 9 Kan 12 Kayab. Changing this Period-ending date into its corresponding Initial Series and solving for its terminal date, the latter date will be found to be 13 Kan 12 Ceh, instead of 9 Kan 12 Kayab. At first this would appear to be even farther from the mark than our preceding attempt, but if the reader will admit a slight correction, the above number can be made to reach the date recorded. The date 13 Kan 12 Ceh is just 5 uinals earlier than 9 Kan 12 Kayab, and if we add one bar to the four dots of the uinal coefficient, this passage can be explained in the above manner, and yet agree in all particulars. This is true since 9.15.9.9.4 reaches the date 9 Kan 12 Kayab. On the above grounds the writer is inclined to believe that the last three Serpent numbers on plate 32, which were shown to have proceeded from a date 9 Kan 12 Kayab, were counted from the date 9.15.9.9.4 9 Kan 12 Kayab. {276}

TEXTS RECORDING ASCENDING SERIES

There remains one other class of numbers which should be described before closing this chapter on the codices. The writer refers to the series of related numbers which cover so many pages of the Dresden Codex. These commence at the bottom of the page and increase toward the top, every other number in the series being a multiple of the first, or beginning number. One example of this class will suffice to illustrate all the others.

In the lower right-hand corner of plate 31 a series of this kind commences with the day 9 Ahau.[264] Of this series the number 8.2.0 just above the 9 Ahau is the first term, and the day 9 Ahau the first terminal date. As usual in Maya texts, the starting point is not expressed; by calculation, however, it can be shown to be 1 Ahau[265] in this particular case.

Counting forward then 8.2.0 from 1 Ahau, the unexpressed starting point, the first terminal date, 9 Ahau, will be reached. See the lower right-hand corner in the following outline, in which the Maya numbers have all been reduced to units of the first order:

151,840[266] 113,880[266] 75,920[266] 37,960[266] 1 Ahau 1 Ahau 1 Ahau 1 Ahau 185,120 68,900 33,280 9,100 1 Ahau 1 Ahau 1 Ahau 1 Ahau 35,040 32,120 29,200 26,280 6 Ahau 11 Ahau 3 Ahau 8 Ahau 23,360 20,440 17,520 14,600 13 Ahau 5 Ahau 10 Ahau 2 Ahau 11,680[267] 8,760 5,840 2,920 7 Ahau 12 Ahau 4 Ahau 9 Ahau (Unexpressed starting point, 1 Ahau.)

In the above outline each number represents the total distance of the day just below it from the unexpressed starting point, 1 Ahau, _not_ the distance from the date immediately preceding it in the series. For example, the second number, 5,840 (16.4.0), is not to be counted forward from 9 Ahau in order to reach its terminal date, 4 Ahau, but from the unexpressed starting point of the whole series, the day 1 Ahau. Similarly the third number, 8,760 (1.4.6.0), is not to be counted forward from 4 Ahau in order to reach 12 Ahau, but from 1 Ahau instead, and so on throughout the series. {277}

Beginning with the number 2,920 and the starting point 1 Ahau, the first twelve terms, that is, the numbers in the three lowest rows, are the first 12 multiples of 2,920.

2,920 = 1 × 2,920 20,440 = 7 × 2,920 5,840 = 2 × 2,920 23,360 = 8 × 2,920 8,760 = 3 × 2,920 26,280 = 9 × 2,920 11,680 = 4 × 2,920 29,200 = 10 × 2,920 14,600 = 5 × 2,920 32,120 = 11 × 2,920 17,520 = 6 × 2,920 35,040 = 12 × 2,920

The days recorded under each of these numbers, as mentioned above, are the terminal dates of these distances from the starting point, 1 Ahau. Passing over the fourth row from the bottom, which, as will appear presently, is probably an interpolation of some kind, the thirteenth number--that is, the right-hand one in the top row--is 37,960. But 37,960 is 13 × 2,920, a continuation of our series the twelfth term of which appeared in the left-hand number of the third row. Under the thirteenth number is set down the day 1 Ahau; in other words, not until the thirteenth multiple of 2,920 is reached is the terminal day the same as the starting point.

With this thirteenth term 2,920 ceases to be the unit of increase, and the thirteenth term itself (37,960) is used as a difference to reach the remaining three terms on this top line, all of which are multiples of 37,960.

37,960 = 1 × 37,960 or 13 × 2,920 75,920 = 2 × 37,960 or 26 × 2,920 113,880 = 3 × 37,960 or 39 × 2,920 151,840 = 4 × 37,960 or 52 × 2,920

Counting forward each one of these from the starting point of this entire series, 1 Ahau, each will be found to reach as its terminal day 1 Ahau, as recorded under each. The fourth line from the bottom is more difficult to understand, and the explanation offered by Professor Förstemann, that the first and third terms and the second and fourth are to be combined by addition or subtraction, leaves much to be desired. Omitting this row, however, the remaining numbers, those which are multiples of 2,920, admit of an easy explanation.

In the first place, the opening term 2,920, which serves as the unit of increase for the entire series up to and including the 13th term, is the so-called Venus-Solar period, containing 8 Solar years of 365 days each and 5 Venus years of 584 days each. This important period is the subject of extended treatment elsewhere in the Dresden Codex (pp. 46-50), in which it is repeated 39 times in all, divided into three equal divisions of 13 periods each. The 13th term of our series 37,960 is, as we have seen, 13 × 2,920, the exact number of {278} days treated of in the upper divisions of pages 46-50 of the Dresden Codex. The 14th term (75,920) is the exact number of days treated of in the first two divisions, and finally, the 15th, or next to the last term (113,880), is the exact number of days treated of in all three divisions of these pages.

This 13th term (37,960) is the first in which the tonalamatl of 260 days comes into harmony with the Venus and Solar years, and as such must have been of very great importance to the Maya. At the same time it represents two Calendar Rounds, another important chronological count. With the next to the last term (113,880) the Mars year of 780 days is brought into harmony with all the other periods named. This number, as just mentioned, represents the sum of all the 39 Venus-Solar periods on pages 46-50 of the Dresden Codex. This next to the last number seems to possess more remarkable properties than the last number (151,840), in which the Mars year is not contained without a remainder, and the reason for its record does not appear.

The next to the last term contains:

438 Tonalamatls of 260 days each 312 Solar years of 365 days each 195 Venus years of 584 days each 146 Mars years of 780 days each 39 Venus-Solar periods of 2,920 days each 6 Calendar Rounds of 18,980 days each

It will be noted in plate 31 that the concealed starting point of this series is the day 1 Ahau, and that just to the left on the same plate are two dates, 1 Ahau 18 Kayab and 1 Ahau 18 Uo, both of which show this same day, and one of which, 1 Ahau 18 Kayab, is accompanied by its corresponding Initial Series 9.9.9.16.0. It seems not unlikely, therefore, that the day 1 Ahau with which this series commences was 1 Ahau 18 Kayab, which in turn was 9.9.9.16.0 1 Ahau 18 Kayab of the Long Count. This is rendered somewhat probable by the fact that the second division of 13 Venus-Solar periods on pages 46-50 of the Dresden Codex also has the same date, 1 Ahau 18 Kayab, as its terminal date. Hence, it is not improbable (more it would be unwise to say) that the series of numbers which we have been discussing was counted from the date 9.9.9.16.0. 1 Ahau 18 Kayab.

The foregoing examples cover, in a general way, the material presented in the codices; there is, however, much other matter which has not been explained here, as unfitted to the needs of the beginner. To the student who wishes to specialize in this field of the glyphic writing the writer recommends the treatises of Prof. Ernst Förstemann as the most valuable contribution to this subject.

* * * * *

{279}

INDEX

ABBREVIATION IN DATING, use, 222, 252 ADDITION, method, 149 ADULTERY, punishment, 9-10 AGUILAR, S. DE, on Maya records, 36 AHHOLPOP (official), duties, 13 AHKULEL (deputy-chief), powers, 13 AHPUCH (god), nature, 17 ALPHABET, nonexistence, 27 AMUSEMENTS, nature, 10 ARABIC SYSTEM OF NUMBERS, Maya parallel, 87, 96 ARCHITECTURE, development, 5 ARITHMETIC, system, 87-155 ASCENDING SERIES, texts recording 276-278 ASTRONOMICAL COMPUTATIONS-- accuracy, 32 in codices, 31-32, 276-278 AZTEC-- calendar, 58-59 ikomomatic hieroglyphics, 29 rulership succession, 16

BACKWARD SIGN-- glyph, 137 use, 137, 268 BAKHALAL (city), founding, 4 BAR, numerical value, 87-88 BAR AND DOT NUMERALS-- antiquity, 102-103 examples, plates showing, 157, 167, 170, 176, 178, 179 form and nature, 87-95 BATAB (chief), powers, 13 BIBLIOGRAPHY, xv-xvi BOWDITCH, C. P.-- cited, 2, 45, 65, 117, 134, 203 on dating system, 82-83, 214-215, 272 on hieroglyphics, 30, 33, 71 on Supplementary Series, 152 works, vii-viii BRINTON, _Dr._ D. G.-- error by, 82 on hieroglyphics, 3, 23, 27-28, 30, 33 on numerical system, 91

CALENDAR-- harmonization, 44, 215 starting point, 41-43, 60-62, 113-114 subdivisions, 37-86 _See also_ CALENDAR ROUND; CHRONOLOGY; DATING; LONG COUNT. CALENDAR ROUND-- explanation, 51-59 glyph, 59 CALENDAR-ROUND DATING-- examples, 240-245 limitations, 76 CHAKANPUTAN (city), founding and destruction 4 CHICHEN ITZA (city)-- history, 3, 4, 5, 202-203 Temple of the Initial Series, lintel, interpretation, 199 CHILAN BALAM-- books of, 3 chronology based on, 2 CHRONOLOGY-- basis, 58 correlation, 2 duration, 222 starting point, 60-62, 113-114, 124-125, 147-148 _See also_ CALENDAR. CITIES, SOUTHERN-- occupancy of, diagram showing, 15 rise and fall of, 2-5 CIVILIZATION, rise and fall, 1-7 CLOSING SIGN of Supplementary Series, glyph, 152-153, 170 CLOSING SIGNS. _See_ ENDING SIGNS. CLOTHING, character, 7-8 COCOM FAMILY, tyranny, 5-6, 12 CODEX PERESIANUS, tonalamatls named in, 265 CODEX TRO-CORTESIANUS, texts, 262-265 CODICES-- astronomical character, 31-32, 276-278 character in general, 31, 252 colored glyphs used in, 91, 251 dates of, 203 day signs in, 39 errors, 270-271, 274 examples from, interpretation, 251-278 glyphs for twenty (20) used in, 92, 130 historical nature, 32-33, 35-36 Initial-series dating in, 266 examples, 266-273 interpretation, 31-33, 254-278 numeration glyphs used in, 103-104, 129-134 order of reading, 22, 133, 135, 137, 252-253 tonalamatls in, 251-266 zero glyph used in, 94 COEFFICIENTS, NUMERICAL. _See_ NUMERICAL COEFFICIENTS. COGOLLUDO, C. L., on dating system, 34, 84 COLORED GLYPHS, use of, in codices, 91, 251 COMMERCE, customs, 9 COMPUTATION, possibility of errors in, 154-155 CONFEDERATION, formation and disruption, 4-5 {280} COPAN (city)-- Altar Q, error on 246, 248 Altar S, interpretation 231-233 Altar Z, interpretation 242 history 15 Stela A, interpretation 169-170 Stela B, interpretation 167-169 Stela D, interpretation 188-191 Stela J, interpretation 191-192 Stela M, interpretation 175-176 Stela N, error on 248-249 interpretation 114-118, 248-249 Stela P, interpretation 185 Stela 2, interpretation 223 Stela 4, interpretation 224-225 Stela 6, interpretation 170-171 Stela 8, interpretation 229 Stela 9, antiquity 173 interpretation 171-173 Stela 15, interpretation 187-188 CRESSON, H. T., cited 27 CUSTOMS. _See_ MANNERS AND CUSTOMS. CYCLE-- glyphs 68 length 62, 135 number of, in great cycle 107-114 numbering of, in inscriptions 108, 227-233 CYCLE 8, dates 194-198, 228-229 CYCLE 9-- dates 172, 183, 185, 187, 194, 222 prevalence in Maya dating 194 CYCLE 10, dates 199-203, 229-233 CYCLE, GREAT-- length 135, 162 number of cycles in 107-114 CYCLES, GREAT, GREAT, AND HIGHER-- discussion 114-129 glyphs 118 omitted in dating 126

DATES-- abbreviation 222, 252 errors in computing 154-155 errors in originals 245-250, 270-271, 274 interpretation, in Initial Series 157-222, 233-245 in Period Endings 222-245 in Secondary Series 207-222, 233-245 monuments erected to mark 33-35, 249-250 of same name, distinction between 147-151 repetition 147 shown by red glyphs in codices 251 DATES, INITIAL. _See_ INITIAL-SERIES DATING. DATES, INITIAL AND SECONDARY, interpretation 207-222 DATES, INITIAL, SECONDARY, AND PERIOD-ENDING, interpretation 233-245 DATES, PERIOD-ENDING. _See_ PERIOD-ENDING DATES. DATES, PROPHETIC-- examples 229-233 use 271-272 DATES, SECONDARY. _See_ SECONDARY-SERIES DATING. DATES, TERMINAL-- absence 218 finding 138-154 importance 154-155 position 151-154 DATING-- methods 46-47, 63-86 change 4 _See also_ CALENDAR-ROUND DATING; INITIAL-SERIES; PERIOD-ENDING; SECONDARY-SERIES. starting point 60-62, 113-114, 124-125 determination 135-136 DAY-- first of year 52-53 glyphs 38, 39, 72, 76 coefficients 41-43, 47-48 position 127-128 omission 127-128, 208 identification 41-43, 46-48 names 37-41, 112 numbers 111-112 position in solar year 52-58 round of 42-44 DAYS, INTERCALARY, lack of 45 DAYS, UNLUCKY, dates 45-46 DEATH, fear of 11, 17 DEATH GOD-- glyph 17, 257 nature 17 DECIMAL SYSTEM, parallel 129 _See also_ VIGESIMAL SYSTEM. DESTRUCTION OF THE WORLD, description 32 DIVINATION, codices used for 31 DIVORCE, practice 9 DOT, numerical value 87-88 DOT AND BAR NUMBERS. _See_ BAR AND DOT NUMBERS. DRESDEN CODEX-- date 271-273 publication iii texts 254-262, 266-278 plates showing 32, 254, 260, 266, 273 DRUNKENNESS, prevalence 10

EK AHAU (god), nature 17-18 ENDING SIGNS-- in Period-ending dates 102 in "zero" 101-102 ENUMERATION-- systems 87-134 comparison 133 _See also_ NUMERALS. ERRORS IN TEXTS-- examples 245-250, 270-271, 274 plate showing 248

FEATHERED SERPENT (god), nature 16-17 FIBER-PAPER BOOKS. _See_ CODICES. FISH, used in introducing glyph 65-66, 188 FIVE-TUN PERIOD. See HOTUN. FÖRSTEMANN, _Prof._ ERNST-- cited 26, 137 investigations iii, 265, 276 methods of solving numerals 134 on hieroglyphics 30 on prophetic dates 272 FULL-FIGURE GLYPHS-- nature 67-68, 188-191 plate showing 188 _See also_ TIME PERIODS. FUNERAL CUSTOMS, description 11-12 FUTURE LIFE, belief as to 19

{281} GLYPH BLOCK, definition, 156 GLYPHS. _See_ HIEROGLYPHS. GODS, nature, 16-19 GOODMAN, J. T.-- chronologic tables of, 134 cited, 2, 44, 116-117, 123 investigation, iii-iv on introducing glyph, 66 on length of great cycle, 108 on Supplementary Series, 152 GOVERNMENT, nature, 12-16 GREAT CYCLE-- length, 135 number of cycles in, 107-114

HAAB (solar year)-- first day, 52-56 glyph, 47 nature, 44-51 position of days in, 48, 52-58 subdivisions, 45 HABITAT OF THE MAYA, 1-2 map, 1 HAIR, method of dressing, 7 HALACH UINIC (chief), powers, 12-13 HAND, used as ending sign, 101-102 HEAD-VARIANT NUMERALS-- antiquity, 73, 102-103 characteristics, 97-103 derivation, 74 discovery, iii explanation, 24-25, 87, 96-104 forms, 96-104 value, 103 identification, 96-103 parallel to Arabic numerals, 87 plates showing, 167, 170, 176, 178, 179, 180 use of, in time-period glyphs, 67-74, 104 _See also_ FULL-FIGURE GLYPHS. HEWETT, _Dr._ E. L., cited 164, 192 HIEROGLYPHS-- antiquity, iii, 2 proofs, 173, 175 character, iv, 26-30 classification, 26 decipherment, 23-25, 31, 249-250 errors in interpretation, 154-155 errors in original text, 245-250 methods, 134-155 inversion of significance, 211 mat pattern, 191-194 materials inscribed upon, 22 modifications, 23-25 order of reading, 23, 129, 133, 135, 136-138, 156, 170, 268 original errors, 245-250 progress, iv, 250 symmetry, 23-24, 88-91, 128 textbooks, vii _See also_ NUMERALS. HIEROGLYPHS, CLOSING, use, 101-102, 152-153, 170 HIEROGLYPHS, INTRODUCING, use in dating, 64-68 HISTORY-- codices containing, 32-33 dates, 179, 221-222, 228-229, 249-250 decipherment, iv-v, 26, 250 dates only, 249-250 outline, 2-7 recording, methods, 33-36 HODGE, F. W., letter of transmittal, iii-v HOLMES, W. H., cited, 196 HOSPITALITY, customs, 10 HOTUN PERIOD, 166 HUNTING, division of spoils, 9

IDEOGRAPHIC WRITING, argument for 27-28 IKONOMATIC WRITING, nature 28-29 INITIAL-SERIES DATING-- bar and dot numbers in, examples, 157-167, 176-180 plates showing, 157, 167, 170, 176, 178, 179 disuse, 84-85, 199 examples, interpretation, 157-222, 233-240 plates showing, 157, 167, 170, 176, 178, 179, 180, 187, 188, 191, 207, 210, 213, 218, 220, 233, 235, 248 explanation, 63-74, 147-148 head-variant numbers, examples, 167-176, 180-188 plates showing, 167, 170, 176, 178, 179, 180 introducing glyph, identification by, 136 irregular forms of, examples, 191-194, 203-207 order of reading, 129, 136-138, 170, 268 position of month signs in, 152-154 reference to Long Count, 147-151 regular forms of, interpretation, 157-191 replacement by u kahlay katunob dating, 84-85 starting point, 108, 109, 113-114, 125-126, 136, 159, 162, 203-207 used in codices, 266 examples, 266-273 plate showing, 266 used on monuments, 85 INSCRIPTIONS ON MONUMENTS-- cycles in, numbering, 108-113 date of, contemporaneous, 179, 194, 203, 209-210, 213, 220-222 date of carving, usual, 194 day signs in, 38 errors, 245-250 historical dates, 179 interpretation, 33-35 examples, 156-250 method, 134-155 length of great cycle used in, 107-114 numeration glyphs. _See_ NUMERALS. _See also_ MONUMENTS; STELÆ. INTRODUCING GLYPH-- lack, 208 nature, 64-68, 125-127, 136, 157-158 INVERTED GLYPH, meaning, 211 ITZAMNA (god), nature, 16

JUSTICE, rules of, 9

KATUN (time period)-- glyph, 68-69 identification in u kahlay katunob, 79-82 length, 62, 135 monument erected to mark end, 250 naming, 80-82 series of, 79-86 use of, in Period-ending dates, 222-225 {282} KIN. _See_ DAY. KUKULCAN (god), nature, 16-17

LABOR, customs, 9 LANDA, BISHOP DIEGO DE-- biography, 7 on Maya alphabet, 27 on Maya calendar, 42, 44, 45, 84 on Maya customs, 7, 13-14, 19 on Maya records, 34, 36 LANDRY, M. D., investigations, 194 LEYDEN PLATE, interpretation, 179, 194-198 LITERATURE, list, xv-xvi See also BIBLIOGRAPHY. LONG COUNT-- date fixing in, 147-151, 240-245 nature, 60-63 See also CHRONOLOGY.

MAIZE GOD, nature, 18 MALER, TEOBERT-- cited, 162, 166, 170, 176, 177, 178, 207, 210, 224, 226, 227, 231 on Altar 5 at Tikal, 244 MANNERS AND CUSTOMS, description, 7-21 MARRIAGE CUSTOMS, 8-9 MARS-SOLAR PERIOD, relation to tonalamatl, 278 MAT PATTERN OF GLYPHS, 191-194 MAUDSLAY, A. P.-- cited 157, 167, 169, 170, 171, 173, 175, 179, 180, 181, 183, 185, 186, 188, 191, 203, 205, 213, 215, 218, 220, 223, 224, 225, 226, 227, 228, 229, 230, 235, 240, 242 on zero glyph, 93 MAYA, surviving tribes, 1-2 MAYA, SOUTHERN-- cities, 2-4 occupancy of, diagram showing, 15 government, 15-16 rise and fall, 2-4 MAYAPAN (city)-- history, 4-6 mortuary customs, 12 time records, 33-34 MILITARY CUSTOMS, nature 10-11 MINUS SIGN. _See_ BACKWARD SIGN. MONTH. See UINAL. MONUMENTS-- age, 249-250 date of erection, 179, 194, 203, 209-210, 213, 220-222 historical dates on, 179 period-marking function, 33-35, 249-250 texts. _See_ INSCRIPTIONS. _See also_ STELÆ. MOON, computation of revolutions, 32 MORLEY, S. G., on Books of Chilan Balam, 3 MYTHOLOGY, dates, 179, 180, 194, 228

NACON (official), duties, 13 NAHUA, influence on Maya, 5-6 NARANJO (city)-- antiquity, 15 Stela 22, interpretation, 162-164 Stela 23, error in, 248 interpretation, 224 Stela 24, interpretation, 166-167 Supplementary Series, absence, 163-164 NORMAL DATE, fixing, of 61 NORMAL FORMS OF TIME-PERIOD GLYPHS. _See_ TIME PERIODS. NORTH STAR, deification, 18 NUMBERS, EXPRESSION-- high, 103-134 thirteen to nineteen, 96, 101, 111-112 NUMERALS-- bar and dot system, 87-95 examples, plates showing, 157, 167, 170, 176, 178, 179 colors, 91, 251 combinations of, for higher numbers, 105-107 forms, 87-104 head-variant forms, 24-25, 87, 96-104 plates showing, 167, 170, 176, 178, 179, 180 one to nineteen, bar and dot forms, 88-90 head-variant forms, 97-101 order of reading, 23, 129, 133, 137-138, 156, 170 ornamental variants, 89-91 parallels to Roman and Arabic systems, 87 solution, 134-155 systems, 87-134 comparison, 133 _See also_ VIGESIMAL SYSTEM. transcribing, mode 138 _See also_ HIEROGLYPHS; THIRTEEN; TWENTY; ZERO. NUMERICAL COEFFICIENTS 127-128

PALENQUE (city)-- history, 15 palace stairway inscription, interpretation, 183-185 Temple of the Cross, tablet, interpretation, 205-207, 227 Temple of the Foliated Cross, tablet, interpretation, 180-181, 223-224, 227 Temple of the Inscriptions, tablet, interpretation, 84, 225-226 Temple of the Sun, tablet, interpretation, 181-182 PERIOD-ENDING DATES-- ending glyph, 102 examples, interpretation, 222-240 plates showing, 223, 227, 233, 235 glyphs, 77-79,102 katun used in, 222-225 nature, 222 tun used in, 225-226 PERIOD-MARKING STONES. _See_ MONUMENTS. PHONETIC WRITING-- argument for, 26-30 traces discovered, iv, 26-30 PIEDRAS NEGRAS (city)-- altar inscription, interpretation, 227 antiquity, 15 Stela 1, interpretation, 210-213 Stela 3, interpretation, 233-235 PLONGEON, F. LE, cited, 27 PONCE, ALONZO, on Maya records, 36 PRIESTHOOD, organization, 20-21 PROPHESYING, codices used for, 31 PROPHETIC DATES-- examples, 229-233 use, 271-272 {283}

QUEN SANTO (city)-- history, 231 Stela 1, interpretation, 199-201 Stela 2, interpretation, 201-203 QUIRIGUA (city)-- Altar M, interpretation, 240-242 five-tun period used at, 165-166 founding of, possible date, 221-222 monuments, 192 Stela A, interpretation, 179-180 Stela C, interpretation, 173-175, 179, 203-204, 226 Supplementary Series, absence, 175 Stela D, interpretation, 239 Stela E, error in, 247-248 interpretation, 235-240 Stela F, interpretation, 218-222, 239-240 plates showing, 218, 220 Stela H, interpretation, 192-194 Stela I, interpretation, 164-166 Stela J, interpretation, 215-218, 239-240 Stela K, interpretation, 213-215 Zoömorph G, interpretation, 186-187, 229-230, 239-240 Zoömorph P, interpretation 157-162

READING, order of, 23, 129, 133, 135, 138, 156, 170, 268 RELIGION, nature, 16-21 RENAISSANCE, commencement, 4 ROCHEFOUCAULD, F. A. DE LA, alphabet devised by, 27 ROMAN SYSTEM OF NUMBERS, parallel, 87 ROSNY, LEON DE, cited, 27 RULERSHIP-- nature, 12-13 succession, 13-14

SCARIFICATION, practice, 7 SCHELLHAS, _Dr._ PAUL, investigations, 265 SCULPTURE, development 2-3 SECONDARY-SERIES DATING-- examples, interpretation, 207-222, 233-240 plates showing, 207, 210, 213, 218, 220, 233, 235 explanation, 74-76, 207 irregular forms, 236 order of reading, 129, 137-138, 208 reference to Initial Series, 209-211, 217-218 starting point, 76, 135-136, 208-210, 218, 240-245 determination, 240-245 SEIBAL (city)-- antiquity, 15 Stela 11, interpretation, 230-231 SELER, _Dr._ EDUARD-- cited, 2, 43, 199 on Aztec calendar, 58 on hieroglyphics, 30 SERPENT NUMBERS-- interpretation, 273-275 nature, 273 range, 32, 273 SLAVES, barter in, 9 SOUTHERN MAYA. _See_ MAYA, SOUTHERN. SPANISH CONQUEST, influence, 6-7 SPECTACLE GLYPH, function, 94 SPINDEN, _Dr._ H. J.-- cited, 187 works, 4 STELÆ-- character, 22 dates, 33, 83-84 inscriptions on, 22, 33-35 See also MONUMENTS, and names of cities. STONES, inscriptions on 22 SUPERFIX, effect 120-122 SUPPLEMENTARY SERIES-- closing-sign, 152-153, 170 explanation, 152, 161 lack of, examples, 163-164, 175 position, 152, 238 SYMMETRY IN GLYPHS, modifications due to, 23-24, 88-91, 128

TERMINAL DATES-- determination, 138-151 importance as check on calculations, 154-155 position, 151-154 TEXTBOOKS, need for, vii THIRTEEN-- glyphs, 96, 205 numbers above, expression, 96, 101, 111-112 THOMAS, _Dr._ CYRUS-- cited, 31 on Maya alphabet, 27 THOMPSON, E. H., investigations 11 TIKAL (city)-- Altar 5, interpretation, 242-245 antiquity, 127 history, 15 Stela 3, importance, 179 interpretation, 178-179 Stela 5, interpretation, 226 Stela 10, interpretation, 114-127 Stela 16, association with Altar 5, 244 interpretation, 224, 244 TIME-- counting backward, 146-147 counting forward, 138-146 glyphs for, only ones deciphered, 26, 31 lapse of, determination, 134-155 expression, 63-64, 105-107 indicated by black glyphs, 251 marked by monuments, 33-35, 249-250 method of describing, 46-48 recording, 33-36 use of numbers, 134 starting point, 60-62, 113-114, 124-125 _See also_ CHRONOLOGY. TIME-MARKING STONES. _See_ MONUMENTS. TIME PERIODS-- full-figure glyphs, 67-68, 188-191 plate showing, 188 head-variant glyphs, 67-74 plates showing, 167, 170, 176, 178, 179, 180 length, 62 normal glyphs, 67-74 plate showing, 157 omission of, 128 reduction to days, 134-135 _See also_ CYCLE; GREAT CYCLE; HAAB; KATUN; TONALAMATL; TUN; UINAL. TONALAMATL (time period)-- graphic representation, 93 interpretation, 254-266 {284} nature, 41-44, 265 relation to zero sign, 93-94 starting point, 252-253 subdivisions, 44 texts recording, 251-266 essential parts of, 265 use of glyph for "20" with, 92, 130, 254, 260, 263 used in codices, 251-266 plates showing, 254, 260, 262, 263 used in divination, 251 wheel of days, 43 _See also_ YEAR, SACRED. TRANSLATION OF GLYPHS-- errors, 154-155 methods, 134-155 progress, 250 TUN (time period)-- glyph, 70 length, 62, 135 use of, in Period-ending dates, 225-226 TUXTLA STATUETTE, interpretation, 179, 194-196 TWENTY-- glyphs, 91-92, 130 need for, in codices, 92, 130 needlessness of, in inscriptions, 92 use of in, 254, 260, 263

UINAL-- days, 42 first day, 53 glyph, 94 glyph, 70-71 length, 45, 62, 135 list, 45 names and glyphs for, 48-51 U KAHLAY KATUNOB DATING-- accuracy, 82 antiquity, 82-85 explanation, 79-86 katun sequence, 80-82 order of reading, 137 replacement of Initial-series dating by, 84-86 UXMAL (city), founding, 4

VENUS-SOLAR PERIOD-- divisions, 31-32 relation to tonalamatl, 32, 277-278 VIGESIMAL NUMERATION-- discovery, iii explanation, 62-63, 105-134 possible origin, 41 used in codices, 266-273 VILLAGUTIERE, S. J., on Maya records, 36

WAR GOD, nature, 17 WEAPONS, character, 10-11 WORLD, destruction, prophecy, 32 WORLD EPOCH, glyph, 125-127 WORSHIP, practices, 19-20 WRITING. _See_ HIEROGLYPHICS; NUMERALS; READING.

XAMAN EK (god), nature 18

YAXCHILAN (city)-- lintel, error in, 245-246 Lintel 21, interpretation, 207-210 Stela 11, interpretation, 176-177 Structure 44, interpretation, 177-178 YEAR, SACRED, use in divination, 251 _See also_ TONALAMATL. YEAR, SOLAR. _See_ HAAB. YUCATAN-- colonization, 3-4 Spanish conquest, 6-7 water supply, 1 YUM KAAX (god), nature. 18

ZERO-- glyphs, 92-95, 101-102 origin, 93-94 variants, 93

* * * * *

NOTES

[1] All things considered, the Maya may be regarded as having developed probably the highest aboriginal civilization in the Western Hemisphere, although it should be borne in mind that they were surpassed in many lines of endeavor by other races. The Inca, for example, excelled them in the arts of weaving and dyeing, the Chiriqui in metal working, and the Aztec in military proficiency.

[2] The correlation of Maya and Christian chronology herein followed is that suggested by the writer in "The Correlation of Maya and Christian Chronology" (_Papers of the School of American Archæology_, No. 11). See Morley, 1910 b, cited in BIBLIOGRAPHY, pp. XV, XVI. There are at least six other systems of correlation, however, on which the student must pass judgment. Although no two of these agree, all are based on data derived from the same source, namely, the Books of Chilan Balam (see p. 3, footnote 1). The differences among them are due to the varying interpretations of the material therein presented. Some of the systems of correlation which have been proposed, besides that of the writer, are:

1. That of Mr. C. P. Bowditch (1901 a), found in his pamphlet entitled "Memoranda on the Maya Calendars used in The Books of Chilan Balam."

2. That of Prof. Eduard Seler (1902-1908: I, pp. 588-599). See also _Bulletin 28_, p. 330.

3. That of Mr. J. T. Goodman (1905).

4. That of Pio Perez, in Stephen's Incidents of Travel in Yucatan (1843: I, pp. 434-459; II, pp. 465-469) and in Landa, 1864: pp. 366-429.

As before noted, these correlations differ greatly from one another, Professor Seler assigning the most remote dates to the southern cities and Mr. Goodman the most recent. The correlations of Mr. Bowditch and the writer are within 260 years of each other. Before accepting any one of the systems of correlation above mentioned, the student is strongly urged to examine with care The Books of Chilan Balam.

[3] It is probable that at this early date Yucatan had not been discovered, or at least not colonized.

[4] This evidence is presented by The Books of Chilan Balam, "which were copied or compiled in Yucatan by natives during the sixteenth, seventeenth, and eighteenth centuries, from much older manuscripts now lost or destroyed. They are written in the Maya language in Latin characters, and treat, in part at least, of the history of the country before the Spanish Conquest. Each town seems to have had its own book of Chilan Balam, distinguished from others by the addition of the name of the place where it was written, as: The Book of Chilan Balam of Mani, The Book of Chilan Balam of Tizimia, and so on. Although much of the material presented in these manuscripts is apparently contradictory and obscure, their importance as original historical sources can not be overestimated, since they constitute the only native accounts of the early history of the Maya race which have survived the vandalism of the Spanish Conquerors. Of the sixteen Books of Chilan Balam now extant, only three, those of the towns of Mani, Tizimin, and Chumayel, contain historical matter. These have been translated into English, and published by Dr. D. G. Brinton [1882 b] under the title of "The Maya Chronicles." This translation with a few corrections has been freely consulted in the following discussion."--MORLEY, 1910 b: p. 193.

Although The Books of Chilan Balam are in all probability authentic sources for the reconstruction of Maya history, they can hardly be considered contemporaneous since, as above explained, they emanate from post-Conquest times. The most that can be claimed for them in this connection is that the documents from which they were copied were probably aboriginal, and contemporaneous, or approximately so, with the later periods of the history which they record.

[5] As will appear later, on the calendric side the old system of counting time and of recording events gave place to a more abbreviated though less accurate chronology. In architecture and art also the change of environment made itself felt, and in other lines as well the new land cast a strong influence over Maya thought and achievement. In his work entitled "A Study of Maya Art, its Subject Matter and Historical Development" (1913), to which students are referred for further information, Dr. H. J. Spinden has treated this subject extensively.

[6] The confederation of these three Maya cities may have served as a model for the three Nahua cities, Tenochtitlan, Tezcuco, and Tlacopan, when they entered into a similar alliance some four centuries later.

[7] By Nahua is here meant the peoples who inhabited the valley of Mexico and adjacent territory at this time.

[8] The Ball Court, a characteristically Nahua development.

[9] One authority (Landa, 1864: p. 48) says in this connection: "The governor, Cocom--the ruler of Mayapan--began to covet riches; and for this purpose he treated with the people of the garrison, which the kings of Mexico had in Tabasco and Xicalango, that he should deliver his city [i. e. Mayapan] to them; and thus he brought the Mexican people to Mayapan and he oppressed the poor and made many slaves, and the lords would have killed him if they had not been afraid of the Mexicans."

[10] The first appearance of the Spaniards in Yucatan was six years earlier (in 1511), when the caravel of Valdivia, returning from the Isthmus of Darien to Hispaniola, foundered near Jamaica. About 10 survivors in an open boat were driven upon the coast of Yucatan near the Island of Cozumel. Here they were made prisoners by the Maya and five, including Valdivia himself, were sacrificed. The remainder escaped only to die of starvation and hardship, with the exception of two, Geronimo de Aguilar and Gonzalo Guerrero. Both of these men had risen to considerable prominence in the country by the time Cortez arrived eight years later. Guerrero had married a chief's daughter and had himself become a chief. Later Aguilar became an interpreter for Cortez. This handful of Spaniards can hardly be called an expedition, however.

[11] Diego de Landa, second bishop of Merida, whose remarkable book entitled "Relacion de las Cosas de Yucatan" is the chief authority for the facts presented in the following discussion of the manners and customs of the Maya, was born in Cifuentes de l'Alcarria, Spain, in 1524. At the age of 17 he joined the Franciscan order. He came to Yucatan during the decade following the close of the Conquest, in 1549, where he was one of the most zealous of the early missionaries. In 1573 he was appointed bishop of Merida, which position he held until his death in 1579. His priceless _Relacion_, written about 1565, was not printed until three centuries later, when it was discovered by the indefatigable Abbé Brasseur de Bourbourg in the library of the Royal Academy of History at Madrid, and published by him in 1864. The _Relacion_ is the standard authority for the customs prevalent in Yucatan at the time of the Conquest, and is an invaluable aid to the student of Maya archeology. What little we know of the Maya calendar has been derived directly from the pages of this book, or by developing the material therein presented.

[12] The excavations of Mr. E. H. Thompson at Labna, Yucatan, and of Dr. Merwin at Holmul, Guatemala, have confirmed Bishop Landa's statement concerning the disposal of the dead. At Labna bodies were found buried beneath the floors of the buildings, and at Holmul not only beneath the floors but also lying on them.

[13] Examples of this type of burial have been found at Chichen Itza and Mayapan in Yucatan. At the former site Mr. E. H. Thompson found in the center of a large pyramid a stone-lined shaft running from the summit into the ground. This was filled with burials and funeral objects--pearls, coral, and jade, which from their precious nature indicated the remains of important personages. At Mayapan, burials were found in a shaft of similar construction and location in one of the pyramids.

[14] Landa, 1864: p. 137.

[15] As the result of a trip to the Maya field in the winter of 1914, the writer made important discoveries in the chronology of Tikal, Naranjo, Piedras Negras, Altar de Sacrificios, Quirigua, and Seibal. The occupancy of Tikal and Seibal was found to have extended to 10.2.0.0.0; of Piedras Negras to 9.18.5.0.0; of Naranjo to 9.19.10.0.0; and of Altar de Sacrificios to 9.14.0.0.0. (This new material is not embodied in pl. 2.)

[16] As will be explained in