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An Introduction to the Study of the Maya Hieroglyphs

An Introduction to the Study of the Maya Hieroglyphs

Chapter 6 THE CODICES

6 Chapters

Chapter 1 THE MAYA

Chapter 2 THE MAYA HIEROGLYPHIC WRITING

Chapter 3 HOW THE MAYA RECKONED TIME

Chapter 4 MAYA ARITHMETIC

Chapter 5 THE INSCRIPTIONS

Chapter 6 THE CODICES

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Chapter 6 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.

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 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.

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.

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 27

PAGE 12 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN ALL THREE DIVISIONS

The beginning day of the next subdivision of the tonalamatl may now be calculated from the day 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 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.

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

1st Division 2d Division 3d Division 4th Division 5th 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 vertebr?. 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 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:

1st Division 2d Division 3d Division 4th 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. In this manner all of the beginning days could be worked out as below:

1st Division 2d Division 3d Division 4th Division 5th 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 Division 2d Division 3d Division 4th Division 5th 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.

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 28

PAGE 15 OF THE DRESDEN CODEX, SHOWING TONALAMATLS IN ALL THREE DIVISIONS

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 Division 2d Division 3d Division 4th Division 5th 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 Division 2d Division 3d Division 4th Division 5th Division 6th Division 7th Division 8th Division 9th Division 10th Division

1st part, 12 days,

beginning with day 3 Lamat 3 Ix 3 Ahau 3 Cimi 3 Eb 3 Eznab 3 Kan 3 Oc 3 Cib 3 Ik

2d part, 14 days,

beginning with day 2 Ahau 2 Cimi 2 Eb 2 Eznab 2 Kan 2 Oc 2 Cib 2 Ik 2 Lamat 2 Ix

Total number of days 26 26 26 26 26 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 Division 2d Division 3d Division 4th 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:

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 29

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

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 30

PAGE 102 OF THE CODEX TRO-CORTESIANO, SHOWING TONALAMATLS IN THE LOWER THREE SECTIONS

1st Division 2d Division 3d Division 4th 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,

beginning with day 6 Ahau[249] 6 Chicchan[249] 6 Oc[249] 6 Men[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 Division 2d Division 3d Division 4th Division 5th Division

1st part, 2 days,

beginning with day 4 Manik 4 Cauac 4 Chuen 4 Akbal 4 Men

2d part, 7 days,

beginning with day 6 Muluc 6 Imix 6 Ben 6 Chicchan 6 Caban

3d part, 2 days,

beginning with day 13 Cib 13 Lamat 13 Ahau 13 Eb 13 Kan

4th part, 10 days,

beginning with day 2 Eznab 2 Oc 2 Ik 2 Ix 2 Cimi

5th part, 9 days,

beginning with day 12 Lamat 12 Ahau 12 Eb 12 Kan 12 Cib

6th part, 22 days,

beginning with day 8 Caban 8 Muluc 8 Imix 8 Ben 8 Chicchan

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 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 Division 2d Division 3d Division 4th Division 5th 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:

1st Division 2d Division 3d Division 4th Division 5th 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 F?rstemann 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 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.

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 31

PAGE 24 OF THE DRESDEN CODEX, SHOWING INITIAL SERIES

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

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 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

----

1,272,921

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 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 F?rstemann[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 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 F?rstemann (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 F?rstemann 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 F?rstemann 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 F?rstemann 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.

BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 32

PAGE 62 OF THE DRESDEN CODEX, SHOWING THE SERPENT NUMBERS

Texts Recording Serpent Numbers

The Dresden Codex contains another class of numbers which, so far as known, occur nowhere else. These have been called the Serpent numbers because their various orders of units are depicted between the coils of serpents. Two of these serpents appear in plate 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

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.

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 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.

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.

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 F?rstemann, 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 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 F?rstemann as the most valuable contribution to this subject.

* * *

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 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 Arch?ology, 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 chapter V, the writer has suggested the name hotun for the 5 tun, or 1,800 day, period.

[17] Succession in the Aztec royal house was not determined by primogeniture, though the supreme office, the tlahtouani, as well as the other high offices of state, was hereditary in one family. On the death of the tlahtouani the electors (four in number) seem to have selected his successor from among his brothers, or, these failing, from among his nephews. Except as limiting the succession to one family, primogeniture does not seem to have obtained; for example, Moctezoma (Montezuma) was chosen tlahtouani over the heads of several of his older brothers because he was thought to have the best qualifications for that exalted office. The situation may be summarized by the statement that while the supreme ruler among the Aztec had to be of the "blood royal," his selection was determined by personal merit rather than by primogeniture.

[18] There can be no doubt that F?rstemann has identified the sign for the planet Venus and possibly a few others. (See F?rstemann, 1906: p. 116.)

[19] Brasseur de Bourbourg, the "discoverer" of Landa's manuscript, added several signs of his own invention to the original Landa alphabet. See his introduction to the Codex Troano published by the French Government. Leon de Rosny published an alphabet of 29 letters with numerous variants. Later Dr. F. Le Plongeon defined 23 letters with variants and made elaborate interpretations of the texts with this "alphabet" as his key. Another alphabet was that proposed by Dr. Hilborne T. Cresson, which included syllables as well as letters, and with which its originator also essayed to read the texts. Scarce worthy of mention are the alphabet and volume of interlinear translations from both the inscriptions and the codices published by F. A. de la Rochefoucauld. This is very fantastic and utterly without value unless, as Doctor Brinton says, it be taken "as a warning against the intellectual aberrations to which students of these ancient mysteries seem peculiarly prone." The late Dr. Cyrus Thomas, of the Bureau of American Ethnology, was the last of those who endeavored to interpret the Maya texts by means of alphabets; though he was perhaps the best of them all, much of his work in this particular respect will not stand.

[20] Thus the whole rebus in figure 14 reads: "Eye bee leaf ant rose can well bear awl four ewe." These words may be replaced by their homophones as follows: "I believe Aunt Rose can well bear all for you."

Rebus writing depends on the principle of homophones; that is, words or characters which sound alike but have different meanings.

[21] The period of the synodical revolution of Venus as computed to-day is 583.920 days.

[22] According to modern calculations, the period of the lunar revolution is 29.530588, or approximately 29? days. For 405 revolutions the accumulated error would be .03×405=12.15 days. This error the Maya obviated by using 29.5 in some calculations and 29.6 in others, the latter offsetting the former. Thus the first 17 revolutions of the sequence are divided into three groups; the first 6 revolutions being computed at 29.5, each giving a total of 177 days; and the second 6 revolutions also being computed at 29.5 each, giving a total of another 177 days. The third group of 5 revolutions, however, was computed at 29.6 each, giving a total of 148 days. The total number of days in the first 17 revolutions was thus computed to be 177+177+147=502, which is very close to the time computed by modern calculations, 502.02.

[23] This is the tropical year or the time from one equinox to its return.

[24] Landa, 1864: p. 52.

[25] Cogolludo, 1688: I, lib. IV, V, p. 186.

[26] For example, if the revolution of Venus had been the governing phenomenon, each monument would be distant from some other by 584 days; if that of Mars, 780 days; if that of Mercury, 115 or 116 days, etc. Furthermore, the sequence, once commenced, would naturally have been more or less uninterrupted. It is hardly necessary to repeat that the intervals which have been found, namely, 7200 and 1800, rest on no known astronomical phenomena but are the direct result of the Maya vigesimal system of numeration.

[27] It is possible that the Codex Peresianus may treat of historical matter, as already explained.

[28] Since the sequence of the twenty day names was continuous, it is obvious that it had no beginning or ending, like the rim of a wheel; consequently any day name may be chosen arbitrarily as the starting point. In the accompanying example Kan has been chosen to begin with, though Bishop Landa (p. 236) states with regard to the Maya: "The character or letter with which they commence their count of the days or calendar is called Hun-ymix [i. e. 1 Imix]". Again, "Here commences the count of the calendar of the Indians, saying in their language Hun Imix (*) [i. e. 1 Imix]." (Ibid., p. 246.)

[29] Professor Seler says the Maya of Guatemala called this period the kin katun, or "order of the days." He fails to give his authority for this statement, however, and, as will appear later, these terms have entirely different meanings. (See Bulletin 28, p. 14.)

[30] As Bishop Landa wrote not later than 1579, this is Old Style. The corresponding day in the Gregorian Calendar would be July 27.

[31] This is probably to be accounted for by the fact that in the Maya system of chronology, as we shall see later, the 365-day year was not used in recording time. But that so fundamental a period had therefore no special glyph does not necessarily follow, and the writer believes the sign for the haab will yet be discovered.

[32] Later researches of the writer (1914) have convinced him that figure 19, c, is not a sign for Uo, but a very unusual variant of the sign for Zip, found only at Copan, and there only on monuments belonging to the final period.

[33] The writer was able to prove during his last trip to the Maya field that figure 19, f, is not a sign for the month Zotz, as suggested by Mr. Bowditch, but a very unusual form representing Kankin. This identification is supported by a number of examples at Piedras Negras.

[34] The meanings of these words in Nahuatl, the language spoken by the Aztec, are "year bundle" and "our years will be bound," respectively. These doubtless refer to the fact that at the expiration of this period the Aztec calendar had made one complete round; that is, the years were bound up and commenced anew.

[35] Bulletin 28, p. 330.

[36] All Initial Series now known, with the exception of two, have the date 4 Ahau 8 Cumhu as their common point of departure. The two exceptions, the Initial Series on the east side of Stela C at Quirigua and the one on the tablet in the Temple of the Cross at Palenque, proceed from the date 4 Ahau 8 Zotz-more than 5,000 years in advance of the starting point just named. The writer has no suggestions to offer in explanation of these two dates other than that he believes they refer to some mythological event. For instance, in the belief of the Maya the gods may have been born on the day 4 Ahau 8 Zotz, and 5,000 years later approximately on 4 Ahau 8 Cumhu the world, including mankind, may have been created.

[37] Some writers have called the date 4 Ahau 8 Cumhu, the normal date, probably because it is the standard date from which practically all Maya calculations proceed. The writer has not followed this practice, however.

[38] That is, dates which signified present time when they were recorded.

[39] This statement does not take account of the Tuxtla Statuette and the Holactun Initial Series, which extend the range of the dated monuments to ten centuries.

[40] For the discussion of the number of cycles in a great cycle, a question concerning which there are two different opinions, see pp. 107 et seq.

[41] There are only two known exceptions to this statement, namely, the Initial Series on the Temple of the Cross at Palenque and that on the east side of Stela C at Quirigua, already noted.

[42] Mr. Bowditch (1910: App. VIII, 310-18) discusses the possible meanings of this element.

[43] For explanation of the term "full-figure glyphs," see p. 67.

[44] See the discussion of Serpent numbers in Chapter VI.

[45] These three inscriptions are found on Stela N, west side, at Copan, the tablet of the Temple of the Inscriptions at Palenque, and Stela 10 at Tikal. For the discussion of these inscriptions, see pp. 114-127.

[46] The discussion of glyphs which may represent the great cycle or period of the 6th order will be presented on pp. 114-127 in connection with the discussion of numbers having six or more orders of units.

[47] The figure on Zo?morph B at Quirigua, however, has a normal human head without grotesque characteristics.

[48] The full-figure glyphs are included with the head variants in this proportion.

[49] Any system of counting time which describes a date in such a manner that it can not recur, satisfying all the necessary conditions, for 374,400 years, must be regarded as absolutely accurate in so far as the range of human life on this planet is concerned.

[50] There are a very few monuments which have two Initial Series instead of one. So far as the writer knows, only six monuments in the entire Maya area present this feature, namely, Stel? F, D, E, and A at Quirigua, Stela 17 at Tikal, and Stela 11 at Yaxchilan.

[51] Refer to p. 64 and figure 23. It will be noted that the third tooth (i. e. day) after the one named 7 Akbal 11 Cumhu is 10 Cimi 14 Cumhu.

[52] This method of dating does not seem to have been used with either uinal or kin period endings, probably because of the comparative frequency with which any given date might occur at the end of either of these two periods.

[53] In Chapter IV it will be shown that two bars stand for the number 10. It will be necessary to anticipate the discussion of Maya numerals there presented to the extent of stating that a bar represented 5 and a dot or ball, 1. The varying combinations of these two elements gave the values up to 20.

[54] The u kahlay katunob on which the historical summary given in Chapter I is based shows an absolutely uninterrupted sequence of katuns for more than 1,100 years. See Brinton (1882 b: pp. 152-164). It is necessary to note here a correction on p. 153 of that work. Doctor Brinton has omitted a Katun 8 Ahau from this u kahlay katunob, which is present in the Berendt copy, and he has incorrectly assigned the abandonment of Chichen Itza to the preceding katun, Katun 10 Ahau, whereas the Berendt copy shows this event took place during the katun omitted, Katun 8 Ahau.

[55] There are, of course, a few exceptions to this rule-that is, there are some monuments which indicate an interval of more than 3,000 years between the extreme dates. In such cases, however, this interval is not divided into katuns, nor in fact into any regularly recurring smaller unit, with the single exception mentioned in footnote 1, p. 84.

[56] On one monument, the tablet from the Temple of the Inscriptions at Palenque, there seems to be recorded a kind of u kahlay katunob; at least, there is a sequence of ten consecutive katuns.

[57] The word "numeral," as used here, has been restricted to the first twenty numbers, 0 to 19, inclusive.

[58] See p. 96, footnote 1.

[59] In one case, on the west side of Stela E at Quirigua, the number 14 is also shown with an ornamental element (*). This is very unusual and, so far as the writer knows, is the only example of its kind. The four dots in the numbers 4, 9, 14, and 19 never appear thus separated in any other text known.

[60] In the examples given the numerical coefficients are attached as prefixes to the katun sign. Frequently, however, they occur as superfixes. In such cases, however, the above observations apply equally well.

[61] Care should be taken to distinguish the number or figure 20 from any period which contained 20 periods of the order next below it; otherwise the uinal, katun, and cycle glyphs could all be construed as signs for 20, since each of these periods contains 20 units of the period next lower.

[62] The Maya numbered by relative position from bottom to top, as will be presently explained.

[63] This form of zero is always red and is used with black bar and dot numerals as well as with red in the codices.

[64] It is interesting to note in this connection that the Zapotec made use of the same outline in graphic representations of the tonalamatl. On page 1 of the Zapotec Codex Féjerváry-Mayer an outline formed by the 260 days of the tonalamatl exactly like the one in fig. 48, a, is shown.

[65] This form of zero has been found only in the Dresden Codex. Its absence from the other two codices is doubtless due to the fact that the month glyphs are recorded only a very few times in them-but once in the Codex Tro-Cortesiano and three times in the Codex Peresianus.

[66] The forms shown attached to these numerals are those of the day and month signs (see figs. 16, 17, and 19, 20, respectively), and of the period glyphs (see figs. 25-35, inclusive). Reference to these figures will explain the English translation in the case of any form which the student may not remember.

[67] The following possible exceptions, however, should be noted: In the Codex Peresianus the normal form of the tun sign sometimes occurs attached to varying heads, as (*). Whether these heads denote numerals is unknown, but the construction of this glyph in such cases (a head attached to the sign of a time period) absolutely parallels the use of head-variant numerals with time-period glyphs in the inscriptions. A much stronger example of the possible use of head numerals with period glyphs in the codices, however, is found in the Dresden Codex. Here the accompanying head (?) is almost surely that for the number 16, the hatchet eye denoting 6 and the fleshless lower jaw 10. Compare (?) with fig. 53, f-i, where the head for 16 is shown. The glyph (?) here shown is the normal form for the kin sign. Compare fig. 34, b. The meaning of these two forms would thus seem to be 16 kins. In the passage in which these glyphs occur the glyph next preceding the head for 16 is "8 tuns," the numerical coefficient 8 being expressed by one bar and three dots. It seems reasonably clear here, therefore, that the form in question is a head numeral. However, these cases are so very rare and the context where they occur is so little understood, that they have been excluded in the general consideration of head-variant numerals presented above.

[68] It will appear presently that the number 13 could be expressed in two different ways: (1) by a special head meaning 13, and (2) by the essential characteristic of the head for 10 applied to the head for 3 (i. e., 10 + 3 = 13).

[69] For the discussion of Initial Series in cycles other than Cycle 9, see pp. 194-207.

[70] The subfixial element in the first three forms of fig. 54 does not seem to be essential, since it is wanting in the last.

[71] As previously explained, the number 20 is used only in the codices and there only in connection with tonalamatls.

[72] Whether the Maya used their numerical system in the inscriptions and codices for counting anything besides time is not known. As used in the texts, the numbers occur only in connection with calendric matters, at least in so far as they have been deciphered. It is true many numbers are found in both the inscriptions and codices which are attached to signs of unknown meaning, and it is possible that these may have nothing to do with the calendar. An enumeration of cities or towns, or of tribute rolls, for example, may be recorded in some of these places. Both of these subjects are treated of in the Aztec manuscripts and may well be present in Maya texts.

[73] The numerals and periods given in fig. 56 are expressed by their normal forms in every case, since these may be more readily recognized than the corresponding head variants, and consequently entail less work for the student. It should be borne in mind, however, that any bar and dot numeral or any period in fig. 56 could be expressed equally well by its corresponding head form without affecting in the least the values of the resulting numbers.

[74] There may be three other numbers in the inscriptions which are considerably higher (see pp. 114-127).

[75] These are: (1) The tablet from the Temple of the Cross at Palenque; (2) Altar 1 at Piedras Negras; and (3) The east side of Stela C at Quirigua.

[76] This case occurs on the tablet from the Temple of the Foliated Cross at Palenque.

[77] It seems probable that the number on the north side of Stela C at Copan was not counted from the date 4 Ahau 8 Cumhu. The writer has not been able to satisfy himself, however, that this number is an Initial Series.

[78] Mr. Bowditch (1910: pp. 41-42) notes a seeming exception to this, not in the inscription, however, but in the Dresden Codex, in which, in a series of numbers on pp. 71-73, the number 390 is written 19 uinals and 10 kins, instead of 1 tun, 1 uinal, and 10 kins.

[79] That it was a Cycle 13 is shown from the fact that it was just 13 cycles in advance of Cycle 13 ending on the date 4 Ahau 8 Cumhu.

[80] See p. 156 and fig. 66 for method of designating the individual glyphs in a text.

[81] The kins are missing from this number (see A9, fig. 60). At the maximum, however, they could increase this large number only by 19. They have been used here as at 0.

[82] As will be explained presently, the kin sign is frequently omitted and its coefficient attached to the uinal glyph. See p. 127.

[83] Glyph A9 is missing but undoubtedly was the kin sign and coefficient.

[84] The lowest period, the kin, is missing. See A9, fig. 60.

[85] The use of the word "generally" seems reasonable here; these three texts come from widely separated centers-Copan in the extreme southeast, Palenque in the extreme west, and Tikal in the central part of the area.

[86] A few exceptions to this have been noted on pp. 127, 128.

[87] The Books of Chilan Balam have been included here as they are also expressions of the native Maya mind.

[88] This excludes, of course, the use of the numerals 1 to 13, inclusive, in the day names, and in the numeration of the cycles; also the numerals 0 to 19, inclusive, when used to denote the positions of the days in the divisions of the year, and the position of any period in the division next higher.

[89] Various methods and tables have been devised to avoid the necessity of reducing the higher terms of Maya numbers to units of the first order. Of the former, that suggested by Mr. Bowditch (1910: pp. 302-309) is probably the most serviceable. Of the tables Mr. Goodman's Arch?ic Annual Calendar and Arch?ic Chronological Calendar (1897) are by far the best. By using either of the above the necessity of reducing the higher terms to units of the first order is obviated. On the other hand, the processes by means of which this is achieved in each case are far more complicated and less easy of comprehension than those of the method followed in this book, a method which from its simplicity might be termed perhaps the logical way, since it reduces all quantities to a primary unit, which is the same as the primary unit of the Maya calendar. This method was first devised by Prof. Ernst F?rstemann, and has the advantage of being the most readily understood by the beginner, sufficient reason for its use in this book.

[90] This number is formed on the basis of 20 cycles to a great cycle (20×144,000=2,880,000). The writer assumes that he has established the fact that 20 cycles were required to make 1 great cycle, in the inscriptions as well as in the codices.

[91] This is true in spite of the fact that in the codices the starting points frequently appear to follow-that is, they stand below-the numbers which are counted from them. In reality such cases are perfectly regular and conform to this rule, because there the order is not from top to bottom but from bottom to top, and, therefore, when read in this direction the dates come first.

[92] These intervening glyphs the writer believes, as stated in Chapter II, are those which tell the real story of the inscriptions.

[93] Only two exceptions to this rule have been noted throughout the Maya territory: (1) The Initial Series on the east side of Stela C at Quirigua, and (2) the tablet from the Temple of the Cross at Palenque. It has been explained that both of these Initial Series are counted from the date 4 Ahau 8 Zotz.

[94] In the inscriptions an Initial Series may always be identified by the so-called introducing glyph (see fig. 24) which invariably precedes it.

[95] Professor F?rstemann has pointed out a few cases in the Dresden Codex in which, although the count is backward, the special character indicating the fact is wanting (fig. 64). (See Bulletin 28, p. 401.)

[96] There are a few cases in which the "backward sign" includes also the numeral in the second position.

[97] In the text wherein this number is found the date 4 Ahau 8 Camhu stands below the lowest term.

[98] It should be noted here that in the u kahlay katunob also, from the Books of Chilan Balam, the count is always forward.

[99] For transcribing the Maya numerical notation into the characters of our own Arabic notation Maya students have adopted the practice of writing the various terms from left to right in a descending series, as the units of our decimal system are written. For example, 4 katuns, 8 tuns, 3 uinals, and 1 kin are written 4.8.3.1; and 9 cycles, 16 katuns, 1 tun, 0 uinal, and 0 kins are written 9.16.1.0.0. According to this method, the highest term in each number is written on the left, the next lower on its right, the next lower on the right of that, and so on down through the units of the first, or lowest, order. This notation is very convenient for transcribing the Maya numbers and will be followed hereafter.

[100] The reason for rejecting all parts of the quotient except the numerator of the fractional part is that this part alone shows the actual number of units which have to be counted either forward or backward, as the count may be, in order to reach the number which exactly uses up or finishes the dividend-the last unit of the number which has to be counted.

[101] The student can prove this point for himself by turning to the tonalamatl wheel in pl. 5; after selecting any particular day, as 1 Ik for example, proceed to count 260 days from this day as a starting point, in either direction around the wheel. No matter in which direction he has counted, whether beginning with 13 Imix or 2 Akbal, the 260th day will be 1 Ik again.

[102] The student may prove this for himself by reducing 9.0.0.0.0 to days (1,296,000), and counting forward this number from the date 4 Ahau 8 Cumhu, as described in the rules on pages 138-143. The terminal date reached will be 8 Ahau 13 Ceh, as given above.

[103] Numbers may also be added to or subtracted from Period-ending dates, since the positions of such dates are also fixed in the Long Count, and consequently may be used as bases of reference for dates whose positions in the Long Count are not recorded.

[104] In adding two Maya numbers, for example 9.12.2.0.16 and 12.9.5, care should be taken first to arrange like units under like, as:

9. 12. 2. 0. 16

12. 9. 5

-------

9. 12. 14. 10. 1

Next, beginning at the right, the kins or units of the 1st place are added together, and after all the 20s (here 1) have been deducted from this sum, place the remainder (here 1) in the kin place. Next add the uinals, or units of the 2d place, adding to them 1 for each 20 which was carried forward from the 1st place. After all the 18s possible have been deducted from this sum (here 0) place the remainder (here 10) in the uinal place. Next add the tuns, or units of the 3d place, adding to them 1 for each 18 which was carried forward from the 2d place, and after deducting all the 20s possible (here 0) place the remainder (here 14) in the tun place. Proceed in this manner until the highest units present have been added and written below.

Subtraction is just the reverse of the preceding. Using the same numbers:

9. 12. 2. 0. 16

12. 9. 5

-------

9. 11. 9. 9. 11

5 kins from 16 = 11; 9 uinals from 18 uinals (1 tun has to be borrowed) = 9; 12 tuns from 21 tuns (1 katun has to be borrowed, which, added to the 1 tun left in the minuend, makes 21 tuns) = 9 tuns; 0 katuns from 11 katuns (1 katun having been borrowed) = 11 katuns; and 0 cycles from 9 cycles = 9 cycles.

[105] The Supplementary Series present perhaps the most promising field for future study and investigation in the Maya texts. They clearly have to do with a numerical count of some kind, which of itself should greatly facilitate progress in their interpretation. Mr. Goodman (1897: p. 118) has suggested that in some way the Supplementary Series record the dates of the Initial Series they accompany according to some other and unknown method, though he offers no proof in support of this hypothesis. Mr. Bowditch (1910: p. 244) believes they probably relate to time, because the glyphs of which they are composed have numbers attached to them. He has suggested the name Supplementary Series by which they are known, implying in the designation that these Series in some way supplement or complete the meaning of the Initial Series with which they are so closely connected. The writer believes that they treat of some lunar count. It seems almost certain that the moon glyph occurs repeatedly in the Supplementary Series (see fig. 65).

[106] The word "closing" as used here means only that in reading from left to right and from top to bottom-that is, in the normal order-the sign shown in fig. 65 is always the last one in the Supplementary Series, usually standing immediately before the month glyph of the Initial-series terminal date. It does not signify, however, that the Supplementary Series were to be read in this direction, and, indeed, there are strong indications that they followed the reverse order, from right to left and bottom to top.

[107] In a few cases the sign shown in fig. 65 occurs elsewhere in the Supplementary Series than as its "closing" glyph. In such cases its coefficient is not restricted to the number 9 or 10.

[108] In the codices frequently the month parts of dates are omitted and starting points and terminal dates alike are expressed as days only; thus, 2 Ahau, 5 Imix, 7 Kan, etc. This is nearly always the case in tonalamatls and in certain series of numbers in the Dresden Codex.

[109] Only a very few month signs seem to be recorded in the Codex Tro-Cortesiano and the Codex Peresianus. The Tro-Cortesiano has only one (p. 73b), in which the date 13 Ahau 13 Cumhu is recorded thus (*). Compare the month form in this date with fig. 20, z-b'. Mr. Gates (1910: p. 21) finds three month signs in the Codex Peresianus, on pp. 4, 7, and 18 at 4c7, 7c2, and 18b4, respectively. The first of these is 16 Zac (**). Compare this form with fig. 20, o. The second is 1 Yaxkin (?). Compare this form with fig. 20, i-j. The third is 12 Cumhu (??); see fig. 20, z-b'.

[110] As used throughout this work, the word "inscriptions" is applied only to texts from the monuments.

[111] The term glyph-block has been used instead of glyph in this connection because in many inscriptions several different glyphs are included in one glyph-block. In such cases, however, the glyphs within the glyph-block follow precisely the same order as the glyph-blocks themselves follow in the pairs of columns, that is, from left to right and top to bottom.

[112] Initial Series which have all their period glyphs expressed by normal forms are comparatively rare; consequently the four examples presented in pl. 6, although they are the best of their kind, leave something to be desired in other ways. In pl. 6, A, for example, the month sign was partially effaced though it is restored in the accompanying reproduction; in B of the same plate the closing glyph of the Supplementary Series (the month-sign indicator) is wanting, although the month sign itself is very clear. Again, in D the details of the day glyph and month glyph are partially effaced (restored in the reproduction), and in C, although the entire text is very clear, the month sign of the terminal date irregularly follows immediately the day sign. However, in spite of these slight irregularities, it has seemed best to present these particular texts as the first examples of Initial Series, because their period glyphs are expressed by normal forms exclusively, which, as pointed out above, are more easily recognized on account of their greater differentiation than the corresponding head variants.

[113] In most of the examples presented in this chapter the full inscription is not shown, only that part of the text illustrating the particular point in question being given. For this reason reference will be made in each case to the publication in which the entire inscription has been reproduced. The full text on Zo?morph P at Quirigua will be found in Maudslay, 1889-1902: II, pls. 53, 54, 55, 56, 57, 59, 63, 64.

[114] All glyphs expressed in this way are to be understood as inclusive. Thus A1-B2 signifies 4 glyphs, namely, A1, B1, A2, B2,

[115] The introducing glyph, so far as the writer knows, always stands at the beginning of an inscription, or in the second glyph-block, that is, at the top. Hence an Initial Series can never precede it.

[116] The Initial Series on Stela 10 at Tikal is the only exception known. See pp. 123-127.

[117] As will appear in the following examples, nearly all Initial Series have 9 as their cycle coefficient.

[118] In the present case therefore so far as these calculations are concerned, 3,900 is the equivalent of 1,427,400.

[119] It should be remembered in this connection, as explained on pp. 47, 55, that the positions in the divisions of the year which the Maya called 3, 8, 13, and 18 correspond in our method of naming the positions of the days in the months to the 4th, 9th, 14th, and 19th positions, respectively.

[120] As stated in footnote 1, p. 152, the meaning of the Supplementary Series has not yet been worked out.

[121] The reasons which have led the writer to this conclusion are given at some length on pp. 33-36.

[122] For the full text of this inscription see Maler, 1908 b: pl. 36.

[123] Since nothing but Initial-series texts will be presented in the plates and figures immediately following, a fact which the student will readily detect by the presence of the introducing glyph at the head of each text, it is unnecessary to repeat for each new text step 2 (p. 135) and step 3 (p. 136), which explain how to determine the starting point of the count and the direction of the count, respectively; and the student may assume that the starting point of the several Initial Series hereinafter figured will always be the date 4 Ahau 8 Cumhu and that the direction of the count will always be forward.

[124] As will appear later, in connection with the discussion of the Secondary Series, the Initial-series date of a monument does not always correspond with the ending date of the period whose close the monument marks. In other words, the Initial-series date is not always the date contemporaneous with the formal dedication of the monument as a time-marker. This point will appear much more clearly when the function of Secondary Series has been explained.

[125] For the full text of this inscription see Hewett, 1911: pl. XXXV C.

[126] So far as the writer knows, the existence of a period containing 5 tuns has not been suggested heretofore. The very general practice of closing inscriptions with the end of some particular 5-tun period in the Long Count, as 9.18.5.0.0, or 9.18.10.0.0, or 9.18.15.0.0, or 9.19.0.0.0, for example, seems to indicate that this period was the unit used for measuring time in Maya chronological records, at least in the southern cities. Consequently, it seems likely that there was a special glyph to express this unit.

[127] For the full text of this inscription see Maler, 1908 b: pl. 39.

[128] The student should note that from this point steps 2 (p. 139) and 3 (p. 140) have been omitted in discussing each text (see p. 162, footnote 3).

[129] In each of the above cases-and, indeed, in all the examples following-the student should perform the various calculations by which the results are reached, in order to familiarize himself with the workings of the Maya chronological system.

[130] The student may apply a check at this point to his identification of the day sign in A4 as being that for the day Eb. Since the month coefficient in A7 is surely 10 (2 bars), it is clear from Table VII that the only days which can occupy this position in any division of the year are Ik, Manik, Eb, and Caban. Now, by comparing the sign in A4 with the signs for Ik, Manik, and Caban, c, j, and a', b', respectively, of fig. 16, it is very evident that A4 bears no resemblance to any of them; hence, since Eb is the only one left which can occupy a position 10, the day sign in A4 must be Eb, a fact supported by the comparison of A4 with fig. 16, s-u, above.

[131] The full text of this inscription will be found in Maudslay, 1889-1901: I, pls. 35-37.

[132] The full text of this inscription is given in Maudslay, 1889-1902: I, pls. 27-30.

[133] Note the decoration on the numerical bar.

[134] So far as known to the writer, this very unusual variant for the closing glyph of the Supplementary Series occurs in but two other inscriptions in the Maya territory, namely, on Stela N at Copan. See pl. 26, Glyph A14, and Inscription 6 of the Hieroglyphic Stairway at Naranjo, Glyph A1 (?). (Maler, 1908 b: pl. 27.)

[135] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 105-107.

[136] In this glyph-block, A4, the order of reading is irregular; instead of passing over to B4a after reading A4a (the 10 tuns), the next glyph to be read is the sign below A4a, A4b, which records 0 uinals, and only after this has been read does B4a follow.

[137] Texts illustrating the head-variant numerals in full will be presented later.

[138] The preceding hotun ended with the day 9.12.5.0.0 3 Ahau 3 Xul and therefore the opening day of the next hotun, 1 day later, will be 9.12.5.0.1 4 Imix 4 Xul.

[139] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 109, 110.

[140] The oldest Initial Series at Copan is recorded on Stela 15, which is 40 years older than Stela 9. For a discussion of this text see pp. 187, 188.

[141] An exception to this statement should be noted in an Initial Series on the Hieroglyphic Stairway, which records the date 9.5.19.3.0 8 Ahau 3 Zotz. The above remark applies only to the large monuments, which, the writer believes, were period-markers. Stela 9 is therefore the next to the oldest "period stone" yet discovered at Copan. It is more than likely, however, that there are several older ones as yet undeciphered.

[142] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 17-19.

[143] Although this date is considerably older than that on Stela 9 at Copan, its several glyphs present none of the marks of antiquity noted in connection with the preceding example (pl. 8, B). For example, the ends of the bars denoting 5 are not square but round, and the head-variant period glyphs do not show the same elaborate and ornate treatment as in the Copan text. This apparent contradiction permits of an easy explanation. Although the Initial Series on the west side of Stela C at Quirigua undoubtedly refers to an earlier date than the Initial Series on the Copan monument, it does not follow that the Quirigua monument is the older of the two. This is true because on the other side of this same stela at Quirigua is recorded another date, 9.17.5.0.0 6 Ahau 13 Kayab, more than three hundred years later than the Initial Series 9.1.0.0.0 6 Ahau 13 Yaxkin on the west side, and this later date is doubtless the one which referred to present time when this monument was erected. Therefore the Initial Series 9.1.0.0.0 6 Ahau 13 Yaxkin does not represent the period which Stela C was erected to mark, but some far earlier date in Maya history.

[144] For the full text of this inscription see Maudslay, 1889-1902: I, pl. 74.

[145] For the full text of this inscription see Maler, 1903: II, No. 2, pls. 74, 75.

[146] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 79, 2.

[147] For the full text of this inscription see Maler, 1911: V, No. 1, pl. 15.

[148] As used throughout this book, the expression "the contemporaneous date" designates the time when the monument on which such a date is found was put into formal use, that is, the time of its erection. As will appear later in the discussion of the Secondary Series, many monuments present several dates between the extremes of which elapse long periods. Obviously, only one of the dates thus recorded can represent the time at which the monument was erected. In such inscriptions the final date is almost invariably the one designating contemporaneous time, and the earlier dates refer probably to historical, traditional, or even mythological events in the Maya past. Thus the Initial Series 9.0.19.2.4 2 Kan 2 Yax on Lintel 21 at Yaxchilan, 9.1.0.0.0 6 Ahau 13 Yazkin on the west side of Stela C at Quirigua, and 9.4.0.0.0 13 Ahau 18 Yax from the Temple of the Inscriptions at Palenque, all refer probably to earlier historical or traditional events in the past of these three cities, but they do not indicate the dates at which they were severally recorded. As Initial Series which refer to purely mythological events may be classed the Initial Series from the Temples of the Sun, Cross, and Foliated Cross at Palenque, and from the east side of Stela C at Quirigua, all of which are concerned with dates centering around or at the beginning of Maya chronology. Stela 3 at Tikal (the text here under discussion), on the other hand, has but one date, which probably refers to the time of its erection, and is therefore contemporaneous.

[149] There are one or two earlier Initial Series which probably record contemporaneous dates; these are not inscribed on large stone monuments but on smaller antiquities, namely, the Tuxtla Statuette and the Leyden Plate. For the discussion of these early contemporaneous Initial Series, see pp. 194-198.

[150] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 4-7.

[151] For the full text of this inscription see Maudslay, 1889-1902: IV, pls. 80-82.

[152] As explained on p. 179, footnote 1, this Initial Series refers probably to some mythological event rather than to any historical occurrence. The date here recorded precedes the historic period of the Maya civilization by upward of 3,000 years.

[153] For the full text of this inscription see Maudslay, 1889-1902; IV, pls. 87-89.

[154] For the full text of this inscription, see Maudslay, 1889-1902: IV, pl. 23.

[155] It is clear that if all the period coefficients above the kin have been correctly identified, even though the kin coefficient is unknown, by designating it 0 the date reached will be within 19 days of the date originally recorded. Even though its maximum value (19) had originally been recorded here, it could have carried the count only 19 days further. By using 0 as the kin coefficient, therefore, we can not be more than 19 days from the original date.

[156] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 88, 89.

[157] While at Copan the writer made a personal examination of this monument and found that Mr. Maudslay's drawing is incorrect as regards the coefficient of the day sign. The original has two numerical dots between two crescents, whereas the Maudslay drawing shows one numerical dot between two distinct pairs of crescents, each pair, however, of different shape.

[158] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 41-44.

[159] For the text of this monument see Spinden, 1913: VI, pl. 23, 2.

[160] For the discussion of full-figure glyphs, see pp. 65-73.

[161] The characteristics of the heads for 7, 14, 16, and 19 will be found in the heads for 17, 4, 6, and 9, respectively.

[162] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 47, 48.

[163] The student will note also in connection with this glyph that the pair of comblike appendages usually found are here replaced by a pair of fishes. As explained on pp. 65-66, the fish represents probably the original form from which the comblike element was derived in the process of glyph conventionalization. The full original form of this element is therefore in keeping with the other full-figure forms in this text.

[164] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 66-71.

[165] The student should remember that in this diagonal the direction of reading is from bottom to top. See pl. 15, B, glyphs 7, 8, 9, 10, 11, 12, etc. Consequently the upper half of 13 follows the lower half in this particular glyph.

[166] For the full text of this inscription see Hewett, 1911: pl. XXII B.

[167] A few monuments at Quirigua, namely, Stel? F, D, E, and A, have two Initial Series each. In A both of the Initial Series have 0 for the coefficients of their uinal and kin glyphs, and in F, D, E, the Initial Series which shows the position of the monument in the Long Count, that is, the Initial Series showing the katun ending which it marks, has 0 for its uinal and kin coefficients.

[168] In 1913 Mr. M. D. Landry, superintendent of the Quirigua district, Guatemala division of the United Fruit Co., found a still earlier monument about half a mile west of the main group. This has been named Stela S. It records the katun ending prior to the one on Stela H, i. e., 9.15.15.0.0 9 Ahau 18 Xul.

[169] For the full text of this inscription see Holmes, 1907: pp. 691 et seq., and pls. 34-41.

[170] For a full discussion of the Tuxtla Statuette, including the opinions of several writers as to its inscription, see Holmes, 1907: pp. 691 et seq. The present writer gives therein at some length the reasons which have led him to accept this inscription as genuine and contemporaneous.

[171] For the full text of these inscriptions, see Seler, 1902-1908: II, 253, and 1901 c: I, 23, fig. 7. During his last visit to the Maya territory the writer discovered that Stela 11 at Tikal has a Cycle-10 Initial Series, namely, 10.2.0.0.0. 3 Ahau 3 Ceh.

[172] Missing.

[173] At Seibal a Period-ending date 10.1.0.0.0 5 Ahau 3 Kayab is clearly recorded, but this is some 30 years earlier than either of the Initial Series here under discussion, a significant period just at this particular epoch of Maya history, which we have every reason to believe was filled with stirring events and quickly shifting scenes. Tikal, with the Initial Series 10.2.0.0.0 3 Ahau 3 Ceh, and Seibal with the same date (not as an Initial Series, however) are the nearest, though even these fall 10 years short of the Quen Santo and Chichen Itza Initial Series.

[174] Up to the present time no successful interpretation of the inscription on Stela C at Copan has been advanced. The inscription on each side of this monument is headed by an introducing glyph, but in neither case is this followed by an Initial Series. A number consisting of 11.14.5.1.0 is recorded in connection with the date 6 Ahau 18 Kayab, but as this date does not appear to be fixed in the Long Count, there is no way of ascertaining whether it is earlier or later than the starting point of Maya chronology. Mr. Bowditch (1910: pp. 195-196) offers an interesting explanation of this monument, to which the student is referred for the possible explanation of this text. A personal inspection of this inscription failed to confirm, however, the assumption on which Mr. Bowditch's conclusions rest. For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 39-41.

[175] For the full text of this inscription, see ibid.: II, pls. 16, 17, 19.

[176] Table XVI contains only 80 Calendar Rounds (1,518,400), but by adding 18 Calendar Rounds (341,640) the number to be subtracted, 98 Calendar Rounds (1,860,040), will be reached.

[177] Counting 13.0.0.0.0 backward from the starting point of Maya chronology, 4 Ahau 8 Cumhu, gives the date 4 Ahau 8 Zotz, which is no nearer the terminal date recorded in B5-A6 than the date 4 Ahau 3 Kankin reached by counting forward.

[178] For the full text of this inscription, see Maudslay, 1889-1902: IV, pls. 73-77.

[179] As noted in Chapter IV, this is one of the only two heads for 13 found in the inscriptions which is composed of the essential element of the 10 head applied to the 3 head, the combination of the two giving 13. Usually the head for 13 is represented by a form peculiar to this number alone and is not built up by the combination of lower numbers as in this case.

[180] Although at first sight the headdress resembles the tun sign, a closer examination shows that it is not this element.

[181] Similarly, it could be shown that the use of every other possible value of the cycle coefficient will not give the terminal date actually recorded.

[182] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 56.

[183] From this point on this step will be omitted, but the student is urged to perform the calculations necessary in each case to reach the terminal dates recorded.

[184] Since the introducing glyph always accompanies an Initial Series, it has here been included as a part of it, though, as has been explained elsewhere, its function is unknown.

[185] The number 15.1.16.5 is equal to 108,685 days, or 297? years.

[186] It is interesting to note in this connection that the date 9.16.1.0.0 11 Ahau 8 Tzec, which is within 9 days of 9.16.1.0.9 7 Muluc 17 Tzec, is recorded in four different inscriptions at Yaxchilan, one of which (see pl. 9, A) has already been figured.

[187] For the full text of this inscription see Maler, 1901: II, No. 1, pl. 12.

[188] The month-sign indicator appears in B2 with a coefficient 10.

[189] Not expressed.

[190] The writer has recently established the date of this monument as 9.13.15.0.0 13 Ahau 18 Pax, or 99 days later than the above date.

[191] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 47-49.

[192] Although the details of the day and month signs are somewhat effaced, the coefficient in each case is 3, agreeing with the coefficients in the Initial-series terminal date, and the outline of the month glyph suggests that it is probably Yax. See fig. 19, q, r.

[193] Since the Maya New Year's day, 0 Pop, always fell on the 16th of July, the day 3 Yax always fell on Jan. 15th, at the commencement of the dry season.

[194] Since 0 Pop fell on July 16th (Old Style), 18 Kayab fell on June 19th, which is very near the summer solstice, that is, the seeming northern limit of the sun, and roughly coincident with the beginning of the rainy season at Quirigua.

[195] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 46.

[196] Bracketed dates are those which are not actually recorded but which are reached by numbers appearing in the text.

[197] Although not recorded, the number 1.14.6 is the distance from the date 9.15.5.0.0 reached by the Secondary Series on one side to the starting point of the Secondary Series on the other side, that is, 9.15.6.14.6 6 Cimi 4 Tzec.

[198] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 37, 39, 40. For convenience in figuring, the lower parts of columns A and B are shown in B instead of below the upper part. The numeration of the glyph-blocks, however, follows the arrangement in the original.

[199] This is one of the two Initial Series which justified the assumptions made in the previous text that the date 12 Caban 5 Kayab, which was recorded there, had the Initial-series value 9.14.13.4.17, as here.

[200] This is the text in which the Initial-series value 9.15.6.14.6 was found attached to the date 6 Cimi 4 Tzec.

[201] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 38, 40.

[202] The frontlet seems to be composed of but one element, indicating for this head the value 8 instead of 1. However, as the calculations point to 1, it is probable there was originally another element to the frontlet.

[203] See Maudslay, 1889-1902: I, pl. 102, west side, glyphs A5b-A7a.

[204] See ibid.: IV, pl. 81, glyphs N15 O15.

[205] See Maler, 1908 b: IV, No. 2, pl. 38, east side, glyphs A17-B18.

[206] See ibid., 1911: V, pl. 26, glyphs A1-A4.

[207] See Maudslay, 1889-1902: I, pl. 104, glyphs A7, B7.

[208] See Maudslay, 1889-1902: IV, pl. 60, glyphs M1-N2.

[209] Maler, 1911: V, pl. 17, east side, glyphs A4-A5.

[210] See Maudslay, 1889-1902: II, pl. 19, west side, glyphs B10-A12.

[211] See Maudslay, 1889-1902: IV, pl. 75, glyphs D3-C5.

[212] See Maler, 1901: II, No. 1, pl. 8, glyphs A1-A2.

[213] See Maudslay, op. cit., pl. 81, glyphs C7-D8.

[214] It will be remembered that Uayeb was the name for the xma kaba kin, the 5 closing days of the year. Dates which fall in this period are exceedingly rare, and in the inscriptions, so far as the writer knows, have been found only at Palenque and Tikal.

[215] See Maudslay, 1889-1902: IV, pl. 77, glyphs P14-R2. Glyphs Q15-P17 are omitted from pl. 22, G, as they appear to be uncalendrical.

[216] See Maudslay, 1889-1902: I, pl. 100, glyphs C1 D1, A2.

[217] This excludes Stela C, which has two Initial Series (see figs. 68 and 77), though neither of them, as explained on p. 175, footnote 1, records the date of this monument. The true date of this monument is declared by the Period-ending date figured in pl. 21, H, which is 9.17.0.0.0 6 Ahau 13 Kayab. (See p. 226.)

[218] See Maudslay, 1889-1902: II, pl. 44, west side, glyphs G4 H4, F5.

[219] The dates 10.2.5.0.0 9 Ahau 18 Yax and 10.2.10.0.0 2 Ahau 13 Chen on Stel? 1 and 2, respectively, at Quen Santo, are purposely excluded from this statement. Quen Santo is in the highlands of Guatemala (see pl. 1) and is well to the south of the Usamacintla region. It rose to prominence probably after the collapse of the great southern cities and is to be considered as inaugurating a new order of things, if not indeed a new civilization.

[220] See Maler, 1908 a: IV, No. 1, pl. 9, glyphs E2, F2, A3, and A4.

[221] The student will note that the lower periods (the tun, uinal, and kin signs) are omitted and consequently are to be considered as having the coefficient 0.

[222] The usual positions of the uinal and kin coefficients in D4a are reversed, the kin coefficient 10 standing above the uinal sign instead of at the left of it. The calculations show, however, that 10, not 11, is the kin coefficient.

[223] In this number also the positions of the uinal and kin coefficients are reversed.

[224] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 28-32.

[225] The student will note that 12, not 13, tuns are recorded in A5. As explained elsewhere (see pp. 247, 248), this is an error on the part of the ancient scribe who engraved this inscription. The correct tun coefficient is 13, as used above.

[226] This Secondary-series number is doubly irregular. In the first place, the kin and uinal coefficients are reversed, the latter standing to the left of its sign instead of above, and in the second place, the uinal coefficient, although it is 14, has an ornamental dot between the two middle dots.

[227] Since we counted backward 1.14.6 from 6 Cimi 4 Tzec to reach 10 Ahau 8 Chen, we must subtract 1.14.6 from the Initial-series value of 6 Cimi 4 Tzec to reach the Initial-series value of 10 Ahau 8 Chen.

[228] It is obvious that the kin and uinal coefficients are reversed in A17b since the coefficient above the uinal sign is very clearly 19, an impossible value for the uinal coefficient in the inscriptions, 19 uinals always being written 1 tun, 1 uinal. Therefore the 19 must be the kin coefficient. See also p. 110, footnote 1.

[229] The first glyph of the Supplementary Series, B6a, very irregularly stands between the kin period glyph and the day part of the terminal date.

[230] Incorrectly recorded as 12. See pp. 247, 248.

[231] In this table the numbers showing the distances have been omitted and all dates are shown in terms of their corresponding Initial-series numbers, in order to facilitate their comparison. The contemporaneous date of each monument is given in bold-faced figures and capital letters, and the student will note also that this date not only ends a hotun in each case but is, further, the latest date in each text.

[232] The Initial Series on the west side of Stela D at Quirigua is 9.16.13.4.17 8 Caban 5 Yaxkin, which was just 2 katuns later than 9.14.13.4.17 12 Caban 5 Kayab, or, in other words, the second katun anniversary, if the term anniversary may be thus used, of the latter date.

[233] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 50.

[234] For the full text of this inscription, see Maudslay, 1889-1902: I, pl. 112.

[235] Every fourth hotun ending in the Long Count was a katun ending at the same time, namely:

9. 16. 0. 0. 0 2 Ahau 13 Tzec

9. 16. 5. 0. 0 8 Ahau 8 Zotz

9. 16. 10. 0. 0 1 Ahau 3 Zip

9. 16. 15. 0. 0 7 Ahau 18 Pop

9. 17. 0. 0. 0 13 Ahau 18 Cumhu

etc.

[236] Maler, 1911: No. 1, p. 40.

[237] For a seeming exception to this statement, in the codices, see p. 110, footnote 1.

[238] That is, the age of one compared with the age of another, without reference to their actual age as expressed in terms of our own chronology.

[239] See Chapter II for the discussion of this point and the quotations from contemporary authorities, both Spanish and native, on which the above statement is based.

[240] As explained on p. 31, tonalamatls were probably used by the priests in making prophecies or divinations. This, however, is a matter apart from their composition, that is, length, divisions, dates, and method of counting, which more particularly concerns us here.

[241] The codices are folded like a screen or fan, and when opened form a continuous strip sometimes several yards in length. As will appear later, in many cases one tonalamatl runs across several pages of the manuscript.

[242] If there should be two or more columns of day signs the topmost sign of the left-hand column is to be read first.

[243] In the original this last red dot has disappeared. The writer has inserted it here to avoid confusing the beginner in his first acquaintance with a tonalamatl.

[244] This and similar outlines which follow are to be read down in columns.

[245] The fifth sign in the lower row is also a sign of the Death God (see fig. 3). Note the eyelashes, suggesting the closed eyes of the dead.

[246] The last sign Chuen, as mentioned above, is only a repetition of the first sign, indicating that the tonalamatl has re-entered itself.

[247] As previously stated, the order of reading the glyphs in columns is from left to right and top to bottom.

[248] The right-hand dot of the 13 is effaced.

[249] The manuscript has incorrectly 7.

[250] In the title of plate 30 the page number should read 102 instead of 113.

[251] The manuscript incorrectly has 24.

[252] Incorrectly recorded as 13 in the text.

[253] Incorrectly recorded as 15 in the text.

[254] Bull. 28, Bur. Amer. Ethn., p. 400.

[255] The terminal dates reached have been omitted, since for comparative work the Initial-series numbers alone are sufficient to show the relative positions in the Long Count.

[256] The manuscript incorrectly reads 10.13.3.13.2; that is, reversing the position of the tun and uinal coefficients.

[257] The manuscript incorrectly reads 10.8.3.16.4. The katun coefficient is changed to 13, above. These corrections are all suggested by Professor F?rstemann and are necessary if the calculations he suggests are correct, as seems probable.

[258] The manuscript incorrectly reads 8.16.4.11.0. The uinal coefficient is changed to an 8, above.

[259] The manuscript incorrectly reads 10.19.6.0.8. The uinal coefficient is changed to 1, above.

[260] The manuscript incorrectly reads 9.16.4.10.18. The uinal coefficient is changed to 11, above.

[261] The manuscript incorrectly reads 9.19.8.7.8. The tun coefficient is changed to 5, above.

[262] Bowditch, 1909: p. 279.

[263] The manuscript has incorrectly 16 Uo. It is obvious this can not be correct, since from Table VII Kan can occupy only the 2d, 7th, 12th, or 17th position in the months. The correct reading here, as we shall see, is probably 17 Uo. This reading requires only the addition of a single dot.

[264] In the text the coefficient appears to be 8, but in reality it is 9, the lower dot having been covered by the marginal line at the bottom.

[265] Counting backward 8.2.0 (2,920) from 9 Ahau, 1 Ahau is reached.

[266] Professor F?rstemann restored the top terms of the four numbers in this row, so as to make them read as given above.

[267] The manuscript reads 1.12.5.0, which Professor F?rstemann corrects to 1.12.8.0; in other words, changing the uinal from 5 to 8. This correction is fully justified in the above calculations.

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