Aids to the Study of the Maya Codices Part 2

As colors are not used in these figures the red numerals are indi cated[TN-2] by hollow or outline dots and lines and the black numerals by solid lines and dots.[272-1]

In order further to a.s.sist those unacquainted with the symbols the same line is here given in another form, in which the names of the days are subst.i.tuted for the symbols, Roman numerals for the red numbers, and Arabic for the black: 10, XI Men; 15, XIII Oc; 9, IX Cauac; 11, VII Oc; S, I Oc; 10, XI Ahau.

The S is introduced to represent a numeral symbol different from the lines and dots and will be explained when reached in the course of the ill.u.s.tration.

Starting from 11 Men, found in the twelfth figure column of Table I, and counting forward fifteen days, we come to 13 Oc of the thirteenth figure column, the second day of the above quoted line. Counting nine days from 13 Oc[273-1] brings us to 9 Cauac, the third day of the line; eleven days more, to 7 Oc, the fourth day of the line. Following this day in the line, instead of a black numeral of the usual form, is this symbol: [Ill.u.s.tration: Hieroglyph] represented by S in the second form, where the names and numbers are subst.i.tuted for the symbols. Taking for granted, from the position it occupies in the line, that it is a numeral character, it must represent 20, as the day which follows is 1 Oc, and counting twenty days from 7 Oc brings us to 1 Oc. Counting ten days more we reach 11 Ahau, the last day of the line given above.

In this example the black numerals appear to have been used simply as counters, or as numbers indicating intervals; for example, 15 is the interval between 11 Men and 13 Oc.[273-2]

This furnishes a clew which, if followed up, may lead to important results. That it explains the signification of one symbol undetermined until this relation of the numerals to one another was discovered, is now admitted. In the work of Dr. Forstemann before alluded to the discovery of the symbol for 20 is announced. Although I was not aware of the signification of this symbol until after my second paper, "Notes on certain Maya and Mexican ma.n.u.scripts," was written, I had made this discovery as early as 1884.[273-3]

As there will be occasion to refer to the days of the four different series of years (the Cauac, Kan, Muluc, and Ix years), a combined calendar, similar to an ordinary counting house calendar, is introduced here. For the Cauac years the left or Cauac column is to be used; for the Kan years, the Kan column, and so on.

TABLE II.--_Names and numbers of the four series of years of the Maya system._

__________________________________________________________________________________ | | | | {Numbers Cauac | Kan | Muluc | Ix | 1 2 3 4 5 6 7 8 9 10 11 12 13{of the column. |column. |column. |column. |14 15 16 17 18 {months.

--------+--------+--------+--------+--+--+--+--+--+--+--+--+--+--+--+--+--+------- | | | | | | | | | | | | | | | | |Days of | | | | | | | | | | | | | | | | |month.

Cauac |Kan |Muluc |Ix | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1 Ahau |Chicchan|Oc |Men | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2 Ymix |Cimi |Chuen |Cib | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3 Ik |Manik |Eb |Caban | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4 Akbal |Lamat |Been |Ezanab | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5 Kan |Muluc |Ix |Cauac | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6 Chicchan|Oc |Men |Ahau | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7 Cimi |Chuen |Cib |Ymix | 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8 Manik |Eb |Caban |Ik | 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9 Lamat |Been |Ezanab |Akbal |10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3| 10 Muluc |Ix |Cauac |Kan |11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4| 11 Oc |Men |Ahau |Chicchan|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5| 12 Chuen |Cib |Ymix |Cimi |13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6| 13 Eb |Caban |Ik |Manik | 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 14 Been |Ezanab |Akbal |Lamat | 2| 9| 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 15 Ix |Cauac |Kan |Muluc | 3|10| 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 16 Men |Ahau |Chicchan|Oc | 4|11| 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 17 Cib |Ymix |Cimi |Chuen | 5|12| 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 18 Caban |Ik |Manik |Eb | 6|13| 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 19 Ezanab |Akbal |Lamat |Been | 7| 1| 8| 2| 9| 3|10| 4|11| 5|12| 6|13| 20 ----------------------------------------------------------------------------------

As this table has been explained in my previous papers it is only necessary to add here that the thirteen figure columns form a single series; therefore, when we reach the bottom of the thirteenth column we go back to the top of the first. The day reached will be the one directly opposite (that is, in the same horizontal line) in the day column for the given year.

For example, taking the fifth column of numbers (the one having 3 for the top figure) and counting down nine days from the top number we reach the number 12. This will be 12 Lamat if a Cauac year, 12 Been if a Kan year, 12 Ezanab if a Muluc year, and 12 Akbal if an Ix year. Therefore it is necessary in counting to refer always to the year (year column) with which the count begins. So long as the particular year referred to is unknown (as is Usually the case, the day series being apparently of general rather than of special application) it is immaterial which day column is selected, as the result will be the same with any. This will be apparent if we bear in mind that, when 260 days with their numbers attached have been written down in proper order as a series, we have therein all the possible combinations of days and numbers. This, it is true, does not give us all the months and years (to include these it is necessary to write out fifty-two entire years), but the same series of numerals will be applicable to each of the four year series (Kan, Muluc, Ix, and Cauac years). As any one of the thirteen figure columns of the table may be taken as the commencement of a year and any of the four day columns may be used, it is apparent that we have all the possible combinations (4 13 = 52).

I say above that "it is necessary in counting to refer always to the year (year column) which the count begins." This I admit does not agree with the generally received idea of the Maya calendar, upon which Table II is constructed, as, according to this theory (which I have accepted in my previous papers), after pa.s.sing through a year of one series (corresponding with one of the day columns of the table), we should enter upon a year of the next series; for example, when the year 1 Kan is completed we should enter upon the year 2 Muluc.

Although this calendar system seems to have been in vogue at the time of the conquest and is indicated in one or two of the codices, and possibly in the one now under consideration, the chronological series of the latter, as will hereafter appear, do not seem to be based upon it or to agree with it.

These explanations, with the further statement that the lines in the codex are to be read from left to right and the columns from the top downward, except where variations from this rule are noted, will enable the reader to follow the discussion. Another reason for using a table with only thirteen columns (though it would be difficult to devise a combined calendar of any other form) is that the 260 days they contain form one complete cycle, which, as will appear in the course of this discussion, was one of the chief periods in Maya time computations.

Examining Plates 33 to 39 of the codex the reader will observe that the line already alluded to extends continuously through division _c_, commencing with the two characters over the figure (picture) in the lower right hand corner of Plate 33.

The first of these characters as given in Kingsborough's work is the symbol of the day Ezanab, with the red numeral 13 to the left of it and the black numeral 9 over it; but referring to Forstemann's photolithographic copy of the codex it is found to be the symbol of Ahau.

The entire line, with this correction (that is to say, as given by Forstemann), is represented in Fig. 360. In order to a.s.sist the reader, the names of the days and numbers of the symbols have been added immediately below the characters.

As the year to which the line relates is unknown, we select the Muluc series, designated "Muluc column" in Table II, and commence with 13 Ahau, the twelfth number of the third figure column. Counting 9 days from this brings us to 9 Muluc, the top number of the fourth figure column and also the second day of the line above given. (the symbol is a face in Kingsborough's copy, but is plainly the Muluc sign in Forstemann's photograph). Eleven days more bring us to 7 Ahau, the third day of the above line; 20 more to 1 Ahau, the fourth day of the line (the 20 here is the symbol represented by S); 10 more to 11 Oc, the fifth day of the line; 15 more to 13 Chicchan, the sixth day of the line; 9 more to 9 Ix, the seventh day of the line; 11 more to 7 Chicchan, the eighth day of the line; line; 20 (S) more to 1 Chicchan, the ninth day of the line; 10 more to 11 Men, the tenth day of the line, and so on to the end.

[Ill.u.s.tration: FIG. 360. Line of day and numeral characters.

Pl. 33 XIII Ahau IX Muluc Pl. 34 11 VII Ahau | 20 I Ahau | 10 XI Oc | 15 XIII Chicchan Pl. 35 9 IX Ix | 11 VII Chicchan | 20 I Chicchan Pl. 36 10 XI Men | 15 XIII Oc | 9 IX Cauac Pl. 37 11 VII Oc | 20 I Oc | 10 XI Ahau Pl. 38 15 XIII Men | 9 IX Kan | 11 VII Men Pl. 39 20 I Men(?) | 10 XI Chicchan | 15 XIII Ahau]

That the order of the series may be clearly seen the numbers are given here as they stand in the line, omitting the days: XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII; 9, IX; 11, VII; 20, I; 10, XI; 15, XIII.

By adding together a black numeral and the preceding red one and casting out thirteen (or thirteens, as the case maybe), when the sum exceeds this number, we obtain the following red one, thus: XIII + 9 - 13 = IX; IX + 11 - 13 = VII; VII + 20 - 13 - 13 = I; I + 10 = XI, and so on through the entire series. Attention is also called to the fact that the sum of the black (Arabic) numbers 9, 11, 20, 10, 15, 9, 11, 20, 10, 15, 9, 11, 20, 10, 15, 9, 11, 20, 10, 15, is 260, a multiple of 13.

If this relation of days and numerals holds good as a general thing throughout the codex, it is apparent that where the break is not too extensive it will enable the student to restore the missing and defective numerals and day symbols, to detect the errors of both copyists and original artists, and to determine the proper relation of the plates to one another. By it he learns, as before stated, that the symbol (see page 273) denotes 20, and if phonetic probably stands for the Maya word _Kal_.

Comparing Plates 42 and 43 with Plates 1 and 2, the resemblance is found to be so strong as to lead to the belief that they belong together. It is apparent from the figures, numerals, and characters[277-1] in the middle division (_b_) of Plates 1 and 2 that they belong together, as they now stand in Kingsborough's work and Forstemann's copy; that Plates 42 and 43 are properly placed in regard to each other is also apparent from the figures and numerals in divisions _a_ and _b_.

Taking for granted that the lines are to be read from left to right and the plates to follow each other in the same order, our next step is to ascertain on which side of the pair (Plates 42 and 43) Plates 1 and 2 should be placed.

The series of days and of numbers in Plate 43_b_ and Plate 1_b_, which evidently belong together, can only be brought into proper relation by placing the latter to the right of the former. Yet, strange as it may appear, the days and numerals in this division are to be read from right to left, while all the other numeral series of these four plates are to be read as usual, from left to right. This change in the order of the pages also brings together the similar figures in the upper division of these plates. That Plate 42 properly follows Plate 41 is apparent from the line of alternate red and black numerals in division _b_. As shown in a previous work[278-1] and as will appear hereafter, these horizontal lines of alternate red and black numerals without day symbols interspersed are usually, if not always, connected at the left with a column of days over which there is a red numeral, as in the Codex Troano.

Running back along the line of numerals in the middle division of Plates 42 and 41, the day column with which it is connected is found at the left margin of Plate 38. Unfortunately the red numeral over this column is obliterated, but can easily be restored. Starting with the first black numeral to the right of this, the entire line, which ends in the second column of the middle division of Plate 43 (representing the black numerals by Arabic numbers and the red by Roman numbers), is as follows: 16, IX; 8, IV; 11, II; 10, XII; 1, XIII; 12, XII; 6, VI(?); 12, IV; 11, II; 11, XIII; 6, VI; 12, V; 7, XII; 6, V; S + 1, XIII; 6, VI.

The number over the day column, Plate 38, must have been VI, as VI + 16 - 13 = 9, a conclusion which is sustained by Forstemann's copy, which shows here very plainly the red character for VI.

By adding the black (Arabic) numeral to the preceding red (Roman) one and casting out the thirteens, as heretofore explained, we obtain the following red (Roman) numerals, thus: VI + 16 - 13 = IX; IX + 8 - 13 = IV; IV + 11 - 13 = II; II + 10 = XII; XII + 1 = XIII; XIII + 12 - 13 = XII; XII + 6 - 13 = V.

Here the result differs from what is found at this point in the line, as we obtain V instead of VI. In this case the mistake, if one has been made, cannot be attributed to Lord Kingsborough's copyist; the Maya artist must have made a mistake or there must be an error in the theory here advanced. But let us continue according to our own figures: V + 12 - 13 = IV; IV + 11 - 13 = II; II + 11 = XIII; XIII + 6 - 13 = VI; VI + 12 - 13 = V; V + 7 = 12; XII + 6 - 13 = V; V + 20 + 1 - 13 = XIII; XIII + 6 - 13 = VI.

There is no doubt, therefore, that the line forms one continuous series, and if so it links together pages 38 and 43 as they are now numbered. It follows, then, that if Plates 1 and 2 and Plates 42 and 43 belong together, the former pair must be placed to the right of 43. This is conceded by Dr. Forstemann,[278-2] as he says that, Dr. Karl Schultz-Sellack having pointed out the error in his paging, he changed pages 1 and 2 to 44 and 45 and pages 44 and 45 to 1 and 2; that is to say, the two leaves containing these pages were loosened from the strip and reversed, so that page 1 would be 44 and page 2 would be 45.

Having brought together these plates so that 1 and 2 stand to the right of 43, attention is called to the lines of day symbols running through division _c_. Subst.i.tuting names and numbers as heretofore, they are as follows:

Plate 42: IV Ahau; XII Lamat; VII Cib; II Kan; X Eb; V Ahau; XIII Lamat.

17 8 8 8 8 8 8

Plate 43: IV Chicchan; XII Been; VII Ymix; II Muluc; X Caban; V Chicchan; XIII Been.

17 8 8 8 8 8 8

Plate 1: IV Oc; XII Ezanab; VII Cimi; II Ix; X Ik; V Oc; (?) Ezanab.

17 8 8 8 8 8 8

Plate 2: IV Men; XIII Akbal; VII Chuen; II Cauac; X Manik; V Men; XIII Akbal.

17 8 8 8 8 8 8

The chief objects in view at present in selecting this series are, as before indicated, to prove the relation of the plates to one another and to determine the use of the black numerals which stand under the day symbols. These numerals consist of but two different numbers, the first on each page being 17, the rest 8's.

As the particular year or years to which the series refers is unknown we turn to our calendar--Table II--and select the Kan column, as we find that 4 Ahau, the first day of the series, is the seventeenth day of the year 1 Kan. This corresponds with the first black numeral. Counting 8 days from this we reach 12 Lamat, the second day of our series; 8 more bring us to 7 Cib, the third day of the series; 8 more to 2 Kan; 8 more to 10 Eb; 8 more to 5 Ahau; 8 more to 13 Lamat, and 17 more to 4 Chicchan. The red numeral at this point in some of the colored copies of Kingsborough's work is III, but a close inspection shows the missing dot which has not been colored. IV Chicchan is therefore correct.

Continuing our count, 8 days more bring us to 12 Been: 8 more to 7 Ymix; 8 more to 2 Muluc; 8 more to 10 Caban; 8 more to 5 Chicchan; 8 more to 13 Been; 17 more to 4 Oc; 8 more to 12 Ezanab; 8 more to 7 Cimi; 8 more to 2 Ix; 8 more to 10 Ik; 8 more to 5 Oc, and 8 more to 13 Ezanab. Here the red numeral is wanting, but a comparison of the numbers on the different plates and the order of the series make it evident that it should be XIII.

Continuing our count, 17 more bring us to 4 Men (here a dot is missing in Kingsborough's copy, but is present in the photograph); 8 more to 12 Akbal. Here there is one dot too many, which we may attribute to a mistake of the original artist. a.s.suming XII to be correct, 8 more bring us to 7 Chuen; 8 more to 2 Cauac; 8 more to 10 Manik; 8 more to 5 Men; 8 more to 13 Akbal, and to the end of our table; thus, if we include the first seventeen days, completing the series of thirteen months or 260 days.

These ill.u.s.trations will probably satisfy any one that the black numerals in these lines denote the intervals between the days indicated by the symbols and that the series so far examined are to be read from left to right.

Although the succession of days and numbers in the lines of the last example would seem to furnish conclusive evidence that the whole is one continuous series, yet the peculiar combinations of numbers used by the Maya priests render these series very deceptive. There can be no doubt that the black numbers--8's--are used to indicate the intervals between the days specified; but there is another possible way of explaining the 17 with which the lines on the different plates begin.

Here are four plates, evidently closely related to one another; the lines of days and numbers in the lowest division of each are precisely alike, except as to the days indicated; in the left hand column of characters of each is one of the cardinal point symbols. It is possible, therefore, that these four plates relate to the four different years or series of years; that is to say, one to the Kan years, one to the Muluc years, and so on. This view is somewhat strengthened by the fact that 4 Ahau, first of the line on Plate 42, is the seventeenth day of the first month of the year 1 Kan; 4 Chicchan, first of the line on plate 43, the seventeenth day of the first month of the year 1 Muluc; 4 Oc, the seventeenth day of 1 Ix, and 4 Men the seventeenth day of 1 Cauac. The four figures in the middle division of Plates 1 and 2 seem also to favor this idea, not so much by the peculiar animals represented (of which we have no explanation to give) as by the double symbols from which they are suspended, which I am quite confident denote the union of years or the time at which two years meet--the close of one and the commencement of another--although fully aware that Dr. Forstemann has interpreted them as symbols of the heavenly bodies.[280-1]

In the text above these figures are seen two characters or symbols of this type, which in all probability, as will hereafter appear, denote or symbolize the "tying of the years." We may also add that the five days of each plate or group are the five a.s.signed, as I have explained in "Notes on certain Maya and Mexican ma.n.u.scripts," to the cardinal points. For example, those on Plate 42 are Ahau, Eb, Kan, Cib, Lamat.[280-2] Still it must be admitted, on the other hand, that as the four lines form precisely one complete cycle of 13 months or 260 days there is a very strong inference that they together form one continuous series and that the arrangement into four parts or divisions has reference to the four seasons or four cardinal points. The final decision on this point therefore still remains in doubt.

As it has been shown that Plates 33 to 39 and Plates 38 to 43 are properly placed as they stand in Kingsborough's copy and also in Forstemann's and that Plates 1 and 2 follow Plate 43, we have proof that the following plates succeed one another to the right, as here given: 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 2.

A slight inspection is sufficient to show that Plates 29 to 33 follow one another in the same order, a conclusion which is easily verified by testing the lines of numerals in the manner explained. It is apparent, therefore, that the following plates form one unbroken series, running from left to right: 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 2; a conclusion which Dr. Forstemann, who has had the opportunity of studying the original, has now reached.

Having ascertained the object and use of at least one cla.s.s of black numerals and the relation they bear to the days and day numbers, it may be well to test further the discovery by other examples, in order to see how far it holds good and what new facts it may bring out. In doing this it will be necessary to repeat in part what has already been shown by Dr.

Forstemann in his late work; but as these discoveries were made independently and before this work came to hand, and as our conclusions differ in some respects from those reached by him, the plan and scope of this paper would be incomplete without these ill.u.s.trations.