Chapter I: The Numerals in the Dresden Codex (3)

By counting on the calendar (our Table II), as heretofore explained, the reader will observe that the interval from 8 Cib to 7 Cimi is 4 months and 10 days; from 7 Cimi to 10 Cib is 12 months and 10 days; from 10 Cib to 5 Kan is 8 days; from 5 Kan to 7 Ahau is 11 months and 16 days; from 7 Ahau to 6 Oc, 4 months and 10 days; from 6 Oc to 9 Ahau, 12 months and 10 days; from 9 Ahau to 4 Lamat, 8 days; from 4 Lamat to 6 Kan, 11 months and 16 days, and so on to the end of the series on Plate 50. Referring to the codex the reader will observe at the bottom of each plate and directly under--that is to say, in the same vertical lines as the day columns--two lines of red numerals. It is impossible to determine these in Kingsborough's copy (except on Plate 50), but they can readily be made out on the photographed plates. (See the copy of Plate 50, given in Fig. 362.) Those on a single plate are as follows:

{ XI, IV, XII, 0,
{ XVI, X, X, VIII.

The 0 here represents a red, diamond shaped symbol.

If the upper line represents months and the lower line days, these numbers will indicate the intervals between the columns and are properly placed. For example, the XI and XVI signify 11 months and 16 days, the interval between the last column of the preceding plate and the first column of the plate on which they stand; the IV and X, the interval of 4 months and 10 days between the first and second columns; XII and X, the interval of 12 months and 10 days between the second and third columns; and 0, VIII, the interval of 8 days between the third and fourth columns. It is apparent from this that the red, diamond shaped symbol represented by 0 over the VIII denotes a cipher or nought, a conclusion reached independently by Foerstemann.

If this supposition as to the arrangement of the series and the signification of these numbers be correct, it is apparent that the plates are to be taken in the order in which they are paged, that is, from left to right, as the others so far noticed, an inference borne out by another fact now to be mentioned.

Immediately below each of these four column day series are four lines of characters (hieroglyphics), and immediately under the latter three horizontal lines of black numerals, with here and there a red, diamond shaped symbol inserted. As these numerals stand directly in the vertical lines of the day columns, it is possible the two have some connection with each other, a supposition somewhat strengthened by what has been observed in regard to the red numerals at the bottom of the plates. To test this and also for the reason that we propose to discuss their relations and their use, we give here the bottom line of days of each of the five series (or plates), together with their week numbers attached; also, the numbers of the three lines of black numerals mentioned, taking them in the order of the paging as here shown:

_Plate_ 46:
VIII Cib. VII Cimi. X Cib. V Kan.
1 1
11 16 10 11
16 6 16 4

_Plate_ 47:
VII Ahau. VI Oc. IX Ahau. IV Lamat.
2 2 3 3
5 9 4 4
0 10 0 8

_Plate_ 48:
VI Kan. V Ix. VIII Kan. III Eb.
3 4 4 4
16 2 15 15
3(?) 14 4 12

_Plate_ 49:
V Lamat. IV Ezanab. VII Lamat. II Cib.
5 5 6 6
9 13 8 8
8 18 8 16

_Plate_ 50:
IV Eb. III Ik. VI Eb. 1 Ahau.
7 7 8 8
3 7 1 2
12 2 12 0

In considering these horizontal lines it is to be understood that the series runs through the five pages, 46-50.

Let us proceed upon the supposition that the figures of the lowest of the three lines denote days of the month, the numbers of the middle line months, and those of the upper line years. As already shown, the interval between 8 Cib and 7 Cimi is 4 months and 10 days; adding 4 months and 10 days to 11 months and 16 days (bearing in mind that 20 days make a month and 18 months a year), the sum is found to be 16 months and 6 days, precisely the figures under 7 Cimi. As already ascertained, the interval between 7 Cimi and 10 Cib is 12 months and 10 days; this added to 16 months and 6 days gives 1 year, 10 months, 16 days, precisely the figures under 10 Cib. The interval between 10 Cib and 5 Kan is 8 days; this added to the 1 year, 10 months, and 16 days gives 1 year, 11 months, and 4 days, the figures under 5 Kan. The interval between 5 Kan and 7 Ahau is 11 months, 16 days, which, added to the preceding, gives 2 years, 5 months, 0 day, agreeing with the figures under 7 Ahau, if the symbol represented by 0 signifies nought. That this rule holds good throughout the entire series, by making one correction, is shown by the following additions:

Years. Months. Days.
11 16 Under VIII Cib, Plate 46.
4 10
-- --
16 6 Under VII Cimi, Plate 46.
12 10
-- --
1 10 16 Under X Cib, Plate 46.
8
-- -- --
1 11 4 Under V Kan, Plate 46.
11 16
-- -- --
2 5 0 Under VII Ahau, Plate 47.
4 10
-- -- --
2 9 10 Under VI Oc, Plate 47.
12 10
-- -- --
3 4 0 Under IX Ahau, Plate 47.
8
-- -- --
3 4 8 Under IV Lamat, Plate 47.
11 16
-- -- --
3 16 4[300-1] Under VI Kan, Plate 48.
4 10
-- -- --
4 2 14 Under V Ix, Plate 48.
12 10
-- -- --
4 15 4 Under VIII Kan, Plate 48.
8
-- -- --
4 15 12 Under III Eb, Plate 48.
11 16
-- -- --
5 9 8 Under V Lamat, Plate 49.
4 10
-- -- --
5 13 18 Under IV Ezanab, Plate 49.
12 10
-- -- --
6 8 8 Under VII Lamat, Plate 49.
8
-- -- --
6 8 16 Under II Cib, Plate 49.
11 16
-- -- --
7 2 12 Under IV Eb, Plate 50.
4 10
-- -- --
7 7 2 Under III Ik, Plate 50.
12 10
-- -- --
8 1 12 Under VI Eb, Plate 50.
8
-- -- --
8 2 0 Under I Ahau, Plate 50.

The proof of the correctness of the theory advanced may, therefore, be considered conclusive, as it amounts, in fact, to a mathematical demonstration.

Dr. Foerstemann, who considers these lines of black numbers, standing one above another, as representing different grades of units--thus, the lowest, single units; the second, units twenty-fold the lower; the third, eighteen-fold the second; the fourth, twenty-fold the third, &c.--has found the correct intervals of the series, which he states are 236, 90, 250, and 8 days, agreeing with our 11 months, 16 days; 4 months, 10 days; 12 months, 10 days, and 8 days.

As all the discoveries mentioned herein were made previous to the receipt of Dr. Foerstemann's work, I give them according to my own method, acknowledging any modification due to his work. Although I shall compare special results from time to time, an explanation of Dr. Foerstemann's method is reserved for a future paper, as his work was not received until I was revising my notes for publication.

The foregoing explanation of the series shows it to be very simple and makes it clear that it relates to the day columns at the top of the pages. Still, there is one point somewhat difficult to understand. Are the numbers of the third or lowest line intended to denote the positions in the month of the days in the columns above? If so, the month must have commenced with Ymix, as can readily be shown in the following manner:

TABLE III.

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

If we write in a column in proper order the 20 days of the Maya month, commencing with Ymix, and number them consecutively, as in Table III, we shall find by comparison that the numbers in the lower line indicate the position, in this column, of the days directly over them. Take, for example, the lower line of black numerals on Plate 46, writing over them the respective days of the columns, thus:

Cib. Cimi. Cib. Kan.
16 6 16 4

Referring to Table III we see that Cib is the sixteenth day, Cimi the sixth, and Kan the fourth.

The days and numbers of Plate 47 are:

Ahau. Oc. Ahau. Lamat.
0 10 0 8

Ahau is the twentieth day--here is the diamond shaped symbol--Oc is the tenth, and Lamat the eighth, and so on to the end of the series on Plate 50.

It may be justly argued that such relation to some given day of the month would necessarily follow in any series of this kind made up by adding together intervals of days and months. Still it is not at all likely that these series were made up without reference to fitted and determinable dates. If so, the months given must be months of certain determinable years, and the days denoted must be days of particular months. In other words, if we had the proper starting point we should be able to determine the position in the calendar of any day or month mentioned in the series.

First. It is easily seen by reference to the calendar (Table II) that Cib is not the sixteenth day of the month of any of the four years, nor is Cimi the sixth nor Kan the fourth. The idea that the figures of this lower line represent the days of the month must, therefore, be given up unless we assume that the year commenced with Ymix. It may be worthy of notice at this point that the list of days on the so-called "title page" of the Manuscript Troano begins with Ymix. It is also true that the remarkable quadruple series in the Codex Cortesianus on Plates 13-18 commences with Ymix; as this is evidently some kind of a calendar table, its bearing on the question now before us is important.

Second. It can easily be shown that the months referred to in the series, if the numbers given denote specific months, are not those of the Kan years. The first, 8 Cib, if in the eleventh month, must be in the year 4 Kan; counting forward from this 4 months and 10 days to 7 Cimi brings us into the sixteenth month of the year 4 Kan; this agrees with our figures on Plate 46. Counting forward 12 months and 10 days to 10 Cib, we reach the tenth month of the next year; 8 days more carry us to the eleventh month, which still agrees with the figures in the codex. Counting 11 months and 16 days more to 7 Ahau, we reach but do not pass the fourth month of the next year; hence the result does not correspond with the series, which has at this point a 5 in the middle line. The same will be found true in regard to the other years as given in our calendar (Table II). This result, as a matter of course, must follow if the figures in the lower line of the series do not denote the month days of some one of the year series as usually given.

Another fact also becomes apparent here, viz, that the 5 supplemental days of the year are not brought into the count, the year consisting throughout of 360 days. There is, in fact, nothing here indicating the four year series as given in the authorities and as represented in our calendar table; yet this ought to appear wherever a series extends over more than one year.

Dr. Foerstemann says that this entire series of black numerals covers 2,920 days, or 8 years of 365 days. This is true, but the concluding figures show that it is given by the writer of the codex as 8 years and 2 months, which would also be 2,920 days, counting the years at 360 days each and the months 20 days each; moreover, the members of the series are based throughout upon the year of 360 days. His theory that the intervals of the series relate to the movements of the planet Venus is, as yet, a mere hypothesis, which needs further proof before it can demand acceptance; but his discovery of the methods of identifying the month symbols on the five plates now under consideration is important. Although I had noticed that most of the characters which he mentions are month symbols, I did not succeed in identifying all of them.

According to his conclusion, which appears to be justified not only by the evidence he gives but by an additional fact that I shall, presently mention, there are four of these symbols in the upper row of the middle group of written characters on each plate and four in the upper and lower lines of the lower group on each plate (see, for example, Fig. 362). Each of these symbols (except three or four) has a black number attached to it which denotes the day of the month represented by the symbol.

These months and days as given by Dr. Foerstemann are as follows, the positions of the lines as here given corresponding with those of the plates:

TABLE IV.--_Table showing months and days._

_____________________________________________________________________
| Month. Day. | Month. Day. | Month. Day. | Month. Day.
|--------------+--------------+--------------+--------------
Plate 46 | 7 4 | 11 14 | 5 19 | 6 7
| 11 8 | 15 18 | 10 4 | 10 12
| 1 14 | 6 4 | 18 14 | 1 2
Plate 47 | 18 3 | 4 8 | 16 18 | 17 6
| 4 3 | 8 13 | 2 18 | 3(not 2) 6
| 10 10 | 15 3 | 9 8 | 9 16
Plate 48 | 10 17 | 15 7 | 9 12 | 10 20
| 15 2 | 1 7 | 13 17 | 14 5
| 3 7 | 7 17 | 2 2 | 2 10
Plate 49 | 3 11 | 8 1 | 2 6 | 2 14
| 7 16 | 12 6 | 6 11 | 6 19
| 14 6 | 18 16 | 13 1 | 13 9
Plate 50 | 14 10 | 18 20 | 13 5 | 13 13
| 18 15 | 5 20 | 17 10 | 17 18
| 6 20 | 11 10 | 5 15 | 6 3
---------------------------------------------------------------------

An examination of the plates will show that Dr. Foerstemann has filled out the following obliterated or wanting day numbers, to wit, the first of the upper line of Plate 46, the fourth of the upper line of Plate 47, and the second of the middle line and first of the lower line of Plate 50. He has also ventured to change the first day number of the lower line of Plate 46 from 16 to 14. Where the number 20 is found in his list there is no corresponding number in the codex, the month symbol only being given. It is evident he has proceeded in these cases upon the theory that the absence of a number indicated that the month was completed. Although probably correct in this conclusion, the question will arise, Does the symbol in such cases denote the _month completed_ or the _month reached?_

The intervals between these dates are as follows, the left hand column being those between the first and second columns of Foerstemann's list (our Table IV), the second column those between the second and third columns of his list, the third column those between the third and fourth columns of his list, and the fourth column those between the last date of one plate and the first of the next:

TABLE V.--_Table showing intervals between dates._

_____________________________________________________________________
| Month. Day. | Month. Day. | Month. Day. | Month. Day.
|--------------+--------------+--------------+--------------
| | | |
Plate 46 | 4 10 | 12 5 | 0 8 | 11 16
| 4 10 | 12 6_b_| 0 8 | 11 11
| 4 10 | 12 10 | 0 8 | 9 8_d_
Plate 47 | 4 5 | 12 10 | 0 8 | 11 11
| 4 10 | 12 5 | 0 8_c_| 11 16_e_
| 4 13_a_| 12 5 | 0 8 | 11 11
Plate 48 | 4 10 | 12 5 | 8 | 11 11
| 4 5 | 12 10 | 0 8 | 11 11
| 4 10 | 12 5 | 0 8 | 11 16
Plate 49 | 4 10 | 12 5 | 0 8 | 11 16
| 4 10 | 12 5 | 0 8 | 11 16
| 4 10 | 12 5 | 0 8 | 11 11
Plate 50 | 4 10 | 12 5 | 0 8 | 11 11
| 4 5 | 12 10 | 0 8 | 11 10
| 4 10 | 12 5 | 0 8 | 12 11_g_
---------------------------------------------------------------------

Although it is apparent that the variations from the intervals of the black numeral and day series above them are too numerous and too uniform to be considered mistakes, yet there is little reason to doubt that these month numbers are connected with and depend upon the day series given in the columns above.

That there are some errors is quite clear; for instance, the variation at _a_ arises from the fact that Dr. Foerstemann gives the date here as 10 months, 10 days, whereas the codex has it 10 months, 13 days. Making this correction the interval will be 4 months, 10 days. The correction will make the interval at _d_ 9, 11, instead of 9, 8. Still there is a variation of two months from the usual interval, which, if corrected on the supposition that Dr. Foerstemann has mistaken the month, would necessitate a change of the remainder of the series given in this line. The interval at _c_, according to the figure given by Dr. Foerstemann, would be retrograde, that is, minus 12. This arises from the fact that he gives the last date in the middle line on Plate 47 as 2 months, 6 days, whereas the symbol is very distinctly that of the third month, and the eight day series is unbroken if this correction is made.

When these evident errors are corrected the series of intervals show very clearly a system and periodicity depending on the day column series in the upper part of the pages. In the first column (Table V) the interval is usually 4 months, 10 days, precisely the same as between the first and second day columns, but occasionally it is 4 months, 5 days, which will still bring it to one of the four day series, including the day indicated by the date--4 months, 10 days. This will be understood by examining our calendar (Table II). The corresponding days in the four year columns were, by the Maya system, necessarily brought together in the calendar; for example, they are arranged in the series pictured on Plates 13-18 of the Cortesian Codex precisely as given in our Table II. This skip of five days is also apparent in the second and fourth columns of differences (Table V). Whether Dr. Foerstemann is correct in all his identifications of months among the symbols on the five plates now under consideration is a question I feel unqualified to answer without a much more careful comparison and study of these characters than I have given them.

Running through the upper division of Plates 53 to 58 and continued through the lower division of Plates 51 to 58--that is to say, commencing in the upper division of 53 and running into 58, then back to the lower division of 51 and ending in 58--is a remarkable compound series. It consists, first, of a three line series of black numerals standing above; second, a middle series of short, three day columns, or columns each of three day symbols, with red numerals attached; and, third, below, a two line series of numerals, those of the upper line red and of the lower black numbers.

As this series is a very important one in the study of the relations of the numerals to one another and to the days indicated, an exact copy of it is given in Figs. 363-370, each figure representing a page and the whole standing in the same order as in the original. The red numerals and red symbols are, as usual, given in outline as an indication of their color.

In order to assist those not familiar with the numeral and day symbols, the entire series is given in the following tables in names and Arabic and Roman numerals, as usual. The obliterated symbols and numbers are restored.

TABLE VI.--_Table of numeral and day symbols._ (Plate 51_b_.)

______________________________________________________________________
14 | 15 | 15 | 16 | 16 | 17
16 | 7 | 16 | 7 | 16 | 5
14 | 11 | 8 | 5 | 2 | 10
IV Ik. | XII Cauac.| VII Cib. | II Been.| X Oc. | II Ezanab.
V Akbal.|XIII Ahau. |VIII Caban. |III Ix | XI Chuen|III Cauac.
VI Kan. | I Ymix. | IX Ezanab.| IV Men. |XII Eb. | IV Ahau.[VI-1]
VIII | VIII | VIII | VIII | VIII | VII
17 | 17 | 17 | 17 | 17 | 8
----------------------------------------------------------------------

[VI-1] The symbol in this case is that of Been, but this is a manifest error, as Ahau follows Cauac.

TABLE VII.--_Table of numeral and day symbols._ (Plate 52_b_.)

____________________________________________________________
| 17 | 18 | 18 | 19
| 14 | 5 | 14 | 4
| 8 | 5 | 2 | 19
| XI Cib. | VI Been.| I Oc. | IX Manik.
[Picture.] | XII Caban. | VII Ix. | II Chuen.| X Lamat.
| XIII Ezanab. |VIII Men. |III Eb. | XI Muluc.
| VIII | VIII | VIII | VIII
|17? (18)[VII-1]| 17 | 17 | 17
------------------------------------------------------------

[VII-1] The variation from the rule found here is explained a little further on.

TABLE VIII.--_Table of numeral and day symbols._ (Plate 53_a_.)

______________________________________________________________________________________
| 1 | 1 | | 2 | 2 |
7 | 17 | 7 | | 15 | 6 | 15
17 | 18 | 2 | |14?(19)[VIII-1]| 16 | 13
VI Kan. | I Ymix. | VI Muluc.|[Picture.]| I Cimi. |IX Akbal. |IV Ahau.
VII Chicchan.| II Ik. | VII Oc. | | II Manik. | X Kan. | V Ymix.
VIII Cimi. |III Akbal.|VIII Chuen.| | III Lamat. |XI Chicchan.|VI Ik.
VIII | VIII | VII | | VIII | VIII | VIII
17 | 17 | 8 | | 17 | 17 | 17
--------------------------------------------------------------------------------------

[VIII-1] The 14 here is manifestly an error, one of the lines in the number symbol having been omitted; it should be 19.

TABLE IX.--_Table of numeral and day symbols._ (Plate 53_b_.)

_____________________________________________________________________
| 1 | | 1 | 1 | 1
19 | 0 | | 0 | 1 | 1
13 | 3 | | 12 | 2 | 11
16 | 4 | | 1 | 18 | 15
IV Kan. |IX Eb. |[Picture.]|IV Muluc.| XII Cimi. | VII Akbal.
V Chicchan.| X Been.| | V Oc. |XIII Manik.|VIII Kan.
VI Cimi. |XI Ix. | |VI Chuen.| I Lamat.| IX Chicchan.
VIII | VII | | VIII | VIII | VIII
17 | 8 | | 17 | 17 | 17
---------------------------------------------------------------------

TABLE X.--_Table of numeral and day symbols._ (Plate 54_a_.)

____________________________________________________________________________________
3 | 3 | 4 | 4 | 5 | 5 | 6
6 | 15 | 6 | 15 | 5 | 10 | 4
11 | 8 | 5 | 5 | 19 | 16 | 4
XIII Ezanab.|VIII Men. |III Eb. | XI Muluc.| VI Cib. | I Akbal. | VI Chuen.
I Cauac. | IX Cib. | IV Been.| XII Oc. | VII Caban. | II Kan. | VII Eb.
II Ahau. | X Caban.| V Ix. |XIII Chuen.|VIII Ezanab.|III Chicchan.|VIII Been.
VIII | VIII | VIII | VIII | VIII | VIII | VII
17 | 17 | 17 | 17 | 17 | 17 | 8
------------------------------------------------------------------------------------

TABLE XI.--_Table of numeral and day symbols._ (Plate 54_b_.)

_______________________________________________________________
1 | 1 | 1 | 1 | | 1
2 | 2 | 3 | 3 | | 4
2 | 11 | 2 | 9 | | 0[XI-1]
12 | 9 | 6 | 14 | | 11
II Ahau.| X Caban. | V Ix. | X Ik. |[Picture]| V Cauac.
III Ymix.| XI Ezanab.| VI Men.| XI Akbal.| | VI Ahau.
IV Ik. |XII Cauac. |VII Cib.|XII Kan. | |VII Ymix.
VIII | VIII | VIII | VII | | VII[XI-2]
17 | 17 | 17 | 8 | | 17
---------------------------------------------------------------

[XI-1] The 0 inserted at various points in these tables denotes as usual the red, diamond shaped symbol, which apparently signifies "nought."

[XI-2] The numeral symbol in this case, both in Kingsborough's copy and in the photograph, is VII, one dot having been omitted by a mistake of the original artist.

TABLE XII.--_Table of numeral and day symbols._ (Plate 55_a_.)

____________________________________________________________________________
| 8 | 7 | 7 | 8 | 8
| 13 | 3 | 12 | 3 | 12
| 2 | 18 | 16 | 13 | 10
| II Muluc.[XII-1]| X Cimi. | V Akbal. |XIII Ahau.|VIII Caban.
[Picture]|III Oc. | XI Manik.| VI Kan. | I Ymix.| IX Ezanab.
| IV Chuen. |XII Lamat.|VII Chicchan.| II Ik. | X Cauac.
| VIII | VIII | VIII | VIII | VIII
| 17 | 17 | 17 | 17 | 17
----------------------------------------------------------------------------

[XII-1] In Kingsborough's work the symbol in this case is that of Been, but should be Muluc, as it is in the photograph.

TABLE XIII.--_Table of numeral and day symbols._ (Plate 55_b_.)

__________________________________________________________________________________________
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
4 | 5 | 5 | 6 | 6 | 6 | 7 | 7
9 | 0 | 9 | 0 | 8 | 17 | 8 | 15
8 | 6 | 3 | 0 | 17 | 14 | 11 | 19
XIII Cib. |IX Ix. |IV Chuen.| XII Lamat.| VII Chicchan.| II Ik. | X Cauac.| II Manik.
I Caban. | X Men.| V Eb. |XIII Muluc.|VIII Cimi. |III Akbal.| XI Ahau. |III Lamat.
II Ezanab.|XI Cib.|VI Been. | I Oc. | IX Manik. | IV Kan. |XII Ymix. | IV Muluc.
VIII | VIII | VIII | VIII | VIII | VIII | VIII | VII
17 |17?(18)| 17 | 17 | 17 | 17 | 17 | 8
------------------------------------------------------------------------------------------

TABLE XIV.--_Table of numeral and day symbols._ (Plate 56_a_.)

____________________________________________________________
9 | | 9 | 10 | 10
1 | | 10 | 1 | 10
18 | | 15 | 12 | 9
XIII Chicchan.| |VIII Ik. |III Cauac.| XI Cib.
I Cimi. |[Picture]| IX Akbal.| IV Ahau. | XII Caban.
II Manik. | | X Kan. | V Ymix. |XIII Ezanab.
VII | | VIII | VIII | VIII
8 | | 17 | 17 | 17
------------------------------------------------------------

TABLE XV.--_Table of numeral and day symbols._ (Plate 56_b_.)

_________________________________________________________
| 1 | 1 | 1 | 1
| 8 | 8 | 9 | 9
| 6 | 15 | 6 | 15
| 16 | 14 | 11 | 8
[Picture]| X Kan. | VI Ik. | I Cauac.|IX Cib.
| XI Chicchan.| VII Akbal.| II Ahau. | X Caban.
|XII Cimi. |VIII Kan. |III Ymix. |XI Ezanab.
| VIII | VIII | VIII | VIII
| 17 | 17?(8) | 17 | 17
---------------------------------------------------------

TABLE XVI.--_Table of numeral and day symbols._ (Plate 57_a_.)

______________________________________________________
11 | 11 | 12 | 12 |
1 | 10 | 1 | 8 |
6 | 4 | 0 | 8 |
VII Ix. | II Chuen.| X Lamat.| II Cib. |
VIII Men.|III Eb. | XI Muluc.|III Caban. |[Picture]
IX Cib.| IV Been. |XII Oc. | IV Ezanab. |
VIII | VIII | VIII | VIII[XVI-1]|
17 | 17 | 17 | 17[XVI-2]|
------------------------------------------------------

[XVI-1] This should be VII.

[XVI-2] This should be 8.

TABLE XVII.--_Table of numeral and day symbols._ (Plate 57_b_.)

__________________________________________________________________
1 | 1 | 1 | | 1 | 1
10 | 10 | 11 | | 11 | 12
6 | 15 | 4 | | 13 | 4
5 | 2 | 10 | | 7 | 4
IV Been.| XII Oc. |IV Ezanab.|[Picture]| XII Men. | VII Eb.
V Ix. |XIII Chuen.| V Cauac. | |XIII Cib. |VIII Been.
VI Men. | I Eb. |VI Ahau. | | I Caban.| IX Ix.
VIII | VIII | VII | | VIII | VIII
17 | 17 | 8 | | 17 | 17
------------------------------------------------------------------

TABLE XVIII.--_Table of numeral and day symbols._ (Plate 58_a_.)

____________________________________________
12 | 13 | 13 | 14
17 | 8 | 17 | 7
5 | 2 | 0 | 17
X Been.| V Oc. | I Lamat.|II Chicchan.
XI Ix. | VI Chuen.| II Muluc.| X Cimi.
XII Men. |VII Eb. |III Oc. |XI Manik.
VIII | VIII | VIII | VIII
17 | 17 | 17 | 17
--------------------------------------------

TABLE XIX.--_Table of numeral and day symbols._ (Plate 58_b_.)

________________________________
1 | 1 |
12 | 13 |
13 | 3 |
1 | 18 |
II Muluc.| X Cimi. |[Picture.]
III Oc. | XI Manik.|
IV Chuen.|XII Lamat.|
VIII | VIII |
17 | 17 |
--------------------------------

The spaces in the lists indicate the positions of the pictures of persons and curtain-like ornaments inserted here and there, as seen in Figs. 363-370.

In order to explain this series, we commence with that portion of it found in the lower division of Plate 51 (Fig. 363).

Omitting any reference for the present to the black numbers over the day columns, we call attention first to the days and to the red numerals attached to them. Those in the division selected as an illustration are as follows:

IV Ik. XII Cauac. VII Cib. II Been. X Oc. II Ezanab.
V Akbal. XIII Ahau. VIII Caban. III Ix. XI Chuen. III Cauac.
VI Kan. I Ymix. IX Ezanab. IV Men. XII Eb. IV Ahau.[317-1]

It will be observed that the week numbers of the days in each single column follow one another in regular arithmetical order, thus: in the first column, 4, 5, 6; in the second, 12, 13, 1; in the third, 7, 8, 9; and so on throughout the entire series. The interval, therefore, between the successive days of a column is 1; or, in other words, the days follow one another in regular order, as in the month series, so that having the first day of a column given we know at once the other two. It is apparent, therefore, that the intervals between the three correspondingly opposite days of any two associate columns are the same; that is to say, the interval between 5 Akbal and 13 Ahau, in the first two columns given above is the same as that between 4 Ik and 12 Cauac, and also as that between 6 Kan and 1 Ymix. This is also true if the attached week numbers are omitted; for instance, the interval between Ik and Cauac, counting on the list of days forming the month, is 17 days, and it is the same between Kan and Ymix. Taking the second and third columns we find here the same interval. This holds good in that part of the series above given until we reach the last two columns; here the interval between Oc and Ezanab is 8 days and it is the same between the other days of these two columns.

This being ascertained, the next step is to determine the true interval between the first days of these columns, taking the numbers attached to them into consideration. Referring to our calendar (Table II) and (for reasons which will be given hereafter) using the Muluc column and counting from 4 Ik, as heretofore explained, we find the interval between this and 12 Cauac to be 8 months and 17 days; counting in the same way from 12 Cauac, 8 months and 17 days more bring us to 7 Cib; 8 months and 17 days more to 10 Oc. So far the intervals have been the same; but at this point we find a variation from the rule, as the interval between 10 Oc and 2 Ezanab (first of the next column) is 7 months and 8 days.

These intervals furnish the explanation of the red and black numerals below the day columns.

These numerals, as the reader will observe by reference to Fig. 363 or the written interpretation thereof in Table VI, are 8 and 17 under the first five columns, but 7 and 8 under the sixth column, the red (8 under the first five and 7 under the sixth) indicating the months and the black (17 under the first five and 8 under the sixth) the days of the intervals. This holds good throughout all that portion of the series running through the lower divisions of Plates 51 to 58, with three exceptions, which will now be pointed out.

In order to do this it will be necessary to repeat here a part of the series on Plate 51_b_ and part of that on Plate 52_b_; that is, the two right hand columns of the former and the two left hand columns of the latter, between which is the singular picture shown in the _lower left hand corner_ of our Fig. 364:

___________________________________________________________________
Plate 51_b_. || Plate 52_b_.
--------------------------++---------------------------------------
X Oc. | II Ezanab. || | XI Cib. | VI Been.
XI Chuen. | III Cauac. || | XII Caban. | VII Ix.
XII Eb. | IV Ahau. || [Picture.] | XIII Ezanab. | VIII Men.
VIII | VII || | VIII | VIII
17 | 8 || | 17 | 17
-------------------------------------------------------------------

As before stated, the interval between 10 Oc and 2 Ezanab is 7 months and 8 days, as indicated by the red and black numerals under the latter. According to the red and black numbers under the column commencing with 11 Cib, the interval between 2 Ezanab and 11 Cib should be 8 months and 17 days, the usual difference, when, in fact, as we see by counting on the calendar, it is 8 months and 18 days. That this variation cannot be attributed to a mistake on the part of the author or of the artist is evident from the fact that the interval between 11 Cib and 6 Been (first of the next column) is 8 months and 17 days and that the difference throughout the rest of the series follows the rule given; that is to say, each is 8 months and 17 days, except at two other points where this variation is found and at the regular intervals where the difference of 7 months and 8 days occurs.[319-1] Precisely the same variation occurs on Plate 55_b_ in passing from the first to the second column and on Plate 56_b_ between columns 1 and 2.

Why these singular exceptions? It is difficult, if not impossible, for us, with our still imperfect knowledge of the calendar system formerly in vogue among the Mayas, to give a satisfactory answer to this question. But we reserve further notice of it until other parts of the series have been explained.

Reference will now be made to the three lines of black numerals immediately above the day columns. Still confining our examinations to the lower divisions, the reader's attention is directed to these lines, as given in Tables VI, VII, IX, XI, XIII, XV, XVII, and XIX. As there are three numbers in each short column we take for granted, judging by what has been shown in regard to the series on Plates 46-50, that the lowest of the three denotes days, the middle months, and the upper years, and that the intervals are the same between these columns as between the day columns under them. The correctness of this supposition is shown by the following additions: Starting with the first or left hand column on Plate 51_b_, we add successively the differences indicated by the corresponding red and black numbers under the day columns. If this gives in each case (save the two or three exceptions heretofore referred to) the numbers in the next column to the right throughout the series, the demonstration will be complete.

Years. Months. Days.
14 16 14 First column on Plate 51_b_.
8 17
-- -- --
15 7 11 Second column on Plate 51_b_.
8 17
-- -- --
15 16 8 Third column on Plate 51_b_.
8 17
-- -- --
16 7 5 Fourth column on Plate 51_b_.
8 17
-- -- --
16 16 2 Fifth column on Plate 51_b_.
7 8
-- -- --
17 5 10 Sixth column on Plate 51_b_.
8 18[319-1]
-- -- --
17 14 8 First column on Plate 52_b_.
8 17
-- -- --
18 5 5 Second column on Plate 52_b_.
8 17
-- -- --
18 14 2 Third column on Plate 52_b_.
8 17
-- -- --
19 4 19 Fourth column on Plate 52_b_.
8 17
-- -- --
19 13 16 First column on Plate 53_b_.
7 8
-- -- --
20 3 4 Second column on Plate 53_b_.

At this point in the original, instead of 20 in the year series, we find a diamond shaped symbol, represented by 0 in our tables, with one black dot over it. From this it would seem that when this codex was written the Maya method of counting years was by periods of 20 each, as in the case of the month days. Whether there is any reference here to the ahaues is uncertain. I am inclined to think with Dr. Foerstemann that it was rather in consequence of the use of the vigesimal system in representing numbers. It would have been very inconvenient and cumbersome to represent high numbers by means of dots and lines; hence a more practicable method was devised. It is evident, from the picture inserted at this point in the series, that some important chronological event is indicated. Here also in the written characters over this picture is the symbol for 20. The last number given in the above addition may therefore, in order to correspond with the method of the codex, be written as follows:

Twenty year periods. Years. Months. Days.
1 0 3 4

Continuing the addition in this way the result is as follows:

Twenty year periods. Years. Months. Days.
1 0 3 4
8 17
-- -- -- --
1 0 12 1 Third column on Plate 53_b_.
8 17
-- -- -- --
1 1 2 18 Fourth column on Plate 53_b_.
8 17
-- -- -- --
1 1 11 15 Fifth column on Plate 53_b_.
8 17
-- -- -- --
1 2 2 12 First column on Plate 54_b_.
8 17
-- -- -- --
1 2 11 9 Second column on Plate 54_b_.
8 17
-- -- -- --
1 3 2 6 Third column on Plate 54_b_.
7 8
-- -- -- --
1 3 9 14 Fourth column on Plate 54_b_.
8 17
-- -- -- --
1 4 0 11 Fifth column on Plate 54_b_.
8 17
-- -- -- --
1 4 0 8 First column on Plate 55_b_.
8 18[321-1]
-- -- -- --
1 5 0 6 Second column on Plate 55_b_.
8 17
-- -- -- --
1 5 9 3 Third column on Plate 55_b_.
8 17
-- -- -- --
1 6 0 0 Fourth column on Plate 55_b_.
8 17
-- -- -- --
1 6 8 17 Fifth column on Plate 55_b_.
8 17
-- -- -- --
1 6 17 14 Sixth column on Plate 55_b_.
8 17
-- -- -- --
1 7 8 11 Seventh column on Plate 55_b_.
7 8
-- -- -- --
1 7 15 19 Eighth column on Plate 55_b_.
8 17
-- -- -- --
1 8 6 16 First column on Plate 56_b_.
8 18[321-2]
-- -- -- --
1 8 15 14 Second column on Plate 56_b_.
8 17
-- -- -- --
1 6 6 11 Third column on Plate 56_b_.
8 17
-- -- -- --
1 9 15 8 Fourth column on Plate 56_b_.
8 17
-- -- -- --
1 10 6 5 First column on Plate 57_b_.
7 8
-- -- -- --
1 10 15 2 Second column on Plate 57_b_.
7 8
-- -- -- --
1 11 4 10 Third column on Plate 57_b_.
8 17
-- -- -- --
1 11 13 7 Fourth column on Plate 57_b_.
8 17
-- -- -- --
1 12 13 1 Fifth column on Plate 57_b_.
8 17
-- -- -- --
1 12 13 1 First column on Plate 58_b_.
8 17
-- -- -- --
1 13 3 18 Second column on Plate 58_b_.

The proof, therefore, that the theory advanced in regard to the order and the plan of the series is correct seems to be conclusive. This probably would have been conceded without the repeated additions given, but these were deemed necessary because of several irregularities found in that portion running through Plates 53_a_-58_a_, which constitutes the first half of the series.

Turning back to our Table VIII, representing that part of the series on Plate 53_a_, we will consider the three lines of black numerals above the day columns, discussing the irregularities as we proceed.

The numbers in the first column are 7/17,[TN-6] or, according to the explanation given, 7 months and 17 days. There is apparently a mistake here, the correct numbers being 8 months and 17 days, as it is the usual custom of the codex to commence numeral series with the prevailing interval; moreover this correction, which has also been made by Dr. Foerstemann, is necessary in order to connect rightly with what follows; the counters under this first column require this correction, as they are 8 months, 17 days. Making this change we proceed with the addition.

Years. Months. Days.
8 17 First column, Plate 53_a_ (corrected).
8 17
-- --
17 14 Second column. Plate 53_a_.

Here the author of the codex has made another mistake or varied from the plan of the series. As several similar variations or errors occur in this part of the series, it will be as well to discuss the point here as elsewhere. Dr. Foerstemann, in discussing the series, takes it for granted that these variations are errors of the aboriginal scribe; he remarks that "It is seen here that the writer has corrected several of his mistakes by compensation. For instance, the two first differences should be 177 [8 months, 17 days] and 148 [7 months, 8 days], not 176 and 149," &c.

This is a strained hypothesis which I hesitate to adopt so long as any other solution of the difficulty can be found. It is more likely that the writer would have corrected his mistakes, if observed, than that he would compensate them by corresponding errors.

Going back to that part of the series in the lower divisions which has already been examined and commencing with Plate 51_b_ (see Table VI), we observe that the numbers in the lowest of the three lines of black numerals, immediately over the day columns, and the first day of these columns are as follows (omitting the week days attached):

14 11 8 5 2 10
Ik. Cauac. Cib. Been. Oc. Ezanab.

Turning to the calendar (Table II) and using the Muluc column, we notice that the figures of this third line of black numerals denote respectively the month numbers of the days under them; that is to say, Ik is the fourteenth day of the month in Muluc years, Cauac the eleventh, Cib the eighth, Been the fifth, Oc the second, and Ezanab the tenth. This holds good through Plates 52_b_ to 58_b_ without a single exception, provided the diamond shaped symbol in the fourth column of Plate 55_b_ is counted as 20. This test, therefore, presents fewer exceptions than are found in counting the intervals as before explained; yet, after all, this would necessarily result from the fact that the day Muluc was selected as the commencement of the series, and hence may have no signification in reference to or bearing on the question of the year series, especially as the years counted are evidently of 360 days.

Returning now to our Table VIII, representing Plate 53_a_, we observe that the number immediately over Kan in the first column is 17, whereas Kan is the sixteenth day of the month. Is it not possible that the intention was to designate as the ceremonial day Chicchan, standing immediately below, which is the seventeenth day of the month in Muluc years? Even though there is no reference to Muluc years, the intervals may be given upon the same idea, that of reaching, for some particular reason, the second or third day of the column instead of the first. This would account for the compensation of which Dr. Foerstemann speaks, without implying any mistake on the part of the writer. These irregularities would then be intentional variations from the order of the series, yet so as not to break the general plan.

The interval between 6 Kan of the first column (with the month number corrected) and 1 Ymix of the second is 8 months and 17 days, as it should be; between 6 Muluc and 1 Cimi, 8 months and 17 days; and between 1 Cimi and 9 Akbal, 8 months and 17 days, thus conforming to the rule heretofore given, a fact which holds good as a general rule throughout that portion of the series in the upper division.

Continuing the addition as heretofore we note the variations.

Years. Months. Days. Column. Plate.
17 14 Second. 53_a_.
7 8
-- -- --
1 7 3 Third. 53_a_.
8 17
-- -- --
1 15 19[323-1] Fourth. 53_a_.
8 17
-- -- --
2 6 16 Fifth. 53_a_.
8 17
-- -- --
2 15 13 Sixth. 53_a_.
8 18[323-2]
-- -- --
3 6 11 First. 54_a_.
8 17
-- -- --
3 15 8 Second. 54_a_.
8 17
-- -- --
4 6 5 Third. 54_a_.
8 17
-- -- --
4 15 2[324-1] Fourth. 54_a_.
8 17
-- -- --
5 5 19 Fifth. 54_a_.
8 17
-- -- --
5 14[324-2] 16 Sixth. 54_a_.
7 8
-- -- --
6 4 4 Seventh. 54_a_.
8 18[324-3]
-- -- --
6[324-4] 13 2 First. 55_a_.
8 17
-- -- --
7 3 19[324-5] Second. 55_a_.
8 17
-- -- --
7 12 16 Third. 55_a_.
8 17
-- -- --
8 3 13 Fourth. 55_a_.
8 17
-- -- --
8 12 10 Fifth. 55_a_.
7 8
-- -- --
9 1 18 First. 56_a_.
8 17
-- -- --
9 10 15 Second. 56_a_.
8 17
-- -- --
10 1 12 Third. 56_a_.
8 17
-- -- --
10 10 9 Fourth. 56_a_.
8 17
-- -- --
11 1 6 First. 57_a_.
8 17
-- -- --
11 10 3 Second. 57_a_.
8 17
-- -- --
12 1 0 Third. 57_a_.
7 8[325-1]
-- -- --
12 8 8 Fourth. 57_a_.
8 17
-- -- --
12 17 5 First. 58_a_.
8 17
-- -- --
13 8 2 Second. 58_a_.
8 18[325-2]
-- -- --
13 17 0 Third. 58_a_.
8 17
-- -- --
14 7 17 Fourth. 58_a_.
8 17
-- -- --
14 16 14 First. 51_b_.[325-3]

We have in what has thus far been given a satisfactory explanation of the meaning and use of the lines of numerals and also of their relation to the day columns, but we still fall short of a complete interpretation, inasmuch as we are unable to give the series a definite location in the Maya calendar or in actual time. It is apparent, however, that the series cannot by any possible explanation be made to agree with the calendar system as usually accepted, as there is nothing in it indicating the four series of years or the year of 365 days. It may be safely assumed, I think, from what has been shown, that the year referred to in the series is one of 360 days, with probably a periodic addition of one day, but the reason of the addition is not yet apparent.

If the numbers in the lowest line of numerals over the day columns indicate the days of the month, and those of the middle line the respective months of the year, it is evident, as before stated, that Muluc is the first day of the year throughout, a conclusion irreconcilable with the Maya calendar as hitherto understood. It is probable, however, that the month and day numbers do not refer to particular months and days, but are used only as intervals of time counted from a certain day, which must in this case have been Muluc.

The sum of the series as shown by the numbers over the second column of Plate 58_b_ is 33 years, 3 months, and 18 days. As this includes only the top day of this column (10 Cimi), we must add two days to complete the series, which ends with 12 Lamat. This makes the sum of the entire series 33 years, 4 months, or 11,960 days, precisely 46 cycles of 13 months, or 260 days each, the whole and also each cycle commencing with 13 Muluc and ending with 12 Lamat. It is also worthy of notice that in the right hand column of characters (hieroglyphics) over the inverted figure in Plate 58_b_ two numbers, 13 and 12, are found attached to characters which appear to be abnormal forms of month symbols.

On Plates 63 and 64 are three series of ten day columns each and three lines of numerals over each series. These are as follows, so far as they can be made out, the numbers over the upper series being mostly obliterated. The 0 denotes the red, diamond shaped symbol which is here sometimes given in fanciful forms.

TABLE XX.--_Table showing series of day columns, with lines of numerals._

UPPER DIVISION.
__________________________________________________________________________
| |
Plate 63. | Plate 64. |
--------------------------------------------+-----------------------------|
4 | 3 | | | 0 |
8 | 6 | | 0 | 16 |
0 | 0 | 0 | 0 | 0 |
III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
Kan. | Kan. | Kan. | Kan. | Kan. |
Ix. | Ix. | Ix. | Ix. | Ix. |
Cimi. | Cimi. | Cimi. | Cimi. | Cimi. |
XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |
______________|______________|______________|______________|______________|
|
Plate 64. |
____________________________________________ _____________________________|
| | | | |
0 | 0 | | | |
12 | 8 | 3 | 3 | |
0 | 0 | 0 | 0 | 0 |
III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.| III Chicchan.|
Kan. | Kan. | Kan. | Kan. | Kan. |
Ix. | Ix. | Ix. | Ix. | Ix. |
Cimi. | Cimi. | Cimi. | Cimi. | Cimi. |
XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |XIII Akbal. |
______________|______________|______________|______________|______________|

MIDDLE DIVISION.[TN-7]
___________________________________________________________________________
| | | | |
XIX 5 | 4 | 4 | 4 | 4 |
IV 1 | 14 | 9 | 5 | 0 |
IV 0 | 0 | 0 | 7 | 16 |
III Chicchan.| III Ix. | III Akbal. | III Eb. | III Ymix. |
Kan. | Been. | Ik. | Chuen. | Ahau. |
Ix. | Akbal. | Eb. | Ymix. | Oc. |
Cimi. | Men. | Kan. | Been. | Ik. |
XIII Akbal. |XIII Eb. |XIII Ymix. |XIII Oc. |XIII Cauac. |
______________|______________|______________|______________|______________|
| | | | |
3 | 3 | 3 | 3 | 2 |
14 | 9 | 5 | 0 | 14 |
5 | 14 | 3 | 12 | 1 |
III Oc. | III Cauac. | III Lamat. | III Caban. | III Cimi. |
Muluc. | Ezanab. | Manik. | Cib. | Chicchan.|
Cauac. | Lamat. | Caban. | Cimi. | Men. |
Chuen. | Ahau. | Muluc. | Ezanab. | Manik. |
XIII Lamat. |XIII Caban. |XIII Cimi. |XIII Men. |XIII Kan. |
______________|______________|______________|______________|______________|