Dr. Forstemann 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. Forstemann 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. Forstemann 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 Forstemann'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. Forstemann 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. Forstemann 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. Forstemann, 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. Forstemann 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.

[Ill.u.s.tration: FIG. 363. Copy of Plate 51, Dresden Codex.]

[Ill.u.s.tration: FIG. 364. Copy of Plate 52, Dresden Codex.]

[Ill.u.s.tration: FIG. 365. Copy of Plate 55, Dresden Codex.]

[Ill.u.s.tration: FIG. 366. Copy of Plate 54, Dresden Codex.]

[Ill.u.s.tration: FIG. 367. Copy of Plate 55, Dresden Codex.]

[Ill.u.s.tration: FIG. 368. Copy of Plate 56, Dresden Codex.]

[Ill.u.s.tration: FIG. 369. Copy of Plate 57, Dresden Codex.]

[Ill.u.s.tration: FIG. 370. Copy of Plate 58, Dresden Codex.]

In order to a.s.sist 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.