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 Forstemann.

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. Forstemann, 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. Forstemann'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. Forstemann'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 a.s.sume that the year commenced with Ymix. It may be worthy of notice at this point that the list of days on the so-called "t.i.tle page"

of the Ma.n.u.script Troano begins with Ymix. It is also true that the remarkable quadruple series in the Codex Cortesia.n.u.s 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 pa.s.s 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.