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:
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. Förstemann, 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. Förstemann’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. Förstemann’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: