Second. That a number of minor changes and additions have been made by a subsequent hand, possibly after it had assumed its present form.
Third. That the year referred to in the larger series is one of 360 days; also, that in instances of this kind the count is continuous, and hence not consistent with the generally received idea of the Maya calendar, in which, the four year series forms a necessary part of the system, unless some other method of accounting for the five supplemental days can be discovered than that which has hitherto been accepted.
Fourth. On the other hand, indications of the four year series are certainly found in all of the Maya manuscripts; for example, in Plates 25-28 of the Dresden Codex and Plates XX-XXIII of the Manuscript Troano,[339-1] which seem to be based on this series; in fact, the numbers attached to the days in the latter can be accounted for in no other way. Plates 3-6 of the Cortesian Codex are apparently based upon the same system. The numbers in the loops on Plates 71, 72, and 73, Dresden Codex, heretofore alluded to and represented in [Fig. 371], apparently defy explanation on any supposition except that they refer to the numbers of the ahaues, which are based upon the four year series.[339-2] The frequent occurrence in connection and in proper order of both the first and the terminal days of the year apparently refers to the same system. Many of the quadruple series no doubt relate to the four cardinal points and the four seasons; yet there are some which cannot be explained on this theory alone.
It is impossible, therefore, to exclude this system from consideration in studying the chronology of the codices, although there are a number of the numerical series of the Dresden manuscript which cannot be made to fit into it on any hypothesis so far suggested. The same thing is also found to be true in regard to some, in fact most, of the series found in the Mexican manuscripts. This confusion probably arises in part from the apparently well established fact that two methods of counting time prevailed among both Mexicans and Mayas: one, the solar year in ordinary use among the people, which may be termed the vulgar or common calendar; the other, the religious calendar used by the priests alone in arranging their feasts and ceremonies, in which the cycle of 260 days was taken as the basis. But this supposition will not suffice as an explanation of some of the long series of the Dresden Codex, in which the year of 360 days appears to have been taken as a unit of measure, unless we assume—as Förstemann seems to have done—that what have been taken as years are simply high units and counting the whole as so many days, refer the sum to the cycle of 260 days, which will in almost every case measure them evenly as a whole, or by its leading factor, 13. That the smaller series attached to day columns are all multiples of 13 and referable to the cycle of 260 days has been shown by Förstemann as well as in the preceding part of this paper. But it is worthy of note that the difficulty mentioned occurs only in reference to series found in that portion of the Dresden manuscript which Förstemann has designated Codex B (page 24 being considered as belonging thereto).
The red unit number symbol, with a circle of dots around it, seen occasionally in the Manuscript Troano, seems to have some connection with the four year series. Take, for example, the one in the lowest division of Plate VII.
The series commences in the lower right hand corner of Plate VIII, where the day column with which it is connected is found. The days of this column, reading downward, are as follows: Ahau, Eb, Kan, Cib, Lamat, and the number over them is I, but without any dots around it, while the terminal I of the series is inclosed in the circle of dots. What is the meaning of this marked distinction? It is evident that it is something which does not apply equally to all the days of the columns; yet, as it is the terminal number, it must relate to some one of them. If we examine the series carefully I think the reason for the distinction will be explained; Written out in full, it is as follows:
| I. | ||
| Ahau | ||
| Eb | } | 10, XI; 10, VIII; 10, V; 10, II; 12[?], Ⓘ. |
| Kan | ||
| Cib | ||
| Lamat |
The last black number is 10 in Brasseur’s fac simile, but should be 12. Making this correction, the series is regular and of the usual form. The sum of the black numbers is 52, which is the interval between the days, and the number over the column is the same as the final red number.
If we turn now to the calendar ([Table II]) and select Ahau of the Kan column, and 1, the seventeenth number of the eighth figure column, and count 52 days, we reach 1 Eb, the second day of our column as given above; 52 days more bring us to 1 Kan, the first day of the first month in the calendar and third day of our column. If the theory of the four year series be correct, then 1 Kan of the Kan series must be the first day of the first year of an Indication or week of years. This fact was probably considered by the aboriginal artist of sufficient importance to give this day a mark of distinction. As it is not possible for any of the other days of the column to be thus distinguished, it is fair to presume this peculiar marking of the final number refers to Kan. Moreover, this distinction would not occur if any other than the Kan series were used.
In the upper division of Plate IX of the same manuscript is the following series: