Going back to the series on Plate 29_c_ of the Dresden Codex, we observe not only that the days of the column are the four year bearers, but also that one of the four cardinal symbols is found--in the superscription--in each of the four compartments through which the series extends. It is possible, therefore, that the series is intended to be applied separately to each of the four years. Supposing this to be the case, counting 64 days from 3 Ix would bring us to 2 Ezanab; 64 days from 3 Cauac to 2 Akbal; 64 days from 3 Kan to 2 Lamat; and 64 days from 3 Muluc to 2 Been.
It is significant that in each case the day reached is that on which the given year terminates; for example, the Ix years (counting the five added days) terminate on Ezanab; the Cauac years on Akbal &c. If the intention was to have the series terminate with the end of the respective years, then these years must necessarily have been 2 Ix, 2 Cauac, 2 Kan, and 2 Muluc. I must confess that this explanation is not satisfactory; it is thrown out simply as a suggestion.
Running through the middle division of Plates 30 and 31 is this series:
3, VIII; 3, VIII; 3, VIII; 3, VIII 5, Oc 5, Men 5, Ahau 5, Chicchan.
Commencing with 8 Oc (omitting for the present the 3 and 5 to the left) and counting thence 3 months and 5 days we reach 8 Men; 3 months and 5 days more and we reach 8 Ahau; 3 months and 5 days more bring us to 8 Chicchan, and 3 months and 5 days more bring us again to 8 Oc, thus completing a cycle of 260 days (13 months) and also accounting for the first pair of numerals--3 and 5 in the series. It appears to be a pretty general rule to commence a series of this type with the difference between the numbers of the series. One reason for this is apparent: that is, to complete the cycle of 260 days, to which most, if not all, of these groups appear to refer.
Dr. Forstemann says in regard to this line:[293-1]
This is the place where I first discovered how numbers of several figures are to be read; here for the first time I understood that the figure 3 with 5 below it is nothing but 3 20 + 5, or 65, and that they mean nothing else than the interval between the days, such as we have frequently met with so far; 4 65 is again the well known period of 260 days.
Plate 3 appears to be isolated and unfinished; at least it presents nothing on its face by which it can be directly connected with any other plate of the codex, notwithstanding the change made by Dr. Forstemann, by which 45 was brought next to it. The day column in this case is in the middle compartment of the upper division and consists of the following days: Ahau, Eb, Kan, Cib, Lamat; the red numeral over it is I. The numerals and days are arranged as follows:
(?) (?) 4, V(?) 15, XIII
I Ahau 8, XIII Eb Kan Cib 14 (?) Lamat
As numerals belonging to two different series are never found in the same compartment it is fair to a.s.sume that those of the middle and right compartments pertain to one series. But what shall we say in reference to those in the left compartment, the upper pair of which is almost entirely obliterated? So far we have found no series extending to the left of the day column. Is this an exceptional case? I am inclined to believe it is, for the following reasons:
Taking the 4, V over the bird as the first pair of the series, we have I + 4 = V, which is so far correct; after this follows the pair in the lower left hand corner, 8, XIII, as V + 8 = XIII. It is probable that the obliterated pair in the upper left hand corner followed next, then the pair in the upper right hand corner, and last the partly obliterated one in the lower right hand corner. In this case the obliterated pair in the upper left hand corner should be 11, XI, as XIII + 11 - 13 = XI, and XI + 15 - 13 = XIII, and XIII + 14 - 13 - 13 = I, which makes the terminal red number of the series the same as that over the day column. This restoration requires no change of any of the numbers which can be distinctly read. By adding together the black numbers 4, 8, 11, 15, 14, the sum is found to be 52, precisely the interval between the days of the column. These facts are sufficient to render it more than probable that the restoration and the order as here given are correct. The series as thus given, including the number over the day column, is: I; 4, V; 8, XIII; 11, XI; 15, XIII; 14, I.
This is repeated, because on turning to Dr. Forstemann"s comment on this series I find that he has restored and amended it so as to read thus: I; 10, XI; 4, V; 15, XIII; 9, XIII; 14, I; and he remarks that all would be plain sailing if, for the V before and the XIII after 15, we could read II and IV. This is true, but these numbers are too distinct to justify such change; moreover his "9" is not to be found on the page; it is true that the three dots over the line are not exactly s.p.a.ced, but there are no indications of a fourth; the number is 8 and should, I think, be so read. His 10 is the obliterated black numeral; of course the value attributed to it depends upon the order given to the series. The fragments remaining of the red number of this pair I think warrant his making it XI.
Plates 46, 47, 48, 49, and 50 are peculiar and seemingly have no direct relation to any other part of the codex. In the upper left hand corner of each are four day columns, all more or less injured, but each column evidently contained, originally, thirteen days, or, more correctly speaking, the symbol for one day repeated thirteen times. In every case the day in the first (left hand) column and that in the third column are the same. As the numbers attached to them are absolutely unreadable in Kingsborough and much obliterated in the photograph, I give here restorations for the benefit of those studying this codex. This restoration is easily made by finding the order of the series, which can be obtained from Plates 49 and 50 of the photographic copy.
_Plate_ 46: III Cib. II Cimi. V Cib. XIII Kan.
XI Cib. X Cimi. XIII Cib. VIII Kan.
VI Cib. V Cimi. VIII Cib. III Kan.
I Cib. XIII Cimi. III Cib. XI Kan.
IX Cib. VIII Cimi. XI Cib. VI Kan.
IV Cib. III Cimi. VI Cib. I Kan.
XII Cib. XI Cimi. I Cib. IX Kan.
VII Cib. VI Cimi. IX Cib. IV Kan.
II Cib. I Cimi. IV Cib. XII Kan.
X Cib. IX Cimi. XII Cib. VII Kan.
V Cib. IV Cimi. VII Cib. II Kan.
XIII Cib. XII Cimi. II Cib. X Kan.
VIII Cib. VII Cimi. X Cib. V Kan.
_Plate_ 47: II Ahau. I Oc. IV Ahau. XII Lamat.
X Ahau. IX Oc. XII Ahau. VII Lamat.
V Ahau. IV Oc. VII Ahau. II Lamat.
XIII Ahau. XII Oc. II Ahau. X Lamat.
VIII Ahau. VII Oc. X Ahau. V Lamat.
III Ahau. II Oc. V Ahau. XIII Lamat.
XI Ahau. X Oc. XIII Ahau. VIII Lamat.
VI Ahau. V Oc. VIII Ahau. III Lamat.
I Ahau. XIII Oc. III Ahau. XI Lamat.
IX Ahau. VIII Oc. XI Ahau. VI Lamat.
IV Ahau. III Oc. VI Ahau. I Lamat.
XII Ahau. XI Oc. I Ahau. IX Lamat.
VII Ahau. VI Oc. IX Ahau. IV Lamat.
As the arrangement and the order of the series are readily seen from the two examples given, only the top and bottom lines of the remaining series will be presented.
_Plate_ 48: I Kan. XIII Ix. III Kan. XI Eb.
* * * * * * * [TN-4]
VI Kan. V Ix. VIII Kan. III Eb.
_Plate_ 49: XIII Lamat. XII Ezanab. II Lamat. X Cib.
V Lamat. IV Ezanab. VII Lamat. II Cib.
_Plate_ 50: XII Eb. XI Ik. I Eb. IX Ahau.
IV Eb. III Ik. VI Eb. I Ahau.
A careful examination of these groups will bring to light the following relations of the numbers, days, columns, and series to one another:
The numerals of any one column, counting downwards, differ from one another by 8; that is to say, by adding 8 to any one and casting out 13 when the sum exceeds that number, the next lower number will be obtained; or, reversing the operation and counting upward, the difference is found to be 5. The true interval between the days of the columns (counting downwards) is 3 months (60 days), a rule which holds good as to all the series and each column. Thus, from 3 Cib to 11 Cib is 3 months, or 60 days; from 11 Cib to 6 Cib, 3 months; from 2 Cimi to 10 Cimi, 3 months, and from 13 Kan to 8 Kan, 3 months.
Counting on the list of the days of the month, without reference to the week numbers attached to them, it will be found that from Cib to Cimi is an interval of 10 days, and from Cib to Kan is an interval of 8 days.
This rule holds good as to all the series, showing that all are arranged upon precisely the same plan. The true interval between any day of the first column of either series (the week number attached being considered) and the opposite or corresponding day in the second column, is 4 months and 10 days, that between the corresponding days of the second and third columns is 12 months and 10 days, that between the days of the third and fourth columns is 8 days, and that between the corresponding days of the fourth or last column of one series or plate and the first column of the following series or plate (taking the plates in the order they are paged) is 11 months and 16 days.
In order to ill.u.s.trate this we will run through the lowest line of each series, taking them in the order of the pages.[296-1]
These are as follows:
_Plate_ 46: VIII Cib. VII Cimi. X Cib. V Kan.
_Plate_ 47: VII Ahau. VI Oc. IX Ahau. IV Lamat.
_Plate_ 48: VI Kan. V Ix. VIII Kan. III Eb.
_Plate_ 49: V Lamat. IV Ezanab. VII Lamat. II Cib.
_Plate_ 50: IV Eb. III Ik. VI Eb. I Ahau.
[Ill.u.s.tration: FIG 362. Copy of Plate 50, Dresden Codex.[TN-5]]
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.