Commencing with the day column in the middle of Plate 35_b_ and extending through Plates 36_b_ and 37_b_ to the right margin of the latter, is a line of alternate red and black numerals, which may be taken as an example of the most common series found in the Dresden and other codices.
It is selected because it is short, complete, and has no doubtful symbols or numerals in it.
Using names and numbers in place of the symbols, it is as follows:
I.
Caban, 11, XII; 6, V; 9, I; 4, V; 7, XII; 9, VIII; 6, I.
Muluc.
Ymix.
Been.
Chicchan.
In this case the red numeral over the day column is I. It is to be observed that the last number of the series is also I, a fact which it will be well to keep in mind, as it has an important bearing on what is now to be presented. But it is proper to show first that this series is continuous and is connected with the day column.
Adding the I over the column to the 11, the first black numeral; gives XII, the red numeral following the 11. That this holds good in all cases of this kind will become apparent from the examples which will be given in the course of this discussion. Adding together the remaining pairs, as follows: XII + 6 - 13 = V; V + 9 - 13 = 1; 1 + 4 = V; V + 7 = XII; XII + 9 - 13 = VIII; VIII + 6 - 13 = I, we obtain proof that the line is one unbroken series. It is apparent that if the black numerals are simply counters used to indicate intervals, as has been suggested, then, by adding them and the red numerals over the column together and casting out the thirteens, we should obtain the last red number of the series. In this case the sum of the numbers 1, 11, 6, 9, 4, 7, 9, 6, is 53; casting out the thirteens the remainder is 1, the last of the series. If we take the sum of the black numbers, which in this case is 52, and count the number of days on our calendar (Table II) from 1 Caban, the fourteenth day of the first month of the year 1 Kan, we shall find that it brings us to 1 Muluc, the sixth day of the fourth month; 52 days more to 1 Ymix; 52 more to 1 Been, and 52 more to 1 Chicchan, thus completing the day column in the example given. This proves, in this case at least, that the red numeral over the day column applies to all the days of the column and that the whole numeral series--that is to say, the sum of the counters--represents the interval between the successive days of the column. The total number of days from 1 Caban, first of the column, to 1 Chicchan, the last, is 208. Adding 52 more gives 260 and brings us back to 1 Caban, our starting point.
It will be observed that the sum of the black numbers--which denotes the interval between the days of the column--is 52, which is a multiple of 13, the number of days in a Maya week. It follows, therefore, that so far as this rule holds good the last red numeral of the series must be the same as that over the day column. In a former work[282-1] I explained the method of ascertaining the relations of the days of a column to one another by means of the intervals without reference to the numbers attached to them, a subject to which Charency had previously called attention;[282-2] by the explanation now given we ascertain the true intervals between the days _as numbered_. The two modes therefore form checks to each other and will aid very materially in restoring obliterated and doubtful days.
There is another point in regard to these series which may as well be ill.u.s.trated by means of the example given as any other. What is the signification of the red numerals of the series? They are unnecessary if the only object in view was to indicate the intervals between the days of the column. Nor will the supposition that the Mayas had not discovered a means of representing higher numbers than 20 suffice, as the introduction of 13 would have lessened the labor and shortened the calculation. But one answer to this inquiry appears possible, viz, that these numbers are intended to denote certain intermediate days to which importance was for some reason attached. These intermediate days can readily be determined from the data given, and in the present example are as follows:
(1) Between 1 Caban and 1 Muluc they are 12 Lamat, 5 Ix, 1 Akbal, 5 Manik, 12 Ix, and 8 Akbal.
(2) Between 1 Muluc and 1 Ymix they are 12 Ahau, 5 Cimi, 1 Men, 5 Cauac, 12 Cimi, and 8 Men.
(3) Between 1 Ymix and 1 Been they are 12 Eb, 5 Ezanab, 1 Manik, 5 Chuen, 12 Ezanab, and 8 Manik.
(4) Between 1 Been and 1 Chicchan they are 12 Kan, 5 Oc, 1 Cauac, 5 Akbal, 12 Oc, and 8 Cauac.
These, as will be readily perceived, are found by counting on the calendar from 1 Caban, 1 Muluc, &c., as heretofore explained.[283-1]
Our interpretation of the series of this particular cla.s.s is now complete, except as to their application or the object in view in forming them and the determination of the particular years to which they apply.
Possibly they may be of general application, so far as consistent with the calendar system. The conclusion on this point depends largely upon the conclusion as regards the system, as it is evident their location in time--if the year of 365 days and the four series of years formed the basis of the system--would not correspond with their position in a system based upon the year of 360 days, in which the four year series does not play any necessary part.
Dr. Forstemann calls attention to the fact that the pairs of numerals representing the intermediate days are usually placed in separate compartments, each containing a figure or a picture generally symbolic or of a priest dressed to indicate some particular G.o.d. It is therefore very probable that these intermediate days are to be devoted to ceremonies relating to the divinities or subjects indicated by these figures.
In order to confirm the theory we are now discussing and at the same time show some of the different varieties of the series of the type now under consideration, the following additional examples are given.
In the middle division of Plate 5 is a day column and a numeral series, as follows:
I.
Manik } Cauac } 16, IV; 9, XIII; S + 5, XII; 2, I.
Chuen } Akbal Men
This series terminates with I, as it should according to the theory. The sum of the black numerals--16, 9, 20, 5, 2--is 52, a multiple of thirteen, and the interval between the successive days, reading downwards, is 52, agreeing in these particulars with the theory. It will also be observed that the symbol represented by S answers to the number 20.
In the lowest division of the same plate is another similar series, as follows:
XII Ezanab } Akbal } 20 + 9, II; 11, XIII; 18, V; 7, XII.
Lamat } Been Ezanab
This terminates with XII, the number over the column; the sum of the black numbers is 65, a multiple of thirteen and precisely the interval between the successive days of the column, taking the week numbers into consideration, which is always to be understood in speaking of these intervals unless the contrary is expressly stated.
[Ill.u.s.tration: FIG. 361.]
In the middle division of Plate 8 is a short series connected with a day column containing the following days, reading downwards, as usual: Manik, Cauac, Chuen, Akbal, Men. The symbol for Akbal (Fig. 361), is a very unusual one, reminding us strongly of a skull, which may possibly have given origin to the symbol. The numerals of the series are as follows: 20 + 6, VIII; 20 + 6, VIII; the number over the column, VIII; and the interval between the days, 52.
In Plate 15, division _c_, is the following series, which differs from those given in having two day columns instead of one:
III III Lamat Ix Ahau Cimi } Eb Ezanab } 12, II; 14, III.
Kan Oc Cib Ik
The final number is the same as that over the columns; the sum of the black numbers is 26, which is a multiple of 13; but in this case in counting the intervals the days are to be taken alternately from the two columns.
Commencing with 3 Lamat on our calendar and counting 26 days brings us to 3 Ix; 26 more to 3 Ahau; 26 more to 3 Cimi, and so on to the end.
In the lower division of Plate 9 is a series arranged as follows:
III III VI VIII Cauac Been 3 2 {XI II Chuen Chicchan { 3 4 {VI VII Akbal Caban { 4 1 Men Muluc I III Manik Ymix 7 2
The sum of the black numerals is 26 and the final red number is III, the same as that over the columns. The interval between the days, taken alternately from the two columns, as in the preceding example, is 26. The numbers are also to be taken alternately from the two number columns.
It is apparent that these examples sustain the theory advanced. This will also be found true in regard to all the series of this type in this and the other codices where the copy is correct. Bra.s.seur"s copy of the Ma.n.u.script Troano is so full of mistakes that no satisfactory examination of this codex can be made until a photographic copy is obtained; nevertheless a few examples are given as proof of the above statement.
In the third division of Plate XI* is the following series:
IV Ahau } Eb } 17, VIII; 13, VIII; 10 V; 12, IV.
Kan } Cib Lamat
As will be readily seen, after the explanations given, this agrees with the theory advanced.
The last red number is the same as that over the day column, the sum of the black numbers is 52, and the interval between the days 52.
Commencing in the right margin of the lowest division of Plate XXIII* and running through Plates XXII* and XXI*, is the series here represented:
VII VII Cib Cimi } Ik Eb } 7, I; 7, VIII; 7, II; 5, VII.
Lamat Ezanab } Ix Kan Ahau Oc
An examination of this shows it to be of the type of the double column series of the other codex, except that here the days of one column are to be taken in the order in which they stand before proceeding to the other column. The sum of the black numbers is 26 and the interval between 7 Cib and 7 Ik 26 days. The interval between 7 Ik and 7 Lamat, 7 Lamat and 7 Ix, and between 7 Ix and 7 Ahau is, in each case, 26 days. The interval between 7 Ahau, last day of the left hand column, and 7 Cimi, the first day of the right hand column, is also 26 days.
The order in which the days of these double column series of this ma.n.u.script follow one another is not uniform, as in some cases (see Plate XXV*, division _a_) they are to be taken alternately from the two columns, as in the examples heretofore given from the Dresden Codex.
In the middle division (Plate x.x.xIII*, same codex) is a series of the following form, but with the days so nearly obliterated that restoration is necessary:
{ VI I { 5 8 I { VI I Ymix (?) { 5 8 Cimi (?) { VI I Chuen { 5 8 Cib (?) { VI I (?) { 5 8 { VI I { 5 8
The symbol of the first day has only the upper circle of dots to indicate that it is Ymix, that of the second day is almost obliterated, the third is clearly Chuen, the lower half of the fourth is obliterated, and the interior of the fifth is a blank.
Fortunately there are sufficient data by which to make the restoration.
Chuen, we observe, is the middle of the column; that is, two days are above it and two days below it; the sum of the black numerals is 65; hence the interval between the days, considering the week numbers as attached, is 65, and the simple interval in the month series, without regard to the week numbers, is 5. Counting back on our calendar (Table II) 65 days from 1 Chuen we reach 1 Cimi, and 65 more bring us to 1 Ymix. In like manner we find the fourth day to be 1 Cib and the fifth 1 Ymix. The numbers in the figure columns are to be taken alternately, thus: 5, VI; 8, I; 5, VI; 8, I, &c.