Part 18

Hieroglyph 1a admits of explanation. It consists of four parts:--the left top is Kin, meaning sun or day, the right top is the sign of the year, the right bottom is the knife as symbol of separation or division, and the left bottom, which is especially decisive, is the month Ceh. Hence I read 1a thus:--the day of the change of year in the month Ceh. The sign 1b is the familiar Kin-Akbal signifying either the beginning day or the day Akbal. If the year should be named from this sign, then this would mean a Kan year, as in the preceding section the beginning lay in the year 9 Kan. If the year in the latter section had been as equally divided as the one in question here, it would have furnished us with some very remarkable parallels.

Again the four groups:--4, 11, 18 and 25, which are alike, are important. The cross in sign _a_, combined with the three dotted lines passing from top to bottom, may refer to the wind and this meaning is further confirmed by the Ik sign (wind) in c. Further the sign _b_ between them is that for the Bacab, the wind deity itself.

The most important events of the year are obviously the sowing and harvesting of the maize together with the beginning and end of the rainy season. Now we find the first two in connection with the god E, the maize-god, who is represented in 6c and 13c, 91 days apart, corresponding to the end of May and the beginning of August. Generally speaking, sixty days only were reckoned as the time between sowing and reaping, but here a quarter of a year may have been taken as a round number and it may also have reference to a more elevated region.

I am inclined to think that the beginning and end of the rainy season are referred to in signs 8c and 16c, where, as it seems to me, three lines of drops are falling from a rectangle denoting the sky (as is usual) like the representation of rain dropping from a cloud at the bottom of page 36 (second picture). The serpent 8b as symbol of water may also refer to the same thing, especially as it is combined with an Akbal (often denoting beginning). The sign, which I think denotes the rainy season, is very similar, but not the same as another one, which is common to the Dresdensis and Tro-Cortesianus, the significance of which is certainly very close to the idea of the week of 13 days.

I have some other ideas on this subject, which, however, are mere conjectures, advanced with some hesitation. If the Chuen sign in 7a is actually a serpent's jaw, then it might refer to the beginning of the astronomical year in May, since the serpent so often designates that time.

In 9b we find a crouching figure with the sign which is usually considered that of the death-bird. In another place (Zur Entzifferung IV, 12) I have regarded the naked human figure placed upside down on page 58 as the sign for Mercury, and on page 60 at the bottom, left, I also regarded the crouching figure as representing Mercury vanquished by Venus. But in 9b, which belongs to the 105th-117th days of the year, a 115 day revolution of Mercury is computed. A crouching figure, like that in 9b, likewise appears on page 65a in the second series of 91 days after 11 + 13 = 24 days of this series have elapsed, _i.e._, directly after the 115 days of the apparent revolution of Mercury.

In 10b, and it is the only place in this passage, we find the hieroglyph of B, the leading god of this Manuscript. This corresponds with the time of the greatest power of the sun and of the change in the civil year (July 16th). In Group 12, do _a_ and _c_ mean the year and is _b_ the head with the Akbal eye, thus denoting the beginning of the civil year? It ought really to have formed group 11, but there was no room for it, since it was necessary that the signs for the period of 91 days should be set down there.

Signs 14a and the combined signs 15bc are almost alike and suggest 1a. Is it intended to designate here the ritual year, the time of the autumnal equinox (September 10th?). In 15a two hooks, turned in opposite directions proceed from one side of the sun-glyph. Do they signify two halves of the year and does the 3 in front of them signify the third quarter of the year?

20b is the sign of the death-god A, probably not placed accidentally here at the end of the month Xul, which denotes the end; but the end of what?

The hieroglyph in 23a is a black bird, with two hooks, one pointing up and the other down, projecting from its head. Usually these hooks belong to K, and by means of them this bird becomes the storm-bird; the year symbol is below. Does this hieroglyph signify the time of the shortest day, when darkness predominates?

A peculiarity of this passage is the striking frequency of the sign looked upon as that of the death-bird as well as of the cognate sign, which is commonly considered as that of the rising Moan. The first bird is in the 14th group, in the 9th it is combined with the apparent Mercury sign, and in the 17th with the year sign. The second bird with the prefixed Yax is in the 2nd group. But it is especially striking that several times both signs, and this is the case nowhere else, are combined into a single sign in groups 9, 13 and 26 and also probably in 19 where, however, the Moan sign seems to be effaced.

This is all I have to say at the present time in reference to this calendar. Some of my statements are positive and some are only conjectures. Compare my treatise "Zwei Hieroglyphenreihen in der Dresdener Mayahandschrift" (Zeitschrift für Ethnologie, 1905, 2 and 3).

Having disposed in this way of the two supplementary subjects of this section, I will now proceed to consider the principal theme, viz:--the two series and whatever is connected with them.

1. The 54-Series of the Day IX Ix.

As with the other series, we begin here at the right, _i.e._, with page 73. There in the last column we find the superscription as it were. It is true that nothing positive can be gathered from the top part consisting of five hieroglyphs, which are mostly destroyed. The third hieroglyph seems to be the sign in group 2a discussed above. The fourth is an Akbal with a prefixed arm as on pages 8a, 36a, and the fifth is an Ik with a prefix.

Below these are three numbers:--14,040, 702 and 54, which are in the proportion of 260, 13 and 1, so that the 14,040 is a Tonalamatl, as it were, of 260 periods of 54 days each. The fact that 54 is chosen here as the difference of the following series is curious, because usually only parts of 260 or of 364 are selected. But 54 is probably only a secondary matter, while 14,040, with its marvellous property of divisibility into the most varied and important periods, is the chief subject.

There is a 9 in a red circle under the three numbers. It is meant to denote the starting-point of the series, the day IX Ix. Perhaps these two as well as the 54 are connected with the 9 "señores de las noches."

In passing on to the left, I shall not consider the hieroglyphs and numbers in the next two columns in the upper third, since they are only set down here in order to secure space for them. They will be discussed later.

The series itself begins in the upper third of page 71, in the next to the last column; it is continued on page 72 and on page 73 as far as the third column. The first twelve numbers are written from left to right contrary to the usual practice, doubtless occasioned by the passage above the series, which has already been discussed. And below, again contrary to rule, we find not the week and month days, but only the week days and they are in red circles. If written in the usual way, the series would have the following form (with the usual omission of the initial day IX Ix):--

54 108 162 216 270 324 378 XI Lamat XIII Ik II Cib IV Oc VI Kan VIII Ezanab X Eb 432 486 540 594 648 XII Cimi I Ahau III Ix V Lamat VII Ik.

The series must now continue with the 702 already specified on page 73, which it proceeds to do from right to left in the middle of page 71, and continues from there on with regularly added dates and with the 702 itself as the difference. At the same time, since 702 = 54 × 13, the week-days are forced to come to a standstill on the IX, while each of the month days ascends by two (702 = 35 × 20 + 2). The 4914 = 7 × 702 is obtained in the next to the last column of page 70. On page 71 the 702 is incorrectly set down as 1. 15. 2. instead of 1. 17. 2. The series continues on page 71 in the same way beyond the 702, until in 7020 a number is obtained which is also divisible by 260, so that now the accompanying day must be IX Ix. Now we ought to expect to see here the double of 7020, the very 14,040 abovementioned, but it is omitted just because it was set down on page 73. Nevertheless this very number forms the new difference with which the series returns from page 70 to the top line of page 71, where the numbers are mostly effaced, but enough remains to enable us to assume that the last number on page 71 is the 10th multiple of 14,040, and this may be followed by the 11th and 12th multiples, the last number being 168,480.

2. The 65-Series of the Day IV Eb.

This series begins in the middle of page 73 with the day IV Caban, the zero-point therefore being IV Eb. It then advances to the left across 28 members, until on page 71 it reaches the number 1820 = 5 years of 364 days = 7 Tonalamatls. From there on, 1820 itself is the difference, and the accompanying day therefore remains IV Eb. Then, in the two lowest sections of pages 71 and 70, the fourth multiple of 1820, _i.e._, 7280, is the third difference and thus the series advances to 15 × 7280 = 109,200 on page 71, after which on page 70 the omitted 8 × 7280 = 58,240 is written out. Close beside this number are the figures 1. 0. 12. 3. and a 0 below the latter, which was not successfully erased; this would be the number 7443 of which I can make nothing at all.

The initial dates of the two series, IX Ix and IV Eb, are 138 days apart and reversely 122 days.

3. The Groups of Hieroglyphs.

The transition, as it were, from the series to the large numbers is formed by a few groups of hieroglyphs.

The first of these groups is at the top of pages 69-70; its first top line is completely effaced. The remainder I will designate by the following numbers:--

1 2 5 6 9 13 3 4 7 8 10 14 11 15 12 16.

The date IX Kan 12 Kayab, set down under 3 and 4 does not belong there but to the serpent below and will be discussed later.

I take sign 1 to be that of a Bacab, 2 I do not understand and it is half obliterated; it seems to occur again on page 73 in the column to the extreme right. 3 and 7 are the elongated head _q_ with an unusual superfix, 4 and 8 correspond with one another, but I cannot explain them. 5, 10 and 14 denote the beginning, 6, 11 and 15, the end. 9 and 13 both designate the 8th day of the month Kayab and over them IV Ahau must have been set down twice. 12 and 16 are two heads of gods, 12 is probably D's with the sign for west and 16, B's with that of the east.

On page 70, in the middle of the third and fourth columns, the day IX Ix occurs twice. In one case it ought to have been IV Eb and the scribe has really changed the IX to IV, but he omitted changing the Ix to Eb. Directly below these dates we find the second group, consisting of two rows of four hieroglyphs.

I think these eight hieroglyphs can be interpreted as follows:--

1) 13 Pax 2) 20 Pop or 25 Cumhu 3) VIII Ahau 4) 13 Yaxkin 5) 10 Muan 6) 37,960 7) 20 8) 1 Zec.

The following is to be noted in this connection:--

3 is really set down X Ahau, but an VIII is written above the Ahau by way of correction. The day VIII Ahau will presently prove to be important.

6, a compound of Imix and the superfix denoting multiplication, is the sign for 18,980, and its prefix seems to me to denote duplication. We have long known how important the 37,960 = 146 × 260 = 104 × 365 is, and, if my theory is correct, we shall see directly that it occurs again here.

8 seems really to be 1 Zec, but the composite prefixes demand further examination.

Impenetrable darkness still shrouds the meaning of the whole group. Though it is clear that in several cases certain days are specified according to their position in the year, their distance apart does not agree with the interval between days IV Eb, IX Ix and IV Ahau under discussion here.

If signs 3 and 4 ought to be read together as VIII Ahau 13 Yaxkin, then this date would come in the year 7 Muluc. In the Zeitschrift für Ethnologie I explained the five hieroglyphs in the third column at the bottom of page 70 (the third group) as civil years of 360 and astronomical years of 365 days:--

1) 8,760 = 24 × 365 = 15 × 584 2) 2,920 = 8 × 365 = 5 × 584 3) 7,200 = 20 × 360 4) 18,720 = 52 × 360 = 72 × 260 5) 360 ------ 37,960.

This, it is true, is a striking explanation and certainly a surprising one!

Now the date IX Ix 12 Kayab is at the very bottom of the fourth column. This, without apparent reason, would refer to the year 4 Kan. Should it not be read IX Kan 12 Kayab (4 Ix), thus indicating that the entire passage is only the preparation for the date from which the serpent numbers proceed? The scribe may have had in mind the IX Ix of the series.

The fourth and last group on page 73, above the two numbers 83,474 and 34,732, consists of four hieroglyphs. The two upper hieroglyphs on the left are effaced, and the top one on the right. I think it probable that the day VIII Ahau, which will be discussed later, may have stood in the top line, and possibly with a month date. Of the two remaining signs of the fourth group, the upper is the moon and the lower Imix, probably with the hieroglyph of the east as a prefix; but there is nothing to be done with it owing to the obliteration of the sign above it. In the Zeitschrift für Ethnologie, 1891, page 153, I have endeavored to explain these three signs on the right above 34,732, by suggesting for them the values

18,980 = 52 × 365 8,760 = 24 × 365 7,200 = 20 × 360 ------ 34,940

and calling special attention to the fact that between IV Eb and IV Ahau there are 208 days, and that the 34,732 placed below them in the Manuscript, increased by 208, is equal to 34,940. This group then seems really to belong to the day IV Eb and to the 65-series, while manifold problems are still to be encountered in interpreting the other groups.

4. The Large Numbers.

The Manuscript offers material with which to work, beginning on page 70:--

1,394,120 1,437,020 1,567,332 1,520,654 (606) (1646) IV Eb IX Ix IV Ahau IV Ahau VIII Ahau; 13 Yaxkin (7 Muluc). 8 Cumhu 8 Cumhu IX Ix IV Eb 1,201,200 1,202,240 111,554 101,812 (86) (208) IV Ahau IV Ahau 8 Cumhu 8 Cumhu

This is followed at the right top of page 73 by

83,474 34,732 IX Ix IV Eb.

Two of the numbers and two of the dates are conjectural:--

I read the 1,202,240 as 8. 6. 19. 10. 0. while the Manuscript has 16 instead of 6. I read the 101,812 as 14. 2. 14. 12. the Manuscript has 16 instead of the second 14. And in two places in the third column of page 70, I have restored the day IV Eb, where the Manuscript incorrectly repeats the IX Ix, and does the same thing on page 73.

Let us now first consider the construction of those large numbers, which are connected with the day IX Ix and thus with the 54-series. These numbers are the two upper ones of columns 1 and 2 and the lower one of column 1 on page 70.

174 is the starting-point, the number of the day is IX Ix, which seems to have been chosen because it divides the Tonalamatl approximately in the proportion of 2 to 1. (IV Ahau - IX Ix = 174.)

The 5359th, 5520th and 4619th multiples of 260 have been added to 174; why precisely these multiples were chosen remains a mystery. In this way were obtained the following numbers, which the Manuscript suppresses. I will give them with their corresponding dates:--

1,393,514 = IX Ix 12 Muan (5 Kan). 1,435,374 = IX Ix 17 Chen (3 Cauac). 1,201,114 = IX Ix 7 Mac (11 Muluc).

When we add to the above the three encircled numbers 606, 1,646 and 86, the resulting sums are the three numbers found in the Manuscript:--

1,394,120 = IV Ahau 8 Chen (7 Ix). 1,437,020 = IV Ahau 23 Cumhu (7 Cauac). 1,201,200 = IV Ahau 13 Kayab (11 Muluc).

I am placing the first two not far from the present and the third in the past.

As multiples of 260 these three numbers have the following form:--

1,394,120 = 5362 × 260. 1,437,020 = 5527 × 260. 1,201,200 = 4620 × 260.

Some curious facts come to light with regard to their magnitude and their mutual relation.

The two largest numbers are 165 × 260 = 660 × 65 apart; this recalls the 65-series. The third lowest number is 165 × 7280 and thus contains not only the 65 but = 165 × 65 × 112.

The ritual year (364) and its excess over the Tonalamatl (104) is likewise contained in these numbers, at least in the first and third:--

1,394,120 = 3830 × 364 = 13,405 × 104. 1,201,200 = 3300 × 364 = 11,550 × 104.

The three encircled numbers are connected with one another because the first = 2 × 260 + 86, the second = 6 × 260 + 86 and the third is 86 itself. The larger encircled numbers are, therefore, 1040 = 4 × 260 apart, and this is also the interval between the two numbers near the bottom. 1040, however, also = 5 × 208, and 208 is the interval from IV Eb to IV Ahau. Now it is curious that the two numbers below are 5775 × 208 and 5780 × 208, though the third belongs to day IX Ix and the fourth to IV Eb. One result of this is that 1,201,200 = 1155 × 1040 and 1,202,240 = 1156 × 1040.

As these three numbers relate to day IX Ix and the 54-series, so the fourth relates to IV Eb and the 65-series.

Here the starting-point is the number 52, which belongs to day IV Eb and this is separated from IV Ahau by 208 days _i.e._, it divides the Tonalamatl in the proportion of 1 to 4.

To the number 52 then, for unknown reasons was added 4623 × 260 = 1,201,980, and thus the number 1,202,032, suppressed in the Manuscript, was obtained for the day IV Eb. To this sum the encircled number 208 was then added and the result was 1,202,240, the number in the Manuscript.

The number = 23,120 × 52 = 4624 × 260, which is self-evident, but it also = 5780 × 208, _i.e._, it is a multiple of the encircled number. It consequently also = 11,560 × 104, and thus it is related to the first and third numbers just now discussed.

The position of this number is IV Ahau 18 Kankin (1 Kan) and the position of the suppressed number is IV Eb 10 Zotz (also 1 Kan).

We ought now to discuss the last two numbers of this section amounting to millions:--1,567,332 and 1,520,654, which are in the third and fourth columns at the top of page 70. But before going further, we must examine four other numbers, two of which, 111,554 and (with my correction) 101,812, are in column 4 on the lower part of page 70, and the other two, 83,474 and 34,732, are on the top of page 73. Although these four numbers are not ornamented with circles, they all have the significance of the numbers enclosed in circles and are designations of differences between suppressed and specified numbers.

Let us first of all examine their curious relation to one another:--

The Manuscript should have set down under these numbers the day IX Ix twice and IV Eb twice, from which days the numbers in question must be computed; but here the two errors already mentioned were made. 111,554 - 101,812 is 9742, the very same number which we shall afterward find as the difference of the serpent numbers on page 69.

83,474 - 34,732 = 48,742. If 9472 be subtracted from this, the remainder is exactly 39,000 = 150 Tonalamatls = 50 revolutions of Mars. I have already found this number on page 31a, and also the double of it, 78,000, on page 24, and this I found by using 68,900 + 9100 for my computation.

111,554 - 83,474 = 28,080, _i.e._, exactly the double of the important 14,040, which is recorded on page 73.

101,812 - 34,732 = 67,080, _i.e._, = 258 Tonalamatls or 86 revolutions of Mars.

111,554 - 34,732 = 76,822; if 122, the interval from IV Eb to IX Ix be subtracted from this, the remainder is 76,700 = 295 Tonalamatls.

101,812 - 83,474 = 18,338; if 138, the interval from IX Ix to IV Eb, be subtracted from 18,338, the remainder is 18,200 = 70 Tonalamatls = 50 ritual years of 364 days each, _i.e._, exactly the double of the 9100 specified on page 24.

Now we also have the following equations for the four numbers:--

111,554 = 429 × 260 + 14. 83,474 = 321 × 260 + 14. 101,812 = 391 × 260 + 152. 34,732 = 133 × 260 + 152.

A day VIII Ahau is 14 days back of the day IX Ix, and another VIII Ahau is 152 days back of IV Eb.

Thus a day VIII Ahau hitherto unmentioned is introduced into the computations. This day has no doubt been chosen, because it divides the Tonalamatl beginning with IV Ahau into two parts of 160 and 100 days, which are in the proportion of 8 to 5, _i.e._, the same proportion as the Venus year to the solar year.

This day VIII Ahau may also figure in the large numbers of the first two columns on page 70, for 1,394,120 and 1,201,200 are both divisible by 14, the interval between VIII Ahau and IX Ix.

Now I believe that the large numbers were constructed in the following twofold manner (I add the corresponding dates):--

160 1,408,940 = 5419 × 260 --------- 1,409,100 = VIII Ahau 3 Yax (9 Cauac). 111,554 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc).

160 1,437,020 = 5527 × 260 --------- 1,437,180 = VIII Ahau 18 Mol (8 Kan). 83,474 --------- 1,520,654 = IX Ix 7 Zip (3 Muluc).

160 1,465,360 = 5636 × 260 --------- 1,465,520 = VIII Ahau 8 Uo (8 Ix). 101,812 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc).

160 1,532,440 = 5894 × 260 --------- 1,532,600 = VIII Ahau 13 Pax (9 Muluc). 34,732 --------- 1,567,332 = IV Eb 5 Pop (1 Muluc).

The last record of the date of VIII Ahau seems to throw light on the date 13 Pax (page 70, column 3), which is directly above the date VIII Ahau, and which I have already mentioned in the discussion of the groups of hieroglyphs.

Indeed, it seems as if a day VIII Ahau occurred a fifth time in that passage, for in consequence of the correction made by the scribe we read here VIII Ahau 13 Yaxkin. This would point to a year 7 Muluc, the position of which between the other four is, of course, undetermined.

If the two large numbers in the Manuscript were treated in the same way as the other large numbers, they would not be recorded at all, but instead of them there would have been two numbers belonging to the day IV Ahau and under them would have been the encircled numbers 208 and 86, or these numbers increased by a multiple of 260. This passage would then read about as follows:--

1,567,540 (IV Ahau) 1,520,740 (IV Ahau) 208 (IV Eb) 86 (IX Ix).

These two numbers for IV Ahau are equal to 6029 and 5849 Tonalamatls. If 5549 × 260 be subtracted from these, the remainders are 480 and 300 Tonalamatls respectively, _i.e._, 124,800 and 78,000, and these are in the proportion of 8 to 5.

Now the two large numbers have the difference 46,678 = 179 × 260 + 138; the latter is the interval from IX Ix to IV Eb.

The four numbers of the days VIII Ahau seem to stand in very irregular relation to one another and yet they show the following striking results, if the first and third and also the second and fourth numbers be combined (as I combined them under page 24):--

In the first case we see the following:--