Part 5

The subject now passes into the province of astronomy. This is already proved by sign 1, which represents the clouds, between which the sun or moon is usually pictured; the sun is probably omitted here merely owing to limited space. Sign 3 suggests the storm-god K (compare pages 7a and 47 left) to which in 2 the Ahau might be appropriately added, inasmuch as it rules the year here under consideration as on pages 25b to 26c. On account of the Ben-Ik sign I see in 4 one of the months of 28 days as a more exact determination of time. Below the Ben-Ik a head is represented with eyes apparently closed, and this head is repeated in 6 and 10, though, probably for lack of space, without the Ben-Ik. In each of the three places a sign is used as an affix which might readily be the year sign, contracted laterally.

The two similar hieroglyphs 5 and 9, which have the following form, are especially worthy of consideration:--

The part on the right recalls by its trisection the sign _r_, which I regard as the week of 13 days and, in fact, the interval between the two hieroglyphs is 13 days. On the left is the inverted figure of a person in a squatting attitude, the head surrounded by stars as on pages 57b and 58b and a sign on the back which may be a suggestion of the sun-glyph. In this figure, which occurs also in the Tro-Cort. and in the inscriptions, I see the planet Mercury and I believe that that planet's retrogression (which lasts 17-18 days) or disappearance into the light of the sun during this week, is the subject of this passage. 7 and 8 are the sign for D with the usual Ahau, and 11 and 12 are the hieroglyphs of the death-god A.

Instead of three pictures there is only one here, viz:--a woman with nose-peg, sitting on a mat and apparently waiting for something. We also find figures sitting on mats elsewhere, for example on pages 7b and 68b.

Page 21b.

VII VII 7 I 7 VIII 7 II 5 VII Oc Ahau Cib Cimi Ik Eb Lamat Ezanab Ix Kan.

This is also a Tonalamatl of 10 parts (10 × 26). The first column should be read first from top to bottom and then the second. The days are exactly the same as on page 21a, and here too Cimi and Eb have changed places.

The hieroglyphs run thus:--

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

The signs forming the hieroglyphs into groups are, in addition to the cross in 2, 6, 10 and 14, the heads in 1, 5, 9 and 13 with an Akbal sign (indistinct in 9) which, by the lock of hair in 5, 9 and 13, refer to a woman. This lock of hair is replaced by a hand in 1.

Sign 3, with which _m_ in 4 is associated as a determinative, shows that the first group ought to have a picture of the black god L grouped with a female figure.

The second group is the only one with a picture. On the right there is a female figure, which, judging by the headdress, we have already met on page 19a. Opposite her sits the dog which we saw on page 13c. Here (in sign 7), as on page 13c, the hieroglyph of the dog is combined with a Cimi sign, and this hieroglyph is repeated in 8 with the sign _c_, which is so closely allied to Cimi.

For the third group the god A should have been represented with the woman, as is proved by sign 11 so peculiarly combined with _r_ as a superfix. To this hieroglyph _a_ is added, doubtless referring to the good days, as if merely to fill space.

The hieroglyphs of the fourth group do not, I think, convey a clear idea as to which deity belongs here. His sign is 15, which is compounded of Manik and Chuen with a superfix, nor does the Cimi added in 16 shed light on the subject. As for 15 we have already found it on page 13c with the prefixed 4, which I find prefixed in this way in at least 12 different signs.

Pages 21c--22c.

Caban 5 21 16 10 Muluc Imix Ben Chicchan.

This is a Tonalamatl of five parts in which the red numerals are wanting.

The hieroglyphs are in the following order:--

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

Among these are hieroglyphs which are common to all the groups:--the cross in 1, 5 and 9 and the woman in 3, 7 and 15. In 13 this cross is replaced by another sign, perhaps that for the year of 360 days, and in 12 the sign for woman is replaced by the universal a.

Each of the three pictures contains a woman facing a deity. I will consider first the second picture in which H is the deity, as is proved by hieroglyph 6 to which an Imix is added in 8, with the uplifted arm prefixed as in 10c and 13a.

Between the first and third pictures there is some confusion. The first is D, for while his type inclines more to that of N, the other old god of the Maya Olympus, comparison with 23c clearly shows that D is intended here. But the year-sign on his head also suggests in some measure the Uayeyab god N and moreover this sign does not belong to D and only occurs again with him on page 23c. Further, there is no hieroglyph at all for D and instead we find in 2, 5 Zac, the regular sign of N. Also sign 4 fits N better than it does D. Furthermore this passage relates to the day Ik, which might very well be the last day of the year.

On the other hand the third picture contains, unquestionably, the figure of N. I look for his sign in the 11th hieroglyph, which is the head of an old man with a prefixed 4, referring to the four different forms of N in the Kan, Muluc, Ix and Cauac years. The Ahau in 12, however, does not fit N, but D.

This confusion can only be adjusted by transferring D from the first group to the third and also, perhaps, the sign of the woman in 3, which applies to all the three groups, and by transferring to the first group N and the 11th sign of the third group.

The fourth group has no picture. It should have, as hieroglyph 14 shows, the god F, who represents death by violence in human sacrifice and the chase. The hieroglyph Cimi in the 16th place is a suitable sign for this deity.

Pages 22c--23c.

II 10 XII 12 XI 9 VII 6 XIII 7 VII 8 II Oc Ik Ix Cimi Ezanab.

The hieroglyphs are arranged in the following order:--

1 2 5 6 9 13 14 17 18 21 22 3 4 7 8 10 15 16 19 20 23 24. 11 12

This Tonalamatl, the fifth and last of this section, presents much that is irregular and puzzling.

It can hardly be said that there are comprehensive hieroglyphs here, forming the heading of the six groups. The sign for woman occurs only in 2, 8 and 24, and the cross _b_ only in 14 and 18, but it is sufficient to make it clear that here, too, connection with a woman is the principal theme. Let us pass, therefore, directly to the single groups.

The first group contains A and a woman. The god, however, is not facing the woman but sits beside her. The Cimi sign in 1, the familiar _c_ in 3 and the unknown sign in 4 (=6) hardly explain this particular proceeding.

The second group contains two persons who sit facing each other, but the representation is so obscure and peculiar that it is difficult to determine which is the male figure and which the female. The hair of the person sitting on the right stands up in a manner not found elsewhere. It forms a figure similar to that which is issuing from the mouth of the dog on pages 13c and 21b. The Cimi sign in 5 and the sign _c_ in 7 are familiar, but the infrequent 6=4 remains a puzzle.

Uncertainty regarding the third group is increased by the fact that there is no picture belonging to it. The well-known signs, 10 (Cimi) and 12 (_q_) afford no explanation, nor does the head with the uplifted arm in 11, which we find with the same hieroglyph on pages 8a and 36a. The most puzzling is the 9th sign, which is composed of two crouching persons leaning back to back, and who also appear in the astronomical sections of the Manuscript on page 68a, not merely in the form of a hieroglyph, but also carried out in a picture. In my article on the Maya chronology published in the Zeitschrift für Ethnologie of the year 1891, I attempted to explain this Janus picture as meaning the change of the year, but that interpretation would make no sense here.

The fourth group contains the woman opposite D, who is clad in the gala mantle and has on his head a bird and apparently the sign for a year, and is designated by the Ahau in 16, while Imix-Kan in 13, _b_ in 14 and _a_ in 15 are rather meaningless.

The fifth group represents the woman united with A, who is designated by the Cimi sign in 17. 18 with its _b_ and 19 with its _q_ display little that is characteristic, _r_ in 20, which I think is the sign for the week of 13 days, invites further study. The sixth picture, which is the last, is very peculiar; it represents three women sitting side by side denoting perhaps the virgins who still remain. Sign 21 as Imix-Kan, 23 as _a_ and 24 as sign of femininity supply nothing in the way of explanation. As 6, 9 and 20 are the characteristic signs in the preceding groups, so here the characteristic sign is 22--an open hand holding the day Ben--which perhaps designates these virgins by referring to the house in which they are held fast by the hand. Cf. Tro. 23* d.

Now of the entire woman section closing with page 23 only the two Tonalamatls on pages 22b-23b remain. These Tonalamatls again display very many peculiarities and seem to be but loosely connected with the five Tonalamatls last discussed.

Page 22b.

III 13 III 13 III 13 III 13 III Akbal Men Manik Cauac Chuen.

This is a regular Tonalamatl, in which the 52 days are divided into four equal parts.

The hieroglyphs are in the following order:--

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

An Ahau is added here as the 17th sign, which is very unusual.

We find elements here forming the hieroglyphs into groups in three different ways.

1. The signs 1, 5, 9 and 13 designate the four cardinal points as they so often stand together in this Manuscript in the order of East, North, West and South, _i.e._, in the sequence of the annual and not of the diurnal course of the sun.

2. The hieroglyphs 2, 6, 10 and 14 are all alike and are the head with the Akbal eye, which in 6 is closed.

3. The three persons pictured here all carry a Kan sign in their hands, probably as the offering they have received. Similarly we found the Kan sign held in the hand twice on page 16b.

The first picture is B; his sign is the third with the _q_ in 4 as a determinative, which has above it a Ben-Ik sign.

The second figure is a goddess with a serpent as head-ornament, though we find in the 7th sign, not her hieroglyph, but merely the one generally used to denote a woman. 8 is the usual _a_, which in my opinion is the sign for the _good_ days, to which also the Kan sign refers in the hands of the three personages.

The third picture is that of the sun-god G; his hieroglyph is the 11th, to which in 12 is added the sign _q_, the sign for the bad days, with a superfix.

The fourth picture is wanting. According to the 15th hieroglyph it should be the maize deity E. My theory that 16 is the sign for the week of 13 days is supported by the fact that the division into 4 × 13 days is the prevailing one.

Page 23b.

VIII 12 VII 12 VI 12 V 12 IV 12 III 5 VIII Kan Muluc Ix Cauac Lamat.

This is a Tonalamatl of 4 × 65 days divided as evenly as possible into 5 × 12 + 5. The 5th day added after the 16th must be a mistake (suggested by the 5th day of the last section) for it is usually the first of the days, which is repeated superfluously.

The hieroglyphs are:--

1 2 7 11 15 19 23 3 4 8 12 16 20 24 5 6 9 13 17 21 25 10 14 18 22 26.

Contrary to practice the first section has six hieroglyphs, and the other five but four each.

As the characteristic hieroglyph we find in 1, 7, 11, 15, 19 and 23 a sign, the meaning of which is still undetermined and which we shall meet again on page 60, where it may refer to darkness.

The groups have in common, furthermore, the head without an underjaw and the hair gathered up in a tuft in 4, 10, 14, 22 and 25 (in 18 perhaps represented by _q_, the evil days). We shall find this sign on pages 25, 28, 30-35, 42-44 and 65-69, repeated a number of times in many instances. I consider it the sign for fast-days. It appears also in the Tro-Cort. Associated with this sign here as in other passages are the four sacrifices derived from the animal kingdom:--a haunch of venison, a bird, an iguana and a fish. The fish is beyond doubt denoted by 3, the mammal by 21 and the bird by 13, and I believe, therefore, that the iguana with its spiny back is denoted by 9. We find the four animals, though in a different order, also on pages 29b-30b, 30b-31b and 40c-41c, as well as in Cort. 3-6 and 8, for example. They seem to have a certain reference also to the four cardinal points.

Only the first of the six groups has a picture (I?). This represents a woman with a serpent in her hair, holding in her hand a dish containing a fish. The woman is denoted by the fifth hieroglyph and the fish by the third. The 6th sign is an Ahau, which is not quite intelligible here. Sign 2=5 Zac is very remarkable; it is the hieroglyph of the Uayeyab days and of their god N. If this Ahau refers, as it often does, to the god D, it suggests the relation between D and N, which follows from page 21c.

According to the 8th sign, the second group might refer to the serpent deity H, and the 9th sign would not improperly denote the iguana.

In the same way sign 12 in the third group probably denotes the storm-god K, with whom the bird in 13 accords very well.

In the fourth group both the animal and the sign of fasting, belonging to it, are wanting, while 16 and 17 as well as the unlucky day in 18 clearly refer to the death-deity A.

The fifth passage belongs, as sign 20 shows, to the maize deity E and to this is added the haunch of venison in 21.

In the sixth group we recognize Imix-Kan, the sign for food derived from the vegetable kingdom. It stands beside the grain-deity E of the fifth group. I do not understand the vulture-head in 26.

The five deities specified here may be compared with those on page 24, which are denoted by hieroglyphs 21-25 of the second column, though the agreement is not perfect.

This ends the first great section of the Manuscript, in which Tonalamatls are represented in uninterrupted succession. We come now to a page which stands quite alone, being the first which treats of astronomy and which ends the front of the first part of the Manuscript.

Page 24.

In my article "Zur Entzifferung IV" I discussed this remarkable page in detail and in what follows I shall conform to that treatise, though omitting many things which since then have become the established possession of science, and shall endeavor to shed a still clearer light upon other points.

This page presents in brief the subject which is more fully treated of on the front of the second part of the Manuscript (pages 46-60).

The first problem it presents is to find periods in which the solar year (365 days) is brought into accord with the apparent Venus year (584 days). This takes place in a term of 2920 days = 8 × 365 = 5 × 584. Sequent to this is the still higher aim of bringing the Tonalamatl (260) into harmony with this period, which is accomplished in 37,960 days (= 146 × 260 = 104 × 365 = 65 × 584).

The revolution of the moon (28), the ritual year (364 = 28 × 13) and the apparent revolution of Mercury (115) come in question as secondary matters.

I will now give an approximate reproduction of the page:--

Hieroglyphs.

1 17 29 151,840 113,880 75,920 37,960 2 18 30 (4 × 37,960) (3 × 37,960) (2 × 37,960) (13 × 2920) 3 19 31 I Ahau I Ahau I Ahau I Ahau

4 20 32 185,120 68,900 33,280 9100 5 21 33 I Ahau I Ahau I Ahau I Ahau

6 22 34 35,040 32,120 29,200 26,280 7 23 35 (12 × 2920) (11 × 2920) (10 × 2920) (9 × 2920) 8 24 36 VI Ahau XI Ahau III Ahau VIII Ahau

9 25 37 23,360 20,440 17,520 14,600 10 26 38 (8 × 2920) (7 × 2920) (6 × 2920) (5 × 2920) 11 27 39 XIII Ahau V Ahau X Ahau II Ahau 12 28 40 13 11,680 8,760 5,840 2920 14 (4 × 2920) (3 × 2920) (2 × 2920) VII Ahau XII Ahau IV Ahau IX Ahau 15 16 2,200 1,366,560 1,364,360 IV Ahau I Ahau I Ahau 8 Cumhu 18 Kayab 18 Zip.

First let me observe that I have restored the four large numbers at the top, which are almost entirely effaced, as follows:--

1 15 10 5 1 16 10 5 1 6 16 8 14 0 0 0. 0

And furthermore, at the right, bottom, I have substituted the third month for the second of the Manuscript, which proceeding will be justified later on.

The least difficult portion of the contents of this page is the first series consisting of 16 members, each being a multiple of 2920. It begins with the date I Ahau (which is always concealed in these series), regularly stops at the month day Ahau (since 2920 = 146 × 20), but necessarily advances in the week days by 8 days each (since 2920 = 224 × 13 + 8), until 37,960 is reached, when the day I Ahau again appears (since 37,960 = 146 × 260).

According to my method of filling in the numbers, the top row of the page consists only of multiples of 37,960.

On the other hand, the four numbers of the second row from the top are more difficult. They are, it is true, all divisible without remainder by 260, but otherwise they seem to be without rule, and they give one somewhat the impression of a subsidiary computation such as one might jot down on a slip of paper in the course of some important mathematical work.

Nevertheless, the following remarkable results are obtained when the first and third and the second and fourth numbers are combined by addition or subtraction:--

1) 185,120 + 33,280 = 218,400, which is just 600 years of 13 × 28 = 364 days, 280 Mars years of 780 days, 840 Tonalamatls of 260 days or 7800 months of 28 days.

2) 185,120 - 33,280 = 151,840, _i.e._, precisely the highest number of the top row, = 416 solar years of 365 days each or 260 Venus years of 584 days each, _i.e._, the product of the days of the Tonalamatl multiplied by the Venus years. We shall again find the 151,840 on page 51, and Seler ("Quetzalcoatl and Kukulcan," p. 400) finds this same period on a relief of Chichen Itza.

3) 68,900 + 9100 = 78,000, _i.e._, 100 Mars years or 300 Tonalamatls. The half of this number, or 39,000, we shall find again on pages 69-73 by computation; also the whole 78,000.

4) 68,900 - 9100 = 59,800, _i.e._, 520 Mercury years of 115 days, or 230 Tonalamatls, or five times the period of 11,960 days, in which these two periods are united. By computation again we find the 59,800 on page 58. This period of 11,960 days is, however, to the period of 37,960 in the proportion of 23:73, _i.e._, 23 × 520:73 × 520. 23 is the fifth part of the apparent Mercury year, as 73 is of the solar year.

Let us now turn to the numbers, which form the bottom of my transcription, but only the left hand lower corner in the Manuscript. Here, in the latter, we find the following (with the correction already mentioned of the second to the third month):--

2200 1,366,560 1,364,360 IV Ahau I Ahau I Ahau 8 Cumhu 18 Kayab 18 Zip.

The first thing to be done is to arrange and fill out these numbers to suit our purpose.

The 2200 is clearly nothing more than the difference between the two high numbers. We can therefore dispense with it.

Further, we find by the usual computation, that the second number belongs to the first date and the third to the second. Hence the number corresponding to the third date is wanting from lack of space. This number can be calculated from that date; it is 1,352,400. It would suit this date equally well if the number were higher or lower by 18,980 or a multiple of 18,980; but it will be seen directly that it agrees with the other two numbers only at the value given above.

Now, if we add to this passage the years in which the dates must lie, they are in the case of the date on the left, the year 9 Ix, in the case of the middle date, the year 3 Kan, and of that on the right hand, the year 10 Kan.

Then if we arrange the three numbers with the dates and years belonging to them, according to the value of the first, this part of the page will run as follows:--

1,352,400 1,364,360 1,366,560 I Ahau I Ahau IV Ahau 18 Zip 18 Kayab 8 Cumhu 10 Kan 3 Kan 9 Ix.

Let us now consider the properties of the three numbers individually.

1) 1,352,400 = 28 × 48,300 and = 115 × 11,760, hence it is divisible by the month days of the year of 364 days and by the Mercury year. At all events this is the least important of the three numbers.

2) 1,364,360. This looks as if it referred particularly to the moon and to Mercury; to the latter since it is equal to 115 × 11,864, and to the former if we assume that the lunar revolution has been fixed at 29-2/3 days, in which case this number is exactly equal to 46,000 such lunations. If this last number be again divided by 115, the number of days required for a revolution of Mercury, the quotient is 400, which is a round number in the vigesimal system and which was therefore denoted by a single word, by Bák in the Maya (according to Stoll) and by Huna in the Cakchiquel (according to Seler). 1,364,360, therefore, is a Huna of lunar revolutions multiplied by the number of days in the Mercury period. Later on we shall find the lunar revolution fixed at 29-2/3 days.

3) 1,366,560. This is the most comprehensive number of the entire Manuscript, for it is divisible into each of the following periods:--Those of the Señores de la noche or Lords of the Cycle (9 × 151,840; this is, however, the first number of the top row), the Tonalamatls (260 × 5256), the old official years (360 × 3796), the solar years (365 × 3744), the Venus years (584 × 2340), the Mars years (780 × 1752), the Venus-solar periods (2920 × 468), the solar year-Tonalamatls (18,980 × 72), the Venus, solar, Tonalamatl periods (37,960 × 36), and the periods which are generally designated Ahau-Katuns (113,880 × 12).

We have next to consider the intervals which elapse between the three dates.

1) From 1,352,400 to 1,364,360 is 11,960 days, which period we have already found once on this page by computation. 11,960, however, is equal to 104 × 115 and 46 × 260, _i.e._, the Mercury revolution and the Tonalamatl combined. 11,960 is again equal to 32 × 365 + 280, and from the year 10 Kan to 3 Kan it is actually 32 years, and from the date 18 Zip to 18 Kayab it is, in fact, 280 days. The day I Ahau must be common to both dates.

2) From 1,364,360 to 1,366,560 is 2200 days, as the Manuscript expressly states. 2200, however, is equal to 8 × 260+120, and the distance from the day I Ahau to IV Ahau is in fact exactly 120 days. Further 2200=6 × 365+10; from the year 3 Kan to 9 Ix it is 6 years and from the date 18 Kayab to 8 Cumhu it is 10 days.