Part 12

Finally the six interesting hieroglyphs set down in a vertical row on the left of each of the four pages are still to be examined. I will give here in the following table what I think is a correct interpretation of them:--

Page 42. 43. 44. 45. South (1) East (7) North (13) West (9). It ends (2) (8) (14) (20) B (3) (9) (15) (21) the time of the Cauac (4), Kan (10), Muluc (16), Ix (22), while Kan (5), Muluc (11), Ix (17), Cauac (23) begins (6) (12) (18) (24).

If that which is actually set down in the Manuscript be compared with this, it will be seen that in 11 of the 24 places the Manuscript corresponds to my hypothesis:--1, 7 and 19 are the familiar signs for the three cardinal points, 8 and 20 are the sign Xul = end, which I have already frequently mentioned, 9 and 21 are the sign for B, 11 is Muluc, 23 is Cauac, where the scribe has added to the correct Kin-Cauac the sign for the year, as if the Cauac _years_ were treated of here as on pages 26 and 27. Finally the two agree in 12 and 18, where the Manuscript has the compound Kan-Imix to denote beginning, _i.e._, the two days beginning the series of twenty days, one of them according to this Manuscript, and the other according to the method resembling that used by the Aztecs.

The other cases have the correct signs, but set down in the wrong place, thus B is changed from 3 to 2, from 15 to 16, the north from 13 to 14, the Xul from 2 to 3, 14 to 15, the E (Kan) from 5 to 4 and 6 and Cauac from 4 to 5, _i.e._, pushed along every time to the next place. This is all in favor of my theory. As one series began at the top, the scribe incorrectly placed the sign for beginning in the thirteenth place.

Strange to say in the tenth place we have the very general sign _a_ in place of Kan. In the 4th, 17th and 22nd, and probably also in the half destroyed 6th sign, the scribe thoughtlessly put down a sign for E, which is proper only with Kan and should come after 5 or 10. Finally in the 24th place he put a sign for A, as if it were the intention that this passage should end exactly like its parallel on page 28. For, as a matter of fact, the two principal sections of the first part of the Dresdensis do end in a very similar way.

* * * * *

PART II.

Pages 46--74.

The first glance at the form and contents of the second part of the Manuscript shows that it is very different from the first. The pages are no longer divided into the usual three parts and there are fewer pictures. The Tonalamatls, which form the principal contents of the first part, disappear wholly, and with them both the vertical columns of day-signs and the horizontal lines of numerals alternating between red and black. On the other hand, the large number series as well as the high numbers significantly increase and we note the appearance of the large vertical columns of hieroglyphs, which were impossible in the triple division of the earlier pages. We also find a large number of hieroglyphs which did not occur in the first part. The contents are essentially astronomical.

And yet the two parts are so closely connected with one another that the idea of two independent Manuscripts must be dismissed. Especially the front side of the second part as far as page 60 is nothing more than an amplification of page 24. The contents of pages 61-74 are of a more independent nature, but special attention should be called to the relation of 31a-32a to 62-63.

Pages 46--50.

The entire contents of these pages must be represented as a unit, for what is in the main true of page 24 is also true of these pages, namely that they treat exclusively of the period of 2920 days, in which five Venus years of 584 days each are brought into accord with eight solar or terrestrial years of 365 days each. Each page is a direct continuation of the preceding one. Each period of 2920 days is taken 13 times, the result being 37,960 days, which are equal to 146 Tonalamatls.

I will give here first a reproduction, as it were, of the left side of the five pages, omitting for greater clearness a few indifferent matters, which are intended only to fill the blank spaces, viz:--

1. The twenty hands pointing to the right, with a knife placed over them, in the middle of the pages, which mean nothing more than that these parts of the Venus year are to be read from left to right.

2. The Venus hieroglyph three lines below, repeated twenty times with the sign of the knife, to denote the _division_ of the Venus revolution.

3. The _Akbal_ sign occurring further down, four times on each page, except on pages 46 and 47. This is the last of the day-signs, again counting forward from the day Kan, and means only that henceforth the _close_ of the four periods of the Venus year is indicated below, as the beginning is indicated above.

4. The sixteen Venus signs also occurring below, except on page 48. This sign likewise occurs in a very similar form on Altar R of Copan.

With these omissions, the left side of these pages presents the following appearance:--

Page 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

4 Yaxkin 14 Zac 19 Zec 7 Xul North. West South East Gods. 236 326 576 584 9[1] Zac 19[1] Muan 4 Yax 12 Yax Gods East North West South 19 Kayab 4 Zotz 14 Pax 2 Kayab 236 90 250 8

Page 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

3 Cumhu 8 Zotz 18 Pax 6 Kayab North West South East Gods. 820 910 1160 1168 3 Zotz 13 Mol 18 Uo 6 Zip Gods East North West South 13 Yax 3 Pax 8 Chen 16 Chen 236 90 250 8

Page 48.

I Kan XIII Ix III Kan XI Eb IX Kan VIII Ix XI Kan VI Eb IV Kan III Ix VI Kan I Eb XII Kan XI Ix I Kan IX Eb VII Kan VI Ix IX Kan IV Eb II Kan I Ix IV Kan XII Eb X Kan IX Ix XII Kan VII Eb V Kan IV Ix VII Kan II Eb XIII Kan XII Ix II Kan X Eb VIII Kan VII Ix X Kan V Eb III Kan II Ix V Kan XIII Eb XI Kan X Ix XIII Kan VIII Eb VI Kan V Ix XIII Kan III Eb

17 Yax 7 Pax 12 Chen 0 Yax[2] North West South East Gods 1404 1494 1744 1752 2 Pax 7 Pop 17 Mac 5 Kankin Gods East North West South 7 Zip 17 Yaxkin 2 Uo 10 Uo 236 90 250 8

Page 49.

XIII Lamat XII Ezanab II Lamat X Cib VIII Lamat VII Ezanab X Lamat V Cib III Lamat II Ezanab V Lamat XIII Cib XI Lamat X Ezanab XIII Lamat VII Cib VI Lamat V Ezanab VIII Lamat III Cib I Lamat XIII Ezanab III Lamat XI Cib IX Lamat VIII Ezanab XI Lamat VI Cib IV Lamat III Ezanab VI Lamat I Cib XII Lamat XI Ezanab I Lamat IX Cib VII Lamat VI Ezanab IX Lamat IV Cib II Lamat I Ezanab IV Lamat XII Cib X Lamat IX Ezanab XII Lamat VII Cib V Lamat IV Ezanab VII Lamat II Cib

11 Zip 1 Mol 6 Uo 14 Uo North West South East Gods 1988 2078 2328 2336 16 Yaxkin 6 Ceh 11 Xul 19 Xul Gods East North West South 6 Kankin 16 Cumhu 1 Mac 9 Mac 236 90 250 8

Page 50.

XII Eb XI Ik I Eb IX Ahau VII Eb VI Ik IX Eb IV Ahau II Eb I Ik IV Eb XII Ahau X Eb IX Ik XII Eb VII Ahau V Eb IV Ik VII Eb II Ahau XIII Eb XII Ik II Eb X Ahau VIII Eb VII Ik X Eb V Ahau III Eb II Ik V Eb XIII Ahau XI Eb X Ik XIII Eb VIII Ahau VI Eb V Ik VIII Eb III Ahau I Eb XIII Ik III Eb XI Ahau IX Eb VIII Ik XI Eb VI Ahau IV Eb III Ik VI Eb I Ahau

10 Kankin 20 Cumhu[3] 5 Mac 13 Mac North West South East Gods 2572 2662 2912 2920 15 Cumhu 0 Zec[4] 10 Kayab 18 Kayab Gods East North West South 20 Xul 10 Zac 15 Zec 3 Xul 236 90 250 8

Let us first examine the numbers which are regularly repeated in the lowest line:--236, 90, 250, and 8, and we shall find that the 584 days of the apparent Venus revolution are divided into these four periods.

The number 236 denotes the time of the western elongation, when Venus is the morning star, 90 the time of the invisibility of the planet, during its superior conjunction, 250 that of its eastern elongation, when Venus is the evening star, and 8 the time of its invisibility during inferior conjunction. The disproportion between 236 and 250 is somewhat striking. These periods which need not of course be exactly equal are usually computed at 243 days. The short period of eight days is only calculated for very sharp eyes; we actually find in the Anales del Museo Nacional de Mexico II, 341 (Mex. 1882), that the Aztecs calculated only eight days for the invisibility of Venus, and this period is also mentioned in the Anales de Quauhtitlan. The repetition of the cardinal points in the 15th and 20th lines of the extract given above refer to these periods; in the upper line to their beginning and in the lower to their close. Hence in the lower line the cardinal points must advance one place and the gods belonging to them in the 16th and 19th lines must follow the same course.

The numbers in the 17th line indicate to which day of the period of 2920 days the position has advanced.

But now we see that the indication of days in the lines 1-13, the indication of months in lines 14, 18 and 21, and the numbers in line 17 are separated from those directly to the right of them by a number of days equal to the numbers given in the lowest line.

From this it follows that each day of the thirteen top lines is joined to each of the month dates placed just below them, forming a complete calendar date. Therefore from the III Cib on the left upper corner of page 46 a III Cib 4 Yaxkin, a III Cib 8 Zac, a III Cib 19 Kayab must be formed.

All the 4 × 13 × 5 = 260 day indications combined with three month indications each, show therefore that this whole passage is a huge abbreviation for 780 calendar dates and that the whole refers to 3 × 37,960 days = 113,880 days. But 37,960 which we already found on page 24, is equal to 146 × 260, 104 × 365, 65 × 584, 13 × 2920. I am inclined to think that I also found 113,880 on page 24.

But the 3 × 37,960 = 113,880 days do not form the entire period treated of here. For the three periods begin and end with the days:--

I Ahau 13 Mac (10 Muluc), I Ahau 18 Kayab (3 Kan), I Ahau 3 Xul (4 Cauac).

Hence these three dates, the second of which was found on page 24, prove that the three periods of 37,960 are not consecutive, but that there is an interval between them. Now between the first and second of the three dates the interval is 19 years + 85 days = 7020 days, and between the second and third, the interval is 26 years + 130 days = 9620 days. If these two periods be added to the 113,880 days, the sum is the whole period treated of here, viz:-- 130,520 = 502 × 260 days.

But a truly surprising result is obtained, if, as must often be the case with series, we begin not with the upper of the three dates, but with the lower.

From I Ahau 3 Xul (4 Cauac) to I Ahau 18 Kayab (3 Kan) there is a lapse of 9360 days or 12 apparent Mars years of 780 days, such as we shall find as the principal subject of page 59. 9360, however, equals 25 × 365 + 235 days. We shall meet with this 235 again as a difference on page 63.

But from I Ahau 18 Kayab (3 Kan) to I Ahau 13 Mac (10 Muluc) there are 11,960 days, _i.e._, the 104 Mercury years, which we found on page 24, and which we shall find again as the principal period on pages 51-58. But this is equal to 32 years + 280 or 33 years - 85 days. Now if 113,880, 9360, 11,960 are added together, we have for the entire period under discussion here, 135,200 days, and this is equal to 2 × 260 × 260 days. Thus the Mayas seem actually to have had an idea of a second power.

Finally I would call attention to a singular double connection between the numbers occurring here:--

37,960 - 11,960 = 26,000 = 100 Tonalamatls, 11,960 - 9,360 = 2600 = 10 Tonalamatls.

But if we subtract 2 × 11,960 = 23,920 from 37,960, the remainder is 14,040, _i.e._, an extraordinary number which often occurs and is equal to 54 × 260, 39 × 360 and 18 × 780.

In short, a Mars and a Mercury-lunar period are inserted in the two spaces between the three solar-Venus periods.

Now, let us try to gain a clearer understanding of this subject by approaching from another side.

As we have seen, the beginning of the middle one of the three equal periods of 37,960 days, is the date I Ahau 18 Kayab (3 Kan). Now, however, page 24 furnished us with a day number for this date, 1,364,360, and from this the beginnings of the other two periods may be computed in the following way:--

I Ahau 3 Xul (4 Cauac) = 1,317,040, I Ahau 18 Kayab (3 Kan) = 1,364,360, I Ahau 13 Mac (10 Muluc) = 1,414,280.

Between the first number and the second there are 47,320 days = 2^3 × 5 × 7 × 13^2, and between the second and third 49,920 days = 2^8 × 3 × 5 × 13 days.

But, according to what has been stated above, 47,320 = 37,960 + 9360, and 49,920 = 37,960 + 11,960.

The whole period is therefore divided as follows:--

It begins with a Venus-solar-Tonalamatl-period followed by 12 Mars years, then the great period again followed by 8 × 13 = 104 Mercury years, and lastly, apparently about the present time, comes the third great period, which, as already stated, ends 135,200 days after the first date.

The case assumes a different aspect, if we insert between the three dates the other two from page 24:--

1,317,040 = I Ahau, 1,352,400 = I Ahau, 1,364,360 = I Ahau, 1,366,560 = IV Ahau, 1,414,280 = I Ahau.

Here we have again, as examination of page 24 showed, the difference 11,960 between the second and third numbers, while there is no longer any connection with the periods of 37,960 days.

Of the left halves of the pages we have now examined all except the twenty hieroglyphs of the gods. I shall mention them according to the upper place in line 16; the lower in line 19, where the hieroglyphs move forward only one place, is only referred to when the two signs differ. They offer many problems still unsolved.

The first sign on page 46 is an unknown sign, which, however, is repeated several times on the right side of the pages; the second is probably an Ahau (_i.e._, D) with a prefix suggesting the snail, the symbol of birth; the third is a head also occurring elsewhere, which I have not yet determined; the fourth is A; compare page 24, hieroglyph 25.

Page 47. The first sign is probably K; compare the third picture on page 7a with its hieroglyph; the second is C's hieroglyph with an Akbal appropriate to it; the third sign is Moan with the 13 belonging to it; the fourth sign is N's with a prefixed 4; the year-sign in the lower series is replaced by Zac, which agrees equally well; compare page 24, hieroglyph 21.

Page 48. The first sign is Kin with the Ben-Ik superfix, perhaps denoting G; the second is a figure similar to the year-sign with a prefixed 6. This same sign in the line below has a 6, but is very different in other respects; the third is an Akbal with superfix and prefix, perhaps denoting D; the fourth is a head which might easily be F's; compare page 24, hieroglyph 22.

Page 49. The first sign is B's; the second, A's; the 3d, K's; compare page 24, hieroglyph 38; the fourth is H's with a prefixed 1; compare page 24, hieroglyphs 23 and perhaps 37.

Page 50. The first sign is E's; compare page 24, hieroglyph 38; the second is L, the black deity; compare page 24, hieroglyph 32; the third is an unknown hieroglyph with a prefixed 7, which also occurs on page 5a and 19b; the fourth is the bat-god; compare page 24, hieroglyph 24.

I find it impossible to discover any relation between these hieroglyphs and the periods and I have as little success with the hieroglyphs apparently belonging to the same cardinal point. Perhaps we should follow Seler here (Quetzalcoatl and Kukulcan, p. 403), who thinks these passages suggest constellations with which Venus is in conjunction; this question, owing to the retrogression of the planet, raises increased difficulties. It is curious that the fourth of these signs on page 46 is like the fourteenth on page 49 (A), and perhaps the two following refer to the same god K; the first two are separated by 1494 days and the latter by 1508 days.

We come now to the _right_ half of the pages. Interpretation is rendered impossible by the destruction of the top part. For we do not even know whether the upper hieroglyphs occupied three or four rows each, the latter being the case at least in part, and there may have been a superscription over the day signs in the left half.

These upper signs are always followed by a picture, then three rows of hieroglyphs, then a second picture and next two rows of hieroglyphs and lastly a third picture.

Let us first examine the pictures:--

At the top of pages 46-49 there is on each page a deity, who with his right arm extended is offering or receiving something. He is seated on astronomical signs; on page 46 B's head accompanies these signs. On pages 46 and 48 the deity is undoubtedly the old woman with tiger claws, who usually pours streams of water from a jug (compare pages 39, 43 and 74). I cannot identify the personage on pages 47 and 49. The object in the deity's hand seems invariably to be a cup of foaming pulque. On page 49 another object is placed above the cup, which I am unable to determine. The fifth, page 50, differs from the other four and forms the connecting link, as it were, between the upper row of pictures and the middle and lower ones. Here, too, a personage is represented sitting on astronomical signs and exhibiting symptoms of violent anger toward a second person opposite him holding the cup in his hands. Both personages are painted as warriors.

The middle pictures on all the pages represent a warrior in a half-kneeling, half-crouching posture, holding spears or a shield in the right hand and brandishing a hatchet in the left. The shield on page 46 is doubtless a representation of the sun-glyph; and on 47 the Venus sign is combined with the head ornament. The hieroglyphs of these deities occupy the first place in the middle line of the three lines above the pictures.

The five lower pictures represent a creature lying on the ground, pierced by arrows and spears. On page 47 it is a jaguar; at any rate it is the same animal found on pages 29a, 30c and 45c; a very similar creature pierced by arrows is given in the Cod. Vat. B.; compare also the pictures in Seler's "Venus-periode," page 371. On the other four pages this creature is in human guise. On page 50 where, differing from the other four pages, this figure is represented lying with the head to the right, it is plainly shedding tears. Seler takes this figure to be E on page 48 and the tortoise on page 49. The varying periods of time occupied by the revolution of the planets is plainly conceived of as contest. But who is the victor in this contest? The planet with the longer or with the shorter period of revolution? Owing to obliteration only a small part of the hieroglyphs of the top section is legible.

On page 46 we see the Venus sign and E's hieroglyph; on page 47 the sign _c_, which occurs frequently on these pages, and is probably always connected with Moan (the Pleiades and thus with the year). The numeral 1, prefixed to an obliterated sign on page 47, is still legible, and we find it repeated on the lower part of the same page. There is rather more to be seen on page 48:--first the elongated head _q_ with the Ben-Ik superfix, then the sign _a_, beside it that for the west with a prefix, in the line below an Ahau, next, an Akbal sign with the prefix of the north, and lastly a Moan sign.

On page 49 we see sign _c_ again occupying the first place, then o with Ben-Ik, and in the lower line the year sign with that for 20 or the moon as a superfix, and to the right of it the head with the Akbal eye, probably denoting D.

This top part of the page is best preserved on page 50. In the third line from the bottom we see the Venus sign and beside it the Moan sign, below, a Cauac, then a Kin with the Ben-Ik superfix, then a Kan-Imix. Finally, in the first place in the lowest row there is a Kin sign and in the second place a sign resembling the year-sign, both having the same superfix, the next sign is again _c_ and the last is a half-effaced sign, of which only a Muluc is distinguishable.

Our knowledge of the middle section of these pages is somewhat more definite. There are twelve hieroglyphs on each page, which I will number in the following order:--