Part 14

It was necessary to discuss all this before I could introduce the entire series itself. In the following table I have set down the numbers and added to them the differences between each number and the preceding one (to the first, the interval between it and the zero point), just as they are given in the Manuscript. An asterisk is added to show that the number has been corrected by me and is wrong in the Manuscript, owing to a mistake either in writing or in computation. The three columns correspond to the three divisions of 3986 days, and the two horizontal lines divide the periods of 1742, 1034 and 1210 days.

Page 53a: | 24. 4163* 177 | 47. 8149 177 1. 177 177 | 25. 4340 177 | 48. 8326 177 2. 354* 177 | 26. 4488 148* | 49. 8474 148 3. 502 148 | Page 58a: | 50. 8651 177* 4. 679* 177 | 27. 4665 177 | Page 55b: 5. 856 177 | 28. 4842 177 | 51. 8828 177 6. 1034* 178* | 29. 5020 178* | 52. 9006 178* Page 54a: | 30. 5197 177 | 53. 9183 177 7. 1211 177 | Page 51b: | 54. 9360 177 8. 1388 177 | 31. 5374 177 | 55. 9537 177 9. 1565 177 | 32. 5551 177 | 56. 9714 177 10. 1742* 177 | 33. 5728 177 | -----------------+-------------------+----------------- 11. 1919 177 | 34. 5905 177 | 57. 9891 177 12. 2096* 177 | 35. 6082 177 | 58. 10068* 177* 13. 2244* 148 | 36. 6230 148 | Page 56b: Page 55a: | Page 52b: | 59. 10216 148* 14. 2422* 178 | 37. 6408 178* | 60. 10394 178* 15. 2599* 177 | 38. 6585 177 | 61. 10571 177 16. 2776 177 | 39. 6762 177 | 62. 10748 177 -----------------+-------------------+----------------- 17. 2953 177 | 40. 6939 177 | Page 57b: 18. 3130 177 | Page 53b: | 63. 10925 177 Page 56a: | 41. 7116 177 | 64. 11102 177 19. 3278 148 | 42. 7264 148 | 65. 11250 148 20. 3455 177 | 43. 7441 177 | 66. 11427 177 21. 3632 177 | 44. 7618 177 | 67. 11604 177 22. 3809 177 | 45. 7795 177 | Page 58b: Page 57a: | Page 54b: | 68. 11781 177 23. 3986 177* | 46. 7972 177 | 69. 11958 177

No one acquainted with the cursoriness of the Maya Manuscripts will be surprised that among 138 numbers I have declared 21 to be wrong. Furthermore the 21 errors are lessened by the fact that six of them are really only one, for in all 6 cases where the difference is 178, the scribe has overlooked this and written down the usual 177, although the numbers and the days of the series very correctly indicate 178. Again the three errors in groups 58 and 59 are also only one, for the author had confused the differences 177 and 148 and had, therefore, to write down 10,039 instead of 10,068. In group 4 the error is merely the omission of a line meaning 5. The scribe must have been at the same time the computer and therefore the actual author of the Manuscript.

Furthermore I must call attention to the regular position of the differences 178 and 148. In the three periods of 1742 days the 178 always occupies the 6th place and in the periods of 1034 it is always in the 4th place. This difference appears, therefore, in groups 6, 14, 29, 37, 52 and 60, _i.e._, 8, 15, 8, 15 and 8 groups apart; but it is entirely lacking in the periods of 1210 days. And in all nine sections the 148 occupies the third place, _i.e._, directly in front of the pictures, which will be discussed immediately, therefore in groups 3, 13, 19, 26, 36, 42, 49, 59, 65, _i.e._, at intervals of 10, 6, 7, 10, 6, 7, 10 and 6 groups. But I must point out an error fraught with consequences. Groups 22 and 23 quite correctly have the difference 177, but in this single instance the scribe has written down 178 and hence has computed the three days belonging to it as VII Ix, VIII Men and IX Cib instead of VI Ben, VII Ix and VIII Men, and from here on to the close he is always one day in advance, so that on page 58 group 69 ends with the days X Cimi, XI Manik and XII Lamat, while it ought to have ended with IX Chicchan, X Cimi and XI Manik.

So much for the series. Vid. on this series my paper "Zwei Hieroglyphenreihen in der Dresdener Mayahandschrift" (Zeitschrift für Ethnologie, 1905, numbers 2 and 3). Let us turn next to the ten pictures which are inserted in this series, three of which appear at the end of each period of 2920 days as on pages 46-50. Let us attempt to advance a step further in the darkness which still surrounds us here.

One of these pictures, the 8th, which is on page 56b, is in the wrong place, owing to the error in computation in Groups 58 and 59 to which I called attention above. It belongs not _before_ but _after_ group 59, the first on page 56b. This is indicated in the Manuscript itself. For in group 59 the two hieroglyphs, usually placed above each group, are missing and we find instead of them the sign resembling a snail, which is doubtless a very much emphasized zero (compare my "Erläuterungen," page 29), which indicates that the section designated by a picture closes with this group.

Having corrected this error we see that the ten pictures are on the following pages and come after the following numbers of the series:--

1. 53a 502 2. 55a 2244 3. 56a 3278 4. 57a 4488 5. 52b 6230 6. 53b 7264 7. 54b 8474 8. 56b 10216 9. 57b 11250 10. 58b 11958.

From this it follows that a picture is assigned to each of the nine sections composing the series. They are placed, however, not at the beginning or end of the section, but always after the expiration of 502 (= 2 × 177 + 148) days. The pictures are thus separated from one another by 1742, 1034 and 1210 days, which intervals correspond exactly to the length of the nine sections. But the last picture is separated from the preceding one by 708 days, and as it has a character quite its own, it must be discussed separately. But these 708 days with the 502 days of the beginning quite regularly amount to 1210 days, and the series is therefore to be considered as a recurring one.

Now these nine pictures might very easily be regarded as forming a new series, which is inserted in the original one and which has the day 502 as its zero-point. In that case, we shall have to subtract 502 every time from the days set down in the Manuscript. This new series may be represented thus:--

1. 53a 0 2. 55a 1742 3. 56a 2776 4. 57a 3986 5. 52b 5728 6. 53b 6762 7. 54b 7972 8. 56b 9714 9. 57b 10748.

It is certainly remarkable that the last number, 10748, corresponds so closely to the time of the revolution of Saturn, which is computed at 10753 days. For owing to the slowness of its progress, the Mayas may have known not only the apparent but also the actual revolution of Saturn. Besides the apparent revolution of Saturn (378 days from one superior conjunction to the next) could not be made to coincide very well with the length of the solar year. I will immediately present a further confirmation of my theory.

All these pictures have rectangles above them, of which I have spoken in my "Erläuterungen," page 16, and which always enclosed two or three hieroglyphs in which, with due hesitation, I assumed to be the signs of the sun, moon, and planets. This theory has as yet called forth no serious opposition.

Now in the passages just mentioned, I indicated the following figures as the signs of Saturn:--

These figures actually occur in all the nine pictures with the exception of the first, which has no rectangle at all, and where in true Maya fashion, the zero-point is concealed.

I go still further in my bold hypothesis. The time of the apparent revolution of Jupiter has been placed at 397 days. The Mayas, I think, computed it at 398 days. In the passage alluded to I regarded the following as the sign for Jupiter:--

We find these signs in pictures 4, 6, 7 and 9. The corresponding numbers reduced for the revolution of Saturn are 3986, 6762, 7972 and 10,748. I assume that the third picture, _i.e._, the number 2776, is another zero-point, in consequence of which the sign is here suppressed, and that still another is the tenth picture with the number 11,958, which has no relation to the revolution of Saturn.

If we compare these numbers with the 398, _i.e._, the apparent revolution of Jupiter, we have the following:--

3. 2776 = 7 × 398 - 10 4. 3986 = 10 × 398 + 6 6. 6762 = 17 × 398 - 4 7. 7972 = 20 × 398 + 12 9. 10748 = 27 × 398 + 2 10. 11958 = 30 × 398 + 18

The differences 10, 6, 4, 12, 2 and 18 are so small in comparison with 398, that the numbers 2776, etc., might very well have been regarded as approximate multiples of the revolution of Jupiter. And the remainders in the seventh and tenth pictures could be still further reduced. In the seventh picture, the first sign is very unusual and one which I do not remember having met with elsewhere. If it should be possible to regard it as the number of the thirteen week days, then it would follow (the Saturn sign being regarded as unimportant) that the contents of the rectangle meant:-- 13 + a multiple of 398, by which this remainder would be reduced to -1.

The tenth picture has the cross _b_ as the beginning of the rectangle. This is the sign for union, very often denoting especially the union of all the twenty days. Thus we have here (aside from the middle sign to be discussed later) the formula:-- 20 + 30 × 398 - 2 = 11,958, or even 20 + 30 × 398 = 11,960.

The regular progression from the 7th multiple to the 10th, 17th, 20th, 27th, and 30th multiples in the above six equations is also somewhat in favor of my theory, while the four rectangles without the Jupiter sign are by no means multiples of the Jupiter revolution:--

1. 502 = 398 + 104 2. 1742 = 4 × 398 + 150 5. 5728 = 14 × 398 + 156 8. 9714 = 24 × 398 + 162.

Let us now try to interpret the meaning of the remaining rectangles (always omitting the Saturn sign as a matter of course.)

In pictures 2 and 8 the rectangle also contains the sign of the moon or of the twenty days. Beside it in picture 2 is the sign, which in my "Erläuterungen," page 16, I regarded as the sign for Mercury. Hence we have here 20 + 15 × 115 = 1745, _i.e._, only 3 units more than the required 1742.

The rectangle with the eighth picture contains in addition to the moon a sign which looks as if it were intended for a whole divided into four parts. Until something better (perhaps the the sign of Venus) is proposed, I will assume that it is the quarter of the Tonalamatl, _i.e._, 65, and I take the required number to be 9714 in the form of 20 + 149 × 65 + 9.

Above the third picture I see a Mercury and a Venus sign and I read 584 + 19 × 115 = 2769, which is only 7 units less than the required 2776.

The fifth picture still remains to be discussed, but I do not know how to unite the Mercury revolution here with the 5728. For the present, however, I am inclined to believe that there is a mistake in this passage.

We pass now from the obscure contents of the rectangles to the equally mysterious pictures themselves.

Aside from the tenth picture, I find human forms in four pictures.

Picture 1, page 53a, is the death-god (A) seated and pointing upward, an appropriate representation for the zero-point of the Saturn series, _i.e._, for the end of the preceding revolution.

Picture 2, page 55a, contains the head of a deity, probably D's with the suggestion of a beard and the sun-sign on his forehead. The head is surrounded by a ring striped black and white.

Picture 3, page 56a, is the head of B, again with a beard and with the sign Kin (sun) above. The head is surrounded by a design, the left part of which is black and the right white.

Picture 6, page 53b, represents a hanged woman, which Schellhas, "Göttergestalten," page 11, takes to be the Maya goddess Ixtab, the goddess of the halter, _i.e._, of the hanged.

The centre of picture 4 on page 57a, contains the suggestion of a face, perhaps in place of the Ahau sign, and on either side of it is a black and white surface.

It is further important to note that four times in this section Kin (sun) forms the centre of the picture, viz:--pictures 5, 7, 8 and 9, pages 52b, 54b, 56b and 57b. In all four cases there is on either side of Kin a black and white surface, such as we have already seen in picture 4 and similar to that in picture 3. Pictures 8 and 9 are vomited up, as it were, by a serpent placed below them, in the same way as B is represented on pages 34b and 35b. In pictures 5 and 8, four objects suggesting arrows extend from the Kin in four directions and probably denote the four cardinal points or the four Bacabs, of which we shall have more to say presently. Two of these arrow-like signs also appear in picture 7, page 54b, but only on the black and not on the white surface.

I will postpone discussing picture 10 until later and pass on to the hieroglyphs above the first nine pictures, about which it is true I have nothing satisfactory to say. There are always properly speaking ten of these hieroglyphs, among them the two signs for the sun and moon. But the scribe introduced the latter only in pictures 1-4, and also with the more elaborate last picture 10. With pictures 5 and 9 he omitted these signs in order to represent the other eight larger and with greater distinctness of detail. Among these hieroglyphs are several of gods, especially that of A with pictures 1, 5 and 9, and H with picture 5, and with pictures 1, 3, 5, 7, 8 and 9 there are other heads, some of them bird-heads, regarding which I am uncertain.

The Ben-Ik sign, to which I have assigned the meaning of a lunar month, belongs with pictures 4, 8 and 9 and occurs twice each with pictures 1 and 10.

I am inclined to see the sign for Mercury in the crouching figure belonging to pictures 9 and 10, which is drawn upside down and combined with the half Venus sign (11958 = 104 × 115 - 2).

Hands grasping a hieroglyph (a sign for 20 days?) are represented in pictures 1, 7, 8 and 10.

The enigmatical numbers, prefixed to the hieroglyphs, occur several times, thus a 1 with pictures 1 and 10, and a 4 twice with picture 8 and a 6 with picture 3.

Now let us examine picture 10 somewhat in detail and also the signs standing above it, since both are of special significance here. This representation treats of the period of 11,960 days in which the Mercury and lunar revolutions meet. And this is proved by the ten hieroglyphs, which I will number as follows:--

1 6 2 7 3 8 4 9 5 10.

I can omit Signs 3 and 8, sun and moon, since they refer to a period of time only in a general way. Sign 1 seems to me, as I have already stated, to have reference to the revolutions of Mercury. Then follows sign 2, the upper part of which is a mat and the lower the Muluc sign. I believe this sign is intended to denote that the beginning of this period is in a Muluc year. Indeed, our examination of pages 51-52 showed that it was the year 6 Muluc. The mat (Pop) is very properly the symbol of beginning, since the first month of the year was likewise called Pop. Sign 7, it seems to me, indicates that this period should be divided into lunar months (denoted by Ben-Ik), and, as I have already demonstrated in my examination of page 24, the length of the period is stated here by Signs 4, 5, 6 and 9, but the dot before the fifth should be placed before the fourth, as is actually the case on page 24. Therefore:--

4 = 21 5 = 7200 6 = 4680 9 = 59 ----- 11960.

It is perhaps not accidental that the ninth sign is that of the fourteenth month, which signifies the expiration of the preceding lunar month, for here the month begins with the first day of the fifteenth month.

Sign 10 is doubtless Xul = end, as it so often is, for example, on pages 61-62 below. But I have not solved the meaning of the two prefixes. The end would be XII Lamat 16 Yax (13 Ix).

The picture represents a human form, which has in place of a head a design somewhat resembling the head of a lance. It is sitting with legs spread apart, and in this respect may be compared with god B of Cort. 9, who is represented in the same way. In the picture before us, the figure holds in its upraised hands the sun and moon signs, which are constantly repeated throughout the series. The Venus sign is placed between the outspread legs. In the rectangle above the figure, this sign is repeated in a more concise form, while on the left the cross _b_ appears as the sign of union or multiplication, and on the right that of Jupiter, whose period of revolution is here multiplied by 30 (30 × 398 = 11,940). And the two Venus signs can mean nothing more than that this period of 11,960 also serves the purpose of filling up the gap between the two large Venus-solar periods of 37,960 days, like the similar process which we saw on pages 46-50.

We have examined first the series and then the pictures with the hieroglyphs belonging to them. Let us pass now, as the third step, to the examination of the two rows of hieroglyphs extending above the numbers throughout the whole section. First of all, I will again set down here the position of each of the sixty-nine groups:--

Page 51. | 52. | 53. | 54. 31.32.33.34.35.36.|37.38.39.40.| 1. 2. 3. 4. 5. 6.| 7. 8. 9.10.11.12.13. | |41.42. 43.44. 45. |46.47.48.49.50.

Page 55. | 56. | 57. | 58. 14.15.16.17.18. |19.20.21.22.|23.24.25.26. |27.28.29.30. 51.52.53.54.56.57.58.|59.60.61.62.|63.64.65.66.67.|68.69.

Since each group contains two hieroglyphs, this makes 138. in all. Of these, however, about 24 on the upper halves of the pages, are wholly or almost wholly effaced which very materially hinders the trustworthy determination of the context.

Furthermore group 59 is entirely lacking or rather group 58, in the place of which the 59th has been set down. The eighth picture was probably already drawn, when the artist saw that there was not room enough left for the 58th and 59th groups. Hence he omitted the 58th, setting down in place of it the 59th and in the place of the latter he set down the zero mentioned above.

The question now arises:--Are these hieroglyphs dependent upon the days and numbers of the series and upon the pictures, or are they entirely independent of them?

I find but _one_ point in favor of the first possibility, viz:--the Venus sign in group 4b (I will designate the upper hieroglyphs by _a_ and the lower by _b_). It is placed in the period indicated in which 502-679 days elapse, and in which, therefore, Venus has finished a revolution of 584 days. It may be, that by way of exception, this significant date was intentionally recorded.

On the other hand, there are many things, which favor an entirely different interpretation of these hieroglyphs. Thus I am of the opinion that the ritual year of 364 days with its four Bacab periods of 91 days each is referred to here, as we have already found it referred to on pages 31a-32a and on page 45a, and shall find it again on pages 65-69 and 71-73. In that case the single groups would be separated from one another by one Maya week = 13 days.

I will now arrange the sixty-nine groups in the following order (the reason for which will become clear directly):--

I 4 11 18 25 32 39 46 53 60 67 II 5 12 19 26 33 40 47 54 61 68 III 6 13 20 27 34 41 48 55 62 69 IV 7 14 21 28 35 42 49 56 63 1 V 8 15 22 29 36 43 50 57 64 2 VI 9 16 23 30 37 44 51 58 65 3 VII 10 17 24 31 38 45 52 59 66.

The groups in a horizontal row are separated from one another by 7 or a multiple of 7. If now a hieroglyph is repeated in those places, which are in the same horizontal row, then this is a confirmation of the supposition that Bacab periods are meant to be represented here. Hence I will examine each row in turn. These rows extend over the long period of 69 × 13 days probably merely for the purpose of filling up the space.

I. In 39b, 46b, 53b and 60b, _i.e._, after every seven groups, perhaps also in 18b, we find the following sign, which I identified as that of a Bacab, in Globus, Vol. LXXI:--

Hence this denotes the beginning of the Bacab period. In 4b the sign is replaced by that for Venus. In 11b, 25b, 32b and 67b we find other signs, it is true, nevertheless the regularity stated above cannot be accidental. The upper signs of groups 39a, 46a, 53a and 60a contain an Imix and corroborate the connection.

II. 5b and 26b (after 3 × 91 days) contain a head very like the preceding, which readily suggests the idea that it is merely a Bacab sign pushed one group ahead, but it also appears in 13b, 50b and 52b.

Then 12b, 54b and 61b correspond, _i.e._, after six groups of 91 days and one more of the same length, but the same sign appears also in 34b, 48b and 56b.

III. 41b and 69a are Xul = end and are therefore separated by 28 × 13 = 4 × 91 days, _i.e._, the length of a year. It is singular that both signs of 41 are like those of 47; if we assume that 47 was set down one group too soon, it would be in excellent keeping with the rest. The Xul also appears in 11b and 28b. 34b and 48b correspond after 2 × 91 days, as already mentioned under II.

IV. 42a and 49b both contain the sign for the sun between clouds.

V. 36b and 57b agree after 3 × 91 days; the same sign appears again in 10b and 20b.

15a and 36a correspond after 3 × 91 days; we shall continue the examination of this sign under pages 71-73.

VI. 37a and 65a agree, _i.e._, after 4 × 91 days = a year. The sign contains a human figure stretching both arms aloft. The passing of a year was likewise indicated in III, but a year coming 52 days later than this.

VII. 10a and 31a agree, _i.e._, after 3 × 91 days. The sign is composed of the crouching figure prefixed to the cross, which we also find in 12b, 35a and 65b; it is prefixed to a different hieroglyph in 30a. In 38b, 52b and 59b (58 in the Manuscript) we see bird-like heads resembling the Bacab sign. We should expect to find a familiar sign in 45, which is drawn between these, but a Moan appears there instead. These signs seem to indicate the end of the Bacab period. Does the Moan sign here, too, suggest the end of the year?

In 38a, 52a and 59a we again see an Imix, and I consider it a corroboration of my theory that all the four signs of groups 38 and 39 are repeated in 52 and 53 after 2 × 91 days.

I believe a further corroboration is the fact that though many of these hieroglyphs have no connection with these periods of 7 × 13, _i.e._, with the divisions of the ritual year, they do correspond with the usual divisions of the Tonalamatl, _i.e._, 4 × 13 and 5 × 13 days.

After 4 × 13 or a multiple of it the signs recur in 20b, 24b, 40b, 44b-12b, 48b, 56b-16b, 32b, 64b-26b, 50b-10a, 30a-37a, 65a-15b, 51b-11b and 47b.

As examples of 5 × 13 I would mention 3b, 63b-10a, 20a, 30a-5b, 50b-24b, 29b-35b, 65b-15b, 20b, 40b.

Finally, I must mention two more hieroglyphs, which are limited almost entirely to these pages:--

In the first sign, which occurred on page 10a, I thought I recognized the lunar month of 28 days. It occurs in this section in connection with the third picture on page 56, and besides in the following groups of hieroglyphs:--16b, 32b and 64b, always combined with a Yax. The regularity of the intervals is striking, but as yet I can neither explain that, nor the crouching personage (Mercury?) in the 10th, 20th and 30th groups and again in the next, the 31st.