8b is a Chuen sign, which, with its prefix (superfix on page 69) always denotes twenty days in the inscriptions. It is multiplied with the same unknown head in 8a, which we have already met with in 3a. 9a contains H's head, and 9b is an unknown head with inserted Kin; the two signs must of necessity indicate the single days still to be added to the period, though as yet we do not know how.
The normal date IV Ahau 8 Cumhu then follows in 10ab. If it refers to the signs just now discussed, then they must denote a number of about the same magnitude as the serpent numbers. 653 or 654 times 18,980 seems to suggest itself, but we shall have more to say later on this subject. My efforts to reach a definite result here have failed.
Nor does the lower part of the two columns lead me to the desired goal. As it seems to consist of several groups, I will first combine 11ab and 12ab. I look upon 11a as denoting 20, and with regard to 11b I have already expressed the surmise in the Zeitschrift für Ethnologie XXIII, page 153, that it may mean 8760 = 24 × 365,i.e., three Venus-solar periods. That would be 20 × 8760 = 480 × 365 = 175,200. The Moan in 12a may have the value 13, for this number is so often combined with the Moan. As we saw under page 51, 12b is = 18,980; 13 × 18,980 = 246,740. Accordingly the four signs taken together may mean 421,940 = 1156 × 365.
The second group, from 13a to 15b, refers, on the other hand, to the year of 360 days. First 13a = 144,000, having in 13b the unknown multiplier, which we have already seen in 3a and 8a. Then follows in 14a, 15 × 7200 = 108,000; in 14b, 9 × 360 = 3240; in 15a, a 20 with a prefixed 1 (21?); and in 15b, three days. It would be more correct to place the 1 beside the following 3. The whole sum would then end with the number 4, which would agree with the day Kan, the date specified below.
In the third group the 16a = 19 × 18,980 = 360,620, remains a mystery; an empty outline of a sign is added in 16b.
17ab also forms a group by itself. 17a contains a sign, which rather suggests the Bacab, upon whose period of 91 days the series belonging here is based. The Imix in 17b with a superfix is still unintelligible.
The columns end in 18 with the date IX Kan XII Kayab, the starting-point of the serpent numbers.
Pages 65—69.
I think it very likely that this section bears the same relation to pages 61-64 as pages 46-50 do to 24 and as 53-58 to 51-52. For here, too, a period of time forming the basis of the earlier section seems to be divided into smaller parts. On page 64 we recognize as the basis of the series the number 91, the quarter of the ritual year of 364 days; here we have to do with the fourfold division of 91 into 13 unequal parts. And the real starting-points on these pages, as on the previous ones, are the days III Chicchan and XIII Akbal.
The four series of numbers, the top one of which I have probably correctly restored from what still remains, are as follows:—
The first two lines, forming together a single period of 182 days, refer to a day III, as we see by the ending, and the last two to XIII, which undoubtedly refers to the III Chicchan and XIII Akbal, the days so significant in the preceding section. Hence an interval of 218 days (III Chicchan to XIII Akbal) is to be assumed between the second and third lines, with the addition of which interval each of the two periods extends over 400 days.
The first and fourth series have the same difference; and the second and third correspond with one another in this respect. In the first and fourth the differences follow a rule, viz:—as if one were walking in a ring having on its edge the numbers 1 to 13, and kept stepping backward four numbers. The differences of the second and third series apparently do not follow any rule. Hence I think that the fourth series follows the third by mistake and ought rightfully to precede it. Only the fifth member in the first and second series has the same day VIII and the day V in the third and fourth series, otherwise the week-days of each series differ from those of the others.
As I regard III Chicchan and XIII Akbal as unquestionably the starting-points, I will here give a table of the days on which each of the twenty-six members of each series must fall and at the same time I will indicate for each day its number from the beginning of the series. Accordingly the first 182 days present the following appearance:—
In the same way I will tabulate the second group of 182 days, but in this case I shall place the fourth line before the third, which is probably correct, and which shows for the first time parallelism of the two rows:—
It would be very essential now to know what place these days occupy in the year, and what year is meant; the answer to one of these questions would at the same time solve the other.
Now I think I come nearer to the solution of this problem by assuming that the pictures and hieroglyphs refer here only tothe more important of the two days, XIII Akbal, and that III Chicchan is represented only by the numbers of the series. Thus both the pictures and the hieroglyphs of the two sections connect without the interval of 218 days, which must be assumed in the case of the numbers.
Here, as is usually the case of series, we have to begin at the bottom. Now the first group of the lower half of page 65 contains the sign 9 Kan. If, as it seems, this actually denotes the year, then the day XIII Akbal must be the first of the eleventh month,i.e., the 201st day of the year. Hence I will again set down the twenty-six dates, but add to them the position in the year.
Let us now prove the correctness of my theory by an examination of groups 22 and 23. In 22 the 160th day of this period, the 361st day of the year is reached,i.e., the first of the five Uayeyab days. The year 9 Kan is ended and the year 10 Muluc is not yet reached. In the corresponding picture we see B occupied in conveying in a bag the image of God K to whom belongs the next year. B is armed with the official staff and the bag also contains water (rain). In the 23d group the 166th day has passed and the second of the year 10 Muluc is reached, which gives the name to this year. The first hieroglyph shows two personages sitting back to back. This representation is repeated on a larger scale below in the Janus picture of B who is sitting on signs of planets. The second hieroglyph, with equal fitness, represents a clamp, which is intended for fastening twoobjects together, and which is repeated twice over the Janus picture, black in one case and white in the other. Rain is pouring over the second half of the picture, for it has long been known that Muluc and rain belong together, and in our examination of page 7a we saw that K is the ruler of the day Muluc (6).
Now, before I begin the examination of the separate pictures and the groups of six hieroglyphs belonging to each picture, I wish to mention three things which are often repeated here.
First, B's picture, which appears in all the twenty-six pictures with the exception of 20, 24 and 25, and represents the god in the most varied positions and activities. These pictures are very similar to those on pages 29-46 and we shall therefore make frequent reference to the section there represented.
Second, the first hieroglyph in groups 1 to 13, strange to say, is not found in the second half. It is hieroglyphf, which appears in exactly the same way in close combination with B in two sections, which differ from each other but are placed side by side on pages 30c-39c. In the present passage it has a distinct prefix resembling the beak of a bird or tortoise, but in the former passage it has rather a stunted appearance. It seems to refer to the eagle in B's hands in group 13.
Third, the head with no underjaw, which is the sixth hieroglyph in groups 1 to 13, but does not occur in groups 14 to 26. It is repeated in a very similar fashion in the last hieroglyph but one on page 23b. I propose to attribute to it the meaning of fasting.
Now for the single groups:—
1. B is seated rowing in a boat, as he is represented also on pages 29c, 36b, 40c and 43c. A creature is swimming beneath him, which may be a crocodile. The fifth hieroglyph is the important 9 Kan already discussed, the fourth isaand the second the crossbcombined with Caban. The day is the 210th of the year.
2. B is walking with the atlatl in his hand, and armed with javelins. Hieroglyph 5, Manik, denotes the chase, but has a prefix, which often seems to have the meaning of 20. 2 is the elongated headqwith the prefix of the east belonging to the Kan years. 4 is a Moan sign (c) with the leaf-shaped prefix. Doesthis perhaps denote the slaying of game in the forest? It is remarkable that B's feet are hidden, as if he were walking in sand or in a bog.
3. B is walking, carrying a large stick like that for tilling the field, as on pages 38b and 39b, and he bears a carrying-frame; there are footprints below him. Hieroglyph 2 is the compound of the signs for south and east, 4 (r) may denote rain, and 5 is two elongated heads with an unknown prefix.
4. B, is seated on astronomical signs as on page 37c. The copal pouch is hanging from his neck and he is brandishing his hatchet. Sign 2 isb, 4 isaand 5 isr, but all three signs have unusual prefixes; the first of these prefixes appears again in the tenth group, 41 days later.
5. B is seated on a head, probably that of D, which, however, is peculiar owing to the ornaments resembling bunches of grapes in place of both the eye and the ear (compare pages 39c and 41a). I do not venture to decide what he holds in his hand nor what are the other objects which he carries. Sign 2 isrwith a prefix, 4 is Imix perhaps with a knife as a prefix, 5 is the skeleton which sometimes belongs to the lightning beast, but also to the 14th month; its prefix is unknown.
6. B is seated on a support, which contains two cross-bones, down to which he points with his right hand, while his left hand holds the hatchet on his knee. Sign 2 is the crouching naked personage, with the crossbprefixed, 4 is the elongated head with a prefixed Yax, and 5 is Kan with a vessel as a prefix (instead of Imix) from which steam or froth is rising. The day is the 234th of the year,i.e., the end of a week of 18 × 13 days.
7. B is sitting on a tree at the root of which his own head appears (compare with this the representations on pages 31c, 33c, and especially 40a, and also 41b and 42b). The second sign is Yax with a prefix; 4 is Kin within which there is a 1, as is several times the case, for example, on pages 61 and 69. The fifth sign is still a mystery to me. The day here is V Manik. Do the hieroglyphs suggest that the interval from the day IX Kan, which gives the name to the year, to V Manik is exactly the sameas that from the normal date IV Ahau to the true starting-point of our passage, the day XIII Akbal? Both intervals are 243.
8. B is seated in a house, on the roof, wall and floor of which are several Caban signs, just as on page 30a; he seems to be pointing forward. Sign 2 is Caban with a prefix, the 4th and also the 5th is Kan with two unusual prefixes.
9. Water is pictured at the bottom of this picture, and in it are a fish, a mussel and a snail (possibly page 37b may be compared with this). There seems to be a suggestion of footprints on the margin of the water, back of which B is walking, his legs hidden as far as the knees. He holds the hatchet uplifted in his left hand and his right holds what may be a long-stemmed aquatic plant (compare page 42b). Sign 2 is composed ofb, Imix, the mouth and nose of C and the object which apparently is a beak, previously met with in sign 1. 4 is Kan-Imix, and 5 is Kan with prefix and suffix.
10. B is seated in an expectant attitude, his hands resting on his knees. We see a very similar representation of him on page 38a, where he faces himself, and in general the remaining pictures of that passage furnish a striking parallel to the present one. Sign 2 is a head (E's?) with a call seemingly issuing from its mouth. 4 is the elongated headqwith the Ben-Ik superfix and an unusual prefix, which we found on page 66c prefixed to the crossb; 5 is Kan with the same prefix, which I regarded as denoting a call in sign 2, and which is probably answered here by an affirmative cry.
11. The expectation has been fulfilled. B is seated on a mat holding a woman in the same position as on page 38a. Sign 2 is the crossbwith the prefixed beak as in 1, and also with another prefix, which seems sometimes to denote the number 20. 4 is exactly the same Kin with 1 and the leaf-shaped prefix, which occurred in the same place with the seventh picture. 5 contains the sign for 73 days; a new period of this length begins here on the 74th day.
12. As in the parallel passage on page 38 B seems to be offering a Kan, so here his gift consists of a kind of wreath, like the one in the fifth picture; he is seated on astronomical signs, which contain the crossbtwice as does also hieroglyph 2. 4 isKin-Akbal, and 5 is a Kan with the prefix which generally belongs to the south as a superfix.
13. B is seated on the elongated headqwith a superfix and a prefix, exactly as on pages 37c and 40a, and this sign is repeated in the hieroglyphs (in 2) just as it is in the two former places. He holds the eagle on his lap and we see him connected with the same bird in a different way on page 43c. Is B represented here as the preventer of evil? Hieroglyph 4 isa, while 5 is Kan, apparently with the sign of the south as a prefix. A Bacab period of 91 days ends here. We come now to the upper series of pictures.
14. B is walking in the rain, with the copal pouch around his neck and the hatchet uplifted in his left hand. An unknown object, possibly held in his right hand, is hanging in front of his legs. Hieroglyphs 1 and 3 are effaced, 2 is indistinct, 5 seems to be a Xul (end, close) and 6 is E's head.
15. B is walking, brandishing the hatchet in his left hand, and holding in his right an object resembling a cornucopia filled with fruit; below this hangs what appears to be a flower. The god wears the copal pouch. Hieroglyph 1 is a hand holding K's head; it is curious that this sign should also occur in the next group as an indication of the approaching Muluc year. 3 is a sign still undetermined; but the prefix is the crouching naked personage with dots suggesting stars around its head. I have often thought that similar figures represented Mercury; it is remarkable that exactly the 115th day of this section is reached here, corresponding with the apparent revolution of Mercury = 115 days. Similarly sign 2 invites computation; it is a face resembling an Ahau sign, with a 3 as a superfix and a 9 as a prefix; compare the other places containing the same face, with 33c. After the fashion of the inscriptions this would denote 9 + 3 × 20 = 69, which by the way is three fifths of the Mercury revolution. 5 is a compound of Akbal and Imix and 6 a compound of a Moan sign (c) witha.
16. B is in a half sitting position and holds a strange object before himself. On top of his own head is K's, which is repeated in sign 2. I do not know how to explain 1, unless it is the bat-god; 3 is a Xul = end (but of what?) combined with Imix,and 5 is the usual Kan-Imix. 6 is a Kin with an 8 back of it (as 36b, 37b, 67a, 68a) and over it is a hand pointing to the right, just like those in groups 20 and 25. This looks as if we ought to count forward 8 days, but what can be the purpose of doing so?
17. B is walking armed with spear and shield. Sign 1 isb, 2 the face resembling an Ahau, which occupied the second place in group 15, 3 is probably Xul again, but with an effaced prefix; of 5 also only an Imix remains; while 6 is the usual compound of Muluc-Caban.
18. We have now reached the day 16 Kayab, a day very close to the day 18 Kayab, which on page 24 we recognized as an especially important day, while in my article "Zur Entzifferung III" I regarded it as the day of the summer solstice. Computed from the normal date IV Ahau 8 Cumhu it may also have denoted the end of a lunar year, as on pages 51-58 where it is the basis of the series. The picture here agrees with this. B is sitting in the pouring rain of the rainy season and gazing upward at the planets, as on page 36c and particularly on 39c; the sun and moon are also represented, but below the planets. The hieroglyphs likewise contain the sun and moon in 1 and 2, in 3, Ahau and Xul with a prefix, as if this were the end of the increase of the sun's power; 5 is Kin-Akbal, day and night, and 6 is Caban with the crossb.
19. B is walking armed with hatchet and shield. He holds a serpent in his hand as on page 40c, but here with the head downward. Hieroglyphs 1 and 2 are destroyed, 3 is the crossbwith a suffix and the horse-shoe prefixe, known to us from pages 5 and 6. 5 is Imix combined with Chuen and probably with Yax, and 6 is E's head.
20. This is the old red woman with the tiger claws, whom we saw on pages 39b and 43b and shall see again on page 74; she reinforces the water falling from the planets by pouring a stream from her jug. The first three hieroglyphs are effaced, 4 is the elongated headq, 5 is Kin-Akbal, 6, as in group 16, is again the enigmatical 8 with a hand pointing to the right.
21. B is walking and bears pouch, spear and shield.Hieroglyph 1 is a hand holding the sign of the rising Moan, just as in 15 a hand holds the head of K; 2 is again K, whose sign is probably effaced several times in the last groups of this series. 3 is E with the sign of the east; 5 is compounded of Imix, Chuen andb, and 6 is Kin with the sign of the north. Here the day of the normal date is reached, but this may be significant only for the year 9 Ix.
22. We come now to the representation of the change of the year, which we have already mentioned. Hieroglyph 1 is curious, consisting of the moon with a stripe running around it like a strap; 3 and 5 are not clear to me and are doubtless closely connected with one another; 3 also contains a trace of K and is perhaps a determinative of the same. 6 is again E, and suggests the tilling of the fields.
23. This picture as well as the first two hieroglyphs have already been discussed above. The crouching personage, repeated again in 3 as a prefix to the crossb, is curious. 5 is again E and 6 is Imix, referring to grain and honey.
24. The picture and three of the hieroglyphs plainly correspond. The grain deity E holds food and drink in his hand. Rain is pouring from the planets, and the wind-beast plunges down, as on pages 44 and 45. Sign 3 is E's hieroglyph, 6 is Kan-Imix and 2 is the wind-beast. B is superfluously added in 4 and the same is true of the crossbin 1, while Kin-Akbal in 5 seems to fit almost everywhere. Pages 29a, 30a and 45c show the lightning-beast in a different form.
25. As is usually the case, rain is pouring from the stars and below them are the sun and moon as before. This time C is sitting in the rain, clad in the gala mantle and holding Kan. Hieroglyphs 1, 2 and 4, the latter apparently representing C, are effaced. The other three are enigmatical, 3 is again Xul with a prefixed 9, 5 a Caban, but with an unintelligible prefix, and 6 is again the mysterious 8.
26. B is sitting on a tree or sacrificial stone, which is colored half blue and half red, and may denote the ceasing of the rainy season; he is brandishing his hatchet. Hieroglyphs 1, 2 and 3are effaced; 4 is B's sign, 5 might be Xul and 6 isawithcadded and thus referring to the Moan. And here the half of the ritual year ends with the 182nd day, which is XIII Chicchan 18 Pop (10 Muluc); and it is left to the reader to imagine or to find hieroglyphs and pictures for the other two series of numeral signs.
I am troubled about the five naked crouching figures of this section, which I am inclined to regard as the sign for Mercury with its apparent revolution of 115 days, which, however, seems sometimes (as on pages 54, 56 and 58 in the upper sections) to be raised to the value of half a Tonalamatl = 130 days. This may be explained by the fact that it is difficult to determine exactly the length of the revolution of Mercury. In group 15 this figure appears exactly on the 115th day of this section, but in group 6 on the 234th day of the year,i.e., approximately at the expiration of two Mercury periods after the beginning of the year. But now for group 23. Here there are three of these crouching figures. The two upper ones leaning back to back must serve the purpose of indicating the change in the year. But they would hardly do so, if the third personage were not added, which may indicate that the solar year consists approximately of three Mercury periods. I look upon this view of the matter merely as the first attempt at an explanation.
Pages 69—73.
The chief subject of the last great section of this Manuscript is two of the usual series, from which large numbers are developed in the usual way and the largest of all is finally recorded in a serpent. This section thus forms a parallel to the contents of pages 61-64, but is somewhat more composite.
Before I begin the discussion of these series, I wish to examine two passages, which I think are not connected with these series, but are independent, like the instance on pages 51-58, where the hieroglyphs were found to be quite independent of the numerals. The Mayas took advantage of space wherever it presented itself, which is admissible in ideographic writing.
The first of these two passages is at the top of pages 71-73.Here there are four horizontal rows of twelve hieroglyphs each. Since, however, the top row is entirely effaced and none of the other three are perfectly preserved, it is quite impossible at present to judge of the interconnection of the whole. But I must point out a certain resemblance to the passage on pages 44b-45b, where a period of 78 days is considered with reference to the wind-deities. The first and sixth columns of pages 71-72 likewise contain the signs for wind and the pierced ears. The fact that the Bacab sign occurs in the eighth column, and in no other, must attract 'attention; if we knew it to be effaced in the first column, then each column might refer to 13 days, though 12 × 13, it is true, does not form a natural whole. C's sign is the only hieroglyph of a god to be found in both passages. E also occurs on pages 44b-45b and may be one of the effaced signs on pages 71-72. There is no trace left of the others. The fact that some hieroglyphs occur in both the passages referred to proves nothing with regard to signs in frequent use and I can find no cases of correspondence among those occurring more rarely. Hence this passage must be left for the present as an almost complete mystery.
I have discussed the second passage in detail in my article "Zur Entzifferung der Mayahandschriften V," of the year 1895, and from it I will borrow the following. This second passage fills the middle and lower thirds of pages 71-73, occupying the same space as the first passage in the upper third, and offering far more reliable material than the latter.
That these hieroglyphs are not connected with the numerals above and below, can be deduced from the fact that the numbers follow one another from right to left and the hieroglyphs in the reversed order. This is proved by the hand pointing to the right, which occurs here at least eight times like the one occurring twenty times on pages 46-50.
But the scribe, misled by the direction of the numeral series, began on page 71 to write thefirstof these hieroglyphs from the right instead of from the left, but after the first four groups he corrected his mistake. Hence I read the groups of three hieroglyphs each, in the following order:—
The number 28 shows that we have to do here with 28 weeks of 13 days each,i.e., with a ritual year of 364 days, as was the case on pages 31-32, 63-64 and 65-69. This year, however, is divided into four parts of 7 x 13 = 91 days,i.e., into four so-called Bacab periods. This is very plainly indicated here, for groups 4, 11, 18 and 25,i.e., those separated by seven groups each, are exactly alike, but in group 4b (I will designate the three hieroglyphs of each group from top to bottom bya,bandc) there is a prefixed 4 which refers to the four Bacabs as does the same 4 prefixed to the Bacab sign at the top of page 72.
Now the question arises as to when this ritual year began. Undoubtedly its beginning day was very different from that of the civil year (360 days) and from that of the astronomical year (365 days).
In this matter I follow Mrs. Zelia Nuttall, who has rendered such estimable service to Aztec science. At the Congress of Americanists at Stockholm in 1894, she submitted an article entitled "Note on the Ancient Mexican Calendar System," in which with keen discernment she pointed out a year beginning with the spring equinox and including in its centre the sacred Tonalamatl,i.e., 260 days, which were preceded and followed by 52 days. I recognize this ritual year also in the present passage of the "Dresdensis," as the one current in the Maya country. It probably began about the 10th of March, at that period about the time of the vernal equinox, according to the Julian Calendar.
Beginning with this date, I will now attempt to tabulate the chronology of this passage. In the first column I will place the number of the group of hieroglyphs in question, in the second I will set down to what day of the Maya year each group refers; in the third, the corresponding day of our year, and finally in the fourth, the 20-day periods which agree in general with the dates.
In the following I will call attention to a few points by which this arrangement is justified.
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 thefamiliar 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 signa, 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) inc. Further the signbbetween 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, doaandcmean the year and isbthe 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 thesign 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 ismeant 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):—
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 newdifference 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:—
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 73in the column to the extreme right. 3 and 7 are the elongated headqwith 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:—
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 hieroglyphsin the third column at the bottom of page 70 (the third group) as civil years of 360 and astronomical years of 365 days:—
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
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:—
This is followed at the right top of page 73 by
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 chosenremains a mystery. In this way were obtained the following numbers, which the Manuscript suppresses. I will give them with their corresponding dates:—
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:—
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:—
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:—
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 daysi.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:—
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):—
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 wouldpoint 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:—
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:—