Commentary on the Maya Manuscript in the Royal Public Library of Dresden/3

Pages 25—28.

As these four pages, which are the beginning of the back of the first part of the Manuscript, not only belong together, but also display a parallel arrangement of their separate parts, the corresponding parts will be considered together as a whole.

There are seven of these parts on each page, viz:—the column of day-signs on the left hand; the top, middle and bottom pictures, and lastly the top, middle and bottom groups of hieroglyphs; but I will consider the pictures and hieroglyphs of the same section as belonging together.

On the left-hand side of each page two days are repeated 13 times. They are as follows:—On page 25 Eb and Ben, on page 26 Caban and Ezanab, on page 27 Ik and Akbal, and on page 28 Manik and Lamat. Cyrus Thomas first made the important discovery that these pages represent the transition from one year into the next, but held the erroneous opinion that the last two days of each of the four kinds of years were treated of on each page. While Seler, on the other hand, found that we have here to do with the last day of one year and the first of the following year, and that, therefore, Ben, Ezanab, Akbal and Lamat are the beginnings of the years and thus of the 20-day periods. The years, however, were always named after their second day (i.e., Kan, Muluc, Ix and Cauac years), since the New Year's Day was considered unlucky and it was the practice of the Mayas to conceal the real starting-point.

These four pages, therefore, extend over 13 × 52 years, that is, over a period of 18,980 days, after which period all the calendar dates are repeated. A list of all these dates is given in "The Maya and Tzental Calendars" by William E. Gates (Cleveland, 1900).

The transition from the Muluc to the Ix years is represented on page 25; from the Ix to the Cauac years on page 26; from the Cauac to the Kan years on page 27, and from the Kan to the Muluc years on page 28. The Ix years are represented first, because the beginning of the historical chronology lies in an Ix year (IV Ahau; 8 Cumhu). This section treats of ceremonies, especially of the setting up of the idols at the changing of the year, which I can pass over here since they have already been described by Diego de Landa and in our own day by Cyrus Thomas in his "Study of the Manuscript Troano," and elsewhere.

The principal representation on all the four pages is a priest, but disguised as an animal with the head of a beast of prey as a mask (always the same one) and also with a tail. He is pictured with the same three articles in each of the four representations, viz:—First, in his right hand, the staff of office with the hand at the top, which, according to Seler, "Mittel-Amerik. Musikinstrum.," p. 112, is the rattle-stick, second the incense-pouch, i.e., for copal, and third in his left hand a rattle, or, according to Schellhas, "Vergleichende Studien" (1880), a fan. There is one point, however, in which the first two pages differ from the other two; on the first two the priest is walking on dry land and on the second two through a stream of water. Was the city, to which this calendar especially refers, bordered in two directions by water, so that the road led across it?

On all the four pages, however, the priest carries on his back a different deity, and I cannot find out by what rule these gods are connected with one another, or with the one which is represented below them, or with the years. On page 25 the god is B, on 26 he has the form of a jaguar (Ix), on 27 he is undoubtedly E, and on page 28 he is the god A, Cimi.

Now to the left of the priest on each page there is one of the familiar Chuen bundles, such as are also frequently found in the the Tro-Cortesianus. Here, on pages 25-28, there are always three of these Chuen signs in a bunch. If Chuen really denotes the eighth day (which, of course, is only possible when Kan = 1), and at the same time the period of 8 days, then in this passage these three Chuen signs would properly designate the 24 days which elapse before the last day of the year, which is the last day of the 18th month. In the same way we shall find the Chuen bundle appropriately given this meaning on pages 42c-45c. Likewise the simple Chuen sign at the top of page 52 seems to denote 8 days. But what do the Chuen bundles in the Tro-Cortesianus mean, some of which are much larger?

In close proximity to these Chuen bundles we find numbers as follows:—on page 25 numbers 8 and 9, on 26 number 13, on 27 number 2 and on 28 number 13. I can offer no opinion, which would be even approximately acceptable in regard to the meaning of these numerals, but we shall discuss them later.

I shall discuss these glyphs in this place, although each group seems to relate not merely to the top picture, but to the whole page. There are 16 on each page, and arranged as follows:—

Unfortunately, the writing at the top is obliterated, which makes it impossible to understand not merely this passage, but also those on all the rest of these pages. Of the 16 signs in the top line only one is legible, and that is the first on page 28. This is the usual cross b; as a comprehensive heading it perhaps occupied places 1 and 9 on each page, alternating with another sign in 2 and 10.

In spite of this obliteration there are a few points which can be profitably discussed here.

I would call attention first to signs 7 and 8 on page 25. The first seems to contain twice repeated the figure, which is thought to represent eagle feathers, and which we found on pages 10b and 13a, for example. As this double character is also used to change the 360-sign into a 7200-sign, so it may also combine the 52 years of this passage. The 8th sign on page 25 is the head with the tuft of hair and no underjaw, which I think refers to fast-days, such as might properly occur at the transition point of one long period to another.

The sign for the year stands five times on the other three pages, which is in keeping with their contents. On page 26 it appears three times. This page treats of the transition of the Ix to the Cauac years. In the 6th place the Ix sign seems actually to be used as a prefix, in 7 the prefix is plainly the Kin-Cauac sign, just as on page 37a, and in 5 the prefix is probably Ezanab, the beginning-day of the Cauac years. At this last place the suffix is the same as that which we often see with the year sign on pages 13c-14c. On page 27, in the 7th place, the year sign has a prefix and a suffix, which seem to indicate that here it was intended to represent 365 as separated into 5 × 73 or 360 + 5. Lastly, on page 28 the 8th sign can be explained as meaning that the ritual year of 364 days is separated into 4 Bacab periods of 91 days each.

Resembling the year sign in form, and placed near it on these pages, is the following sign:—



This sign frequently appears on pages 8b-9b, 16b-17b, 17c-20c. We find it with slight variations once on each of the four pages 25-28. It is the 6th on page 25; the 8th on 26; the 6th on 27; the 6th on 28. Its lower part, especially the (phallic?) sign added at the left, suggests the hieroglyphs of the Bacabs, as we find them on pages 52, 55, 56, etc.; they might refer to the separation of the ritual year of 364 days into 4 × 91 days. On the other hand it has been considered simply as the reproduction of the carrying-frame pictured below it (compare above under page 17c.)

While the hieroglyphs, hitherto discussed, demonstrate the connection between the parts on the left of the four pages, two other signs prove the connection of the portions on the right.

One of these looks like the Ik sign surrounded by a dotted circle; it occurs on page 25 as the 13th sign, on page 26 as the 15th, on page 27 as the 14th and on page 28 as the 15th. To this sign are prefixed successively the numbers 9, 7, 11 and 6.

The second is unquestionably the hieroglyph for the numeral 20 or for the moon. It is effaced on page 25 and on pages 27 and 28 has a prefix, which on page 26 is used as a superfix. This sign is the 14th on page 25, the 16th on page 26, the 15th on page 27 and the 16th on page 28. The prefixed numbers are 7, 16, 5 and 6.

The meaning of these two signs and that of the apparently irregular numbers is still a mystery. The latter will be discussed presently.

The 4th sign on all the four pages seems to refer to a period like the one hitherto discussed. On page 26 the sign resembles that for the 13th Uinal (Mac) and hence appears to refer to the Tonalamatl, as in the first column on page 24. Above it is the sign for the south. The corresponding hieroglyphs of the other pages are obliterated, but strange to say the vestiges suggest that they too had below them the sign for the south. Now the south and the Bacab of the south preside over the fourth quarter of the year from which ensues the transition to the new year in question here.

Among the signs on the left side we should expect to find those of the gods to whom the expiring year belonged. On page 25 it ought to be B. Sign 5, however, though it can with difficulty be identified, points rather to god K. Sign 3 on page 26 corresponds better; this is the hieroglyph of the tiger already known to us, which is carried by the priest in the upper section of page 8a; here its prefix is the sign for the west. On page 27 we ought to see the grain-god E carried by the priest; his hieroglyph may be destroyed, but sign 5, which is Kan-Imix (food and drink) is his determinative. Finally the 5th sign on page 28 is, just as we should expect, the hieroglyph of A and, in addition, we find his determinative in 7.

But what is to be said of the fact that the tiger appears again on page 28 in sign 3, and this time with the sign for the east?

The Ahau on page 27, sign 16, refers to the god D of the middle section.

There maybe some reference here to sacrifice, thus:—the 11th sign on page 25 is Kan-Imix, the 12th on page 27 is Kan, which is followed in the 13th sign on page 27 by another one with a Yax and a suggestion of a second Kan-Imix. Also the curious sign in the 8th place on page 27, which we have already discussed under page 8b, is used to denote the sacrifice on pages 18a and 15b. Here its position with reference to sign 6 is the same as on page 8b. On page 26 the prefix of sign 13, which is half destroyed, may be recognized as a serpent. Signs 12 and 15 on page 25 are unintelligible. Unfortunately the following signs are entirely effaced:—Sign 1 on pages 25, 26 and 27, as well as 2 on all the four pages, 3 on page 25, 9 and 10 on all the four pages, 11 on pages 26, 27 and 28, 12 on pages 26 and 28, 13 on page 28, 14 on pages 26 and 28, and 16 on page 27.

On each page at the right there is a house, the back wall of which is always marked with the cross often met with. In front of the house with his back turned towards it, sits a deity. Each of the four deities has the front of his body covered with a gala mantle. Now we know that the god of the new year was set up before the house of the chieftain. On page 25 the god is K with his eyes apparently destroyed, and on page 26 it is B with a Kin sign on his head covering, hence designated here as a sun or day-god. On page 27 the god is D, and on page 28, A with the cross-bones on his robe, his own hieroglyph on his cheek, and the Akbal sign on his forehead. Only on the last page, therefore, and apparently by mistake, the god in the top picture is the same as in the middle picture.

At the left of each page, i.e., opposite the house and the god, is a flaming altar, bearing the sign Ix equivalent to fire.

The centre, between the gods and the altars, is occupied by vessels of which there are two on each of the first three pages and but one on the fourth; they contain food, without doubt intended for the sacrificial feast. On page 25 the lower vessel contains Kan (maize) and the upper probably a food prepared from Kan. Or are the spines on the back of the iguana indicated on this vessel? (Compare 40c and Cort. 8 and 12c). The contents of the lower vessel on page 26 are still unknown (birds?). The upper vessel contains a Kan, but the sign has a superfix, which corresponds to the sign for the west. On page 27 the lower vessel contains a fish and the upper the sign for the south. Lastly, the single vessel on page 28 contains the cross-bones (mammal?) and above them the Kan sign repeated three times.

Finally here on the last three pages, we find some numbers, which are still undetermined; on page 26 there is a 7 with the lower vessel, and on page 27 with the upper vessel two dots with a cross between them (perhaps this may mean 20 2 = 18, which is used in place of the usual clumsy numeral?). On page 28 we see above the vessel a 6, and below it, in place of a second vessel, a double Chuen sign, as in the upper section of the page, therefore it can hardly be the Akbal sign resembling Chuen.

On each page these signs consist of but one line containing 5, 6, 3 and 3 glyphs respectively. The first of these signs in all of the four places is the same (o), which very suitably refers to the change in the year. The second sign is always the hieroglyph of the god represented in the middle section:—K on page 25, B as the sun-god on page 26, and D on page 27. The second sign on page 28, which is the head without an underjaw and with the prefixed four, probably referring to four fast-days, must, therefore, be an uncommon sign for A, who was similarly designated on page 25 in sign 8 of the upper section.

If the gods in the top thirds are those of the past year and those in the middle the gods of the year just beginning, we should expect to find in each top third the deity who is represented in the middle of the preceding page. But this does not hold good. For then we should expect to find K on page 26 and not the tiger, on page 27 B or G and not E, on page 28 D and not A, and on page 25 A and not B.

Hence there is some confusion here. Yet it seems to be in the nature of a correction, that on page 26 the third sign, next to that of the sun-god, is actually the sign for E who is in the top section on page 27, and that the sixth sign is Kan-Imix belonging to this god.

On pages 25 and 26 this line also refers to the past year, i.e., to the year set down in the top third. The fourth sign on page 25 is a Manik, i.e., originally a grasping hand denoting taking away, disappearance, and the fifth sign on this page is a Muluc, which seems to denote the ending of the Muluc years. The fifth sign on page 26, is, in fact, the tiger pictured above.

The lunar hieroglyph as the third sign on page 25 and the a as the fourth on page 26 are strange and unaccountable. Both appear to be almost without significance here and seem almost like mere points between the names of gods in groups of two each.

The Ahau as the third sign on page 27 is the usual determinative of D, whose hieroglyph stands beside it.

On page 28 the main part of the third sign corresponds to the sixth of the upper section. I do not know, however, how to explain either the upper part suggesting a mat or the familiar leaf-shaped prefix.

In the left-hand lower corner of each page we see the sign for the year of 360 days, which at the same time designates the heap of stones, on which the stelae were erected, the two thick black lines indicating the two columns of hieroglyphs usually found on them. A tree is growing out of this sign, having on its trunk an abbreviated Cauac sign, at least, on pages 26, 27 and 28, which probably refers to rain as the most desired event of the year. The tree on page 25 has no leaves, but the top is carved into the shape of the head of the god B. In the other three cases it has leaves, but instead of ending in the god's head the tree is draped with a mantle and a breech-clout, and a serpent is coiled about it denoting a period of time (here, the year). Furthermore there are foot-prints on the trunk or the drapery of the tree, which represent it as the goal of a pilgrimage.

If the top and middle thirds refer to the mere transportation of the idols, the bottom thirds refer to the feasts connected with this act, or, at any rate, to those dedicated to the new god. For we see here on page 25 the god B, on 26 the god K, on 27 A and on 28 D, i.e., the same deities as in the middle sections, yet so placed that the first two and the last two have changed places.

Each of the four deities hold in one hand a hen with its head cut off; "degollavan una gallina" is the statement made by Landa concerning these feasts. Perhaps all four gods, at any rate the last three, are scattering grain; this was one form of divination; we found the other on page 2. There are besides, on every page, several small objects between the two pictures, just as in the middle section. On page 25 the object is probably an altar, but instead of the flame it has the number 19. Above this is the sign for the west (the Ix days) with that for the sun, and on top of them the sign which we found in the middle section of page 26 as the contents of the lower vessel. On page 26 we see a vessel containing a bird, then another whose contents are indicated by Yax and a double Kan sign. Above it is the sign for the moon or for 20 with a prefix, and above this a 9. At the bottom of page 27 there is a vessel containing two Kan signs and a fish; above this another vessel the contents of which are the same as we found in the vessel in the middle section of page 26 and in that of the lower section of page 25. Above these is again the sign for the moon or 20 with a superfix, which is the same as the prefix on page 26, and beside it is a 16. Page 28 has the usual haunch of venison (Landa:—"una pierna de venado"), above this is a vessel with a bird and Kan and above this again the sign for the moon or for 20 with the same superfix and the numeral 15. I shall discuss below the numbers scattered over these four pages.

These hieroglyphs also form but one line on each page and each line contains six hieroglyphs. The first of each line is always the same (p). It consists of a surface divided into four quadrants thus suggesting the four cardinal points, the four Bacabs presiding over them and the four kinds of years. The superfix seems to be the abbreviated hieroglyph of the north; the sign for the north, however, is Muluc and these four pages begin with the Muluc years.

The second sign is the head of D as the supreme god; to this a Yax is joined on pages 26-28 as the symbol of strength, and on page 25, but probably by mistake, the abbreviated sign for the west.

The third sign always represents one of the four cardinal points:—on page 25 the east, on page 26 the south, on page 27 the west and on page 28 the north; here then the usual order is reversed and the signs are set down according to the diurnal instead of the annual course of the sun, probably occasioned merely by exchanging the sign for the west (Ix), which belongs on page 25, with that for the east (Kan), which belongs on page 27.

The other three signs do not stand in the same order on every page.

The fifth sign on pages 26 and 28 and the fourth on page 27 show correspondence most clearly. This sign is always a head, undoubtedly that of the god pictured in the bottom third. But on page 25 it is the hieroglyph of E, who is pictured on the top of page 27, instead of that of B.

In the same way the 6th sign on page 25, the 4th on page 26, the 5th on page 27 and the 4th on page 28 have something in common. One element of the hieroglyph is always the sign for the year of 360 days, combined on page 25 with cross-bones and the Cauac sign, on 26 with Yax and Kan, and on 27 and 28 simply with Yax.

The most puzzling and divergent of these hieroglyphs are the remaining ones. The 4th on page 25 has an oblique cross (or bones?) and the abbreviated glyph for the west, the 6th on page 26 is the head of E, the 6th on page 27 is the 360-day sign combined with Kin and Cauac, and the 6th on page 28 is the usual Kan-Imix sign. Here, too, there seems to have been a displacement.

Before I leave the four pages 25-28, I will glance at the numerals, which are scattered over them and which apparently have no connection with one another. I have discussed these numerals in my article "Die Mayahieroglyphen" in Volume LXXI, No. 5, of the Globus, and the following is borrowed therefrom.

First of all, I believe that I proved there, that the sign composed of two dots with a cross between them is an abbreviation for the usual clumsy representation of the numeral 18 and designates it like a duodeviginti by 20 2. Next, that in this passage as on pages 18a, 18c, 19c, 46b and 50c, the sign is combined with the hieroglyphs Yax-Kin. Third, that it is closely related to the god D, inasmuch as it stands on page 27b close beside the picture of that god.

Assuming this as a known fact, we find scattered over these four pages the following numbers:—

It is very remarkable that the sum of the numbers on each of the first three pages is equal to 52, and as an accidental freak it would be most surprising; somewhere on the fourth page six units may have been omitted; but perhaps the 6, which stands above the two Chuen signs in the centre, is to be counted twice. The 52, however, designates the very 52 years, which are treated of on these four pages.

As yet I know no reason to account for the fact that the 52 is here separated into these apparently very irregular numbers. The discovery of this reason would be an important step in advance. Or does it means 52 days, perhaps those which follow a Tonalamatl coming in the middle of the year?

Page 28 is followed in the Manuscript by three empty pages. The scribe's object in reserving them is beyond our ken; possibly they were intended to represent the period of 8 years.

Pages 29-45 (i.e., to the end of the first part of the Manuscript) all belong together. After the Maya manner there is very little system displayed in their arrangement, and though here and there there may be occasion to consider the three parts of each page consecutively, I will discuss them here as follows:—First, the top thirds, which are most difficult owing to the destruction of a large portion of them; then the middle, and last the bottom thirds. They all consist in great part, with a few interruptions, of representations of the regular Tonalamatl, such as we find represented from the beginning of the Manuscript to page 23.

The element which these pages have in common is the fact that the god B, who can hardly be Kukulcan or Quetzalcoatl, occurs on almost all of them. He is the god of wind, fire, breath, i.e., the true god of life and is here represented in his relation to the most varied manifestations and activities of a human being, so that this section bears a certain resemblance to the Tro-Cortesianus. With this is closely connected his relation to all four cardinal points, which so often occur. He may have been the local god of the region from whence this Manuscript came; in the Tro-Cort. It seems rather to be C who lays claim to this office.

Pages 29a—30a.

This is a Tonalamatl of 4 × 65 days, each part subdivided into 5 × 13 days. The four days written on the left are those which may begin the year.

In each of the five sections B is pictured in a sitting posture, the first four times on a tree (the tree of life rather than the sacrificial tree).

In the first picture he holds in one hand the haunch of venison, so often occurring as an offering, the last time on page 28; the object above it is probably the Kan sign. There is a vessel at the god's feet, probably a receptacle for the venison, bearing the hieroglyph of the 13th day Cib, which, however, refers rather to a bird.

In the second picture an animal with a protruding tongue lies on its back at the feet of the god, who kneels upon its stomach. This probably represents the lightning-dog as vanquished. The same animal is pictured on the next page and also on page 40b and perhaps on page 60. There are a number of small dots around B's head, which on page 11c we attempted to interpret as the starry sky.

I can find nothing of special importance in the third and fourth pictures, but in the fifth, B is sitting in a house, which is marked repeatedly with the sign Caban (ground). Here the god is holding the hatchet (machete) in his hand, as if prepared for some terrestrial activity. Four hieroglyphs in the usual order belong to each of the five pictures. They are almost entirely destroyed, but the vestiges show that the fourth sign was always that of B, while the third sign with the first picture had the abbreviated hieroglyph of the west as a prefix; with the second picture it had that of the south, and therefore with the third and fourth it must certainly have had the signs of the east and north. We should expect the signs with these prefixes to contain references to Ix, Cauac, Kan and Muluc, but they are not distinguishable.

Thus B is represented in pictures 1-4 as ruler of the four cardinal points and in 5 as the ruler of the earth in general.

Pages 30a—31a.

This passage looks like an amplification of the middle picture on page 29a. Here B is represented with the hatchet in his left hand and holding aloft by the tail with his right hand the animal, which is spitting out something upon a stepped pyramidal structure, probably the pyramid of a teocalli. That this is probably meant to represent lightning is rendered almost a certainty by the picture on page 40b. In this passage there are several red and black numerals scattered around the animal in an irregular manner, which we find nowhere else in our Manuscript, but with which the Tro-Cortesianus has made us familiar. The sum of the black numbers still legible is 23, probably a 3 is effaced and the sum should be 26, the sum which so often occurs in the Cod. Troano 8-13 with the animal represented there. The red numbers likewise do not admit of exact determination. This passage also contained hieroglyphs, four standing side by side on each of the two pages. The legible portion is limited to the Cimi sign in the third place, perhaps an Imix in the second, and possibly an Ahau in the first.

Pages 31a—32a.

In my article "Zur Entzifferung, etc., VI," published in the year 1897, I discussed this passage more in detail, and the following will be in continuation of what I stated there.

The real aim of the computation on these pages is to find a number in which the following periods of time are united with the Tonalamatl of 260 days:—1. The ritual year of 364 days, and consequently also a quarter of it, the Bacab period of 91 days. 2. The period of 104 days, being the number of days which remain after a Tonalamatl has been deducted from a ritual year. The hypothesis advanced by Mrs. Zelia Nuttall ("Note on the Ancient Mexican Calendar System," Stockholm, 1894) and also the entirely different opinion held by Mr. Charles P. Bowditch ("The Lords of the Night and the Tonalamatl of the Codex Borbonicus" in the American Anthropologist, N. S., Vol. II, New York, 1900) prove the existence not only of merely arbitrary Tonalamatls for the purpose of prediction, as those in our Manuscript, but also of Tonalamatls having a fixed position in certain years. But after the manner peculiar to priestcraft, the number sought is found only by an indirect and mysterious process.

In the first place we find on page 32a all the days set down in the following manner:—

That is to say, a series counting from the day XIII Akbal, the New Year's day of the year I Kan, recurring every 52 years, furthermore a series which shows the same difference of 91 from the day XIII Akbal to XIII Ix, XIII Chicchan, etc., and finally ends with XIII Akbal again, after it has run through a period of 20 × 91, i.e., 1820 days = 7 Tonalamatls, like a similar representation of 7 Tonalamatls on page 51. Above these 20 days, and to the left of them, numbers are set down rather irregularly, which begin with 91 and are multiples of that number. The signs of the days corresponding to these numbers are joined to them; but they are omitted with the numbers of lowest value. Hence we have:—91, 182, 273, 364 (4), 455 (5), 546 (6), 637 (7), 728 (8), 819 (9), 910 (10). Then with a bound follow 1456 and 1820; with the last number Akbal is reached in the natural way, which day the scribe had erroneously set down again with 1456 in place of Cauac.

The number 728 already united the numbers 91, 104 and 364, but did not include the number 260. This inclusion is accomplished by the number 3640 on page 32, quite on the left where we find the numbers 10 and 2, under which only a 0 has been omitted. With the usual hiatuses this series seems to end on page 31, where I think the numbers 4, 0, 16 and 0 ought to stand, but they are almost wholly effaced; this would then be 320 × 91, 280 × 104, 112 × 260, 80 × 364 = 29,120.

We have thus gone far in advance of the first problem, but a second always presents itself in these series, it is that of using these periods for larger numbers, which refer to a not too remote past or to a future not too distant. The first numbers are, as a rule, in the neighborhood of 1,252,680, the close of the eleventh Ahau-Katun, and the latter in the neighborhood of 1,480,440, the close of the thirteenth Ahau-Katun. The Manuscript presents the following:—

In connection with this it should be noted first that I have restored the 8 in the statement of the months, and second that the two numbers on the right were found with the aid of page 63 only by an easy conjecture. For with the reading of the Manuscript 10, 13, 3, 13, 2, I do not agree, but read instead 10, 13, 13, 3, 2; the number below, however, is given in the Manuscript as 7, 2 and then a black 14 joined to a red 5; I read this 7, 2, 14, 19.

The three numbers nearest the bottom have red circles around them, indicating subtraction, or, according to my present point of view, addition.

Now let us see how the computer arrived at the large numbers.

Day XIII Akbal, the New Year's day of the 1 Kan years, is given; also the differences of the series 91 and 104, therefore also in the proportion of 7 to 8. If we combine these last two numbers by addition and then by multiplication with 260, the result is (7 + 8) × 260 = 3900. If, however, 7, 8 and 3900 be combined by multiplication the product is 7 × 8 × 3900 = 218,400 = 2400 × 91 = 2100 × 104 = 840 × 260 = 600 × 364 = 1120 × (91 + 104). We have already met with the 218,400 on page 24, which was obtained by the addition of 33,280 + 185,120.

My opinion is as follows:—First 11 Ahau-Katuns = 1,252,680, were taken as a point of departure, and to this sum was added 15,600 = 4 × 3900, and 243 as the interval between the normal date IV Ahau and XIII Akbal. The result was 1,268,523. The position of this day, however, is XIII Akbal 11 Xul (1 Ix).

Then the 3900 mentioned above was added to this number and the result was 1,272,423 = XIII Akbal 16 Pop (12 Muluc).

Then to the 1,268,523 was added the 218,400 and the sum was 1,486,923 = XIII Akbal 1 Kankin (1 Kan), the very place in that year where a Tonalamatl ends.

The following numbers were thus obtained:—

These numbers are suppressed in the Manuscript. But if the encircled numbers are added to them, viz:—121 (interval between XIII Akbal and IV Kan), 17 (interval between XIII Akbal and IV Ahau), and 51,419 (= 197 × 260 + 199; 199, however, is the interval between XIII Akbal and IV Ik), the result is the three large numbers set down in the Manuscript, which have the following properties:—

1) 1,272,544 = IV Kan 17 Xul (12 Muluc). This number = 13,984 × 91 = 12,236 × 104 = 3496 × 364. It also = 4894 × 260 + 104, the interval between IV Ahau and IV Kan.

2) 1,268,540 = IV Ahau 8 Mol (1 Ix) = 4879 × 260 = 3485 × 364 = 74,620 × 17. 17 is the interval between XIII Akbal and IV Ahau.

3) 1,538,342 = IV Ik 15 Zac (12 Muluc). It also = 5916 × 260 + 182. The 182, however, the half of the ritual year of 364 days, is the interval between IV Ahau and IV Ik and between IV Ik and IV Kan. The fact that the interval is the same in each case is clearly the reason for the choice of the days IV Kan and IV Ik, which are otherwise not at all prominent.

It is remarkable that the third number is obtained by the addition of 51,419, i.e., of 197 × 260 + 199 (there are 199 days between XIII Akbal and IV Ik). But it was evidently desirable to obtain as large a number as this. On page 63 a number of nearly similar value is associated with it, viz:—1,535,004. It is set down almost in the middle between the 13th and 14th Ahau-Katuns, for it is 57,902 days greater than 1,480,440, and 55,978 days less than 1,594,320.

Now, however, the Manuscript presents in the last column but one of page 31 a number, 2,804,100, which occupies a very unique position, since it is nearly twice as great as all the other large numbers, with the exception of those in the serpents. It must refer to the year 9 Muluc, and to the date IV Ahau 13 Mol. It has many remarkable properties, for it is:—

1) = 10,785 × 260

2) = 17,975 × 156 (156 = IV Kan - IV Ahau).

3) = 35,950 × 78 (78 = IV Ik - IV Ahau and IV Kan - IV Ik).

4) = 719 × 3900. We have already met with this 3900 above. Now, however, the 2,804,100 by virtue of its magnitude creates the suspicion that it may be composed of two ordinary large numbers. It might be

5) 1,308,580 + 1,495,520, therefore 14,380 (91 + 104).

6) 1,380,600 + 1,423,500, therefore 3,900 (354 + 365).

That is to say, the important 3900 multiplied by the days of the lunar year and also by those of the solar year, hence the 719, referred to under 4, separates into these two parts. The lunar year of 354 = 6 × 29 + 6 × 30 days was not unknown to the Mayas. We shall find its half, 177 days, several times on pages 51-58.

We might also use the two important numbers 14,040 and 18,980, the first of which is divisible by 260 and 360, and the second by 260 and 365, without remainder.

Then we have the large number desired:—

7) 147 × 18,980 + 14,040.

8) 200 × 14,040 - 3900.

What future student will penetrate more deeply into the meaning and purpose of these numbers?

We might now expect to interpret also the upper right-hand corner of page 31, but here almost everything is in a deplorable state of obliteration. In the first three of the five columns over each of the three large numbers there was a date consisting of a numeral and a hieroglyph, but these admit of no certain nor even probable determination.

Four hieroglyphs still remain in the fourth column, respecting which compare my treatise "Zur Maya-Chronologie" in the Berliner Zeitschrift für Ethnologie XXIII, pp. 141-155.

In the top sign I recognize an Imix with a prefix and probably also a superfix. I think this denotes the period of 18,980 days.

I am forced to pass over the second entirely, inasmuch as a red 6 inserted in it remains a mystery (6 × 18,980 = 113,880?).

As I stated in the above-named work, I think the third is three times the sacred period of 2920, i.e., 8760 days.

Finally, the fourth sign certainly denotes the period of 7200 days.

Whether or not there was a fifth sign above the one now at the top is as uncertain as the meaning of the whole.

The most remarkable thing about it is that in three other passages of this Manuscript these three signs appear in close proximity to another. On page 61 we find the third in the 11th place in the second column, the first in the 12th place in the same column, and the fourth in the 14th place in the first column. Page 70 has the first sign in the middle of the 4th column; the second somewhat lower down in the 3d column and the 4th two places below. Finally all three signs appear in succession on the top of page 73 in the same order as on page 31.

The fifth column on page 31 may have contained another numeral belonging to the series, the loss of which is not so serious a matter, but there may have been one or two hieroglyphs above it, the obliteration of which is greatly to be deplored.

Pages 32a—39a.

This is a large section extending over eight pages, which is difficult of interpretation owing to the prevailing disorder and because a large part of the hieroglyphs are effaced. Here, too, the principal subject is the god B, who is represented in manifold activity. A series of numbers extends through the entire representation. I read them as follows:—

There are thus 18 divisions, the different lengths of which reveal no rule. They embrace 208 days, i.e., 2 × 104, which may well be considered as a continuation of the computation in the preceding section, of which the 104 was so important a number. The red numbers are entirely lacking in the beginning, then they are very slightly indicated, and finally they are distinctly written out on pages 36-39. I assume that the scribe has set down the 4th, 3d and 2nd numbers from the end, one too little. The last number has been entirely omitted. I have supplied these omissions though in a manner somewhat different from that adopted by Cyrus Thomas, "Aids," p. 28. I would note in addition that a period such as this, consisting of 208 days = 16 weeks, might be explained in an entirely different way, if there were a column of five days at the left having a difference of 8 days; then the whole would signify four Tonalamatls. But there is no such series of days.

Another point of view presents itself, however. If we take cognizance of the fact that a group of four hieroglyphs usually belongs to a picture, then it is evident that here there are such groups not for 18, but for about 22 subdivisions. It may, therefore, be assumed that about four subdivisions averaging 13 days are not specified, in which case this passage would extend not over 208, but over 260 days. The very irregularity in the arrangement of these numbers is an argument in favor of this hypothesis; it may be occasioned by the fact, that the pictures do not correspond exactly to the subdivisions. For the present, however, we shall discuss the single pictures assuming that there are 18 subdivisions.

1. Pages 32a-33a. Here at the very beginning it is uncertain whether the signs at the end of page 32 and at the beginning of page 33 are to be regarded as a single group of 8 hieroglyphs, as seems to follow from the numbers, or as two groups of 4 hieroglyphs each. At the end of page 32 we see two persons facing one another, one of whom, to be sure, is barely visible. The other wears a head-covering like a man's silk hat, similar to that worn by the priests on the inscriptions of Palenque. It is a remarkable fact that of the four hieroglyphs above these figures, 1, 2 and 4 (the last probably the god C) seem to have the sign for the west as a prefix, while the prefix of 3 (Imix) suggests the usual representation of the tortoise head. Below the persons there is a Kan sign, the prefix of which is also the sign for the west.

On page 33, B is represented walking and carrying the Caban sign in his hand. The first of the four hieroglyphs is the sign for B, the second is Imix, probably again with the sign for the west as a prefix, the third is an Akbal sign with Kin, and the fourth is the cross-hatched sign with Kan.

2. The rest of 33a is occupied by two persons, one of whom is clad in a gala mantle, but neither admit of further identification. They are occupied in fishing, inasmuch as they are sitting on the shore of a body of water and are either casting a net or drawing it in. There is a fish between them and above it is a vessel with something apparently cooking in it. Of the 8 hieroglyphs belonging to this picture, only the following are distinguishable:—the 1st containing an Akbal, the 3d, which is the common cross b with a 9, the 4th, an Imix also with 9, and of the 7th only the prefix Yax. The 3d and 4th appear again on page 35a, 28 days later.

3. Page 34, like page 3, represents a human sacrifice. The victim, very vaguely drawn, lies on a step-shaped sacrificial stone, or on the pyramid of a teocalli. There is a Caban (earth) sign between the sacrifice and the pyramid, and also on the walls of the buildings; the shrieking of the victim is plainly indicated. As on page 3, there are four persons in the form of gods surrounding the sacrifice, but here they are different ones. The one at the left above is the black god (L?), holding the rattle-stick (Seler, "Mittelamer. Musikinstrumente," p. 111), and at the right, above, F, the companion of the death-god, is sitting with a rattle in his hand. Below, the two have changed places, F is on the left and L on the right. The former is beating the drum and the latter blowing a wind-instrument. The sounds emitted by the two instruments are represented by drawings. This may, therefore, be regarded as an instrumental quartette. The following objects are also in this picture:—at the left above is a vessel the contents of which are cooking; at the left below, another vessel with three Kan signs, and at the right above, a Kan sign with a bird's head and below the food known to us from pages 27b and 29b. These four objects refer to the sacrificial feast. Lastly, at the bottom on the right there is a ladder, probably intended for scaling the pyramid. Ten hieroglyphs in the upper line belong to this picture:—the first, which is effaced, is followed by a Cauac, then comes the cross b, then a Cimi appropriate to the sacrifice, and lastly a head with an Akbal eye, probably D's. The first sign in the lower row is likewise destroyed, the second sign is a Kan, the next is the cross b, both having a different prefix, then here too is the hieroglyph of B with Yax as a prefix, and the last is an unknown sign.

4 and 5. Page 35a. According to the numbers there are two sections here, but neither the pictures nor the hieroglyphs can with certainty be assigned to either. On the left is a house in which C sits holding a Kan sign in his hand; on the roof, as if guarding him, and also holding a Kan sign, lies the god B. In the Cort. 24b-25b, there are six gods lying on houses, within which other gods are also represented in a recumbent position. Then follow two vessels, again denoting the sacrificial feast, the contents of which are probably cooking, and which, from the sign on the second, are probably liquid. Above these are three others, one with the Cimi sign (human flesh?), one with a bird and the third with the haunch of venison. At the right of these is an implement, which is unfamiliar to me and is similar to that held in the god's hand on pages 5c and 6c. And quite on the right sits B with foot-prints pictured below him and on his clothing.

The hieroglyphs on page 35, when they were all legible, numbered 14 and were arranged in two rows. 4 of the upper row are preserved, the lower part of the first is a year-sign (?), similar to that which often appears on pages 25-28, the upper element is the cross, and the prefix is the one resembling a leaf, which occurs so frequently. The second sign is an Imix with a prefixed 9, the third a cross and the fourth a head (probably D's) with Akbal. In the second row there is a cross with a prefixed 9 (sign of the second or third month?). These two signs with the prefixed 9 are perhaps to be read as a calendar date IX Imix 9 Zip (1 Ix), as on page 33a. Ix, however, belongs to the west, which is the predominant cardinal point from 32a onward. The second sign is a compound of Kin and Akbal (day and night) which often occurs here, the third is the compound of the Moan and Caban signs with the number 1 above each, and the fourth is the hieroglyph of B. The fifth sign is unfamiliar to me. The sixth contains an Imix with the sign for the west as a prefix, and the seventh is effaced.

At this point the representations begin to display a more orderly arrangement.

6. Page 36a. Here the head of B forms the head of a serpent (cf. pages 61 and 62) represented in pouring rain, while on page 35b it is emerging from the water. Of the four hieroglyphs 1 and 2 are entirely and 3 for the most part destroyed, and 4 is the usual Kan-Imix.

7. The lightning-beast with flames pouring forth from his forepaws and tail, is plunging down from the rectangle, which primarily designates stars and then the sky in general. This rectangle occurs for the first time here, but will often be met with later. Here it may be a combination of Mars and Venus. Of the four hieroglyphs, 1 is effaced, 2 is a compound of Kan and Kin, 3 a head with Akbal and Kin (D?) with the uplifted arm as a prefix, and 4, corresponding with the picture, is the compound of the rain sign Cauac with the prefix of the storm-god K.

8. Here B himself is the bringer of lightning. In one hand he holds a burning torch and flames are bursting from his carrying-frame. The third hieroglyph is his sign. It is doubtful whether the fourth is the hatchet (machete) or is not rather intended for an ear pierced for the purpose of ritual blood-letting, as on pages 44b and 45b; the first and second signs are rather indistinct.

9. Page 37a. Unless I am entirely mistaken, B is here represented with his arms bound behind his back. Cf. the pictures on page 2, top, and 60, bottom. Are the ends of the rope fluttering in front of the god intended to render this still more plain? Hieroglyph 1 contains the sign t, which resembles, but is not the same as, the year sign. This sign has already occurred frequently, especially on pages 25a-28a, and the last time on page 35 in the first hieroglyph. As on page 35, hieroglyph 4 is the compound Kin-Cauac, but here it is joined to the year-sign, i.e., it denotes the Kin-Cauac year, just as it does on page 26a. 3 is again Cauac and 2 is the hieroglyph for B.

10. Rain is falling from the heavenly shield, already seen on page 36, here however designating different planets (Mars and Mercury?) and the figure represented in the rain is the one which we have already seen on pages 12c, 17a and 21c. It is that of the old Uayeyab god N with a hatchet in one hand and an unfamiliar object in the other like the one on page 39a, and with another unknown object on his back shaped like a shield marked with a Kin. That this figure is really meant to represent N follows from the fourth hieroglyph (which, however, is not his regular sign 5 Zac), which is repeated on the head of the figure. The lower part of the hieroglyph is replaced by the year-sign just as it is in the hieroglyph on page 47, left, middle. The third hieroglyph contains 2 Caban signs, the first and second cannot be clearly identified.

11. This is a deity which I hardly think appears elsewhere. It has an animal's head resembling that of a bear, thus recalling page 7a, and it also has the paws of a bear. Of the hieroglyphs only a Kin-Akbal is recognizable.

12. Page 38a. Here we have another heavenly shield (Mars and Venus?) and under this shield B is represented seated and strangely enough facing himself, the figures not being back to back as on page 68a. Hieroglyphs 1 to 3 are wholly and 4, which is a head, is for the most part destroyed.

13. B is here represented in very close connection with a female figure. Cf. pages 21c-23c. The representation on page 68b is a still closer parallel to this passage. The first hieroglyph is destroyed for the most part, the second is B, the third is probably only a determinative of the latter, but has the sign for the west, and the fourth is Kan-Imix.

14. B holding a Kan sign is sitting on an object, which may be meant for the stone on which the idols were set up at the change of the year. Of the hieroglyphs the third is again B, and the fourth is probably the frequent sign a. The first sign is the most remarkable. In the Zeitschrift für Ethnologie, Vol. XXIII, p. 147, I stated that this was the sign for the change of the year, which is its meaning on pages 41b, 52b and 68a. The Kan year follows here after the Cauac year of page 37. The prefix of the sign is the hieroglyph for the east to which the Kan years belong. The Kan sign in B's hand also corresponds to this. The second hieroglyph is destroyed.

15. Page 39. The picture represents the lightning-beast with two flaming torches walking under the heavenly shield (Mercury and Jupiter?). Of the hieroglyphs the third belongs to B, the fourth has as a prefix the sign of the storm-god K, but otherwise admits as little of determination as do the first and second.

16. Here we see B in the rain holding in one hand a machete, and in the other a strange implement similar to that on page 37a. Of the hieroglyphs the second was the god's sign, the third is a, and the fourth may be an Akbal sign with Kin. The first sign somewhat suggests the sign for the Moan; its prefix is curious.

17. Here in place of the picture and the superscription, owing perhaps to lack of space and in order not to omit the last picture, we have a vertical row of seven hieroglyphs interrupted between the sixth and seventh by the red and black numeral belonging here. The top sign is effaced and the second is B's. I will not venture to determine the third, which contains a Yax. Could it belong to the serpent deity H? The fourth is probably Kan-Imix and the fifth is indistinct. And the same is true of the sixth, the prefix of which we have already met with as the sixteenth hieroglyph on page 24, and shall meet with again on pages 53, 56, 58, 61, etc. The seventh sign, which is quite at the bottom, consists of a vessel with a foot-print beneath it; it seems to be in the place of the picture.

18. The entire section ends with a picture of B, who carries the hatchet and probably the copal pouch. The hieroglyphs are wholly obliterated.

Pages 40a—41a.

The following Tonalamatl, one of the form of 10 × 26, has suffered much from the carelessness of the scribe and from injury. I have attempted to restore it as follows:—

The first row should be read from top to bottom, and then the second in the same order.

The six subdivisions all refer to some activity of B. Among the 6 × 4 hieroglyphs his sign occurs five times as the fourth and only in the last group as the third. Let us now examine the six groups individually.

1. B is traversing the water in a canoe, as on pages 29c and 40c, with the paddle in his hand. All the hieroglyphs belonging to him are obliterated.

2. B is sitting on the laterally elongated head q, which here, as on page 69, is enlarged and drawn with special care. Seler ("Charakter der aztekischen, etc. Handschrift" in the Zeitschrift für Ethnologie, 1888, p. 83) discusses this sign in connection with the day Men. It seems to me to denote unlucky days, the influence of which may here be checked by B. B holds in his hand a hatchet. The head (q) is repeated in the third sign, perhaps also in the second, and the superfix of these two signs is probably the same as that of the sign beneath the picture of B. The first sign is mostly destroyed.

3. As on pages 30a and 31c, and again just as on page 69a, B is sitting on the tree of life or sacrificial tree. A branch of this, which he grasps in one hand, ends in a serpent-head, and the root of the tree also represents B's head. Around the god's head are again the familiar dots, probably signifying stars. Of the hieroglyphs, the first is probably f, the second is destroyed, the third may be a variant of a, although it recalls the sign which, I believe, has the meaning of 73 days on pages 46-50; the prefix of 1 also suggests this meaning.

4. B's head is again surrounded by stars and he holds in one hand the outline of a hieroglyph. He is sitting on a peculiar ornamented structure resembling the crenelations of a wall. This wall displays the spiral which we found also on pages 33b-35b, and which in the treatise, "Zur Maya-Chronologie" (Zeitschrift für Ethnologie XXIII, p. 147), I regarded as an abbreviation for a serpent and hence as a symbol of time. It is further to be noted that B is wet with rain and with this the third hieroglyph is in keeping, if it is actually intended to denote the rainy season and not the week of 13 days ("Zur Entzifferung" V, 6); still the red numeral 13 below is more in keeping with the second meaning. The second sign is an Ahau with the leaf-shaped prefix, which also appears in the first sign of the third group. The first is effaced.

5. B, represented with a gala mantle hanging down in front and with the copal pouch, is sitting on a head, which looks like his own, especially as to the eyes, but which notwithstanding probably belongs to D and is marked with Ik (wind) and Cauac (cumulus clouds). Of the hieroglyphs the first and second do not admit of positive identification, and the third is Kan-Imix.

6. The god is sitting on a mat in a house. All the hieroglyphs except his own are obliterated.

Pages 42a—44a.

Another Tonalamatl of the form of 10 × 26; I have restored the effaced day-signs as follows:—

Thus the month days are the same as in the preceding Tonalamatl, but should be read in a different order:—Oc, Cib, Ik, Lamat, etc.

Here each of the 8 subdivisions has 6 hieroglyphs, and the order is as follows:—

A few of these signs are common to all the groups. Thus the first sign (v), as far as what remains is distinguishable, seems to occur in all the groups. It has the leaf-shaped prefix, but I cannot understand the rest of it; we shall find it again several times on pages 29c-41c.

Again the sign in the sixth place, as far as we can see, is always the head without an underjaw and the tuft of hair tied up on top of it (O, according to Schellhas), which we found above on page 25 and which we shall meet again on pages 65-69 no less than 13 times, with regular intervals of 6 signs between them. Indeed that passage is a remarkable parallel to this one.

That the sign for B, who here too plays the most important part, occurs often, is self-evident. It appears in the fourth place, in the 1st, 3d, 4th, and 7th groups, and in the third of the 8th group; in the 6th group it is destroyed. In the 2nd and 5th groups B has neither picture nor sign.

The hieroglyphs of the cardinal points I shall mention in connection with the separate groups. They are especially conspicuous in this section, being sometimes represented in full and sometimes in an abbreviated form as mere prefixes.

1. B with arms crossed sits above a serpent denoting time, and holding in its coils the cross b, which so often refers to astronomical conditions. Above the head of the serpent is the vessel with the three Kan signs, which we have already found several times on pages 25-28. It is remarkable that the flourish, which usually appears as the nose-ornament of the sun-god G (e.g., pages 11b and c), is added to these Kan signs. As the stars are again indicated on B's head, he plainly denotes a time-god here. The third hieroglyph, the sign of the east, corresponds with this meaning, and the Kan sign, which we see in the fifth hieroglyph probably combined with Ahau, also belongs to the east; the prefix of the fourth hieroglyph is the sign for the west.

2. A deity whom we shall probably have to call F, the god of human sacrifice, is sitting on a stepped pyramidal structure (a teocalli as a place of sacrifice?). He holds something in his hands, resembling a long and broad scroll, joined to which is the head of the god of the north, C, and in the third hieroglyph of this group the sign for the north also appears, prefixed to the head of F, who seems to be repeated in the fourth hieroglyph. The fifth hieroglyph with an Imix is unintelligible to me.

3. Page 43. B is sitting in the water, the copal pouch hangs from his neck and the hatchet is raised as if ready to attack. The second hieroglyph clearly denotes water, while the third is the sign for the west and the fourth is the sign for B, its prefix being the sign for the east abbreviated; the order of the cardinal points is thus exactly the reverse of that in the first group. The fifth hieroglyph is not clear to me, but it appears to be repeated in the same place in the next group.

4. B is sitting here astride a sort of bench again holding the hatchet in his hand. Belonging to this picture in the third hieroglyph is the sign for the south, which is repeated in an abbreviated form in the fourth hieroglyph.

The fifth is Kan, joined to what appears to be the same sign as the one found in this place in the preceding group. The second sign is indistinct.

5. This is an aged deity, probably M according to Schellhas, seated on an indefinite object. In front of the deity is a Cauac sign, which contains exactly the same cumulus clouds as those in the sign 5 Zac, which belongs to N. Cauac, however, belongs to the south, and therefore corresponds with the north of the second group on page 42. Sign 5, a Kan, corresponds exactly with the same sign in the fifth place of the preceding group.

6. Page 44. B seems to be in a state of collapse. Behind him is a second person, who is either trying to support him or to pull him up by some kind of a sling. I think the second person is E, the grain-deity, if it is not Seler's young god. If the hieroglyphs were not completely effaced, they would probably shed some light on this interesting passage.

7. Here we see B, holding a fish in his hand, and sitting on a hieroglyph, which is compounded of Imix and a prefix, which resembles the tortoise head and which appeared once before in this combination on page 32a. This passage recalls page 40a, where B is seated on the laterally elongated head q. Nothing more can be said of the hieroglyphs, than that 6 is the head without an underjaw.

8. B is sitting here in a house; his sign in the third place has Yax as a prefix. Hieroglyph 5, with the number 4 prefixed, recalls the one which we found on page 21c belonging to the baldheaded old man. Hieroglyph 4 is the common Kan-Imix.

Page 45a.

The last page on the front of the first section of this Manuscript is used for a series, which presents itself as a second improved edition of the series which was found on pages 31a-32a. The very fact that the writing is so much better proclaims it an amendment. The chief aim of both series is the same, viz:—to bring into unison the numbers 91, 104, 260 and 364. But the two series gain this end by different means. On page 32 the series begins with 91, and at first has only 91 as a difference, until with 728 a multiple of 104 and 364 is obtained, then it returns to the simple difference 91, in 1456 it obtains again the 104 and 364, loses these two last numbers once more in 1820 and finally in 3640 obtains the desired multiple of all four numbers, which is retained in 7280, 14,560, 21,840 and 29,120. The series on page 45a proceeds much more briefly. It begins at once with 728 (91, 104, 364), loses the 104 in 1092, gains the 260 and loses the 104 in 1820, arrives at divisibility by all four numbers in the 3640, loses the 104 again in 5460, but then comes to a standstill after having obtained the same multiples (double at that) of 3640, which I mentioned just now in the preceding series. Indeed it can be seen from what is legible in the third column above, that the series went still further. But so much is obliterated that I have obtained the numbers 14,560 and 21,840 in both series only by conjecture.

In the earlier passage the starting-point of the series is the day XIII Akbal and in the one before us it is the day XIII Oc. In the former the days specified were 91 days apart from each other, and here they are separated by 104, i.e., XIII Ezanab, XIII Ik, XIII Cimi, XIII Oc.

The initial days of the two series, XIII Oc-XIII Akbal, are separated by 13 days, and the reversed series, XIII Akbal-XIII Oc, by 247 days. Hence the subject of both passages is essentially the week of thirteen days, i.e., the year of 364 (28 × 13) days.

Now this series is also accompanied by a number amounting to millions. It is in the second column of page 45; only, in order to understand it, we must add a zero as the bottom figure; then it becomes 1,278,420. XIII Oc stands below this number as the beginning of the series. The first column has 30 as an encircled number and below it the normal day IV Ahau.

The large number must have been formed as follows:—

The point of departure was 230, the interval between IV Ahau and XIII Oc, to this was added 98 × 260 = 25,480, the sum being 25,710. The result of this number added to 11 Ahau-Katuns = 1,252,680, was 1,278,390, which number is not revealed in the Manuscript. It is concealed in XIII Oc 3 Mol (2 Muluc). But 1,278,390 = 42,613 × 30, i.e., it is divisible by the interval XIII Oc-IV Ahau.

Now if we add to this large number the 30 set down in the Manuscript, the result will be the above-mentioned 1,278,420. This number in the Manuscript has the date IV Ahau 13 Chen. (2 Muluc). It is, of course, divisible by 30 and by 260, hence = 42,614 × 30 and 4917 × 260. It corresponds not merely in this respect with the largest number on page 31a, viz:—2,804,100, but also with regard to its divisibility by 78, 156, 195, which are all multiples of 13.

On page 45a, top left, there were doubtless five hieroglyphs, of which the two topmost ones are effaced. First we see only the sign of the eleventh or twelfth month, Zac or Ceh, with an uncertain number prefixed, then the signs for beginning and end are distinctly legible. Ceh begins and Zac ends the year of 364 days; see page 4 of my treatise "Zur Entzifferung V."

Pages 29b—30b.

We come now to the middle section of pages 29-45, in which we shall not be so hampered by obliteration in our attempts at interpretation, as we were in the upper section.

We have here first a Tonalamatl of the usual kind, arranged as follows:—

That is to say, the 52 days divided into four equal parts.

To these four divisions, as on page 23b, belong the four usual forms of animal food, which are joined in three places to Kan (bread) and probably denote sacrifice. They are, first a mammal, which, however, is erroneously represented by a fish; second, a fish, third an iguana and lastly a bird. I would add, that in the hieroglyphs above, the east, north, west and south correspond in turn with these representations of food.

The hieroglyphs are arranged as follows:—

Of these, 2, 6, 10 and 14 are the cardinal points just mentioned; 4, 8, 12 and 16 are the sign for B, and 1, 5, 9 and 13 are the head with the tuft of hair and the Akbal eye to which I attribute the meaning of beginning. Likewise the remaining four signs, 3, 7, 11 and 15, although they are not exactly alike, have something in common, the 15th being a distinct Imix; they are not yet wholly intelligible to me.

Four pictures of B belong to these hieroglyphs. In the first the god is seated with crossed arms on two of the ordinary astronomical signs (Jupiter and Mars?). In the second, where he is pointing forward with his hand, there are footprints on his seat, as, for example, on page 35a. In the third the seat contains the usual cumulus clouds in clusters. Finally, in the fourth, he is seated on the tree of life or of sacrifice, the hatchet is in his hand and he is clad in the gala mantle; cf. pages 31c, 40a, 69a.

Pages 30b—31b.

This passage is in some respects closely related to the preceding Tonalamatl, but in other respects it differs significantly from this and from what is usual, for the Tonalamatl is divided here into only four principal divisions of 65 days each, which begin very regularly with the days VIII Oc, VIII Men, VIII Ahau and VIII Chicchan. There are neither subdivisions nor the usual pictures belonging to them. But on the other hand each of the longer periods of time written down here have eight hieroglyphs for each section in the usual order.

B's sign occupies the places 6, 4, 4 and 4; from this it follows that here too he forms the principal subject.

Here, as in the preceding Tonalamatl, the first place in each group contains the sign denoting beginning, while the eighth sign is invariably the head without an underjaw, which seems to me to refer to fasting, as if a fast-day fell at the end of every 65 days.

In the fifth place we see in succession the four animals, which in the preceding Tonalamatl are not included in the groups of hieroglyphs. Here they stand in the order of mammal, bird, amphibian and fish, but the bird in the second group is replaced by the sign which usually occurs with the dog (lightning-beast).

The signs in the second place are those of the cardinal points, and they are given in the same order as in the preceding Tonalamatl, i.e., east, north, west and south, so that they do not belong to the same animals as they do there.

The third signs are the cardinal points again, but in the abbreviated form discovered first by Schellhas, and in a different order:—west, north, east and south, and always joined to the head of C around which everything revolves as around the polar star. The Kan sign with different accompanying signs occupies the seventh place in the first group, and the sixth in the other three.

Four signs still remain:—the fourth of the first group I am inclined to consider the abbreviated sign for the sun; the seventh of the second, rain with the sign for the west as a prefix; the seventh of the third, Caban, ground, with the sign for the east as a prefix; the seventh of the fourth is Kan with the Yax sign above it, probably denoting the vegetable kingdom.

Pages 31b—35b.

This entire passage is devoted to a single Tonalamatl, which is divided and written out in an unusual manner. Like the preceding it is divided into four parts of 65 days each, but the remarkable thing about it is that these divisions of 65 days are each subdivided into two periods of 46 and 19 days, and the 46 days again into eight unequal parts, which are exactly the same each time, while the 19 days run their course without further subdivision. On pages 33, 34 and 35 this 19 is always on the left at the bottom, on page 32 it is wanting, probably because it was self-evident and there was no suitable place for it.

We shall next discuss the division of these four periods of 46 days each. This division is indicated with especial exactness on these pages, since not merely the length of the separate divisions and the week days are specified, but also the month days. This representation has the additional peculiarity, that the two columns on each page must be read from bottom to top, and of each group of two days standing side by side, the one on the right is to be read first and then the one on the left. If the Tonalamatl were written in the usual manner, it would have the following form:—

Instead of this we read in greater detail as follows (the pages and the stated length of time are in parentheses):—

In spite of the seemingly wholly irregular division of time, the following relation, which is certainly not accidental, results from this arrangement:—the first of the eight members of each row is one of the days which may begin the year and the months, and the eighth, on the other hand, one of the four regents of the year. The remaining six members are the remaining 12 of the 20 days repeated twice and the second always corresponds with the fifth of its own series, and the third to the sixth and the fourth to the seventh of the following series.

Two pictures of god B belong to each of these periods of 65 days, the first of these pictures referring to the divided period of 46 days and the second to the undivided one of 19. It is also in agreement with this that on pages 61 and 62 the fourth, sixth and eighth pictures represent the god as rising from the jaws of a serpent—the serpent being represented each time as lying in water which invariably contains the number 19.

As the hieroglyphs belonging to the periods of 46 days are allied to one another, and as this is also true of those belonging to the periods of 19 days, I will first consider the hieroglyphs of the first period by themselves, then those of the second, and the pictures shall be treated in the same manner.

Therefore, let us first examine the four pictures (1, 3, 5 and 7) on the right side of the pages:—

1. The first page shows the god walking with the official staff in his right hand, in his left the hatchet raised for a blow and with the copal pouch hanging from his neck.

2. He is walking and holding a flaming torch reversed in his right hand, in his left the hatchet is raised aloft, the pouch hangs from his neck, the mantle is indicated and around his head are the little circles which are so frequently his adjuncts and probably signify stars.

3. He is walking and holding the reversed torch in his left hand and the hatchet in his right.

4. He is walking and holding a torch in each hand. He wears on his head the head of K. He seems to be bringing storm and fire.

Now let us examine the hieroglyphs, which I have numbered thus:—

The first hieroglyph on each page certainly represents one of the cardinal points. They are in the usual order:—east, north, south and west.

2 is the same sign on each page. I take it to be the sign for Xul = end, denoting, it may be, the end of the period of each cardinal point.

In each group 3 is the head with tuft of hair and the Akbal eye; probably the sign denoting beginning. This beginning and end occur most distinctly repeated on page 63, and the end alone eight times at the bottom of pages 61-62.

On page 31, 4 is B's sign, on page 32 B's with the prefix of the north, on page 33 it is B's sign again and although quite indistinct its is plainly joined with the east. On page 34 there is another indistinct sign which may be that of the serpent deity H.

Owing to indistinctness I do not venture to determine the fifth sign on pages 31 and 33; on page 32 it is the laterally elongated head q with the Ben-Ik superfix, and on page 34 the ordinary Kan-Imix.

The sixth sign varies as much as the fifth; it seems here to denote four different gods, perhaps the four given on pages 25-28. On page 31 it is a Cauac, the prefix of which here, however, suggests K, on 32 it is certainly the hieroglyph of E and on 33 possibly of A, on 34 it most resembles Muluc of the day-signs, but also suggests the line crossing F's face from top to bottom.

We come now to the four pictures 2, 4, 6 and 8 and to the hieroglyphs belonging to them, which are on the left side of the pages and belong to the periods of 19 days.

1. B is pictured walking, raising the hatchet in his right hand, and holding an uncertain object in his left; the serpent with the 19 set down in its coils does not appear here. The 2nd, 3d and 4th pictures belong together. In each picture on these three pages there is a serpent with water in its coils and the number 19 in the water, denoting the number of days belonging here. As on pages 61 and 62 B is emerging from the open jaws of the serpent. In each case he is brandishing the uplifted axe in his left hand. The difference in the three pictures consists, first, in the fact that only in the 2nd and 3d B wears the copal pouch, second, that only in the 3d and 4th he has an implement in his right hand (the two implements differ somewhat but are both, apparently, adapted for hanging up) and third, that only in 3 the whole picture is painted blue, which means that the entire scene is enacted under water.

The hieroglyphs are as follows:—

The first in all four cases is a Manik, i.e., originally a grasping hand, perhaps referring to the chase; on page 32 it has a prefix and on pages 33-35 a superfix corresponding to the first.

The second sign on each page is simply B's.

The Cauac sign in the third refers in all four cases to the water represented at the bottom of pages 33b-35b. On page 32 it has an Akbal as a superfix, on 33-35 a prefix, which is familiar and in keeping with the sign and probably also the same suffix, though it is indistinct on page 34.

The fourth sign shows, as do several other things, that the representation on page 32 differs from that on pages 33-35. On the first of these pages we see an Imix with a puzzling 1 prefixed. If the numbering of the days really begins with Kan, as is probable in this Manuscript, then Imix is the 18th day and 1 + 18 might denote the 19, which is not set down here. On pages 33-35 this sign contains the spiral, which refers to the serpent in the picture below (and probably therefore to time). A curious element, however, is the numeral 9 prefixed three times to the spiral. This number is rarely a prefix, but it occurs, for example, on pages 33a and 35a before the cross b and on page 60 right, middle, prefixed to Xul (= end). The interval 9 occurs in this Tonalamatl 16 times, including therefore 117 of the 260 days.

The fifth sign each time contains the head without the under jaw, just as it recurs regularly in the preceding passage, pages 30-31.

The sixth sign in each group is the not uncommon compound of Caban and the sign, which resembles Muluc and which we saw before in the sixth place among the hieroglyphs on the right side of page 34.

Pages 35b—37b.

That is, a regular Tonalamatl of five parts, 5 × 52. That the 52 days are divided into two halves (11 + 6 + 9 = 4 + 7 + 9 + 6), may only be accidental.

I will designate the hieroglyphs of the seven divisions thus:—

I will first consider those signs, which are repeated and by means of which the sections seem to be brought into connection with one another. But I shall attend in detail to those hieroglyphs which contain characteristic references to each picture, when I discuss the latter.

The first place both among the pictures and among the hieroglyphs again belongs unquestionably to B. He is plainly designated in the 10th, 17th, 21st and 26th hieroglyphs, but, for an unknown reason, C's sign is joined to B's in the 16th, probably also in the 6th and perhaps in the 9th, and in 20 and 28 C's sign forms an integral part of a hieroglyph. Now in discussing the great Tonalamatl, pages 4a-10a, I attempted to make it appear probable that C belongs to the eighth day (Chuen) and in that case the Chuen sign in the thirteenth hieroglyph may be probably set down here. Further, in discussing pages 25 to 28, I expressed the conjecture that this Chuen sign might simply mean eight days, if we begin with Kan as the first day, for which proceeding there is some warrant in the "Dresdensis." Now, in hieroglyphs 8 and 24 we find an 8 inscribed; in hieroglyph 8 it is joined to an Imix, exactly as on page 39c; on page 65a it is joined to Kin, and on 67a and 68a to a hand. Is it possible that here also the 8 is intended as a sign for Chuen = C?

Then the familiar Kin-Akbal sign (day and night) is in the fourth place as well as in the eleventh and nineteenth.

The other signs which appear but once, I will discuss in connection with each of the seven pictures:—

1. A serpent in the water, with B emerging from its head, exactly as on pages 36a, Tro. 26 and Cort. 10.

The third sign, that of the serpent-deity H, refers to the serpent. The first sign is the one which I think may be Caban-Muluc, while the second, owing to its indistinctness, eludes interpretation.

2. This also represents a deity sitting in the water, whom we are probably safe in calling H, for the top of his head changes into a serpent, ending, however, in a bird's bill holding a fish. The deity holds up both hands. The union of serpent and bird should be noted in connection with the fourth picture. The deity is represented in the fifth sign; the sixth, seventh and eighth signs have already been discussed.

3. B is traversing the water in a boat, exactly as on pages 29c, 40a and c, and 43c. Here, however, there is a person beside him (probably a woman) whom, from the ninth hieroglyph we recognize as the deity E, unless this sign is C's. In 12 we see with Kan a sign which may suggest the usual hieroglyph denoting a year.

4. A serpent is pictured here, with a bird sitting upon it. We met with the same bird on page 17b. Schellhas, "Maya-handschr.," p. 51, has already expressed the opinion that this is probably a rebus for the name Quetzalcoatl or Kukulcan, and this theory is certainly worthy of consideration. In this connection I would call to mind that it is probably also Kukulcan with serpent and bird who occupies the first place on page 4a. The bird appears again in the fourteenth sign, while the thirteenth is a Chuen, which, according to the statement made above, may be connected with the C in the sixteenth. The fifteenth sign is the cross b, which probably denotes the connection between the thirteenth and sixteenth or else between the bird and serpent. Or is Chuen intended here to represent the serpent and not the ape?

5. This picture represents B carrying a burning torch, with the copal pouch hanging from his neck. His left hand touches a strange object, a kind of frame, the top of which ends in the head of a bird of prey.

The eighteenth sign is obliterated and the twentieth is a curious combination of Caban, C and the front part of K.

6. B is walking, with the hatchet in his left hand and in his right an object which looks like the representation of sounds issuing from musical instruments, as on page 34a. Perhaps B is represented here as the air-god.

The twenty-second sign is the familiar Kan-Imix. The twenty-third sign (w) is not intelligible to me; it occurs on pages 19c, 40b, 58, on the right, with a superfix suggesting K.

7. Water, in which a small human being seems to be emerging from a snail (the symbol of birth). Above the water is B, grasping a serpent which is in the water, as if to protect the new-born being from the serpent. The twenty-fifth (with Kin) is the so-called bat-god, who on page 50 at the left ends the series of twenty gods. The twenty-seventh sign (with Yax) is still undetermined.

Pages 38b—41b.

The sum of the black numbers is 104, the whole is, therefore, a double Tonalamatl = 5 × 104 = 520. While the series on pages 31a-32a primarily brought the 91 and the 104 together, and the series on page 45a accomplished the same result with the 104 and the 364, here, though the process is a different one, the 104 is combined with the 260 in another number.

It is characteristic of this part of the Manuscript, that the astronomical rectangles, which are very rare in the preceding pages, appear here in no less than five of the eleven divisions and six of them represent showers of rain. One is very readily, therefore, led to infer that the 104 days have reference to the rainy season and to its dependence upon the position of the planets. I will now analyse the eleven sections separately.

1. Rain is streaming down from two astronomical signs (Mars and Jupiter? Day and night?) and in the rain stands a black human form, grasping an implement with the right hand held downward and pointing upward with the left. It has the vulture head which occurred on pages 8a and 13c.

Hieroglyphs 1 and 2 represent the sun and moon, both surrounded by half white and half black envelopes, which must denote clouds. The third sign is Imix, which just here might refer to the rainy season productive of nourishment. The fourth sign is the vulture head of the picture.

2. B is walking in the rain and holds in one hand a stick pointed at the lower end. This is doubtless a farming implement, likewise occurring frequently in the Tro-Cort., which was used for making furrows or holes in the ground.

The second hieroglyph is B's, the first is Caban = earth, the fourth might be a compound of Caban and Muluc, referring to the rain, and the third is the familiar Kan-Imix, which, as the designation of food and drink, would be especially appropriate here.

3. B is apparently resting from tilling the soil, since he is sitting on a support consisting of the signs just spoken of, i.e., Caban and Muluc (?).

The latter signs are repeated in the second hieroglyph, while the third is B's with the sun-glyph (?) prefixed; the first is the head apparently open on top with the Akbal eye, probably the sign for beginning, and the fourth is the familiar sign a, which I think signifies a good, auspicious day.

4. Page 39. This represents a violent shower of rain, which might be pronounced a cloud-burst. The old red goddess with tiger-claws and a serpent on her head is pouring water in a stream from a jug. The same goddess occurs on page 43b and on the last page, 74.

Her hieroglyph is the second; it is more distinct in the two other passages. The first part of the third hieroglyph is indistinct, and the second part is the hieroglyph denoting the year. The first hieroglyph is a head with the Akbal sign, and the fourth is the usual compound of Kin and Akbal.

5. The cloud-burst seems to have destroyed the cultivation of the field, for B walks forth again with the implement for tilling the soil, as in the second picture. The second hieroglyph is B's with the prefix of the west, therefore probably denoting sunshine, the first again contains Caban and Muluc and the fourth is Kan-Imix referring again to the produce of the field. I shall not venture to explain the third sign here any more than I did in the previous passages. Compare page 8b.

6. B is again sitting in the rain and under the same astronomical signs as before on page 38. He is pointing downward (to the sprouting seed?). He has the sun-glyph on his back. The first two hieroglyphs are unfamiliar to me (Yax); the third is Imix with the sign for the west, and the fourth is again Muluc.

7. Page 40. B is plunging down headfirst from the same astronomical signs and is brandishing the hatchet.

Hieroglyph 1 is the cross b, 2 is B's sign, 3 probably that of the grain-god E, and 4 being Kan-Imix refers to grain. Favorable weather seems to have set in.

8. The astronomical signs are not the same as those in the three preceding instances (Mercury and sun?). Below them is a deity with tortoise-head—in my opinion, the sign for the longest day—holding a torch in each hand and thus referring to the heat.

Hieroglyph 1 (w) with the superfix suggesting K still puzzles me. 2 is the cross b, 3 is the tortoise-head with the number 4, which probably refers to the Kan, Muluc, Ix and Cauac years, as the 4 sometimes appears prefixed to N's hieroglyph. In exactly the same way the tortoise-head with the tortoise itself occurs frequently in the Cortesianus. 4 is the sign of the year with prefixed Kin and Cauac, i.e., day-Cauac-year.

9. A thunder-storm, which is very appropriate after the longest day. The lightning-beast, likewise holding a burning torch, is plunging down from the astronomical signs, which are different ones again (Venus and the moon?).

The second hieroglyph contains the sign of the dog together with the cross b, while the third is that of the north-god C, and the fourth is Muluc. I cannot explain the first sign; its prefix, which rarely occurs, appears also on pages 23b, 25a, 37b, 63a, and possibly on pages 53b, 62-63a, 69b.

10. Page 41. Another representation of rain. There is an old deity in the rain, who is N rather than F, denoting the end of the old year. He is emerging from a snail (cf. with this page 37b), and is pointing upward; a part of the first hieroglyph is on his head.

This first hieroglyph recalls the sign which, in the Zeitschrift für Ethnologie, XXIII, p. 145, I ventured to connect with the change of the year; but it also suggests the snail pictured below, hence the birth of the new year. The beginning of the year for the Mayas, although of course not for all parts of the country, is fixed, as a rule, to fall on the 16th of July. This would agree admirably with the eighth and ninth sections, which represent the time of the longest day and of thunder-storms.

The second hieroglyph is B's, the fourth the cross b, probably referring here to a union of two years, and the third with its Cauac to the duration of the rainy season or to the god N.

11. The rain seems to fall with less violence. B is seated, clad in the gala mantle with a Kan on his head, as the sign of grain. His headdress also strongly recalls that of the grain-deity E (which is also the case of the headdress on the preceding picture.)

Hieroglyph 1, the upper part of which is very like that of the first sign of the preceding group, looks like a plaited mat. Does it not suggest that the name of the first month of the new year is Pop and that this word is denoted by carpet, mat? Hieroglyph 2 is B's, 3 is the sun between a dark and a bright sky, and 4 is the common Kin-Akbal, day and night.

If the seventh picture really refers to the beginning of the year, then the entire period of 104 days extends from April 15th to August 2nd, which, with the addition of the five days not counted at the end of the year, does indeed make 109 days. All this, however, is only true on the supposition that I have not seen more in these representations than they contain.

Pages 41b—43b.

Another regular Tonalamatl, and like the preceding one apparently referring to the change of the year, the tilling of the soil and the rainy season. B's sign is regularly repeated in the second place of all five groups of hieroglyphs, and moreover each of these groups has six signs. The head with the missing under jaw is in the fourth place of groups 2 and 3, in the sixth of group 5 and might perhaps be intended also in the fourth of 1 and 4. The usual Kan-Imix is in the third sign of group 2, in the fifth of 4, and the fourth of 5; possibly also in the fifth of 1; the third hieroglyph in group 3, at any rate, contains Imix.

Let us now consider the five groups individually:—

1. The rainy season seems to have been delayed; the beginning of the year draws near. B is kneeling on a kind of footstool, the hatchet is in his right hand and his left hand holds a kind of chisel with which he is carving something out of the trunk of a tree. The purpose of the work is indicated by the god's own head directly below (probably placed in front of the tree as a model?). No doubt this is intended to represent the making of the statue of the god of the new year destined for the beginning of the year, as we know it from pages 25-28.

Corresponding with this is the first hieroglyph denoting the year with Yax as a superfix, and also the sixth being the sign to which in the article in the Zeitschrift für Ethnologie cited above, I attributed the meaning of change of the year. I cannot decide whether the third sign is intended for an Imix-Chuen with the sign of the south as a superfix, the fifth for a Kan-Imix and the fourth for the head without the under jaw.

2. Page 42. Prayer for rain. B (that is to say, his priest) is seated apparently on the same footstool. He is gazing upward and presenting a vessel containing an offering, the nature of which is uncertain. The vessel ends in a tube; cf. page 67b.

The first, fifth and sixth hieroglyphs are not finished, and the third is Kan-Imix.

3. The rain-goddess promises aid. B is seated opposite the old red goddess, who is holding intercourse with him. The god is seated on the Caban sign (earth) and the goddess on Muluc (rain?).

The first, fifth and sixth hieroglyphs are also unfinished; the third is Imix with its meaning intensified by the prefixed Yax (the luxuriantly growing grain?).

4. B is again tilling the ground in the manner already familiar to us. Under him lies his own head with the Imix-Kan sign, denoting food and drink, as a superfix. The first hieroglyph is the sign of the eighteenth month Cumhu, i.e., of the end of the year. The third is a Kin-Akbal, the fifth a Kan-Imix, the sixth is not finished, and the fourth may be intended for the head without the lower jaw, but it is carelessly drawn.

5. Page 43. The solicited rain begins. The goddess with the serpent on her head is pouring streams of water from her vessel.

The first hieroglyph repeats the month Cumhu, denoting the beginning of rain, before the close of the year; the third is the sign of the goddess met with on page 39b, here also with the sign for the west as a prefix; the fifth is her determinative, the serpent, and the fourth is Kan-Imix.

If the first sign in the first group is not regarded as the sign of the year, but as that of the sixteenth month (Pax) resembling it, and the fact is taken into consideration that there is an interval of 34 days between the second and fourth groups and of 40 days between the second and fifth, this would be found to correspond with the interval between the months Pax and Cumhu.

Pages 43b—44b.

This is the fourth and last series of the first part of the Manuscript; the first is on page 24, the second on pages 31a to 32a, and the third on page 45a. The first series is quite by itself, but the second and third are similar in form to this fourth, though their initial days are different from those of the latter:—XIII Akbal, XIII Oc and III Lamat. All three begin with differences which are divisible by 13:—91, 104 and 78, equal to 7, 8, and 6 × 13. All three aim and arrive at numbers which are common factors of 260, 104 and 364, and therefore also of 3640, which last number is written out in the other two series, while in this series it can only appear later on and then, increased by multiplication.

Since this series has the difference 78, the week day numbers remain the same, while those of the month days must advance by 18 each, that is, from the hidden starting-point III Lamat they go on to III Cimi, III Kan, III Ik, III Ahau, etc., until the tenth member of the series is 10 × 78, i.e., 3 × 260 and thus comes again to the day III Lamat.

From 780 onward this number is itself always the difference of the higher terms of the present series. At the same time 780 days are the duration of the apparent revolution of Mars, which is here supplementary, as it were, since page 24 treated of the revolutions of the sun and of Venus, and also of those of the moon and of Mercury. Hence in the present passage we find the numbers 1560, 2340, 3120 and 3900, always accompanied by the day III Lamat. The larger numbers require a few corrections; I read them 13,260 (17 × 780), 15,600 (20 × 780), 31,200 (40 × 780), 62,400 (80 × 780) and 72,540 (93 × 780). The very largest again are correctly set down; first 109,200 equal to 140 × 780, but here also equal to 1050 × 104 and 300 × 364, so that in this series the goal aimed at is not reached until later than it is in the two preceding series. Then follows 131,040 = 168 × 780, 1260 × 104, 360 × 364, but finally 151,320, which number = 1455 × 104 and 194 × 780, but is not divisible by 364.

Detached in the usual way from this series on the left of page 43 is the number 1,435,980. Above and below it is the day III Lamat, further down IV Ahau, and between them is 352 in a red circle. This number seems to have been obtained in the following way:—The writer began with the distance between III Lamat and IV Ahau, which is 92, added to it 172 × 260 = 44,720, and subtracted the result 44,812 from 13 Ahau-Katuns = 1,480,440. The remainder was 1,435,628, which number would correspond to the date III Lamat 6 Zotz (4 Kan), which, however, is suppressed in the Manuscript. The 352 = 260 + 92 was added to this sum, and the result was the 1,435,980 written out in the Manuscript, i.e., a day IV Ahau 13 Zip (5 Muluc). Now this number is the one sought; it is 5523 × 260 = 1841 × 780 = 3945 × 364, and hence must also be equal to 263 × 5460, since the 780 and 364 are united in 5460. According to our present knowledge, it would seem to lie in the future, but not far from the present; the solar and Mars revolutions are united in it. There is but a single hieroglyph here, the hieroglyph of the animal which is the chief subject of the next section; from which it appears that the two sections are closely connected.

Pages 44b—45b.

This section supplements the pictures and hieroglyphs belonging to the series just examined. Therefore it likewise extends over 78 days and divides them as follows:—

These five days are plainly intended to be the days III Lamat, IX Manik, II Cimi, VIII Chicchan, III Cimi.

With regard to the real purport of this section, it is my opinion that it has reference to the time of the shortest day and also to the four winds and that this section therefore forms, in a measure, a contrast to pages 38-41, where attention was called to the rainy season, the longest day and the thunderstorms.

We see here in the first place four of the ordinary heavenly shields, with two astronomical signs each. I cannot decide, at present, whether these are 1st, the moon and Saturn, 2nd, Mars and Mercury, 3d, the moon and Mars, and 4th, Jupiter and Venus.

From each of these shields hangs a figure not unlike an heraldic beast. It cannot be the canine lightning-beast; it has no flames, it is cloven-footed and with the upper lip bent upward and the lower lip curved downward suggesting the storm-god K, and therefore probably represents the four winds; this wind-beast repeated four times also occurs on Cort. 2.

Six hieroglyphs belong to each picture. Those in the first place are pierced ears and refer therefore to the ritual bloodletting, which may have been performed at this season. In Tro. 5*b we also find the pierced ear; a pierced tongue (Tro. 17*b), however, does not occur in the Dresdensis. The second place always contains the sign of the beast like the one instance on page 43.

The third place seems to be devoted to the four cardinal points, i.e., to the four winds. First we see Akbal-Kin, i.e., the transition from night to day, the east. The north-god, C, is here in the second group; in the third we see Kin and beside it in the fourth place Akbal, both enveloped by clouds denoting the transition from day to night, the west. The fourth group, it is true, has the year-sign here, but with the compound Kin-Cauac prefixed, and Cauac always belongs to the south. I believe I have found a distinct reference to the season of the year in two other places. The fourth hieroglyph of the second group and the sixth of the fourth both have the familiar prefix suggesting K, the storm-god. The first of the two contains the month Mol (December 3d-22nd); the second might very well be the month Yax (January 12th-31st). This is quite in keeping with the distances 19 + 21 = 40 set down below.

In my "Tagegöttern der Mayas" (Globus LXXIII, 10) and above in my discussion of the great Tonalamatl under pages 4a-10a, I have assigned the day Chuen to C, and Muluc to K, i.e., the first to the dark north and the latter to the wind, which are both under consideration here. In fact, we find the Chuen sign in the fifth place of the fourth group with the same prefix that C has in the second group. The Muluc sign, however, seems to occur three times:—1st, group 1, sign 6, where it may be joined to the month Mol belonging here; 2nd, group 3, sign 5, joined to the Akbal, which also belongs here; 3d, group 4, sign 4, with a usual prefix. In the second group it may be included in the very similar month sign of Mol. Four hieroglyphs remain:—1st, Akbal in group 1, sign 5, hence probably denoting the darker time of the year in general; 2nd, A in 2, sign 5; 3d, E in 2, sign 6; i.e., probably referring to the death of the grain (I do not know to what extent this expression may be used in relation to the Maya country); 4th, Kan-Imix in 3, sign 6, perhaps expressing the hope of new harvests.

This finishes the middle sections of the pages of the first part of the Manuscript, and we must now turn back again to page 29 in order to examine the lower sections.

Pages 29c—30c.

Here is a Tonalamatl of four quarters, 4 × 65.

In the Manuscript 16 is again erroneously set down for 17 and the III following it is omitted. The initial day is exactly the same III Ix, as in section 29b above it, to which in other respects the passage now under consideration shows a great likeness, since the four familiar animals occur here as well as there. But in spite of beginning in the same way the days here are different ones, being the four regents of the year, as on page 9b.

The four parts are grouped together by the sign, which always occupies the first place in each part; I have denoted this sign by f, and I think it must have a very general significance, since from pages 29c to 40c it always begins the groups. The connection between the four parts is further shown by the four cardinal points in the second place:—the north in the first group, the west in the second, the south in the third and the east in the fourth. In the third place these cardinal points are again indicated by their usual abbreviations; the east is erroneously set down in the second group. These abbreviations are here invariably joined to the head of C as the representative of the north, the first of the cardinal points occurring in this passage; the others revolve about the north pole.

As B's sign always occurs in the fourth place, there is nothing further to be said concerning the hieroglyphs. We now come to the pictures:—

1. B is rowing a boat, as we have already seen him several times (36b, 40a, c, and 43c). To the left of his head there is a bird's head and in the left, bottom, corner, a pot in which apparently a soup of fowl is cooking, emitting bubbles. The Cib sign on the pot refers to the cooking or bubbling.

2. B, with his head surrounded by the familiar stars, is seated in water, in which are represented the iguana over a Kan sign, and the familiar spiral probably denoting a serpent. He is painted black (perhaps corresponding to the west?) and holds in his hand an implement not yet determined. Perhaps it may be intended for a tree, past which the water is flowing.

3. The god is seated, holding in one hand the spiral with a Kin sign over it and a Yax on top of that, and in the other hand something which looks like a bird's feather or a fish's fin. Above him is a fish with a Kan sign, as on page 27, where the fish and Kan are also combined.

4. Holding a hunting-spear, he is sitting on an animal slain in the chase, as on page 45c.

Finally, I have remarked that pages 42c-45c, the last part of the first division of the Manuscript, look like an enlargement or amendment of the section just considered.

Pages 30c—33c.

To begin with, the day signs are set down in the following order:—

Here then, as is frequently the case in this Manuscript, all the twenty days are specified. But in order to obtain equal periods of time, the left column should first be read from top to bottom and the following ones should be treated in the same way. Then each succeeding day is 17 days distant from the preceding, but in reality the interval is 117 days, since the same week-day is always implied. The hieroglyphs seem to indicate that these 117 days are divided into three distinct parts, 52, 39 and 26.

117 days, however, are equal to 9 × 13 and hence in what follows we find a black 13 set down 9 times as the interval between the days, and a red XI being the number of the week-day an equal number of times. Now, since the whole series extends over 20 such sections of 117 days, the duration of this calendar is 2340 days or 9 Tonalamatl.

Consequently we find nine pictures of the same god B. In five of them (in Groups 1-4 and 9) he is sitting before or on a sacrificial tree or tree of life; cf. 30b. It is probably not accidental that in these five cases the hieroglyphs refer to the cardinal points. In the eighth group the god is surrounded by the suggestion of one or more trees; he is sitting in water as if in a forest; or in a cave bordered by trees? In the remaining groups, 5, 6 and 7 he is seated on various supports, in 5 on an object, which is not completed and which cannot, therefore, be explained, in 6 on astronomical figures (Mars and Venus?) and in 7 on agave leaves. In 1 and 3 his head is again surrounded by those dots suggesting stars, in 4 there seems to be a bird (quetzal?) seated upon it and in 2 it bears what may be the Kin sign. In 1 and 5 he has the pouch for incense in his hand, while in 3 alone he wears the gala mantle and is painted black, just as he appears in connection with the same hieroglyphs on page 29c. He carries a hatchet in repose in 2, 6 and 9, and raised for a blow in 1 and 7. In 7 he also holds the Imix sign.

The hieroglyphs form nine groups of four signs each. The first hieroglyph, as is always the case in this part of the Manuscript, is the sign which I have denoted by f, and the second is always B's hieroglyph. The cardinal points are everywhere specified by two signs each; in places 3 and 4 of group 1, the west comes first and beside it is the sign for the east, erroneously used for that of the west (a like error occurred in the preceding Tonalamatl); in group 2 there are two signs for the north; in group 3 that for the east with the sign for the west beside it erroneously given for the east, and in group 4 two signs for the south. In groups 5, 6 and 7 we find in the 4th place the head of C, and the same sign in group 7 in the 3d place, where it is joined to another head, which may be that of a woman. The 3d sign of group 5 is incomplete and cannot be determined. The 3d sign of group 6 displays a repetition of the astronomical signs represented below. There still remain the 3d and 4th signs of groups 8 and 9. Of these the 3d in group 8 is w, which is as yet unexplained. The 4th might be interpreted either as Oc (day 7) or as Xul (end). Its prefix is a Yax sign. Finally, in group 9 the 3d sign is Manik (day 4), the 4th the elongated head q with the Ben-Ik superfix, which Seler assigns to Men (day 12).

Pages 33c—39c.

The beginning of this Tonalamatl is indicated by a large red dot on page 33. It resembles the Tonalamatl almost exactly above it on pages 31b-35b, inasmuch as its arrangement is an unusual one. I will here, as I did above, give it the form in which it would present itself if it were set down in the usual order:—

In this passage as in the earlier one, instead of employing the above concise order, a preference has been shown throughout for carrying out the whole series in such a manner that the week days are set down each time and not merely in the left column. It, therefore, has the following form in the Manuscript:—

I have arranged the whole series in four parallel periods of 65 days each, for the 65 appears throughout the computation, although the entire Tonalamatl is written out in one continuous line. On the right of page 35 the scribe seems to have wished to erase an entirely incongruous 4, and in writing the last 15, on page 39, he began to use the red paint prematurely, so that the top one of the three lines is red.

Attention should also be called to the fact that the second of my vertical columns contains the year-regents, the others only the days following immediately after them, while 12 month days do not occur at all. Also the intervening periods 9 + 11 (= 20), 20, 10, 15 doubtless reveal some design.

In order to avoid repetition, I think it proper to mention first, that in the twenty groups of four hieroglyphs each, the sign f always stands in the first place, but the hieroglyph of B, who is represented 20 times, usually appears in the second place, in the first and second groups in the third place, and in the 18th and 19th his sign does not appear at all. I will discuss the remaining hieroglyphs in their place in each of the 20 groups.

1. B is sitting in a house and holding the Kan sign in his hand.

The second hieroglyph is apparently meant for the Ahau sign (referring to the 17th day), which usually does not belong to B. This hieroglyph, which certainly bears a resemblance to Ahau and with which we have become very familiar in the inscriptions, occurs again in this Manuscript on pages 46b, c, 50b, 54b, 65a and 66a. The fourth sign is a combination of Cauac and Manik.

2. B is seated on what may be a tree, below him is the cross b, and he holds the hatchet in his left hand.

The second sign with an emphasized 6 as a prefix (cf. the same sign with the 6 on page 48, bottom, left, below the gods), has the usual Ben-Ik superfix, perhaps to denote that a lunar month has now elapsed, for this passage extends from the 20th to the 40th day of the Tonalamatl. The rest of the hieroglyph is unintelligible. In the 4th place we see a vessel with Imix, probably denoting pulque.

3. B is sitting in water, the hatchet raised in his right hand and his face turned upward.

The 3d hieroglyph is again Imix and the 4th a compound of Ik and Muluc:—wind and clouds.

4. B is seated on a reproduction of his own head or D's, beating a drum with his hand.

The 3d hieroglyph denotes the serpent-god H with the number 3 as a prefix. The 4th hieroglyph is a Chuen with the sign for the south prefixed,—at any rate the upper part of that sign.

5. B is standing in the pouring rain and looking backward.

The 3d sign here is a Caban apparently in a vessel. Following this in 4 is the hieroglyph which I have proposed to interpret as the sign for beginning (Globus, Vol. LXVI, page 79). This sign occurs again in groups 7, 12, 15, 17 and 19, and must therefore be connected with the principal idea embodied in this Tonalamatl.

6. B with folded arms is sitting in a house.

Aside from the usual leaflike prefix, the third sign is composed of two parts. The upper part looks like a plaited mat and suggests that the word for the first month of the year (Pop) is expressed by mat. The lower part is the sign, which occurs frequently especially on pages 25-28, and which very much resembles the familiar sign for a year of 360 days. We shall meet it again in the continuation of this Tonalamatl on pages 36 and 38. The three passages refer to the 74th, 139th, and 204th days of the Tonalamatl, and hence are 65 days apart.

The 4th sign is the cross b, with possibly the sign of the east as a prefix.

7. B is seated on the cross b, which is here undoubtedly meant for an astronomical sign. He holds a Kan sign in his hand and there is an Ahau sign on his back.

The naked crouching personage, pointing upward, should have especial mention here. The same figure recurs above as a prefix to the 4th hieroglyph. We have already seen it in the 39th hieroglyph on page 24, and shall meet it with especial frequency in the second part of the Manuscript. It is placed sometimes, as in this case, before a sign, sometimes after a sign and again two of these figures are placed back to back as on page 22c, and one of them is even placed upside down before another sign, where it seemed to me to be a sign for Mercury ("Zur Entzifferung VII," p. 11). This figure is represented independently only on the right of page 58. In the passage under present consideration this personage appears again on page 38. The two figures are connected one with the 85th and the other with the 215th day, and are, therefore, divided by exactly half a Tonalamatl or 130 days. Here we find it as a prefix of the supposed sign for beginning of which mention was made in discussing the 5th group. The 3d sign is the same astronomical one, which we saw below under B. It might refer to the Moan and to the change of the year, and thus indicate that a Mercury revolution was coincident here with the beginning of the solar year.

8. B is walking in the rain, both arms are stretched upward, and the pouch hangs from his neck. At the left top there is a black spot suggesting those which usually occur beside the sun and moon.

The 3rd sign is Manik, with a prefix. The 4th is an indistinct head, which may be C's, with an Imix sign as a prefix.

9. B is walking with the pouch hanging from his neck, and the hatchet in his hand.

The 3d sign, which is unusual, is very obscure, but suggests the fish on page 44c or that on page 36b. The 4th sign with the prefix of the north is very indistinct.

10. B is standing in water, his face turned upward while water is pouring from a cloud. The third sign is very complex. The top, left, suggests a serpent, the right a hand, the bottom, left, a Chuen and the element at the bottom, right, may be intended for a bird's head. Exactly the same sign, with the 4th part merely indicated, occurs 65 days later on page 38. The 4th sign is the familiar compound Kin-Akbal.

11. B is sitting in a tent, on the roof of which there is a vessel containing food of some kind.

The third sign, which is very complex, is indistinct. The 4th sign likewise consists of four parts, the left, bottom, part is probably the vessel, above it is a spiral (which usually means serpent or time). The right, bottom, is again the sign resembling the year-sign which was spoken of in discussing group 6. The component at the right, top, is indistinct.

12. B is sitting here on no less than four astronomical signs, he has the hatchet in his hand and the design on his back may be a shield or the elaborately ornamented sun-glyph Kin.

The third sign (denoting beginning?) has already been discussed in connection with group 7, which is 65 days earlier. The fourth is the sign of the year of 360 days or the month Pax with the Ben-Ik as a prefix. These signs are here suggestive of the beginning and end of the year.

13. Above B are astronomical signs (Jupiter and Mercury?) and also the sun and moon. The rain is pouring down upon the god, and a fish is placed beside him. He seems to have the same chisel in his hand which we saw him using on page 41b in connection with the beginning of the year. This again would correspond to the date indicated in the preceding picture. The shield (?) also is the same here as in the preceding group.

The third sign ought to represent the fish; the drawing seems to have been unsuccessful and the sign looks more like a bird and also resembles the third sign in the ninth group on page 36. The fourth sign is a Kin-Akbal.

14. B is seated on the elongated head q, which has an ordinary prefix. He is pointing upward with his right hand and the left looks as if opened to receive something.

The third hieroglyph contains a q like the one under the god, the fourth is an indistinct head (C's?) with an unintelligible prefix.

15. B is standing in water while rain is again pouring down upon him. He holds the hatchet raised in his left hand, while the fingers of the right are extended upward in an unusual manner. This is repeated in the third hieroglyph.

The third hieroglyph, however, is the same as the third in the tenth group 65 days earlier, only here the hand is more distinct, while the element below it is vague. The fourth sign is again the one denoting beginning. Compare the fifth group (130 days earlier).

16. B with arms folded is sitting in a house with the Cauac sign below.

The third and fourth hieroglyphs contain the sign resembling that for the year, which was mentioned in discussing the sixth group (130 days earlier). In the third a Kin is prefixed to this sign, while the superfix of the fourth is what I take to be a mat, which also occurred in the sixth group. The prefix is a figure suggesting the serpent-deity, which we have already met with in the tenth and fifteenth groups.

17. B, holding the hatchet, is seated on a Moan head, and the third sign is probably intended to represent the same Moan head, in front of which we find the same crouching person met with in the seventh group, 130 days earlier.

The fourth hieroglyph is again the sign for beginning, which we have already often met with, as, for example, 65 days earlier in the twelfth group.

18. B is sitting in the pouring rain under astronomical signs (Mars and Mercury?) to which those of the sun and moon are added. The god's face is upturned and he holds the hatchet in his hand.

The third hieroglyph may be the vulture head, to which a part of the unintelligible second hieroglyph may also refer. This second sign stands in the place of B's hieroglyph, which is wanting here.

The fourth sign contains the enigmatical numeral 8, which we found on pages 36b and 37b, and has the Imix sign as a prefix, as in the first of these two passages. The same compound appears on pages 67a-68a.

19. B is seated here on his own head, as in the fourth group he is sitting on D's. His hands are empty.

The second sign is again the vulture head instead of B's hieroglyph. The third is probably the head of the lightning beast, and the fourth is again the sign supposed to denote beginning.

20. B is sitting in water and holding in his hands a vessel with a Kan sign upon it.

The water (with Imix prefixed) is denoted by the third sign, while the fourth represents a head (with what is probably a hand pointing to the right above it), which I should prefer to consider the grain-deity E.

In conclusion I would call attention to the remarkable fact that every four pictures, which are separated from each other by four of the other pictures, i.e., after every 65 days, correspond in certain respects with one another, viz:—

1. Pictures 1, 6, 11 and 16. In all, and only in these, B is sitting in a house or tent, in 6 and 16 with his arms folded.

2. Pictures 2, 7, 12 and 17. In the first three the god is seated on astronomical signs and in the fourth on the Moan head, which I think refers to the Pleiades.

3. Pictures 3, 8, 13 and 18. Here in the last two B is sitting beneath astronomical signs. In all four pictures water, clouds and rain are represented.

4. Pictures 4, 9, 14 and 19. In the first and fourth the god is seated on D's head and on his own, and in the third on the elongated head q.

5. Pictures 5, 10, 15 and 20. Like the third of these five classes, these pictures are likewise distinguished by water, clouds and rain.

Now the first set of pictures is between the week days XIII and IX, the second between IX and VII, the third between VII and I, the fourth between I and XI, the fifth between XI and XIII, while the month days are quite different. Hence the conjecture is but natural that the pictures and week days bear some relation to one another, though that relation is still shrouded in obscurity.

Pages 40c—41c.

This is a Tonalamatl of the most ordinary kind, in which an unsuccessful attempt has been made to divide the subdivisions into equal parts.

In the groups of four hieroglyphs each, which belong to each of the six parts, the sign f always occupies the first place, and B the third. Let us now examine the six parts separately.

1. B is sitting in a boat and rowing (as on the top of the same page). Around his head there is again the suggestion of what may denote the starry sky, and in this picture his nose-peg is unusually large.

The second sign is an Imix, but it might also denote the thirteenth month Mac and therefore the Tonalamatl (13 × 20). The fourth sign is a fish forming a connecting link between the water represented below and the rest of the group.

2. B is seated on the Caban sign and his arms are apparently resting on an altar standing in front of him, on which fire is burning, indicated by the Ik sign, while the moon is placed below the altar.

The Caban sign below is repeated in the second hieroglyph, combined here as usual with a sign which may be Muluc.

The fourth sign is a head. I think the scribe meant to set down an 8 before it, but as there was not sufficient space for the heavy line after the three small circles, he indicated it by a black dot below the circles. Now, if we call the head D's, which of course cannot be asserted positively, this would be day VIII Ahau, and this, in fact, is twenty days from the beginning day I Ahau, as it is meant to be in this passage. There is no representation of food; can this have been a fast day?

3. B is seated on four astronomical signs. He wears the gala mantle and holds a serpent in his hand.

The second sign is b, and at the same time one of the astronomical signs. The fourth is the iguana prepared as food, recognizable by the spines on its back, as on page 25b. It is drawn in precisely the same curious fashion in Cort. 8 and 12c; hence it is represented in the picture by the serpent.

4. B is falling down from above headfirst. I believe that the numerous footprints below him are only intended to represent swift motion. The descent from above may only be intended here to bring the god into closer relationship with the head of the bird of prey in the fourth sign. That this head is again as usual joined to Kan, may refer merely to the fact that it was the Maya custom to eat bread with animal food. Compare page 27b. The second sign might be the abbreviation for the south.

5. B is seated on a mat with his hand extended as if to receive something. He is wet with water.

The second sign contains the mat, with what may be the sign below it, and the leaf-shaped prefix probably denoting the plant from which the mat is plaited. The very same combination is given on page 35c and a similar one on 38c. The fourth sign has the prefix of the west followed by two Kans, as if on this day (V Akbal) it had been the custom to eat tortillas without meat.

6. B is standing holding the hatchet. The fourth sign must denote venison, the fourth article of animal food. The second seems to represent the day Eb, with which the remaining 52 days begin, and if the prefixed 9 indicates nothing more than that the ninth day of the month is here meant, it is further evidence that the "Dresdensis" began the days with Kan and not with Imix.

In the discussion of this Tonalamatl I have omitted the mention of a very peculiar feature, which as yet does not admit of explanation. I refer to the numbers below the pictures. With the first picture we find 6 + 20, with the second 20, with the third 19 + 20, with the fourth 6 + 20, with the fifth 19 + 20, and with the sixth 6 + 20, i.e., with the exception of the second, 26 or 39, two multiples of 13. Now the question arises, should not one of these multiples have been set down with the second picture? There was no space left for a prefixed 19. Therefore the idea suggests itself that what we took to be an altar with the sign Ik above it, is intended for nothing else than this 19, and Ik is the 19th day, if we count from Kan as the starting-point.

Pages 42c—45c.

This is a Tonalamatl consisting of 4 × 65 days. If written out in the usual way it would run as follows:—

Since, however, the subdivisions are divided and the individual month days also are given for all the parts of the whole Tonalamatl, the representation follows the order which we have already found on pages 31b-35b and 33c-39c. In this place, as in the two former ones, I will reproduce in four lines what is set down in the Manuscript in one single line extending over all four pages.

Thus the days Chicchan, Lamat, Oc, Ben, Men, Ezanab, Ahau, and Akbal are repeated here twice, and the others occur but once. The 4 (17 + 48) strongly recalls the 4 (19 + 46) on pages 31b-35b. The repetition of six times eight days in each quarter of the Tonalamatl is closely connected with the fact that there are six Chuen signs on each page, two of which, however, are omitted on page 44. From this it follows, as we have already found on pages 25-28, that Chuen really denotes 8 days and that the count of the days in the "Dresdensis" begins with Kan. But the numbers 12, 15, 16 and 17 are entirely unexplained. They show no recognizable order and always stand near the bundle of Chuen signs. They recall the numbers on pages 25-28, which are equally irregular and unintelligible, and upon which, it is probable, light will break at the same time as it does upon these now under consideration.

We come now to the purport of this passage, which seems to be a further amplification of the contents of pages 29c-30c. The meaning is simply as follows:—every 65 days the god B discards a cardinal point and the deity presiding over it and installs another.

From this point of view let us now examine the four pictures.

1. Page 42. B is represented here as a warrior with the front of his body painted red. He is aiming a blow with his hatchet at a person sunk down before him, who, from the ornament above his head, seems to be the grain-deity E, the ruler of Kan and of the east, although the contents of this passage really demand a deity of the south, a ruler of Cauac. In a very similar way on page 27, E occurs with the completed Cauac years, instead of with the Kan years just beginning. Behind B's head is the sign of the discarded cardinal point, the south, while below it is a vessel with food, clearly a piece of venison with Kan.

2. Page 43 deals not with the removal of the old cardinal point, but with the introduction of the new one. Here B is rowing in a boat, as in other passages (29c), and Muluc, the north, has certainly a close relation to water. We see here two kinds of food, while none is represented on page 45. The same bird's head, which we find at the bottom of the corresponding page 28, is placed in front of the canoe, and on 29c it is combined with the representation of rowing a boat. On the left is the picture of a vessel with Kan and the iguana. There is something resembling a net between the boat and the bird.

3. Page 44 likewise refers to the introduction of the new cardinal point, west, which is represented on page 26 by the tiger Ix. The two hieroglyphs in the middle of this passage must surely refer to an animal; the lower is the skeleton of an animal, which we so often find as the sign of the lightning-dog, but also as that of the month Kankin, and the upper I take to be a rather vague picture of the day Oc, which certainly denotes the dog. Below these two signs the fish is represented as the fourth species of animal food.

The picture belonging to these hieroglyphs is very remarkable. B stands opposite a seated personage wearing an animal's snout, which somewhat resembles that of the wind-beast on pages 44b and 45b and also the nose of the storm-god K, who occurs on the corresponding pages 25 and 26 both with the coming and the departing Ix years, as he does here with the coming years. In the picture before us, the two personages seem to be throwing something resembling a rope at each other, as if these ropes were to be tied together. Is this meant to suggest the casting of lots by means of the knotting of cords, as it is represented on page 2? Or of hunting with snares?

Page 45 refers to the displacement of the Ix period by the Cauac period, i.e., of the west by the south. The end of the former is represented here. The lightning-beast, which occurred in the preceding period, here lies on his back and B sits astride his body brandishing in each hand a burning torch as an appropriate symbol of the south. On pages 29a and 30c we already saw the god riding on the lightning-dog.

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:—

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.