The interval between the days, without reference to the numbers attached to them, is 17. It may be well to notice here the relation of the intervals between the days when counted in the two ways: (1) the apparent interval, or that which indicates their position in the month; (2) the true interval between the days, indicated by the symbols and numbers. When the first is 6 the latter, as we have found, is 20; when the first is 12 the latter is 52; when the first is 5 the latter is 65, and when it is 17 the latter is 117.

Particular attention is also called here to the fact that so far no indications of the use of the year period of 365 days have been observed; on the contrary the cycle of 260 days appears to be the period to which reference is chiefly made.

Attached to the day column in Plate 29c and running into 30c is a series which presents a difficulty I am unable to explain. The days and numerals in this case are as follows:

III Ix Cauac } 16, VI; 16, IX; 16, XII; 16, (?) Kan } Muluc

The red numeral over the day column is very distinctly III in Kingsborough's work, but is II, though somewhat blurred, in Foerstemann's photograph. As III + 16 - 13 = VI, and the remaining numerals agree with this result, III must be correct. Adding together the pairs and casting out the thirteens, thus, III + 16 - 13 = VI; VI + 16 - 13 = IX; IX + 16 - 13 = XII; XII + 16 - 13 - 13 = II, we find the last red number, which is wanting in both copies of the codex, to be II, whereas, according to the theory advanced, it should be III. The sum of the black numerals (four 16's) is 64, while the interval between the days is 65. The only way of correcting the mistake, if one has been made, is by arbitrarily changing the last 16 to 17; but uniformity in the black numerals apparently forbids this change and and[TN-3] indicates that the variation from the usual rule must be accounted for in some other way.

In reference to this series, Dr. Foerstemann[292-1] remarks:

The column of the days has the difference 5; the fifth sign (in this case really superfluous), that of the thirteenth day, appears in a remarkable form, apparently as an inscription on a vessel. The black figures ought to give the sum 65, but we get only 4 x 16, or 64. But this appears to be merely an oversight by the copyist, for although in the Codex Troano, also, we find 64 several times instead of 65, still this has always appeared to me merely as a sign of the great negligence of the copyist of that manuscript.

Turning to the Manuscript Troano, Plate XXVIII*b, we find a column consisting of the four terminal days of the year, Been, Ezanab, Akbal, and Lamat, which of course have the same relation to one another as the first days. It is evident from the space that only four were intended to be given. The numerals in Brasseur's fac simile are XI; 20, 12, IV; 9, XIII; 10, X; 13, XI.

The red numeral over the column is XI, as is also the last of the series, but the sum of the black numbers is only 64, which would give X as the final number, as is evident from the following operation: XI + 32 - 13 - 13 - 13 = IV; IV + 9 = XIII; XIII + 10 - 13 = X; X + 13 - 13 = X. The interval between the days is 65. We have, therefore, precisely the same difficulty in this instance as in the case from the Dresden Codex under consideration. Moreover, the only method of correcting the mistake, if there is one, is by adding one to the last black number. It would be hazardous to assume that two mistakes, precisely the same in every respect, should have been made in regard to these exactly similar series. The probability that a mistake has been made is lessened by the fact that on Plate XXIX*b of the manuscript is another four day column, the last days of the years, as the preceding. The numeral over the column is XIII and the series is as follows: 13, XIII; 20, 18, XII; 13, XIII. Adding these and casting out the thirteens, we have this result: XIII + 13 - 13 = XIII; XIII + 20 + 18 - 13 - 13 - 13 = XII; XII + 13 - 13 = XII. This gives XII as the last number when it should be XIII. If a mistake has been made the only method of correcting it is by increasing the last black number by one, as in the other two cases alluded to.

It is proper to state that on the other hand there is another four day column on Plate XXXII*a of the last mentioned codex, the days of which are precisely the same as those on Plate 29c of the Dresden Codex, to wit, Ix, Cauac, Kan, Muluc. The numeral over it is XII and the series is as follows: 13, XII; 13, XII; 13, XII; 13, XII; 13, XII. This presents no difficulty, as it conforms in every respect to the rules given, but only serves to deepen the mystery in the other cases.

Going back to the series on Plate 29c of the Dresden Codex, we observe not only that the days of the column are the four year bearers, but also that one of the four cardinal symbols is found—in the superscription—in each of the four compartments through which the series extends. It is possible, therefore, that the series is intended to be applied separately to each of the four years. Supposing this to be the case, counting 64 days from 3 Ix would bring us to 2 Ezanab; 64 days from 3 Cauac to 2 Akbal; 64 days from 3 Kan to 2 Lamat; and 64 days from 3 Muluc to 2 Been. It is significant that in each case the day reached is that on which the given year terminates; for example, the Ix years (counting the five added days) terminate on Ezanab; the Cauac years on Akbal &c. If the intention was to have the series terminate with the end of the respective years, then these years must necessarily have been 2 Ix, 2 Cauac, 2 Kan, and 2 Muluc. I must confess that this explanation is not satisfactory; it is thrown out simply as a suggestion.

Running through the middle division of Plates 30 and 31 is this series:

3, VIII; 3, VIII; 3, VIII; 3, VIII 5, Oc 5, Men 5, Ahau 5, Chicchan.

Commencing with 8 Oc (omitting for the present the 3 and 5 to the left) and counting thence 3 months and 5 days we reach 8 Men; 3 months and 5 days more and we reach 8 Ahau; 3 months and 5 days more bring us to 8 Chicchan, and 3 months and 5 days more bring us again to 8 Oc, thus completing a cycle of 260 days (13 months) and also accounting for the first pair of numerals—3 and 5 in the series. It appears to be a pretty general rule to commence a series of this type with the difference between the numbers of the series. One reason for this is apparent: that is, to complete the cycle of 260 days, to which most, if not all, of these groups appear to refer.

Dr. Foerstemann says in regard to this line:[293-1]

This is the place where I first discovered how numbers of several figures are to be read; here for the first time I understood that the figure 3 with 5 below it is nothing but 3 x 20 + 5, or 65, and that they mean nothing else than the interval between the days, such as we have frequently met with so far; 4 x 65 is again the well known period of 260 days.

Plate 3 appears to be isolated and unfinished; at least it presents nothing on its face by which it can be directly connected with any other plate of the codex, notwithstanding the change made by Dr. Foerstemann, by which 45 was brought next to it. The day column in this case is in the middle compartment of the upper division and consists of the following days: Ahau, Eb, Kan, Cib, Lamat; the red numeral over it is I. The numerals and days are arranged as follows:

(?) (?) 4, V(?) 15, XIII

I Ahau 8, XIII Eb Kan Cib 14 (?) Lamat

As numerals belonging to two different series are never found in the same compartment it is fair to assume that those of the middle and right compartments pertain to one series. But what shall we say in reference to those in the left compartment, the upper pair of which is almost entirely obliterated? So far we have found no series extending to the left of the day column. Is this an exceptional case? I am inclined to believe it is, for the following reasons:

Taking the 4, V over the bird as the first pair of the series, we have I + 4 = V, which is so far correct; after this follows the pair in the lower left hand corner, 8, XIII, as V + 8 = XIII. It is probable that the obliterated pair in the upper left hand corner followed next, then the pair in the upper right hand corner, and last the partly obliterated one in the lower right hand corner. In this case the obliterated pair in the upper left hand corner should be 11, XI, as XIII + 11 - 13 = XI, and XI + 15 - 13 = XIII, and XIII + 14 - 13 - 13 = I, which makes the terminal red number of the series the same as that over the day column. This restoration requires no change of any of the numbers which can be distinctly read. By adding together the black numbers 4, 8, 11, 15, 14, the sum is found to be 52, precisely the interval between the days of the column. These facts are sufficient to render it more than probable that the restoration and the order as here given are correct. The series as thus given, including the number over the day column, is: I; 4, V; 8, XIII; 11, XI; 15, XIII; 14, I.

This is repeated, because on turning to Dr. Foerstemann's comment on this series I find that he has restored and amended it so as to read thus: I; 10, XI; 4, V; 15, XIII; 9, XIII; 14, I; and he remarks that all would be plain sailing if, for the V before and the XIII after 15, we could read II and IV. This is true, but these numbers are too distinct to justify such change; moreover his "9" is not to be found on the page; it is true that the three dots over the line are not exactly spaced, but there are no indications of a fourth; the number is 8 and should, I think, be so read. His 10 is the obliterated black numeral; of course the value attributed to it depends upon the order given to the series. The fragments remaining of the red number of this pair I think warrant his making it XI.

Plates 46, 47, 48, 49, and 50 are peculiar and seemingly have no direct relation to any other part of the codex. In the upper left hand corner of each are four day columns, all more or less injured, but each column evidently contained, originally, thirteen days, or, more correctly speaking, the symbol for one day repeated thirteen times. In every case the day in the first (left hand) column and that in the third column are the same. As the numbers attached to them are absolutely unreadable in Kingsborough and much obliterated in the photograph, I give here restorations for the benefit of those studying this codex. This restoration is easily made by finding the order of the series, which can be obtained from Plates 49 and 50 of the photographic copy.

Plate 46: III Cib. II Cimi. V Cib. XIII Kan. XI Cib. X Cimi. XIII Cib. VIII Kan. VI Cib. V Cimi. VIII Cib. III Kan. I Cib. XIII Cimi. III Cib. XI Kan. IX Cib. VIII Cimi. XI Cib. VI Kan. IV Cib. III Cimi. VI Cib. I Kan. XII Cib. XI Cimi. I Cib. IX Kan. VII Cib. VI Cimi. IX Cib. IV Kan. II Cib. I Cimi. IV Cib. XII Kan. X Cib. IX Cimi. XII Cib. VII Kan. V Cib. IV Cimi. VII Cib. II Kan. XIII Cib. XII Cimi. II Cib. X Kan. VIII Cib. VII Cimi. X Cib. V Kan.

Plate 47: II Ahau. I Oc. IV Ahau. XII Lamat. X Ahau. IX Oc. XII Ahau. VII Lamat. V Ahau. IV Oc. VII Ahau. II Lamat. XIII Ahau. XII Oc. II Ahau. X Lamat. VIII Ahau. VII Oc. X Ahau. V Lamat. III Ahau. II Oc. V Ahau. XIII Lamat. XI Ahau. X Oc. XIII Ahau. VIII Lamat. VI Ahau. V Oc. VIII Ahau. III Lamat. I Ahau. XIII Oc. III Ahau. XI Lamat. IX Ahau. VIII Oc. XI Ahau. VI Lamat. IV Ahau. III Oc. VI Ahau. I Lamat. XII Ahau. XI Oc. I Ahau. IX Lamat. VII Ahau. VI Oc. IX Ahau. IV Lamat.

As the arrangement and the order of the series are readily seen from the two examples given, only the top and bottom lines of the remaining series will be presented.

Plate 48: I Kan. XIII Ix. III Kan. XI Eb. * * * * * * * [TN-4] VI Kan. V Ix. VIII Kan. III Eb.

Plate 49: XIII Lamat. XII Ezanab. II Lamat. X Cib. * * * * * * * * V Lamat. IV Ezanab. VII Lamat. II Cib.

Plate 50: XII Eb. XI Ik. I Eb. IX Ahau. * * * * * * * * IV Eb. III Ik. VI Eb. I Ahau.

A careful examination of these groups will bring to light the following relations of the numbers, days, columns, and series to one another:

The numerals of any one column, counting downwards, differ from one another by 8; that is to say, by adding 8 to any one and casting out 13 when the sum exceeds that number, the next lower number will be obtained; or, reversing the operation and counting upward, the difference is found to be 5. The true interval between the days of the columns (counting downwards) is 3 months (60 days), a rule which holds good as to all the series and each column. Thus, from 3 Cib to 11 Cib is 3 months, or 60 days; from 11 Cib to 6 Cib, 3 months; from 2 Cimi to 10 Cimi, 3 months, and from 13 Kan to 8 Kan, 3 months.

Counting on the list of the days of the month, without reference to the week numbers attached to them, it will be found that from Cib to Cimi is an interval of 10 days, and from Cib to Kan is an interval of 8 days. This rule holds good as to all the series, showing that all are arranged upon precisely the same plan. The true interval between any day of the first column of either series (the week number attached being considered) and the opposite or corresponding day in the second column, is 4 months and 10 days, that between the corresponding days of the second and third columns is 12 months and 10 days, that between the days of the third and fourth columns is 8 days, and that between the corresponding days of the fourth or last column of one series or plate and the first column of the following series or plate (taking the plates in the order they are paged) is 11 months and 16 days.

In order to illustrate this we will run through the lowest line of each series, taking them in the order of the pages.[296-1]

These are as follows:

Plate 46: VIII Cib. VII Cimi. X Cib. V Kan.

Plate 47: VII Ahau. VI Oc. IX Ahau. IV Lamat.

Plate 48: VI Kan. V Ix. VIII Kan. III Eb.

Plate 49: V Lamat. IV Ezanab. VII Lamat. II Cib.

Plate 50: IV Eb. III Ik. VI Eb. I Ahau.

]

By counting on the calendar (our Table II), as heretofore explained, the reader will observe that the interval from 8 Cib to 7 Cimi is 4 months and 10 days; from 7 Cimi to 10 Cib is 12 months and 10 days; from 10 Cib to 5 Kan is 8 days; from 5 Kan to 7 Ahau is 11 months and 16 days; from 7 Ahau to 6 Oc, 4 months and 10 days; from 6 Oc to 9 Ahau, 12 months and 10 days; from 9 Ahau to 4 Lamat, 8 days; from 4 Lamat to 6 Kan, 11 months and 16 days, and so on to the end of the series on Plate 50. Referring to the codex the reader will observe at the bottom of each plate and directly under—that is to say, in the same vertical lines as the day columns—two lines of red numerals. It is impossible to determine these in Kingsborough's copy (except on Plate 50), but they can readily be made out on the photographed plates. (See the copy of Plate 50, given in Fig. 362.) Those on a single plate are as follows:

{ XI, IV, XII, 0, { XVI, X, X, VIII.

The 0 here represents a red, diamond shaped symbol.

If the upper line represents months and the lower line days, these numbers will indicate the intervals between the columns and are properly placed. For example, the XI and XVI signify 11 months and 16 days, the interval between the last column of the preceding plate and the first column of the plate on which they stand; the IV and X, the interval of 4 months and 10 days between the first and second columns; XII and X, the interval of 12 months and 10 days between the second and third columns; and 0, VIII, the interval of 8 days between the third and fourth columns. It is apparent from this that the red, diamond shaped symbol represented by 0 over the VIII denotes a cipher or nought, a conclusion reached independently by Foerstemann.

If this supposition as to the arrangement of the series and the signification of these numbers be correct, it is apparent that the plates are to be taken in the order in which they are paged, that is, from left to right, as the others so far noticed, an inference borne out by another fact now to be mentioned.

Immediately below each of these four column day series are four lines of characters (hieroglyphics), and immediately under the latter three horizontal lines of black numerals, with here and there a red, diamond shaped symbol inserted. As these numerals stand directly in the vertical lines of the day columns, it is possible the two have some connection with each other, a supposition somewhat strengthened by what has been observed in regard to the red numerals at the bottom of the plates. To test this and also for the reason that we propose to discuss their relations and their use, we give here the bottom line of days of each of the five series (or plates), together with their week numbers attached; also, the numbers of the three lines of black numerals mentioned, taking them in the order of the paging as here shown:

Plate 46: VIII Cib. VII Cimi. X Cib. V Kan. 1 1 11 16 10 11 16 6 16 4

Plate 47: VII Ahau. VI Oc. IX Ahau. IV Lamat. 2 2 3 3 5 9 4 4 0 10 0 8

Plate 48: VI Kan. V Ix. VIII Kan. III Eb. 3 4 4 4 16 2 15 15 3(?) 14 4 12

Plate 49: V Lamat. IV Ezanab. VII Lamat. II Cib. 5 5 6 6 9 13 8 8 8 18 8 16

Plate 50: IV Eb. III Ik. VI Eb. 1 Ahau. 7 7 8 8 3 7 1 2 12 2 12 0

In considering these horizontal lines it is to be understood that the series runs through the five pages, 46-50.

Let us proceed upon the supposition that the figures of the lowest of the three lines denote days of the month, the numbers of the middle line months, and those of the upper line years. As already shown, the interval between 8 Cib and 7 Cimi is 4 months and 10 days; adding 4 months and 10 days to 11 months and 16 days (bearing in mind that 20 days make a month and 18 months a year), the sum is found to be 16 months and 6 days, precisely the figures under 7 Cimi. As already ascertained, the interval between 7 Cimi and 10 Cib is 12 months and 10 days; this added to 16 months and 6 days gives 1 year, 10 months, 16 days, precisely the figures under 10 Cib. The interval between 10 Cib and 5 Kan is 8 days; this added to the 1 year, 10 months, and 16 days gives 1 year, 11 months, and 4 days, the figures under 5 Kan. The interval between 5 Kan and 7 Ahau is 11 months, 16 days, which, added to the preceding, gives 2 years, 5 months, 0 day, agreeing with the figures under 7 Ahau, if the symbol represented by 0 signifies nought. That this rule holds good throughout the entire series, by making one correction, is shown by the following additions:

Years. Months. Days. 11 16 Under VIII Cib, Plate 46. 4 10 — — 16 6 Under VII Cimi, Plate 46. 12 10 — — 1 10 16 Under X Cib, Plate 46. 8 — — — 1 11 4 Under V Kan, Plate 46. 11 16 — — — 2 5 0 Under VII Ahau, Plate 47. 4 10 — — — 2 9 10 Under VI Oc, Plate 47. 12 10 — — — 3 4 0 Under IX Ahau, Plate 47. 8 — — — 3 4 8 Under IV Lamat, Plate 47. 11 16 — — — 3 16 4[300-1] Under VI Kan, Plate 48. 4 10 — — — 4 2 14 Under V Ix, Plate 48. 12 10 — — — 4 15 4 Under VIII Kan, Plate 48. 8 — — — 4 15 12 Under III Eb, Plate 48. 11 16 — — — 5 9 8 Under V Lamat, Plate 49. 4 10 — — — 5 13 18 Under IV Ezanab, Plate 49. 12 10 — — — 6 8 8 Under VII Lamat, Plate 49. 8 — — — 6 8 16 Under II Cib, Plate 49. 11 16 — — — 7 2 12 Under IV Eb, Plate 50. 4 10 — — — 7 7 2 Under III Ik, Plate 50. 12 10 — — — 8 1 12 Under VI Eb, Plate 50. 8 — — — 8 2 0 Under I Ahau, Plate 50.

The proof of the correctness of the theory advanced may, therefore, be considered conclusive, as it amounts, in fact, to a mathematical demonstration.

Dr. Foerstemann, who considers these lines of black numbers, standing one above another, as representing different grades of units—thus, the lowest, single units; the second, units twenty-fold the lower; the third, eighteen-fold the second; the fourth, twenty-fold the third, &c.—has found the correct intervals of the series, which he states are 236, 90, 250, and 8 days, agreeing with our 11 months, 16 days; 4 months, 10 days; 12 months, 10 days, and 8 days.

As all the discoveries mentioned herein were made previous to the receipt of Dr. Foerstemann's work, I give them according to my own method, acknowledging any modification due to his work. Although I shall compare special results from time to time, an explanation of Dr. Foerstemann's method is reserved for a future paper, as his work was not received until I was revising my notes for publication.

The foregoing explanation of the series shows it to be very simple and makes it clear that it relates to the day columns at the top of the pages. Still, there is one point somewhat difficult to understand. Are the numbers of the third or lowest line intended to denote the positions in the month of the days in the columns above? If so, the month must have commenced with Ymix, as can readily be shown in the following manner:

TABLE III.

1. Ymix. 2. Ik. 3. Akbal. 4. Kan. 5. Chicchan. 6. Cimi. 7. Manik. 8. Lamat. 9. Muluc. 10. Oc. 11. Chuen. 12. Eb. 13. Been. 14. Ix. 15. Men. 16. Cib. 17. Caban. 18. Ezanab. 19. Cauac. 20. Ahau.

If we write in a column in proper order the 20 days of the Maya month, commencing with Ymix, and number them consecutively, as in Table III, we shall find by comparison that the numbers in the lower line indicate the position, in this column, of the days directly over them. Take, for example, the lower line of black numerals on Plate 46, writing over them the respective days of the columns, thus:

Cib. Cimi. Cib. Kan. 16 6 16 4

Referring to Table III we see that Cib is the sixteenth day, Cimi the sixth, and Kan the fourth.

The days and numbers of Plate 47 are:

Ahau. Oc. Ahau. Lamat. 0 10 0 8

Ahau is the twentieth day—here is the diamond shaped symbol—Oc is the tenth, and Lamat the eighth, and so on to the end of the series on Plate 50.

It may be justly argued that such relation to some given day of the month would necessarily follow in any series of this kind made up by adding together intervals of days and months. Still it is not at all likely that these series were made up without reference to fitted and determinable dates. If so, the months given must be months of certain determinable years, and the days denoted must be days of particular months. In other words, if we had the proper starting point we should be able to determine the position in the calendar of any day or month mentioned in the series.

First. It is easily seen by reference to the calendar (Table II) that Cib is not the sixteenth day of the month of any of the four years, nor is Cimi the sixth nor Kan the fourth. The idea that the figures of this lower line represent the days of the month must, therefore, be given up unless we assume that the year commenced with Ymix. It may be worthy of notice at this point that the list of days on the so-called "title page" of the Manuscript Troano begins with Ymix. It is also true that the remarkable quadruple series in the Codex Cortesianus on Plates 13-18 commences with Ymix; as this is evidently some kind of a calendar table, its bearing on the question now before us is important.

Second. It can easily be shown that the months referred to in the series, if the numbers given denote specific months, are not those of the Kan years. The first, 8 Cib, if in the eleventh month, must be in the year 4 Kan; counting forward from this 4 months and 10 days to 7 Cimi brings us into the sixteenth month of the year 4 Kan; this agrees with our figures on Plate 46. Counting forward 12 months and 10 days to 10 Cib, we reach the tenth month of the next year; 8 days more carry us to the eleventh month, which still agrees with the figures in the codex. Counting 11 months and 16 days more to 7 Ahau, we reach but do not pass the fourth month of the next year; hence the result does not correspond with the series, which has at this point a 5 in the middle line. The same will be found true in regard to the other years as given in our calendar (Table II). This result, as a matter of course, must follow if the figures in the lower line of the series do not denote the month days of some one of the year series as usually given.

Another fact also becomes apparent here, viz, that the 5 supplemental days of the year are not brought into the count, the year consisting throughout of 360 days. There is, in fact, nothing here indicating the four year series as given in the authorities and as represented in our calendar table; yet this ought to appear wherever a series extends over more than one year.

Dr. Foerstemann says that this entire series of black numerals covers 2,920 days, or 8 years of 365 days. This is true, but the concluding figures show that it is given by the writer of the codex as 8 years and 2 months, which would also be 2,920 days, counting the years at 360 days each and the months 20 days each; moreover, the members of the series are based throughout upon the year of 360 days. His theory that the intervals of the series relate to the movements of the planet Venus is, as yet, a mere hypothesis, which needs further proof before it can demand acceptance; but his discovery of the methods of identifying the month symbols on the five plates now under consideration is important. Although I had noticed that most of the characters which he mentions are month symbols, I did not succeed in identifying all of them.

According to his conclusion, which appears to be justified not only by the evidence he gives but by an additional fact that I shall, presently mention, there are four of these symbols in the upper row of the middle group of written characters on each plate and four in the upper and lower lines of the lower group on each plate (see, for example, Fig. 362). Each of these symbols (except three or four) has a black number attached to it which denotes the day of the month represented by the symbol.

These months and days as given by Dr. Foerstemann are as follows, the positions of the lines as here given corresponding with those of the plates:

TABLE IV.—Table showing months and days.

Month. Day. Month. Day. Month. Day. Month. Day. + + + Plate 46 7 4 11 14 5 19 6 7 11 8 15 18 10 4 10 12 1 14 6 4 18 14 1 2 Plate 47 18 3 4 8 16 18 17 6 4 3 8 13 2 18 3(not 2) 6 10 10 15 3 9 8 9 16 Plate 48 10 17 15 7 9 12 10 20 15 2 1 7 13 17 14 5 3 7 7 17 2 2 2 10 Plate 49 3 11 8 1 2 6 2 14 7 16 12 6 6 11 6 19 14 6 18 16 13 1 13 9 Plate 50 14 10 18 20 13 5 13 13 18 15 5 20 17 10 17 18 6 20 11 10 5 15 6 3 -

An examination of the plates will show that Dr. Foerstemann has filled out the following obliterated or wanting day numbers, to wit, the first of the upper line of Plate 46, the fourth of the upper line of Plate 47, and the second of the middle line and first of the lower line of Plate 50. He has also ventured to change the first day number of the lower line of Plate 46 from 16 to 14. Where the number 20 is found in his list there is no corresponding number in the codex, the month symbol only being given. It is evident he has proceeded in these cases upon the theory that the absence of a number indicated that the month was completed. Although probably correct in this conclusion, the question will arise, Does the symbol in such cases denote the month completed or the month reached?

The intervals between these dates are as follows, the left hand column being those between the first and second columns of Foerstemann's list (our Table IV), the second column those between the second and third columns of his list, the third column those between the third and fourth columns of his list, and the fourth column those between the last date of one plate and the first of the next:

TABLE V.—Table showing intervals between dates.

Month. Day. Month. Day. Month. Day. Month. Day. + + + Plate 46 4 10 12 5 0 8 11 16 4 10 12 6b 0 8 11 11 4 10 12 10 0 8 9 8d Plate 47 4 5 12 10 0 8 11 11 4 10 12 5 0 8c 11 16e 4 13a 12 5 0 8 11 11 Plate 48 4 10 12 5 8 11 11 4 5 12 10 0 8 11 11 4 10 12 5 0 8 11 16 Plate 49 4 10 12 5 0 8 11 16 4 10 12 5 0 8 11 16 4 10 12 5 0 8 11 11 Plate 50 4 10 12 5 0 8 11 11 4 5 12 10 0 8 11 10 4 10 12 5 0 8 12 11g -

Although it is apparent that the variations from the intervals of the black numeral and day series above them are too numerous and too uniform to be considered mistakes, yet there is little reason to doubt that these month numbers are connected with and depend upon the day series given in the columns above.

That there are some errors is quite clear; for instance, the variation at a arises from the fact that Dr. Foerstemann gives the date here as 10 months, 10 days, whereas the codex has it 10 months, 13 days. Making this correction the interval will be 4 months, 10 days. The correction will make the interval at d 9, 11, instead of 9, 8. Still there is a variation of two months from the usual interval, which, if corrected on the supposition that Dr. Foerstemann has mistaken the month, would necessitate a change of the remainder of the series given in this line. The interval at c, according to the figure given by Dr. Foerstemann, would be retrograde, that is, minus 12. This arises from the fact that he gives the last date in the middle line on Plate 47 as 2 months, 6 days, whereas the symbol is very distinctly that of the third month, and the eight day series is unbroken if this correction is made.

When these evident errors are corrected the series of intervals show very clearly a system and periodicity depending on the day column series in the upper part of the pages. In the first column (Table V) the interval is usually 4 months, 10 days, precisely the same as between the first and second day columns, but occasionally it is 4 months, 5 days, which will still bring it to one of the four day series, including the day indicated by the date—4 months, 10 days. This will be understood by examining our calendar (Table II). The corresponding days in the four year columns were, by the Maya system, necessarily brought together in the calendar; for example, they are arranged in the series pictured on Plates 13-18 of the Cortesian Codex precisely as given in our Table II. This skip of five days is also apparent in the second and fourth columns of differences (Table V). Whether Dr. Foerstemann is correct in all his identifications of months among the symbols on the five plates now under consideration is a question I feel unqualified to answer without a much more careful comparison and study of these characters than I have given them.

Running through the upper division of Plates 53 to 58 and continued through the lower division of Plates 51 to 58—that is to say, commencing in the upper division of 53 and running into 58, then back to the lower division of 51 and ending in 58—is a remarkable compound series. It consists, first, of a three line series of black numerals standing above; second, a middle series of short, three day columns, or columns each of three day symbols, with red numerals attached; and, third, below, a two line series of numerals, those of the upper line red and of the lower black numbers.

As this series is a very important one in the study of the relations of the numerals to one another and to the days indicated, an exact copy of it is given in Figs. 363-370, each figure representing a page and the whole standing in the same order as in the original. The red numerals and red symbols are, as usual, given in outline as an indication of their color.



In order to assist those not familiar with the numeral and day symbols, the entire series is given in the following tables in names and Arabic and Roman numerals, as usual. The obliterated symbols and numbers are restored.

TABLE VI.—Table of numeral and day symbols. (Plate 51b.)

14 15 15 16 16 17 16 7 16 7 16 5 14 11 8 5 2 10 IV Ik. XII Cauac. VII Cib. II Been. X Oc. II Ezanab. V Akbal. XIII Ahau. VIII Caban. III Ix XI Chuen III Cauac. VI Kan. I Ymix. IX Ezanab. IV Men. XII Eb. IV Ahau.[VI-1] VIII VIII VIII VIII VIII VII 17 17 17 17 17 8

[VI-1] The symbol in this case is that of Been, but this is a manifest error, as Ahau follows Cauac.

TABLE VII.—Table of numeral and day symbols. (Plate 52b.)

17 18 18 19 14 5 14 4 8 5 2 19 XI Cib. VI Been. I Oc. IX Manik. [Picture.] XII Caban. VII Ix. II Chuen. X Lamat. XIII Ezanab. VIII Men. III Eb. XI Muluc. VIII VIII VIII VIII 17? (18)[VII-1] 17 17 17

[VII-1] The variation from the rule found here is explained a little further on.

TABLE VIII.—Table of numeral and day symbols. (Plate 53a.)

_______________ 1 1 2 2 7 17 7 15 6 15 17 18 2 14?(19)[VIII-1] 16 13 VI Kan. I Ymix. VI Muluc. [Picture.] I Cimi. IX Akbal. IV Ahau. VII Chicchan. II Ik. VII Oc. II Manik. X Kan. V Ymix. VIII Cimi. III Akbal. VIII Chuen. III Lamat. XI Chicchan. VI Ik. VIII VIII VII VIII VIII VIII 17 17 8 17 17 17

[VIII-1] The 14 here is manifestly an error, one of the lines in the number symbol having been omitted; it should be 19.

TABLE IX.—Table of numeral and day symbols. (Plate 53b.)

1 1 1 1 19 0 0 1 1 13 3 12 2 11 16 4 1 18 15 IV Kan. IX Eb. [Picture.] IV Muluc. XII Cimi. VII Akbal. V Chicchan. X Been. V Oc. XIII Manik. VIII Kan. VI Cimi. XI Ix. VI Chuen. I Lamat. IX Chicchan. VIII VII VIII VIII VIII 17 8 17 17 17 -

TABLE X.—Table of numeral and day symbols. (Plate 54a.)

3 3 4 4 5 5 6 6 15 6 15 5 10 4 11 8 5 5 19 16 4 XIII Ezanab. VIII Men. III Eb. XI Muluc. VI Cib. I Akbal. VI Chuen. I Cauac. IX Cib. IV Been. XII Oc. VII Caban. II Kan. VII Eb. II Ahau. X Caban. V Ix. XIII Chuen. VIII Ezanab. III Chicchan. VIII Been. VIII VIII VIII VIII VIII VIII VII 17 17 17 17 17 17 8

TABLE XI.—Table of numeral and day symbols. (Plate 54b.)

___________ 1 1 1 1 1 2 2 3 3 4 2 11 2 9 0[XI-1] 12 9 6 14 11 II Ahau. X Caban. V Ix. X Ik. [Picture] V Cauac. III Ymix. XI Ezanab. VI Men. XI Akbal. VI Ahau. IV Ik. XII Cauac. VII Cib. XII Kan. VII Ymix. VIII VIII VIII VII VII[XI-2] 17 17 17 8 17 -

[XI-1] The 0 inserted at various points in these tables denotes as usual the red, diamond shaped symbol, which apparently signifies "nought."

[XI-2] The numeral symbol in this case, both in Kingsborough's copy and in the photograph, is VII, one dot having been omitted by a mistake of the original artist.

TABLE XII.—Table of numeral and day symbols. (Plate 55a.)

_____________ 8 7 7 8 8 13 3 12 3 12 2 18 16 13 10 II Muluc.[XII-1] X Cimi. V Akbal. XIII Ahau. VIII Caban. [Picture] III Oc. XI Manik. VI Kan. I Ymix. IX Ezanab. IV Chuen. XII Lamat. VII Chicchan. II Ik. X Cauac. VIII VIII VIII VIII VIII 17 17 17 17 17

[XII-1] In Kingsborough's work the symbol in this case is that of Been, but should be Muluc, as it is in the photograph.

TABLE XIII.—Table of numeral and day symbols. (Plate 55b.)

_______________ 1 1 1 1 1 1 1 1 4 5 5 6 6 6 7 7 9 0 9 0 8 17 8 15 8 6 3 0 17 14 11 19 XIII Cib. IX Ix. IV Chuen. XII Lamat. VII Chicchan. II Ik. X Cauac. II Manik. I Caban. X Men. V Eb. XIII Muluc. VIII Cimi. III Akbal. XI Ahau. III Lamat. II Ezanab. XI Cib. VI Been. I Oc. IX Manik. IV Kan. XII Ymix. IV Muluc. VIII VIII VIII VIII VIII VIII VIII VII 17 17?(18) 17 17 17 17 17 8

TABLE XIV.—Table of numeral and day symbols. (Plate 56a.)

9 9 10 10 1 10 1 10 18 15 12 9 XIII Chicchan. VIII Ik. III Cauac. XI Cib. I Cimi. [Picture] IX Akbal. IV Ahau. XII Caban. II Manik. X Kan. V Ymix. XIII Ezanab. VII VIII VIII VIII 8 17 17 17

TABLE XV.—Table of numeral and day symbols. (Plate 56b.)

1 1 1 1 8 8 9 9 6 15 6 15 16 14 11 8 [Picture] X Kan. VI Ik. I Cauac. IX Cib. XI Chicchan. VII Akbal. II Ahau. X Caban. XII Cimi. VIII Kan. III Ymix. XI Ezanab. VIII VIII VIII VIII 17 17?(8) 17 17 -

TABLE XVI.—Table of numeral and day symbols. (Plate 57a.)

_________ 11 11 12 12 1 10 1 8 6 4 0 8 VII Ix. II Chuen. X Lamat. II Cib. VIII Men. III Eb. XI Muluc. III Caban. [Picture] IX Cib. IV Been. XII Oc. IV Ezanab. VIII VIII VIII VIII[XVI-1] 17 17 17 17[XVI-2]

[XVI-1] This should be VII.

[XVI-2] This should be 8.

TABLE XVII.—Table of numeral and day symbols. (Plate 57b.)

___________ 1 1 1 1 1 10 10 11 11 12 6 15 4 13 4 5 2 10 7 4 IV Been. XII Oc. IV Ezanab. [Picture] XII Men. VII Eb. V Ix. XIII Chuen. V Cauac. XIII Cib. VIII Been. VI Men. I Eb. VI Ahau. I Caban. IX Ix. VIII VIII VII VIII VIII 17 17 8 17 17

TABLE XVIII.—Table of numeral and day symbols. (Plate 58a.)

12 13 13 14 17 8 17 7 5 2 0 17 X Been. V Oc. I Lamat. II Chicchan. XI Ix. VI Chuen. II Muluc. X Cimi. XII Men. VII Eb. III Oc. XI Manik. VIII VIII VIII VIII 17 17 17 17

TABLE XIX.—Table of numeral and day symbols. (Plate 58b.)

1 1 12 13 13 3 1 18 II Muluc. X Cimi. [Picture.] III Oc. XI Manik. IV Chuen. XII Lamat. VIII VIII 17 17

The spaces in the lists indicate the positions of the pictures of persons and curtain-like ornaments inserted here and there, as seen in Figs. 363-370.

In order to explain this series, we commence with that portion of it found in the lower division of Plate 51 (Fig. 363).

Omitting any reference for the present to the black numbers over the day columns, we call attention first to the days and to the red numerals attached to them. Those in the division selected as an illustration are as follows:

IV Ik. XII Cauac. VII Cib. II Been. X Oc. II Ezanab. V Akbal. XIII Ahau. VIII Caban. III Ix. XI Chuen. III Cauac. VI Kan. I Ymix. IX Ezanab. IV Men. XII Eb. IV Ahau.[317-1]

It will be observed that the week numbers of the days in each single column follow one another in regular arithmetical order, thus: in the first column, 4, 5, 6; in the second, 12, 13, 1; in the third, 7, 8, 9; and so on throughout the entire series. The interval, therefore, between the successive days of a column is 1; or, in other words, the days follow one another in regular order, as in the month series, so that having the first day of a column given we know at once the other two. It is apparent, therefore, that the intervals between the three correspondingly opposite days of any two associate columns are the same; that is to say, the interval between 5 Akbal and 13 Ahau, in the first two columns given above is the same as that between 4 Ik and 12 Cauac, and also as that between 6 Kan and 1 Ymix. This is also true if the attached week numbers are omitted; for instance, the interval between Ik and Cauac, counting on the list of days forming the month, is 17 days, and it is the same between Kan and Ymix. Taking the second and third columns we find here the same interval. This holds good in that part of the series above given until we reach the last two columns; here the interval between Oc and Ezanab is 8 days and it is the same between the other days of these two columns.

This being ascertained, the next step is to determine the true interval between the first days of these columns, taking the numbers attached to them into consideration. Referring to our calendar (Table II) and (for reasons which will be given hereafter) using the Muluc column and counting from 4 Ik, as heretofore explained, we find the interval between this and 12 Cauac to be 8 months and 17 days; counting in the same way from 12 Cauac, 8 months and 17 days more bring us to 7 Cib; 8 months and 17 days more to 10 Oc. So far the intervals have been the same; but at this point we find a variation from the rule, as the interval between 10 Oc and 2 Ezanab (first of the next column) is 7 months and 8 days.

These intervals furnish the explanation of the red and black numerals below the day columns.

These numerals, as the reader will observe by reference to Fig. 363 or the written interpretation thereof in Table VI, are 8 and 17 under the first five columns, but 7 and 8 under the sixth column, the red (8 under the first five and 7 under the sixth) indicating the months and the black (17 under the first five and 8 under the sixth) the days of the intervals. This holds good throughout all that portion of the series running through the lower divisions of Plates 51 to 58, with three exceptions, which will now be pointed out.

In order to do this it will be necessary to repeat here a part of the series on Plate 51b and part of that on Plate 52b; that is, the two right hand columns of the former and the two left hand columns of the latter, between which is the singular picture shown in the lower left hand corner of our Fig. 364:

Plate 51b. Plate 52b. + - X Oc. II Ezanab. XI Cib. VI Been. XI Chuen. III Cauac. XII Caban. VII Ix. XII Eb. IV Ahau. [Picture.] XIII Ezanab. VIII Men. VIII VII VIII VIII 17 8 17 17 -

As before stated, the interval between 10 Oc and 2 Ezanab is 7 months and 8 days, as indicated by the red and black numerals under the latter. According to the red and black numbers under the column commencing with 11 Cib, the interval between 2 Ezanab and 11 Cib should be 8 months and 17 days, the usual difference, when, in fact, as we see by counting on the calendar, it is 8 months and 18 days. That this variation cannot be attributed to a mistake on the part of the author or of the artist is evident from the fact that the interval between 11 Cib and 6 Been (first of the next column) is 8 months and 17 days and that the difference throughout the rest of the series follows the rule given; that is to say, each is 8 months and 17 days, except at two other points where this variation is found and at the regular intervals where the difference of 7 months and 8 days occurs.[319-1] Precisely the same variation occurs on Plate 55b in passing from the first to the second column and on Plate 56b between columns 1 and 2.

Why these singular exceptions? It is difficult, if not impossible, for us, with our still imperfect knowledge of the calendar system formerly in vogue among the Mayas, to give a satisfactory answer to this question. But we reserve further notice of it until other parts of the series have been explained.

Reference will now be made to the three lines of black numerals immediately above the day columns. Still confining our examinations to the lower divisions, the reader's attention is directed to these lines, as given in Tables VI, VII, IX, XI, XIII, XV, XVII, and XIX. As there are three numbers in each short column we take for granted, judging by what has been shown in regard to the series on Plates 46-50, that the lowest of the three denotes days, the middle months, and the upper years, and that the intervals are the same between these columns as between the day columns under them. The correctness of this supposition is shown by the following additions: Starting with the first or left hand column on Plate 51b, we add successively the differences indicated by the corresponding red and black numbers under the day columns. If this gives in each case (save the two or three exceptions heretofore referred to) the numbers in the next column to the right throughout the series, the demonstration will be complete.

Years. Months. Days. 14 16 14 First column on Plate 51b. 8 17 — — — 15 7 11 Second column on Plate 51b. 8 17 — — — 15 16 8 Third column on Plate 51b. 8 17 — — — 16 7 5 Fourth column on Plate 51b. 8 17 — — — 16 16 2 Fifth column on Plate 51b. 7 8 — — — 17 5 10 Sixth column on Plate 51b. 8 18[319-1] — — — 17 14 8 First column on Plate 52b. 8 17 — — — 18 5 5 Second column on Plate 52b. 8 17 — — — 18 14 2 Third column on Plate 52b. 8 17 — — — 19 4 19 Fourth column on Plate 52b. 8 17 — — — 19 13 16 First column on Plate 53b. 7 8 — — — 20 3 4 Second column on Plate 53b.

At this point in the original, instead of 20 in the year series, we find a diamond shaped symbol, represented by 0 in our tables, with one black dot over it. From this it would seem that when this codex was written the Maya method of counting years was by periods of 20 each, as in the case of the month days. Whether there is any reference here to the ahaues is uncertain. I am inclined to think with Dr. Foerstemann that it was rather in consequence of the use of the vigesimal system in representing numbers. It would have been very inconvenient and cumbersome to represent high numbers by means of dots and lines; hence a more practicable method was devised. It is evident, from the picture inserted at this point in the series, that some important chronological event is indicated. Here also in the written characters over this picture is the symbol for 20. The last number given in the above addition may therefore, in order to correspond with the method of the codex, be written as follows:

Twenty year periods. Years. Months. Days. 1 0 3 4

Continuing the addition in this way the result is as follows:

Twenty year periods. Years. Months. Days. 1 0 3 4 8 17 — — — — 1 0 12 1 Third column on Plate 53b. 8 17 — — — — 1 1 2 18 Fourth column on Plate 53b. 8 17 — — — — 1 1 11 15 Fifth column on Plate 53b. 8 17 — — — — 1 2 2 12 First column on Plate 54b. 8 17 — — — — 1 2 11 9 Second column on Plate 54b. 8 17 — — — — 1 3 2 6 Third column on Plate 54b. 7 8 — — — — 1 3 9 14 Fourth column on Plate 54b. 8 17 — — — — 1 4 0 11 Fifth column on Plate 54b. 8 17 — — — — 1 4 0 8 First column on Plate 55b. 8 18[321-1] — — — — 1 5 0 6 Second column on Plate 55b. 8 17 — — — — 1 5 9 3 Third column on Plate 55b. 8 17 — — — — 1 6 0 0 Fourth column on Plate 55b. 8 17 — — — — 1 6 8 17 Fifth column on Plate 55b. 8 17 — — — — 1 6 17 14 Sixth column on Plate 55b. 8 17 — — — — 1 7 8 11 Seventh column on Plate 55b. 7 8 — — — — 1 7 15 19 Eighth column on Plate 55b. 8 17 — — — — 1 8 6 16 First column on Plate 56b. 8 18[321-2] — — — — 1 8 15 14 Second column on Plate 56b. 8 17 — — — — 1 6 6 11 Third column on Plate 56b. 8 17 — — — — 1 9 15 8 Fourth column on Plate 56b. 8 17 — — — — 1 10 6 5 First column on Plate 57b. 7 8 — — — — 1 10 15 2 Second column on Plate 57b. 7 8 — — — — 1 11 4 10 Third column on Plate 57b. 8 17 — — — — 1 11 13 7 Fourth column on Plate 57b. 8 17 — — — — 1 12 13 1 Fifth column on Plate 57b. 8 17 — — — — 1 12 13 1 First column on Plate 58b. 8 17 — — — — 1 13 3 18 Second column on Plate 58b.

The proof, therefore, that the theory advanced in regard to the order and the plan of the series is correct seems to be conclusive. This probably would have been conceded without the repeated additions given, but these were deemed necessary because of several irregularities found in that portion running through Plates 53a-58a, which constitutes the first half of the series.

Turning back to our Table VIII, representing that part of the series on Plate 53a, we will consider the three lines of black numerals above the day columns, discussing the irregularities as we proceed.

The numbers in the first column are 7/17,[TN-6] or, according to the explanation given, 7 months and 17 days. There is apparently a mistake here, the correct numbers being 8 months and 17 days, as it is the usual custom of the codex to commence numeral series with the prevailing interval; moreover this correction, which has also been made by Dr. Foerstemann, is necessary in order to connect rightly with what follows; the counters under this first column require this correction, as they are 8 months, 17 days. Making this change we proceed with the addition.

Years. Months. Days. 8 17 First column, Plate 53a (corrected). 8 17 — — 17 14 Second column. Plate 53a.

Here the author of the codex has made another mistake or varied from the plan of the series. As several similar variations or errors occur in this part of the series, it will be as well to discuss the point here as elsewhere. Dr. Foerstemann, in discussing the series, takes it for granted that these variations are errors of the aboriginal scribe; he remarks that "It is seen here that the writer has corrected several of his mistakes by compensation. For instance, the two first differences should be 177 [8 months, 17 days] and 148 [7 months, 8 days], not 176 and 149," &c.

This is a strained hypothesis which I hesitate to adopt so long as any other solution of the difficulty can be found. It is more likely that the writer would have corrected his mistakes, if observed, than that he would compensate them by corresponding errors.

Going back to that part of the series in the lower divisions which has already been examined and commencing with Plate 51b (see Table VI), we observe that the numbers in the lowest of the three lines of black numerals, immediately over the day columns, and the first day of these columns are as follows (omitting the week days attached):

14 11 8 5 2 10 Ik. Cauac. Cib. Been. Oc. Ezanab.

Turning to the calendar (Table II) and using the Muluc column, we notice that the figures of this third line of black numerals denote respectively the month numbers of the days under them; that is to say, Ik is the fourteenth day of the month in Muluc years, Cauac the eleventh, Cib the eighth, Been the fifth, Oc the second, and Ezanab the tenth. This holds good through Plates 52b to 58b without a single exception, provided the diamond shaped symbol in the fourth column of Plate 55b is counted as 20. This test, therefore, presents fewer exceptions than are found in counting the intervals as before explained; yet, after all, this would necessarily result from the fact that the day Muluc was selected as the commencement of the series, and hence may have no signification in reference to or bearing on the question of the year series, especially as the years counted are evidently of 360 days.

Returning now to our Table VIII, representing Plate 53a, we observe that the number immediately over Kan in the first column is 17, whereas Kan is the sixteenth day of the month. Is it not possible that the intention was to designate as the ceremonial day Chicchan, standing immediately below, which is the seventeenth day of the month in Muluc years? Even though there is no reference to Muluc years, the intervals may be given upon the same idea, that of reaching, for some particular reason, the second or third day of the column instead of the first. This would account for the compensation of which Dr. Foerstemann speaks, without implying any mistake on the part of the writer. These irregularities would then be intentional variations from the order of the series, yet so as not to break the general plan.

The interval between 6 Kan of the first column (with the month number corrected) and 1 Ymix of the second is 8 months and 17 days, as it should be; between 6 Muluc and 1 Cimi, 8 months and 17 days; and between 1 Cimi and 9 Akbal, 8 months and 17 days, thus conforming to the rule heretofore given, a fact which holds good as a general rule throughout that portion of the series in the upper division.

Continuing the addition as heretofore we note the variations.

Years. Months. Days. Column. Plate. 17 14 Second. 53a. 7 8 — — — 1 7 3 Third. 53a. 8 17 — — — 1 15 19[323-1] Fourth. 53a. 8 17 — — — 2 6 16 Fifth. 53a. 8 17 — — — 2 15 13 Sixth. 53a. 8 18[323-2] — — — 3 6 11 First. 54a. 8 17 — — — 3 15 8 Second. 54a. 8 17 — — — 4 6 5 Third. 54a. 8 17 — — — 4 15 2[324-1] Fourth. 54a. 8 17 — — — 5 5 19 Fifth. 54a. 8 17 — — — 5 14[324-2] 16 Sixth. 54a. 7 8 — — — 6 4 4 Seventh. 54a. 8 18[324-3] — — — 6[324-4] 13 2 First. 55a. 8 17 — — — 7 3 19[324-5] Second. 55a. 8 17 — — — 7 12 16 Third. 55a. 8 17 — — — 8 3 13 Fourth. 55a. 8 17 — — — 8 12 10 Fifth. 55a. 7 8 — — — 9 1 18 First. 56a. 8 17 — — — 9 10 15 Second. 56a. 8 17 — — — 10 1 12 Third. 56a. 8 17 — — — 10 10 9 Fourth. 56a. 8 17 — — — 11 1 6 First. 57a. 8 17 — — — 11 10 3 Second. 57a. 8 17 — — — 12 1 0 Third. 57a. 7 8[325-1] — — — 12 8 8 Fourth. 57a. 8 17 — — — 12 17 5 First. 58a. 8 17 — — — 13 8 2 Second. 58a. 8 18[325-2] — — — 13 17 0 Third. 58a. 8 17 — — — 14 7 17 Fourth. 58a. 8 17 — — — 14 16 14 First. 51b.[325-3]

We have in what has thus far been given a satisfactory explanation of the meaning and use of the lines of numerals and also of their relation to the day columns, but we still fall short of a complete interpretation, inasmuch as we are unable to give the series a definite location in the Maya calendar or in actual time. It is apparent, however, that the series cannot by any possible explanation be made to agree with the calendar system as usually accepted, as there is nothing in it indicating the four series of years or the year of 365 days. It may be safely assumed, I think, from what has been shown, that the year referred to in the series is one of 360 days, with probably a periodic addition of one day, but the reason of the addition is not yet apparent.

If the numbers in the lowest line of numerals over the day columns indicate the days of the month, and those of the middle line the respective months of the year, it is evident, as before stated, that Muluc is the first day of the year throughout, a conclusion irreconcilable with the Maya calendar as hitherto understood. It is probable, however, that the month and day numbers do not refer to particular months and days, but are used only as intervals of time counted from a certain day, which must in this case have been Muluc.

The sum of the series as shown by the numbers over the second column of Plate 58b is 33 years, 3 months, and 18 days. As this includes only the top day of this column (10 Cimi), we must add two days to complete the series, which ends with 12 Lamat. This makes the sum of the entire series 33 years, 4 months, or 11,960 days, precisely 46 cycles of 13 months, or 260 days each, the whole and also each cycle commencing with 13 Muluc and ending with 12 Lamat. It is also worthy of notice that in the right hand column of characters (hieroglyphics) over the inverted figure in Plate 58b two numbers, 13 and 12, are found attached to characters which appear to be abnormal forms of month symbols.

On Plates 63 and 64 are three series of ten day columns each and three lines of numerals over each series. These are as follows, so far as they can be made out, the numbers over the upper series being mostly obliterated. The 0 denotes the red, diamond shaped symbol which is here sometimes given in fanciful forms.

TABLE XX.—Table showing series of day columns, with lines of numerals.

UPPER DIVISION. _____________ Plate 63. Plate 64. + - 4 3 0 8 6 0 16 0 0 0 0 0 III Chicchan. III Chicchan. III Chicchan. III Chicchan. III Chicchan. Kan. Kan. Kan. Kan. Kan. Ix. Ix. Ix. Ix. Ix. Cimi. Cimi. Cimi. Cimi. Cimi. XIII Akbal. XIII Akbal. XIII Akbal. XIII Akbal. XIII Akbal. ___ ___ ___ ___ ___ Plate 64. ________ ______ 0 0 12 8 3 3 0 0 0 0 0 III Chicchan. III Chicchan. III Chicchan. III Chicchan. III Chicchan. Kan. Kan. Kan. Kan. Kan. Ix. Ix. Ix. Ix. Ix. Cimi. Cimi. Cimi. Cimi. Cimi. XIII Akbal. XIII Akbal. XIII Akbal. XIII Akbal. XIII Akbal. ___ ___ ___ ___ ___

MIDDLE DIVISION.[TN-7] _____________ XIX 5 4 4 4 4 IV 1 14 9 5 0 IV 0 0 0 7 16 III Chicchan. III Ix. III Akbal. III Eb. III Ymix. Kan. Been. Ik. Chuen. Ahau. Ix. Akbal. Eb. Ymix. Oc. Cimi. Men. Kan. Been. Ik. XIII Akbal. XIII Eb. XIII Ymix. XIII Oc. XIII Cauac. ___ ___ ___ ___ ___ 3 3 3 3 2 14 9 5 0 14 5 14 3 12 1 III Oc. III Cauac. III Lamat. III Caban. III Cimi. Muluc. Ezanab. Manik. Cib. Chicchan. Cauac. Lamat. Caban. Cimi. Men. Chuen. Ahau. Muluc. Ezanab. Manik. XIII Lamat. XIII Caban. XIII Cimi. XIII Men. XIII Kan. ___ ___ ___ ___ ___

LOWER DIVISION.[TN-7] _____________ 2 2 2 1 1 9 4 0 13 9 10 19 8 17 6 III Men. III Kan. III Been. III Ik. III Chuen. Ix. Akbal. Eb. Ymix. Oc. Kan. Been. Ik. Chuen. Ahau. Cib. Chicchan. Ix. Akbal. Eb. XIII Been. XIII Ik. XIII Chuen. XIII Ahau. XIII Muluc. ___ ___ ___ ___ ___ 1 1 4 0 13 9 4 15 4 13 2 11 III Ahau. III Muluc. III Ezanab. III Manik. III Cib. Cauac. Lamat. Caban. Cimi. Men. Muluc. Ezanab. Manik. Cib. Chicchan. Ymix. Oc. Cauac. Lamat. Caban. XIII Ezanab. XIII Manik. XIII Cib. XIII Chicchan. XIII Ix. ___ ___ ___ ___ ___

By examining carefully the lines and columns of the middle and lower divisions of the plates—those represented in Tables XXI and XXII—we ascertain that the two together form one series; but, contrary to the method which has prevailed in those examined, it is to be read from right to left, commencing with the right hand column of the lower and ending with the left hand column of the middle division.

As proof of this we have only to note the fact that the series of black numerals over the day columns ascends towards the left. Assuming the lowest of the three lines to be days, the middle one months, and the upper one years, the common difference is 4 months and 11 days. Numbering the ten columns of each of our tables from left to right as usual and adding successively the common difference, commencing with the tenth column of the lowest division, of which Cib is the first day, the result will be as follows:

Years. Months. Days. 4 11 Over tenth column, lower division. 4 11 — — 9 2 Over ninth column, lower division. 4 11 — — 13 13 Over eighth column, lower division. 4 11 — — 1 0 4 Over seventh column, lower division. 4 11 — — — 1 4 15 Over sixth column, lower division. 4 11 — — — 1 9 6 Over fifth column, lower division. 4 11 — — — 1 13 17 Over fourth column, lower division. 4 11 — — — 2 0 8 Over third column, lower division. 4 11 — — — 3 4 19 Over second column, lower division. 4 11 — — — 2 9 10 Over first column, lower division. 4 11 — — — 2 14 1 Over tenth column, middle division. 4 11 — — — 3 0 12 Over ninth column, middle division. 4 11 — — — 3 5 3 Over eighth column, middle division. 4 11 — — — 3 9 14 Over seventh column, middle division. 4 11 — — — 3 14 5 Over sixth column, middle division. 4 11 — — — 4 0 16 Over fifth column, middle division. 4 11 — — — 4 5 7 Over fourth column, middle division. 4 11 — — — 4 9 18 Over third column, middle division. 4 11 — — — 4 14 9 Over second column, middle division. 4 11 — — — 5 1 0 Over first column, middle division.

The red numerals over the first column of the middle division, except the lowest diamond shaped one, are omitted, as they do not appear to belong to the series.

It must be borne in mind that the 4 months and 11 days form the common difference between the corresponding days of the columns counting from right to left; that is to say, counting 4 months and 11 days from the top day of any column will bring us to the first or top day of the next column to the left. The interval between the other corresponding days of the columns is also the same if the same week numbers are assigned them.

This question arises here, Does the difference include the time embraced in the entire column? That is to say, Is this interval of 4 months and 11 days (referring, for example, to the tenth and ninth columns of the lower division, our table) the sum of the intervals between 3 Cib and Men; Men and Chicchan; Chicchan and Caban; Caban and 13 Ix, and 13 Ix of the tenth column and 3 Manik of the ninth column? If not, the columns do not form a continuous series or must be taken in some other order.

Although Dr. Foerstemann discovered the order in which the series as a whole was to be read, and also the common difference—given, as is his custom, in days—he failed to furnish further explanation of the group.

In answer to the question presented I call attention to the following facts:

Commencing again with the uppermost day, 3 Cib, of the tenth column, lowest division, and counting on the calendar to 13 Ix of the same year, the interval is found to be 10 months and 18 days, which is much more than the interval between 3 Cib and 3 Manik (first of the ninth column), and of course cannot be included in it.

Reversing the order in reading the columns, but counting forward on the calendar as usual, we find the interval between 13 Ix and 3 Cib to be 2 months and 2 days, and, what is another necessary condition, the intermediate days of the column are included in this period in the order in which they stand, if read upwards. The interval between 3 Cib, uppermost day of the tenth column, and 13 Chicchan, bottom day of the ninth column, is 2 months and 9 days. The sum of these two intervals is 4 months and 11 days, as it should be on the supposition that the entire columns follow one another in regular succession. This proves beyond question that the columns are to be read from bottom to top and that they follow one another from right to left. This enables us to fix the week numbers to the intermediate days and to determine the day to which the entire series is referred as its starting point. The days and their numbers of the tenth and ninth columns of the lower division, writing them in reverse order, that is, from bottom to top, are as follows: 13 Ix; 3 Caban; 11 Chicchan; 8 Men; 3 Cib; 13 Chicchan; 3 Lamat; 11 Cib; 8 Cimi; 3 Manik.

These numbers hold good throughout the series.

Commencing with 13 Ix, the lowest day of the tenth column, lower division, but first day of the series, and ending with 13 Akbal, the bottom of the first column, middle series, the time embraced is 5 years, 1 month, 0 day, less 4 months and 11 days—that is, 4 years, 14 months, 9 days (years of 360 days being understood). This is easily proved by counting on the calendar 4 years, 14 months, and 9 days from 13 Ix, as it brings us to 13 Akbal. If we add to this time 2 months and 2 days—the interval between 13 Akbal and 3 Chicchan (top day of first column, middle division)—we have, as the entire period embraced in the series as it stands—from 13 Ix (first of the series) to 3 Chicchan (the last)—4 years, 16 months, 11 days. Add to this 4 months and 11 days, in order to reach the day with which the count begins, and we have as the entire period 5 years, 3 months, 2 days = 5 years, 1 month, 0 day + 2 months, 2 days. If we count back 4 months and 11 days from 13 Ix (first of the series), we reach 1 Kan, the day to which the series is referred as its starting point. Counting forward from this date 5 years, 3 months and 2 days brings us to 3 Chicchan, the last day of the series.

It is worthy of notice that, although this series appears to be referred to Kan years, it is at variance with the idea of passing from one to the other of the four year series, and is, moreover, based upon the year of 360 days. The order in which it is to be read, which is true also of some other pages, indicates that these extracts pertain to a different original codex than those to which we have heretofore alluded, a conclusion reached by Dr. Foerstemann soon after he commenced the study of the Dresden manuscript.

I was for a time inclined to believe there was a break between Plates 64 and 65, as there appeared to be no day columns with which the lines of numerals running through Plates 65-69 could be connected, but the fact that the sum of the black numbers in each is 91, precisely the interval between the corresponding days of the columns in Plates 63 and 64, will probably warrant the conclusion that they are connected with them. This conclusion is strengthened, so far as those in the lower division are concerned, by the fact that by taking the XIII attached to the lowest days of the columns the numbers properly succeed one another and the series conforms to the rule heretofore given. As proof of this I give here the lower line of the lower division, prefixing the XIII, thus: XIII; 9, IX; 5, I; 1, II; 10, XII; 6, V; 2, VII; 11, V; 7, XII; 3, II; 12, I; 8, IX; 4, XIII; 13, XIII.

Adding together the numbers and casting out the thirteens, thus, XIII + 9 - 13 = IX; IX + 5 - 13 = I, &c., the connection is seen to be regular. The final red numeral is XIII, the same as that with which the series begins, and the sum of the black numbers, 9, 5, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4, 13, is 91, a multiple of 13. The middle line of numerals also connects with the XIII attached to the bottom symbols of the day columns; and the upper line of numerals connects with the III attached to the top symbols of the day columns.

Plates 70 to 73 present some peculiarities difficult to account for. That these pages belong to the same type as 62, 63, and 64 cannot be doubted, and that as a general rule they are to be read from right to left is easily proved; but this method does not seem to be adopted throughout, the order being apparently reversed in a single series.

The aboriginal artist has apparently made up these pages from two older manuscripts or changed and added to his original. The last two columns of Plate 70 and first five of 71 appear to have been thrust in here as an afterthought or as a fragment from some other source, forming apparently no legitimate connection with the series to either the right or to the left of them. It is true, as will be shown, that there is some connection with the lowest series on the right, but it would seem that advantage was here taken of accidental correspondence rather than that this correspondence was the result of a preconceived plan.

Commencing in the lower part of the middle division of Plate 73 and running back (to the left) to the sixth column of 71 and returning to the lower part of the lower division of 73 and ending with the sixth column of 71, is the following series. The columns are given in the order in which they stand on the respective plates, but the plates are taken in reverse order:

TABLE XXIII.—Table giving comparison between Plates 71, 72, and 73.

First Second Third Fourth Fifth column. column. column. column. column. - - - - - - - - Plate 73, 16 13 9 6 3 middle 5 0 15 10 5 division IV Caban. IV Eb. IV Manik. IV Ik. IV Caban. - First Second Third Fourth Fifth Sixth Seventh column. column. column. column. column. column. column. - - - - - - - - Plate 72, 2 1 1 1 1 1 middle 3 17 14 11 8 4 19 division 0 15 10 5 0 15 10 IV Eb. IV Manik. IV Ik. IV Caban. IV Eb. IV Manik. IV Ik. - Sixth Seventh column. column. - - - - - - - - Plate 71, 2 2 middle 9 6 division 10 5 IV Ik. IV Caban. - First Second Third Fourth Fifth column. column. column. column. column. - - - - - - - - Plate 73, 3 3 3 2 2 lower 7 3 1 16 12 division 15 10 5 0 15 IV Manik. IV Ik. IV Caban. IV Eb. IV Manik. - First Second Third Fourth Fifth Sixth Seventh column. column. column. column. column. column. column. - - - - - - - - Plate 72, 4 4 4 4 2 3 3 lower 12 9 6 2 17 14 11 division 10 5 0 15 10 5 0 IV Ik. IV Caban. IV Eb. IV Manik. IV Ik. IV Caban. IV Eb. - Sixth Seventh column. column. - - - - - - - - Plate 71, 5 4 lower 1 15 division 0 15 IV Eb. IV Manik. -

The interval between the successive days, counting to the left, is in each case 3 months and 5 days, corresponding with the numbers over IV Caban, fifth column, middle division, Plate 73. Commencing with this number and adding it successively, we obtain the numbers over the various columns:

Years. Months. Days. 3 5 Over fifth column, middle division, Plate 73. 3 5 — — 6 10 Over fourth column, middle division, Plate 73. 3 5 — — 9 15 Over third column, middle division, Plate 73. 3 5 — — 13 0 Over second column, middle division, Plate 73. 3 5 — — 16 5 Over first column, middle division, Plate 73. 3 5 — — 1 1[333-1] 10 Over seventh column, middle division, Plate 72. 3 5 — — — 1 4 15 Over sixth column, middle division, Plate 72. 3 5 — — — 1 8 0 Over fifth column, middle division, Plate 72. 3 5 — — — 1 11 5 Over fourth column, middle division, Plate 72. 3 5 — — — 1 14 10 Over third column, middle division, Plate 72. 3 5 — — — 1 17 15 Over second column, middle division, Plate 72. 3 5 — — — 2 3 0 Over first column, middle division, Plate 72. 3 5 — — — 2 6 5 Over seventh column, middle division, Plate 71. 3 5 — — — 2 9 10 Over sixth column, middle division, Plate 71. 3 5 — — — 2 12 15 Over fifth column, lower division, Plate 73. 3 5 — — — 2 16 0 Over fourth column, lower division, Plate 73. 3 5 — — — 3 1 5 Over third column, lower division, Plate 73. 3 5 — — — 3 4 10 Over second column, lower division, Plate 73. 3 5 — — — 3 7 15 Over first column, lower division, Plate 73. 3 5 — — — 3 11 0 Over seventh column, lower division, Plate 72. 3 5 — — — 3 14 5 Over sixth column, lower division, Plate 72. 3 5 — — — 3 17 10 Over fifth column, lower division, Plate 72. 3 5 — — — 4 2 15 Over fourth column, lower division, Plate 72. 3 5 — — — 4 6 0 Over third column, lower division, Plate 72. 3 5 — — — 4 9 5 Over second column, lower division, Plate 72. 3 5 — — — 4 12 10 Over first column, lower division, Plate 72. 3 5 — — — 4 15 15 Over seventh column, lower division, Plate 71. 3 5 — — — 5 1 0 Over sixth column, lower division, Plate 71.

It is worthy of notice that the sum of the series as expressed by the final numbers is precisely that of the series on the middle and lower divisions of Plates 63 and 64, heretofore given, and embraces seven complete cycles of 13 months, or 260 days each. Counting back three months and five days from 4 Caban (the day in the fifth column, middle division, of Plate 73) we reach 5 Been as the starting point of the series.

As there can be no doubt that the lines and days of the two divisions form together one unbroken series, it is evident there is no connection between that portion of it in the middle division and what lies to the left of it in Plate 71; but there does appear to be, as before indicated, some connection between the conclusion and what follows to the left in the lower portion of 71. The series which lies to the left at this point is as follows:

TABLE XXIV.—Table showing relations of Plates 70 and 71.

___________ Plate 70. Plate 71. + - 5th 6th 1st 2d 3d 4th 5th 6th column. column. column. column. column. column. column. column. 6 5 4 3 2 1 1 0 0 0 15 10 5 6 2 16 12 8 3 2 1 0 0 0 0 0 0 0 0 IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. -

For the purpose of assisting the reader to see the relation more clearly, the last column of the preceding series—sixth of the lower division on Plate 71—is added at the right as it stands in the original.

It is apparent that the figures in the fifth column of 71 are exactly double those in the sixth column. This and the fact that the day IV Eb is the same as those following are the only indications that there is any connection between the series. Using the 5 years and 1 month as the common difference and adding, the result is as follows:

Years. Months. Days. 5 1 0 Sixth column, lower division, Plate 71. 5 1 0 — — — 10 2 0 Fifth column, lower division, Plate 71. 5 1 0 — — — 15 3 0 Fourth column, lower division, Plate 71.

At this point another change occurs: the former difference is added to the last figures and the sum is doubled.

Twenty year periods. Years. Months. Days. 15 3 0 5 1 0 — — — — 1 0 4 0 2 — — — — 2 0 8 0 Third column lower division, Plate 71. 1 0 4 0 — — — — 3 0 12 0 Second column, lower division, Plate 71. 1 0 4 0 — — — — 4 0 16 0 First column, lower division, Plate 71. 1 0 4 0 — — — — 5 1 2 0 Sixth column, lower division, Plate 70. 1 0 4 0 — — — — 6 1 6 0 Fifth column, lower division, Plate 70.

This series does not end at this point, but is continued in the lines immediately above, which are as follows:

TABLE XXV.—Table showing relations between Plates 70 and 71.

Plate 70. Plate 71. + - 5th 6th 1st 2d 3d 4th 5th column. column. column. column. column. column. column. 1 0 8(?) 15 13 10 9 7 XII 12 1 3 2 2 2 1 II 3 10 6 16 4 0 10 XII 0 0 0 0 (?) 0 0 IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. IV Eb. IV Eb.

Adding the difference, 1, 0, 4, 0, to the final result of the preceding addition we obtain the figures of the right hand column (fifth column, Plate 71) of this series:

6 1 6 0 1 0 4 0 — — — — 7 1 10 0

To obtain the figures of the fourth column this difference must be doubled, thus

7 1 10 0 2 0 8 0 — — — — 9 2 0 0

To obtain the black numbers of the next (third) column, the lower cipher symbol of which is wanting, we add the former difference:

9 2 0 0 1 0 4 0 — — — — 10 2 4 0

This decrease in the difference is unusual and indicates some error. This idea seems to be confirmed in the following way: In order to obtain the numbers of the next (second) column it is necessary to add three times the former difference, thus:

10 2 4 0 3 0 12 0 — — — — 13 2 16 0 Second column, Plate 71.

If the increased difference, 2, 0, 8, 0, were retained after its appearance the result would be as follows:

7 1 10 0 Fifth column, Plate 71. 2 0 8 0 — — — — 9 2 0 0 Fourth column, Plate 71. 2 0 8 0 — — — — 11 2 8 0 Third column, Plate 71. 2 0 8 0 — — — — 13 2 16 0 Second column, Plate 71. 2 0 8 0 — — — — 15 3 6 0 First column, Plate 71.

Adding the difference, 2, 0, 8, 0, to the third column, Plate 71, thus:

10 2 4 0 2 0 8 0 — — — — 12 2 12 0

we obtain the red numerals inserted in the third column. It is probable that the original or some subsequent scribe, observing an error at this point, inserted these figures as a correction. If so, he failed to remedy the confusion apparent in this portion of the series. The sum of the entire series is 303 years (360 days each) and six months, equal to 420 cycles of 260 days.

I am strongly inclined to believe that this section and also pages 24 and 59 are interpolations by some aboriginal artist of a mathematical turn and advanced ability in this direction, who has given these high series more as curiosities than with reference to any specific dates or periods of time.



Commencing in the sixth column of Plate 71a and running through 72a to the second column of 73a, is a numeral series which presents some peculiarities that baffle all attempts at explanation. Contrary to the rule which prevails in these pages it ascends from left to right and has no day symbols connected with it. In addition to this, the numbers of its lowest line are inclosed in loops of the form here shown (Fig. 371) and have no apparent connection with the other lines of the series, but, on the contrary, if taken from right to left, they present in the order usually given the numbers of the ahaues or katunes.[337-1] It is as follows:

1 1 1 1 1 1 1 2 5 8 10 13 16 0 3 6 9 11 14 17 II. 14 8 2 16 10 4 18 12 6 0 14 7(?) 2 XIV [(11)][(13)][(2)][(4)][(6)][(8)][(10)][(12)][(1)][(3)][(5)][(7)][(9)]

The last (thirteenth) column of this series is not in a line with the others, but is found in the lower part of the right hand column of Plate 73, and in connection with it we find the red numerals II and XIV, denoting the difference between the columns, as is apparent from the additions here given:

Years. Months. Days. 2 14 First or left hand column. 2 14 — — 5 8 Second column. 2 14 — — 8 2 Third column. 2 14 — — 10 16 Fourth column. 2 14 — — 13 10 Fifth column. 2 14 — — 16 4 Sixth column[TN-8] 2 14 — — 1 0 18 Seventh column. 2 14 — — — 1 3 12 Eighth column. 2 14 — — — 1 6 6 Ninth column. 2 14 — — — 1 9 0 Tenth column. 2 14 — — — 1 11 14 Eleventh column. 2 14 — — — 1 14 8[338-1] Twelfth column.[TN-9] 2 14 — — — 1 17 2 Thirteenth column.

FOOTNOTES:

[261-1] The work here referred to is entitled Die Mayahandschrift der Koeniglichen oeffentlichen Bibliothek zu Dresden, herausgegeben von Prof. Dr. E. Foerstemann, Hofrat und Oberbibliothekar. It contains, besides the chromolithographs of the 74 plates, an introduction published at Leipzig, 1880, 4^o.

[269-1] A Study of the Manuscript Troano, by Cyrus Thomas, pp. 7-15.

[272-1] This method will be adopted throughout this paper where figures containing numerals are introduced.

[273-1] In the representations of lines and columns of the codex Roman numbers are necessarily used to distinguish the class of numerals, yet in the text, as in this case, the Arabic numbers will be used as most convenient.

[273-2] Strictly speaking, the interval between 11 Men and 13 Oc is fourteen days, but throughout this paper, by "interval between" two days, is to be understood the number of days to be counted from one to and including the other. The one counted from is always excluded and the one reached or with which the interval terminates is always included.

[273-3] Science, p. 459, April 11, 1884.

[277-1] Throughout this paper when the words "figure" and "character" are used in reference to what appears in the codex, they are to be understood as follows: "figure" refers to the picture, as of a person, animal, or other object in the spaces; "character" refers to the hieroglyphics or written symbols.

[278-1] Study of the Manuscript Troano, by Cyrus Thomas, Chapters II and VII.

[278-2] Erlaeuterungen zur Mayahandschrift, p. 2.

[280-1] Erlaeuterungen zur Mayahandschrift, p. 16.

[280-2] Bureau of Eth., Third Ann. Rep., pp. 16 et seq.

[282-1] Study of the Manuscript Troano, by Cyrus Thomas, pp. 15, 16.

[282-2] Dechiffrement des ecritures calculiformes ou Mayas, par M. le C^te H. de Charency, Alencon, 1849; also, Melanges, pp. 185-195.

[283-1] For an explanation of the principle upon which these day columns were formed, see "Notes on certain Maya and Mexican manuscripts," by Cyrus Thomas, published in the Third Annual Report of the Bureau of Ethnology.

[290-1] The symbol for this day in Kingsborough resembles Lamat, but the photographic copy makes it Ix, as it should be.

[290-2] Foerstemann, Erlaeuterungen zur Mayahandschrift, p. 42.

[291-1] Erlaeuterungen zur Mayahandschrift, p. 36.

[292-1] Erlaeuterungen zur Mayahandschrift, p. 60.

[293-1] Erlaeuterungen zur Mayahandschrift, p. 56.

[296-1] The bottom lines are selected because they are less injured in the codex than the top lines, which are in most cases entirely obliterated.

[300-1] 3 days in ms., should be 4.

[317-1] The third symbol in the last day column of Plate 51b is Been in the codex; but this is an evident mistake, as shown by the order of the days, since Ahau, which has been substituted above, always follows Cauac. This may be seen by reference to the middle column of 57b.