the years of the Maya calendar with those dated from the Christian era, if any one can be determined.

The reader will observe that we have so far proceeded upon the assumption that the first year of the cycle was 1 Kan, or in other words, that the Kan column always occupied the extreme left. That the four days, Kan, Muluc, Ix, Cauac-or "year bearers," as they were called by the Mayas-must follow in the order given, is manifest, but that Kan must come first does not follow from anything apparent in the system itself; either day may be the first, without any change in the system, but not without a difference in the result. There are some reasons apparent in the manuscript itself for believing that the author considered Cauac the first, or ruling day, and hence Kan the second, Muluc the third and Ix the fourth. One of these reasons will be given hereafter.

The importance of knowing which one of these days came first will be apparent from the following illustration: A certain event, for example, is dated a particular day in the year, I Ix. By

sary that we construct one. Since the system admits of fifty-two changes in the day on which the year begins, it would require fifty-two calendars to include the years of one cycle, just as fourteen are required to suit all the years of our system-seven for the ordinary and seven for the leap years.

As it would require much time and space to write these out in

1 2 3 4 5 6 7 8 9 10 II 12 13 Numbers of

A CONDENSED MAYA CALENDAR.

Ix
Column.

14 15 16 17 18

full, I have adopted the expedient shown in the following table of

abbreviating the work :

TABLE VI.

As each of the four days (the year bearers) can have but thirteen different numbers, it is unnecessary for us to have more than thirteen columns of numbers; when we reach the thirteenth column, or month, we have passed through all possible changes of numbers, and the fourteenth month begins with one as did the first. Instead, therefore, of having eighteen columns in our table, we need to extend it only so as to include thirteen, as we can use the first, second, third, fourth and fifth respectively for the fourteenth, fifteenth, sixteenth, seventeenth and eighteenth months, as indicated by the numbers of the months which we have placed above the table.

The reader must bear in mind the fact that although we have numbered the months as commencing with the left hand column, which has I for its upper figure; yet this holds good only when the year is I Cauac, 1 Kan, 1 Muluc or 1 Ix, and for none of the other years. The first month of the year may be any one of the thirteen columns, thus, 8 Cauac, 8 Kan, 8 Muluc and 8 Ix have the second column-which has 8 as its top figure-as their first month, then the one with 2 at top will be the second month, and so on to the thirteenth (7 at top) which will be the 12th month. Then we go back to the first column (1 at top) for the 13 month, and so on to the one with 10 at top for the 18th month. As the months always retain the same order and numbers, by knowing the column with which the year begins, we can, by counting in this way, find any month for any possible year. We must here warn the reader against confounding the days of month with the days of the week, the latter being the ones by which the days are usually designated; we must also warn him against confounding the numbers of the months with the top numbers of the columns. I will now show how this table is to be used by giving one or two examples:

Given the day 8 Ahau and the year 11 Kan to find the month and day of the month. As the year is 11 Kan, we must look to the Kan column. By running our eyes down this column we find that Ahau is the 17th day; then by looking along the 17th transverse line we find the figure 8 to be in the column which has 5 at the top, which we find is the second (always counting both) from the column with II at top; hence 8 Ahau of the year II Kan is the 17th day of the 2d month.

In the same way we find that 8 Ahau of the year 11 Muluc is

the 12th day of the 12th month, but in this case we have to count the columns from the one having 11 at top (always inclusive) to the right through to the thirteenth (the one with 7 at top), and then go back to the first and count up to the one in which we find 8 in the twelfth transverse line.

In the Perez manuscript, translated by Stephens and published in his "Yucatan," Vol. II, we find it stated that one Ajpula died "in the year 4 Kan, the 18th day of the month Zip on 9 Ymix." The year 4 Kan begins with the column of our table which has 4 as its top figure; the third month (Zip) will then be the one with 5 at the top; running down this to the eighteenth transverse line, we find the figure 9, we also find that the 18th day of the Kan column is Ymix, agreeing exactly with the date given.

In the Manuscript Troano we find another method of giving dates, which is very common throughout the work, thus:

(red)

(black)

This, according to my interpretation, signifies 13 Ahau of the 13th month. As neither the year nor the day of the month is given, it is evident that we may find four dates satisfying the demand. Turning to our table we commence with the Ahau in the Cauac column, which we find is the second day of the month. The 13 in the second transverse we find in the column having II at the top; by counting back thirteen months (always including the one counted from and to) we find that the first month of the year is the one with 6 at the top, hence the year is 6 Cauac. The backward counting is exactly the reverse of the forward counting-count toward the left until the first colunin is reached, then return to the thirteenth and so on until the number of the month required is reached.

Proceeding in the same way with the Ahau in the Kan, Muluc and Ix columns, we find the years to be 4 Kan, 9 Muluc and I Ix.

We are now prepared to discuss the question as to whether the numerals and day characters are used in the manuscript simply as dates or not.

By counting, I find there are about 235 recognizable columns

of day characters in the work, eight-ninths of which contain five characters each. Why this number? If, as I suppose, and as above illustrated, each has four dates (four different years) this gives to each of these columns twenty years (4 x 5 = 20), or one Katun, for even according to the theory of Perez, four years of his period were not generally counted.

But before testing this suggestion, I wish to call attention to a certain regularity in the order of the days in these columns. The left hand column of the middle division of Plate x is composed of characters representing the following days (always reading from the top downwards) in the order here given: Oc, Cib, Ik, Lamat, Ix. If we turn to the list of days and count from one of these names to the other, we shall find in each case an interval of six days. The other column, same plate and division, contains the characters for Ahau, Cimi, Eb, Ezanab and Kan, with an interval of six days between each two. The column in the middle division. of Plate vi shows an interval of five days between each two; the columns on Plate XVII, of twelve days; a column on Plate XXXI, of sixteen days; but the usual interval is either six or twelve days.

Although the interval is usually the same throughout a column, there are occasional departures from this rule, for example, in the left hand column of the upper division of Plate XIII, they are 6, 6, 4 and 2 days.

This fact, which is a marked characteristic of the work, is sufficient to show, beyond a reasonable doubt, that the days are here used simply as dates, and not for the signification of the words, as Brasseur supposed.

I understand that Charency has noticed a regularity in the order of the days, but as I have had no opportunity of examining his work, I am unable to state whether it is the fact here mentioned or not.

By examining Plates XX-XXIII, we see such a strong resemblance between them that we are forced to believe they relate to one and the same subject; the left hand column of each, which extends the whole length of the plate, is the repetition of a single day character with red numerals over each character. In Plate XXIII the character repeated is Cauac, one of the year bearers; the numerals over them are as follows, and in the following order (reading from the top downwards): 10, 1, 5, 9, 13, 4, 8, 12, (?), 7, (?), 2, 6-two of them being obliterated.