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 VIIIVIII
17 8 1717

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. Förstemann 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.
1034

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.