s red numeral should be II. We may assume
that the Maya artist has made a mistake and written 12 instead of 11,
which is evidently the number to be used in the count; but this
arbitrary correction should not be resorted to so long as any other
explanation is possible. From the fact that immediately under these
numbers there are certain symbols which appear to have some reference to
the termination of one year or cycle and the commencement of another, it
is possible that a supplemental, unnumbered, but not uncounted day has
been added. The fact that this interval of twelve days includes the day
Ymix lends some probability to this supposition. Using 11 instead of 12,
we continue our count as follows: IV + 11 - 13 = II; II + 5 = VII; VII +
8 - 13 = II; II + 11 = XIII. Thirteen is, therefore, the last number of
the series, which is wanting in the codex. The 8 and II next to the last
pair of the series are not in line with the other numbers, but thrust
into and near the bottom of the column of characters in the upper
division of Plate 39. Adding together the black numbers as thus amended
and restored, viz, 11, 8, 20, 13, 6, 20, 12, 19, 5, 1, 20, 12, 6, 8, 5,
7, 11, 5, 8, 11, the sum is found to be 208, which is a multiple of 13,
and the final number of the series is 13. On the other hand, the sum of
the series does not indicate the interval between the days of a column
counting downwards, nor between two consecutive days or the corresponding
days of two adjoining columns in any direction. The number of days from
13 Manik to 13 Chuen is 104, but counting 208 days from 13 Manik brings
us to 13 Men, the third day of the first (left hand) column; 208 more to
13 Akbal, the fifth; 208 more to 13 Chuen, the second; and 208 more to 13
Cauac, the fourth, thus completing the column.

As these columns do not appear to form a continuous series it is possible
they pertain to four different series of years, though the fact that each
includes more than one year would seem to forbid this idea. It is more
probable that they pertain to four different series, to each of which the
line of numerals is to be considered as belonging.

The black numerals above the columns present a problem which I am unable
to explain. The numbers stand in the original as follows:

1
4 13 9 4
15 13 2 11

If we suppose that the lowest line denotes days, the one next above,
months, and the uppermost, in which there is but a single number