3 - 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 29_c_ 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 29_c_ 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