ays and day numbers, it may
be well to test further the discovery by other examples, in order to see
how far it holds good and what new facts it may bring out. In doing this
it will be necessary to repeat in part what has already been shown by Dr.
Foerstemann in his late work; but as these discoveries were made
independently and before this work came to hand, and as our conclusions
differ in some respects from those reached by him, the plan and scope of
this paper would be incomplete without these illustrations.

Commencing with the day column in the middle of Plate 35_b_ and extending
through Plates 36_b_ and 37_b_ to the right margin of the latter, is a
line of alternate red and black numerals, which may be taken as an
example of the most common series found in the Dresden and other codices.
It is selected because it is short, complete, and has no doubtful symbols
or numerals in it.

Using names and numbers in place of the symbols, it is as follows:

I.
Caban, 11, XII; 6, V; 9, I; 4, V; 7, XII; 9, VIII; 6, I.
Muluc.
Ymix.
Been.
Chicchan.

In this case the red numeral over the day column is I. It is to be
observed that the last number of the series is also I, a fact which it
will be well to keep in mind, as it has an important bearing on what is
now to be presented. But it is proper to show first that this series is
continuous and is connected with the day column.

Adding the I over the column to the 11, the first black numeral; gives
XII, the red numeral following the 11. That this holds good in all cases
of this kind will become apparent from the examples which will be given
in the course of this discussion. Adding together the remaining pairs, as
follows: XII + 6 - 13 = V; V + 9 - 13 = 1; 1 + 4 = V; V + 7 = XII; XII +
9 - 13 = VIII; VIII + 6 - 13 = I, we obtain proof that the line is one
unbroken series. It is apparent that if the black numerals are simply
counters used to indicate intervals, as has been suggested, then, by
adding them and the red numerals over the column together and casting out
the thirteens, we should obtain the last red number of the series. In
this case the sum of the numbers 1, 11, 6, 9, 4, 7, 9, 6, is 53; casting
out the thirteens the remainder is 1, the last of the series. If we take
the sum of the black numbers, which in this case is 52, and count the
number of days on our calendar (Table II) from 1 Caban, the fourteenth
day of the first month of the year 1 Kan, we sha