In this example the black numerals appear to have been used simply as counters, or as numbers indicating intervals; for example, 15 is the interval between 11 Men and 13 Oc.[273-2]

This furnishes a clew which, if followed up, may lead to important results. That it explains the signification of one symbol undetermined until this relation of the numerals to one another was discovered, is now admitted. In the work of Dr. Förstemann before alluded to the discovery of the symbol for 20 is announced. Although I was not aware of the signification of this symbol until after my second paper, “Notes on certain Maya and Mexican manuscripts,” was written, I had made this discovery as early as 1884.[273-3]

As there will be occasion to refer to the days of the four different series of years (the Cauac, Kan, Muluc, and Ix years), a combined calendar, similar to an ordinary counting house calendar, is introduced here. For the Cauac years the left or Cauac column is to be used; for the Kan years, the Kan column, and so on.

Table II.—Names and numbers of the four series of years of the Maya system.

Cauac
column.		Kan
column.		Muluc
column.		Ix
column.		1
14		2
15		3
16		4
17		5
18		6
7
8
9
10
11
12
13
{Numbers
of the
months.
Days of
month.
CauacKanMulucIx182931041151261371
AhauChicchanOcMen293104115126137182
YmixCimiChuenCib310411512613718293
IkManikEbCaban411512613718293104
AkbalLamatBeenEzanab512613718293104115
KanMulucIxCauac613718293104115126
ChicchanOcMenAhau718293104115126137
CimiChuenCibYmix829310411512613718
ManikEbCabanIk931041151261371829
LamatBeenEzanabAkbal1041151261371829310
MulucIxCauacKan1151261371829310411
OcMenAhauChicchan1261371829310411512
ChuenCibYmixCimi1371829310411512613
EbCabanIkManik1829310411512613714
BeenEzanabAkbalLamat2931041151261371815
IxCauacKanMuluc3104115126137182916
MenAhauChicchanOc4115126137182931017
CibYmixCimiChuen5126137182931041118
CabanIkManikEb6137182931041151219
EzanabAkbalLamatBeen7182931041151261320

As this table has been explained in my previous papers it is only necessary to add here that the thirteen figure columns form a single series; therefore, when we reach the bottom of the thirteenth column we go back to the top of the first. The day reached will be the one directly opposite (that is, in the same horizontal line) in the day column for the given year.

For example, taking the fifth column of numbers (the one having 3 for the top figure) and counting down nine days from the top number we reach the number 12. This will be 12 Lamat if a Cauac year, 12 Been if a Kan year, 12 Ezanab if a Muluc year, and 12 Akbal if an Ix year. Therefore it is necessary in counting to refer always to the year (year column) with which the count begins. So long as the particular year referred to is unknown (as is Usually the case, the day series being apparently of general rather than of special application) it is immaterial which day column is selected, as the result will be the same with any. This will be apparent if we bear in mind that, when 260 days with their numbers attached have been written down in proper order as a series, we have therein all the possible combinations of days and numbers. This, it is true, does not give us all the months and years (to include these it is necessary to write out fifty-two entire years), but the same series of numerals will be applicable to each of the four year series (Kan, Muluc, Ix, and Cauac years). As any one of the thirteen figure columns of the table may be taken as the commencement of a year and any of the four day columns may be used, it is apparent that we have all the possible combinations (4 × 13 = 52).

I say above that “it is necessary in counting to refer always to the year (year column) which the count begins.” This I admit does not agree with the generally received idea of the Maya calendar, upon which [Table II] is constructed, as, according to this theory (which I have accepted in my previous papers), after passing through a year of one series (corresponding with one of the day columns of the table), we should enter upon a year of the next series; for example, when the year 1 Kan is completed we should enter upon the year 2 Muluc.

Although this calendar system seems to have been in vogue at the time of the conquest and is indicated in one or two of the codices, and possibly in the one now under consideration, the chronological series of the latter, as will hereafter appear, do not seem to be based upon it or to agree with it.