He took the days for granted. First he determined the differences between
them; then he added to each difference a multiple of 260; and the choice of
the multiple seems to have been quite arbitrary. The number thus obtained
he added to 12,412,920, unless it was the smaller, in which case he
subtracted it from 12,412,920, and the result he wrote down in the
serpents.
We shall find the same process, only somewhat amplified, with the serpent
on page 69.
Are the seven numbers intended to denote the destruction of the seven
planets? I hope this question will be answered in the near future.
There now remains of the contents of these pages only the two columns on
the left of page 61, which we will now examine and at the same time compare
them with the corresponding column of page 69, the upper part of which is
exactly the same, and the lower very nearly so. Each column consists of 18
hieroglyphs, which I count from the top downward, designating those of the
first column by _a_ and those of the second by b.
At the first glance these double columns remind one of the inscriptions in
the temples and on the stelae, especially of their beginnings, the
so-called initial series. Here, in the second column, we find the statement
of the usual periods:--144,000, 7200, 360, 20, 1, but in the first column
we find faces belonging to them. In his work "The Archaic Maya
Inscriptions," 1897, which, on the whole, contains more of imagination than
of science, J. T. Goodman unqualifiedly declares these faces to be numbers
by which the periods indicated beside them are to be multiplied, and this
theory has already found considerable recognition; we will therefore try to
follow where he leads.
1a and 1b are effaced on page 61; they probably contained a sort of
superscription as on the inscriptions. 2a is effaced on page 61, but the
sign may be recognized from page 69 as that with which on page 46 the
series of the twenty deities begins after 236 (4 × 59) days. On pages 61
and 69 it takes the place of a face, to which I am inclined to assign the
numerical value 4. In 2b, which is C's head, I am inclined to look for the
value 2,880,000 = 20 × 20 × 20 × 360 days, which is not at all
inappropriate for C, as the sign of the north pole around which everything
revolves. I therefore propose to read 2ab as 4 × 2,880,000 = 11,520,000.
3b, it seems to me, resembles the sign for 144,000, which I found in the
inscriptions and which is repeated in 12a. It must, however, be left
undecided by what this same number in 3a is to be multiplied; 3a is
repeated besides in 8a and 13b. 4a contains the head of E, and 4b that of
the Moan. 4a seems to refer to 5a, and 4b to 5b. But 5a and 5b are the same
sign, which, inserted between the 144,000 and the 7200, can scarcely mean
anything else than the so-called Ahau-Katun of 6 × 18,980 = 113,880 days.
Have we two such periods here? Were they designated by consecutive numbers?
Now comes the 7200 in 6a, and the number 8 with E's head and the inserted
sign for 360 days in 6b (on page 69 without E's head), therefore 8 × 360 =
2880. Seler also thinks 7a has the numerical value 16 (Einiges mehr über
die Monumente von Copan, etc., page 217); 7b belongs to 7a. 7b, a Kin with
a I and a suffix and a leaf-shaped prefix, is inserted between the 360 and
20. What can it mean? Hardly the 260, for this is represented elsewhere
(_e.g._, page 24) by the thirteenth month Mac. Or can it possibly refer to
the month Yaxkin (days 120-140)?
8b is a Chuen sign, which, with its prefix (superfix on page 69) always
denotes twenty days in the inscriptions. It is multiplied with the same
unknown head in 8a, which we have already met with in 3a. 9a contains H's
head, and 9b is an unknown head with inserted Kin; the two signs must of
necessity indicate the single days still to be added to the period, though
as yet we do not know how.
The normal date IV Ahau 8 Cumhu then follows in 10ab. If it refers to the
signs just now discussed, then they must denote a number of about the same
magnitude as the serpent numbers. 653 or 654 times 18,980 seems to suggest
itself, but we shall have more to say later on this subject. My efforts to
reach a definite result here have failed.
Nor does the lower part of the two columns lead me to the desired goal. As
it seems to consist of several groups, I will first combine 11ab and 12ab.
I look upon 11a as denoting 20, and with regard to 11b I have already
expressed the surmise in the Zeitschrift für Ethnologie XXIII, page 153,
that it may mean 8760 = 24 × 365, _i.e._, three Venus-solar periods. That
would be 20 × 8760 = 480 × 365 = 175,200. The Moan in 12a may have the
value 13, for this number is so often combined with the Moan. As we saw
under page 51, 12b is = 18,980; 13 × 18,980 = 246,740. Accordingly the four
signs taken together may mean 421,940 = 1156 × 365.
The second group, from 13a to 15b, refers, on the other hand, to the year
of 360 days. First 13a = 144,000, having in 13b the unknown multiplier,
which we have already seen in 3a and 8a. Then follows in 14a, 15 × 7200 =
108,000; in 14b, 9 × 360 = 3240; in 15a, a 20 with a prefixed 1 (21?); and
in 15b, three days. It would be more correct to place the 1 beside the
following 3. The whole sum would then end with the number 4, which would
agree with the day Kan, the date specified below.
In the third group the 16a = 19 × 18,980 = 360,620, remains a mystery; an
empty outline of a sign is added in 16b.
17ab also forms a group by itself. 17a contains a sign, which rather
suggests the Bacab, upon whose period of 91 days the series belonging here
is based. The Imix in 17b with a superfix is still unintelligible.
The columns end in 18 with the date IX Kan XII Kayab, the starting-point of
the serpent numbers.
Pages 65--69.
I think it very likely that this section bears the same relation to pages
61-64 as pages 46-50 do to 24 and as 53-58 to 51-52. For here, too, a
period of time forming the basis of the earlier section seems to be divided
into smaller parts. On page 64 we recognize as the basis of the series the
number 91, the quarter of the ritual year of 364 days; here we have to do
with the fourfold division of 91 into 13 unequal parts. And the real
starting-points on these pages, as on the previous ones, are the days III
Chicchan and XIII Akbal.
The four series of numbers, the top one of which I have probably correctly
restored from what still remains, are as follows:--
9 XII, 5 IV, 1 V, 10 II, 6 VIII, 2 X, 11 VIII, 7 II, 3 V, 12 IV,
8 XII, 4 III, 13 III.
11 I, 13 I, 11 XII, 1 XIII, 8 VIII, 6 I, 4 V, 2 VII, 13 VII, 6 XIII,
6 VI, 8 I, 2 III.
11 XI, 13 XI, 11 IX, 1 X, 8 V, 6 XI, 4 II, 2 IV, 13 IV, 6 X,
6 III, 8 XI, 2 XIII.
9 IX, 5 I, 1 II, 10 XII, 6 V, 2 VII, 11 V, 7 XII, 3 II, 12 I, 8 IX,
4 XIII, 13 XIII.
The first two lines, forming together a single period of 182 days, refer to
a day III, as we see by the ending, and the last two to XIII, which
undoubtedly refers to the III Chicchan and XIII Akbal, the days so
significant in the preceding section. Hence an interval of 218 days (III
Chicchan to XIII Akbal) is to be assumed between the second and third
lines, with the addition of which interval each of the two periods extends
over 400 days.
The first and fourth series have the same difference; and the second and
third correspond with one another in this respect. In the first and fourth
the differences follow a rule, viz:--as if one were walking in a ring
having on its edge the numbers 1 to 13, and kept stepping backward four
numbers. The differences of the second and third series apparently do not
follow any rule. Hence I think that the fourth series follows the third by
mistake and ought rightfully to precede it. Only the fifth member in the
first and second series has the same day VIII and the day V in the third
and fourth series, otherwise the week-days of each series differ from those
of the others.
As I regard III Chicchan and XIII Akbal as unquestionably the
starting-points, I will here give a table of the days on which each of the
twenty-six members of each series must fall and at the same time I will
indicate for each day its number from the beginning of the series.
Accordingly the first 182 days present the following appearance:--