V. 36b and 57b agree after 3 × 91 days; the same sign appears again in 10b
and 20b.
15a and 36a correspond after 3 × 91 days; we shall continue the examination
of this sign under pages 71-73.
VI. 37a and 65a agree, _i.e._, after 4 × 91 days = a year. The sign
contains a human figure stretching both arms aloft. The passing of a year
was likewise indicated in III, but a year coming 52 days later than this.
VII. 10a and 31a agree, _i.e._, after 3 × 91 days. The sign is composed of
the crouching figure prefixed to the cross, which we also find in 12b, 35a
and 65b; it is prefixed to a different hieroglyph in 30a. In 38b, 52b and
59b (58 in the Manuscript) we see bird-like heads resembling the Bacab
sign. We should expect to find a familiar sign in 45, which is drawn
between these, but a Moan appears there instead. These signs seem to
indicate the end of the Bacab period. Does the Moan sign here, too, suggest
the end of the year?
In 38a, 52a and 59a we again see an Imix, and I consider it a corroboration
of my theory that all the four signs of groups 38 and 39 are repeated in 52
and 53 after 2 × 91 days.
I believe a further corroboration is the fact that though many of these
hieroglyphs have no connection with these periods of 7 × 13, _i.e._, with
the divisions of the ritual year, they do correspond with the usual
divisions of the Tonalamatl, _i.e._, 4 × 13 and 5 × 13 days.
After 4 × 13 or a multiple of it the signs recur in 20b, 24b, 40b, 44b-12b,
48b, 56b-16b, 32b, 64b-26b, 50b-10a, 30a-37a, 65a-15b, 51b-11b and 47b.
As examples of 5 × 13 I would mention 3b, 63b-10a, 20a, 30a-5b, 50b-24b,
29b-35b, 65b-15b, 20b, 40b.
Finally, I must mention two more hieroglyphs, which are limited almost
entirely to these pages:--
[Illustration]
In the first sign, which occurred on page 10a, I thought I recognized the
lunar month of 28 days. It occurs in this section in connection with the
third picture on page 56, and besides in the following groups of
hieroglyphs:--16b, 32b and 64b, always combined with a Yax. The regularity
of the intervals is striking, but as yet I can neither explain that, nor
the crouching personage (Mercury?) in the 10th, 20th and 30th groups and
again in the next, the 31st.
The second sign is found _only_ on these pages and here not less than
eleven times, possibly with the addition of the effaced sign in 6b and 27b
which may have been the same hieroglyph. The eleven places in which it
occurs are as follows:--3b, 15b, 17b, 23b, 24b, 29b, 40b, 44b, 49a, 51b and
63b. Two different prefixes are added to it; one in the first two and the
last two places and also in the last but two joined with Kin, and the other
in the six middle places. Of the eleven groups, 17 and 24, 44 and 51 are 7
groups apart, 3 and 17, 15 and 29, 49 and 63 are 14 groups apart, 23 and 44
are 21 groups apart, and hence 23 and 51 are separated by 28 groups or 1
year. Group 40 alone is not concerned with these intervals of seven or
multiples of seven.
Now, how far may all these periods of time be due to accident and how far
to design? Accident _alone_ is quite out of the question. The frequent
repetition of the sun-sign in groups 49, 50 and 51 on pages 54b and 55b,
seems to me to refer to the conjunctions of the sun with certain stars,
which occur at intervals of thirteen days.
Pages 58--59.
This section is also based on a series occupying the whole of page 59,
which contains nothing but number and day signs. This series has the
difference 78, which we found once before on page 44. There the
starting-point was III Lamat, here it is the day XIII Muluc, probably
coming in the year XIII Muluc, as in Cort. 40b, as I shall have occasion to
suggest later. The series extends, with the usual errors and variations, in
four divisions from top to bottom. The days, which are always two days
behindhand, owing to the number 78, in 780 again reach the day XIII Muluc,
at which point the succeeding members remain stationary, since from here on
the difference is always 780 or a multiple of it. 780 days are, however,
the apparent time of the revolution of Mars, which is the only planet now
left to be discussed, the subject of pages 46-50 having been Venus and the
sun, and of pages 51-58, Mercury and the moon with incidental treatment of
Saturn and Jupiter. With 780 as its difference, the series ascends to 19 ×
780 = 14,820, and then continues with this large number as its difference
until the series is lost in the effaced passages.
Curiously enough, however, directly under the line containing the 14,820,
there is a new series composed of nine members, or ten counting the
suppressed starting-point. But this starting-point is again the day IX Ik,
the difference, as proved by the annexed days, is again 78 and the series
ends with 780. Thus the starting-point is the only difference between the
two series. The principal series contains all the even and the secondary
series all the uneven days. Can the starting-point of the revolution of
Mars have been determined according to different principles? Is it possible
that in one case the beginning of the planet's retrogression was adopted as
the starting-point, and in the other case the date on which the planet,
after completing its retrograde course, again reached the degree of right
ascension at which it had begun its retrogression? This is a difficult
matter to decide, since the period of the retrogression of Mars fluctuates
between 62 and 81 days. The interval from IX Ik to XIII Muluc is 147 and in
reversed order 113 days.
It can hardly be assumed that the 19 of the IX 19 or IX Ik is connected
with the 19 × 780 mentioned above or with the 19 + 19 + 19 + 21 into which
the 78 is divided on pages 44-45, or finally with the 19, which four times
forms the principal part of the sub-divisions of 65 on pages 33-34.
Numbers amounting to millions accompany this series in the usual way. Two
of these are on page 58, viz:--1,426,360 and 1,386,580; but with the sign
of the sixth day, which is important here, between them. Below these
numbers, however, are two month dates:--first the normal date IV Ahau 8
Cumhu and, if I have correctly restored the effaced number before the month
sign, which in its turn is indistinct, the second is XIII Muluc 2 Zac,
which would fall in the year VIII Muluc. The encircled numbers also occur
here. They are set down beside the lower number of seven figures. We find
here a red 12 with a black 1 inserted, below this a black 7 and below this
again, enclosed in a red band, a black 11, which I regard as also
representing the value of a red number. We shall find a similar instance
among the serpent numerals. Then we have here 1. 7. 11. = 511 and 12. 11. =
251. But 511 = 260 + 251 and 251 is the interval between XIII Muluc and IV
Ahau.
With the day XIII Muluc and the interval 9 between IV Ahau and XIII Muluc,
numbers for XIII Muluc have been formed amounting to millions, which,
however, have been suppressed in the Manuscript, just as they were on page
31 where, in like manner, numbers were first formed for day XIII Akbal.
I assume that to begin with, 76 Tonalamatls (= 19,760) were added to this 9
and then 228 Tonalamatls (= 59,280), the 228 being = 3 × 76 and the 59,280
including 76 revolutions of Mars.
The result in one case was 19,769 and in the other 59,289. If the 12
Ahau-Katuns, which are specified as 1,366,560 on page 24b be added here, we
have the following numbers:--
1,386,329 = XIII Muluc 2 Mol (3 Muluc),
1,425,849 = XIII Muluc 2 Zip (12 Muluc),
and if the two encircled numbers of the Manuscript:--251 and 511 be added,
the sums are 1,386,580 and 1,426,360, _i.e._, the two large numbers of the
Manuscript.