which he was told was a part of this monument (Stela 15). This showed the
top parts of two consecutive glyphs, the first of which very clearly had a
coefficient of 12 and the one following of 8. The glyphs to which these
coefficients belonged were missing, but the coincidence of the two numbers
12 (?) 8 (?) was so striking when taken into consideration with the fact
that these were the day and month coefficients reached by calculation, that
the writer was inclined to accept this fragment as the missing part of
Stela 15 which showed the terminal date. This whole Initial Series
therefore reads: 9.4.10.0.0 12 Ahau 8 Mol. It is chiefly interesting
because it shows the earliest use of head-variant numerals known.
In the foregoing texts plate 12, _A_, _B_, figure 69, _A_, _B_, and figure
70, the head-variant numerals 0, 1, 3, 4, 5, 6, 8, 9, 10, 13, 14, 15, 17,
and 18 have been given, and, excepting the forms for 2, 11, and 12, these
include examples of all the head numerals.[161] No more texts specially
illustrating this type of numeral will be presented, but when any of the
head numerals not figured above (2, 7, 11, 12, 16, and 19) occur in future
texts their presence will be noted.
Before taking up the consideration of unusual or irregular Initial Series
the writer has thought best to figure one Initial Series the period glyphs
and numerals of which are expressed by full-figure forms. As mentioned on
page 68, such inscriptions are exceedingly rare, and such glyphs, moreover,
are essentially the same as head-variant forms, since their determining
characteristics are restricted to their head parts, which are exactly like
the corresponding head-variant forms. This fact will greatly aid the
student in identifying the full-figure glyphs in the following text.
In plate 14 is figured the Initial Series from Stela D at Copan.[162] The
introducing glyph is recorded in A1. The variable central element in
keeping with the other glyphs of the inscription appears here as a full
figure, the lower part of which is concealed by the tun-sign.[163]
[Illustration: INITIAL SERIES ON STELA D, COPAN, SHOWING
FULL-FIGURE NUMERAL GLYPHS AND PERIOD GLYPHS]
{189}
The Initial-series number itself appears in B1-B3. The cycle sign is a
grotesque bird, designated by Mr. Bowditch a parrot, an identification
which the hooked beak and claws strongly suggest. The essential element of
the cycle sign, however, the clasped hand, appears only in the head of this
bird, where the student will readily find it. Indeed, the head of this
full-figure form is nothing more nor less than a head-variant cycle glyph,
and as such determines the meaning of the whole figure. Compare this head
with figure 25, _d-f_, or with any of the other head-variant cycle forms
figured in the preceding texts. This grotesque "cycle bird," perhaps the
parrot, is bound to the back of an anthropomorphic figure, which we have
every reason to suppose records the cycle coefficient. An examination of
this figure will show that it has not only the dots on the lower part of
the cheek, but also the beard, both of which are distinctive features of
the head for 9. Compare this head with figure 52, _g-l_, or with any other
head variants for the numeral 9 already figured. Bearing in mind that the
heads only present the determining characteristics of full-figure glyphs,
the student will easily identify B1 as recording 9 cycles.
The katun and its coefficient are represented in A2, the former by a
grotesque bird, an eagle according to Mr. Bowditch, and the latter by
another anthropomorphic figure. The period glyph shows no essential element
recognizable as such, and its identification as the katun sign therefore
rests on its position, immediately following the cycle sign. The head of
the full figure, which represents the katun coefficient, shows the
essential element of the head for 5, the tun headdress. It has also the
fleshless lower jaw of the head for 10. The combination of these two
elements in one head, as we have seen, indicates the numeral 15, and A2
therefore records 15 katuns. Compare the head of this anthropomorphic
figure with figure 53, _b-e_.
The tun and its coefficient are represented in B2. The former again appears
as a grotesque bird, though in this case of undetermined nature. Its head,
however, very clearly shows the essential element of the head-variant tun
sign, the fleshless lower jaw. Compare this form with figure 29, _e-g_, and
the other head-variant tun signs already illustrated. The head of the
anthropomorphic figure, which denotes the tun coefficient, is just like the
head of the anthropomorphic figure in the preceding glyph (A2), except that
in B2 the head has no fleshless lower jaw.
Since the head in A2 with the fleshless lower jaw and the tun headdress
represents the numeral 15, the head in B2 without the former but with the
latter represents the numeral 5. Compare the head of the anthropomorphic
figure in B2 with figure 51, _n-s_. It is clear, therefore, that 5 tuns are
recorded in B2.
The uinal and its coefficient in A3 are equally clear. The period glyph
here appears as a frog (Maya, _uo_), which, as we have seen {190}
elsewhere, may have been chosen to represent the 20-day period because of
the similarity of its name, _uo_, to the name of this period, _u_, or
uinal. The head of the anthropomorphic figure which clasps the frog's
foreleg is the head variant for 0. Note the clasped hand across the lower
part of the face, and compare this form with figure 53, _s-w_. The whole
glyph, therefore, stands for 0 uinals.
In B3 are recorded the kin and its coefficient. The period glyph here is
represented by an anthropomorphic figure with a grotesque head. Its
identity, as representing the kins of this number, is better established
from its position in the number than from its appearance, which is somewhat
irregular. The kin coefficient is just like the uinal coefficient--an
anthropomorphic figure the head of which has the clasped hand as its
determining characteristic. Therefore B3 records 0 kins.
The whole number expressed by B1-B3 is 9.15.5.0.0; reducing this by means
of Table XIII to units of the first order, we have:
B1 = 9 × 144,000 = 1,296,000
A2 = 15 × 7,200 = 108,000
B2 = 5 × 360 = 1,800
A3 = 0 × 20 = 0
B3 = 0 × 1 = 0
---------
1,405,800
Deducting from this number all the Calendar Rounds possible, 74 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141 respectively),
to the remainder, the terminal date reached will be 10 Ahau 8 Chen.
The day part of this terminal date is recorded in A4. The day sign Ahau is
represented as an anthropomorphic figure, crouching within the customary
day-sign cartouche. The head of this figure is the familiar profile variant
for the day sign Ahau, seen in figure 16, _h', i'_. This cartouche is
clasped by the left arm of another anthropomorphic figure, the day
coefficient, the head of which is the skull, denoting the numeral 10. Note
the fleshless lower jaw of this head and compare it with the same element
in figure 52, _m-r_. This glyph A4 records, therefore, the day reached by
the Initial Series, 10 Ahau.
The position of the month glyph in this text is most unusual. Passing over
B4, the first glyph of the Supplementary Series, the month glyph follows it
immediately in A5. The month coefficient appears again as an
anthropomorphic figure, the head of which has for its determining
characteristic the forehead ornament composed of one part, denoting the
numeral 8. Compare this head with the heads for 8, in figure 52, _a-f_. The
month sign itself appears as a large grotesque head, the details of which
present the essential elements of the month here recorded--Chen. Compare
with figure 19, _o, p_.
[Illustration: INITIAL SERIES ON STELA J, COPAN]
{191}
The superfix of figure 16, _o, p_, has been retained unchanged as the
superfix in A5b. The element () appears just above the eye of the grotesque
head, and the element (**) on the left-hand side about where the ear lobe
should be. The whole glyph unmistakably records a head variant of the month
glyph Chen, and this Initial Series therefore reads 9.15.5.0.0 10 Ahau 8
Chen.
The student will note that this Initial Series records a date just 5 tuns
later than the Initial Series on Stela B at Copan (pl. 7, _A_). According
to the writer's opinion, therefore, Stelæ B and D marked two successive
hotuns at this city.
We come now to the consideration of Initial Series which are either unusual
or irregular in some respect, examples of which it is necessary to give in
order to familiarize the student with all kinds of texts.
The Initial Series in plate 15, _A_,[164] is figured because of the very
unusual order followed by its glyphs. The sequence in which these succeed
each other is given in _B_ of that plate. The scheme followed seems to have
been that of a mat pattern. The introducing glyph appears in position 0
(pl. 15, _B_), and the student will readily recognize it in the same
position in _A_ of the same plate. The Initial Series number follows in 1,
2, 3, 4, and 5 (pl. 15, _B_). Referring to these corresponding positions in
_A_, we find that 9 cycles are recorded in 1, and 13 katuns in 2. At this
point the diagonal glyph- band passes under another band, emerging at 3,
where the tun sign with a coefficient of 10 is recorded. Here the band
turns again and, crossing backward diagonally, shows 0 uinals in 4. At this
point the band passes under three diagonals running in the opposite
direction, emerging at position 5, the glyph in which are recorded 0 kins.
This number 9.13.10.0.0 reduces by means of Table XIII to units of the
first order, as follows:
1 = 9 × 144,000 = 1,296,000
2 = 13 × 7,200 = 93,600
3 = 10 × 360 = 3,600
4 = 0 × 20 = 0
5 = 0 × 1 = 0
---------
1,393,200
Deducting from this number all the Calendar Rounds possible, 73 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date reached will be 7 Ahau 3 Cumhu.
Referring again to plate 15, _B_, for the sequence of the glyphs in this
text, it is clear that the day of this terminal date should be recorded in
6, immediately after the kins of the Initial-series number in 6. It will be
seen, however, in plate 15, _A_, that {192} glyph 6 is effaced, and
consequently the day is missing. Passing over 7, 8, 9, 10, and 11, in _A_
and _B_ of the plate named, we reach in the lower half of 12 the closing
glyph of the Supplementary Series here shown with a coefficient of 10.
Compare this form with figure 65. The month glyph, therefore, should follow
in the upper half of 13.[165] This glyph is very clearly the form for the
month Cumhu (see fig. 19, _g', h'_), and it seems to have attached to it
the bar and dot coefficient 8. A comparison of this with the month
coefficient 3, determined above by calculation, shows that the two do not
agree, and that the month coefficient as recorded exceeds the month
coefficient determined by calculation, by 5, or in Maya notation, 1 bar.
Since the Initial-series number is very clearly 9.13.10.0.0, and since this
number leads to the terminal date 7 Ahau 3 Cumhu, it would seem that the
ancient scribes had made an error in this text, recording 1 bar and 3 dots
instead of 3 dots alone. The writer is inclined to believe, however, that
the bar here is only ornamental and has no numerical value whatsoever,
having been inserted solely to balance this glyph. If it had been omitted,
the month sign would have had to be greatly elongated and its proportions
distorted in order to fill completely the space available. According to the
writer's interpretation, this Initial Series reads 9.13.10.0.0 7 Ahau 3
Cumhu.
The opposite face of the above-mentioned monument presents the same
interlacing scheme, though in this case the glyph bands cross at right
angles to each other instead of diagonally.
The only other inscription in the whole Maya territory, so far as the
writer knows, which at all parallels the curious interlacing pattern of the
glyphs on the back of Stela J at Copan, just described, is Stela H at
Quirigua, illustrated in figure 71.[166] The drawing of this inscription
appears in a of this figure and the key to the sequence of the glyphs in b.
The introducing glyph occupies position 1 and is followed by the Initial
Series in 2-6. The student will have little difficulty in identifying 2, 3,
and 4 as 9 cycles, 16 katuns, and 0 tuns, respectively. The uinal and kin
glyphs in 5 and 6, respectively, are so far effaced that in order to
determine the values of their coefficients we shall have to rely to a large
extent on other inscriptions here at Quirigua. For example, every monument
at Quirigua which presents an Initial Series marks the close of some
particular hotun in the Long Count; consequently, all the Initial Series at
Quirigua which record these Katun endings have 0 for their uinal and kin
coefficients.[167] This {193} absolute uniformity in regard to the uinal
and kin coefficients in all the other Initial Series at Quirigua justifies
the assumption that in the text here under discussion 0 uinals and 0 kins
were originally recorded in glyphs 5 and 6, respectively. Furthermore, an
inspection of the coefficients of these two glyphs in figure 71, _a_, shows
that both of them are of the same general size and shape as the tun
coefficient in 4, which, as we have seen, is very clearly 0. It is more
than probable that the uinal and kin coefficients in this text were
originally 0, like the tun coefficient, and that through weathering they
have been eroded down to their present shape. In figure 72, _a_, is shown
the tun coefficient and beside it in _b_, the uinal or kin coefficient. The
dotted parts in _b_ are the lines which have disappeared through erosion,
if this coefficient was originally 0. It seems more than likely from the
foregoing that the uinal and kin coefficients in this number were
originally 0, and proceeding on this assumption, we have recorded in glyphs
2-6, figure 71, _a_, the number 9.16.0.0.0.
[Illustration: FIG. 71. Initial Series on Stela H, Quirigua: _a_, Mat
pattern of glyph sequence; _b_, key to sequence of glyphs in a.]
Reducing this to units of the first order by means of Table XIII, we have:
5 = 9 × 144,000 = 1,296,000
6 = 16 × 7,200 = 115,200
7 = 0 × 360 = 0
8 = 0 × 20 = 0
9 = 0 × 1 = 0
---------
1,411,200
Deducting from this number all the Calendar Rounds possible, 74 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date 2 Ahau 13 Tzec will be reached.
[Illustration: FIG. 72. The tun, uinal, and kin coefficients on Stela H,
Quirigua: _a_, Tun coefficient; _b_, suggested restoration of the uinal and
kin coefficients like the tun coefficient.]
In spite of some weathering, the day part of the terminal date appears in
glyph 7 immediately after the kin glyph in 6. The coefficient, though
somewhat eroded, appears quite clearly as 2 (2 dots separated by an
ornamental crescent). The day sign itself is the profile variant for Ahau
shown in figure 16, _h', i'_. The agreement of {194} the day recorded with
the day determined by calculations based on the assumption that the kin and
uinal coefficients are both 0, of itself tends to establish the accuracy of
these assumptions. Passing over 8, 9, 10, 11, 12, 13, and 14, we reach in
15 the closing glyph of the Supplementary Series, and in 16 probably, the
month glyph. This form, although badly eroded, presents no features either
in the outline of its coefficient or in the sign itself which would prevent
it representing the month part 13 Tzec. The coefficient is just wide enough
for three vertical divisions (2 bars and 3 dots), and the month glyph
itself is divided into two parts, a superfix comprising about one-third of
the glyph and the main element the remaining two-thirds. Compare this form
with the sign for Tzec in figure 19, _g, h_. Although this text is too much
weathered to permit absolute certainty with reference to the reading of
this Initial Series, the writer nevertheless believes that in all
probability it records the date given above, namely, 9.16.0.0.0 2 Ahau 13
Tzec. If this is so, Stela H is the earliest hotun-marker at Quirigua.[168]
The student will have noticed from the foregoing texts, and it has also
been stated several times, that the cycle coefficient is almost invariably
9. Indeed, the only two exceptions to this rule in the inscriptions already
figured are the Initial Series from the Temples of the Foliated Cross and
the Sun at Palenque (pl. 12, _A_ and _B_, respectively), in which the cycle
coefficient in each case was 1. As explained on page 179, footnote 1, these
two Initial Series refer probably to mythological events, and the dates
which they record were not contemporaneous with the erection of the temples
on whose walls they are inscribed; and, finally, Cycle 9 was the first
historic period of the Maya civilization, the epoch which witnessed the
rise and fall of all the southern cities.
As explained on page 179, footnote 2, however, there are one or two Initial
Series which can hardly be considered as referring to mythological events,
even though the dates which they record fall in a cycle earlier than Cycle
9. It was stated, further, in the same place that these two Initial Series
were not found inscribed on large monuments but on smaller antiquities, one
of them being a small nephrite figure which has been designated the Tuxtla
Statuette, and the other a nephrite plate, designated the Leyden Plate;
and, finally, that the dates recorded on these two antiquities probably
designated contemporaneous events in the historic period of the Maya
civilization. {195}
[Illustration: FIG. 73. The Initial Series on the Tuxtla Statuette, the
oldest Initial Series known (in the early part of Cycle 8).]
[Illustration: FIG. 74. The introducing glyph (?) of the Initial Series on
the Tuxtla Statuette.]
These two minor antiquities have several points in common. Both are made of
the same material (nephrite) and both have their glyphs incised instead of
carved. More important, however, than these similarities is the fact that
the Initial Series recorded on each of them has for its cycle coefficient
the numeral 8; in other words, both record dates which fell in the cycle
immediately preceding that of the historic period, or Cycle 9. Finally, at
least one of these two Initial Series (that on the Leyden Plate), if indeed
not both, records a date so near the opening of the historic period, which
we may assume occurred about 9.0.0.0.0 8 Ahau 13 Ceh in round numbers, that
it may be considered as belonging to the historic period, and hence
constitutes the earliest historical inscription from the Maya territory.
{196}
The Initial Series on the first of these minor antiquities, the Tuxtla
Statuette, is shown in figure 73.[169] The student will note at the outset
one very important difference between this Initial Series--if indeed it is
one, which some have doubted--and those already presented. No period glyphs
appear in the present example, and consequently the Initial-series number
is expressed by the second method (p. 129), that is, numeration by
position, as in the codices. See the discussion of Initial Series in the
codices in Chapter VI (pp. 266-273), and plates 31 and 32. This at once
distinguishes the Initial Series on the Tuxtla Statuette from every other
Initial Series in the inscriptions now known. The number is preceded by a
character which bears some general resemblance to the usual Initial-series
introducing glyph. See figure 74. The most striking point of similarity is
the trinal superfix, which is present in both signs. The student will have
little difficulty in reading the number here recorded as 8 cycles, 6
katuns, 2 tuns, 4 uinals, and 17 kins, that is, 8.6.2.4.17; reducing this
to units of the first order by means of Table XIII, we have:
8 × 144,000 = 1,152,000
6 × 7,200 = 43,200
2 × 360 = 720
4 × 20 = 80
17 × 1 = 17
---------
1,196,017
Solving this Initial-series number for its terminal date, it will be found
to be 8 Caban 0 Kankin. Returning once more to our text (see fig. 73), we
find the day coefficient above reached, 8, is recorded just below the 17
kins and appears to be attached to some character the details of which are,
unfortunately, effaced. The month coefficient 0 and the month sign Kankin
do not appear in the accompanying text, at least in recognizable form. This
Initial Series would seem to be, therefore, 8.6.2.4.17 8 Caban 0 Kankin, of
which the day sign, month coefficient, and month sign are effaced or
unrecognizable. In spite of its unusual form and the absence of the day
sign, and the month coefficient and sign the writer is inclined to accept
the above date as a contemporaneous Initial Series.[170]
[Illustration: FIG. 75. Drawings of the Initial Series: _A_, On the Leyden
Plate. This records a Cycle-8 date and next to the Tuxtla Statuette Initial
Series, is the earliest known. _B_, On a lintel from the Temple of the
Initial Series, Chichen Itza. This records a Cycle-10 date, and is one of
the latest Initial Series known.]
The other Initial Series showing a cycle coefficient 8 is on the Leyden
Plate, a drawing of which is reproduced in figure 75, _A._ This Initial
Series is far more satisfactory than the one just described, and {197} its
authenticity, generally speaking, is unquestioned. The student will easily
identify A1-B2 as an Initial-series introducing glyph, even though the pair
of comblike appendages flanking the central element and the tun tripod are
both wanting. Compare this form with figure 24. The Initial-series number,
expressed by normal-form numerals and head-variant period glyphs, follows
in A3-A7. The former are all very clear, and the number may be read from
them in spite of certain irregularities in the corresponding period glyphs.
For example, the katun head in A4 has the clasped hand, which is the
distinguishing characteristic of the cycle head, and as such should have
appeared in the head in A3. Neither the tun head in A5 nor the kin head in
A7 shows an essential element heretofore found distinguishing these
particular period glyphs. Indeed, the only period glyph of the five showing
the usual essential element is the uinal head in A6, where the large mouth
curl appears very clearly. However, the number recorded here may be read as
8.14.3.1.12 from the sequence of the coefficients--that is, their position
with reference to the introducing glyph--a reading, moreover, which is
confirmed by the only known period glyph, the uinal sign, standing in the
fourth position after the introducing glyph. {198}
Reducing this number to units of the first order by means of Table XIII, we
have:
A3 = 8 × 144,000 = 1,152,000
A4 = 14 × 7,200 = 100,800
A5 = 3 × 360 = 1,080
A6 = 1 × 20 = 20
A7 = 12 × 1 = 12
---------
1,253,912
Deducting from this number all the Calendar Rounds possible, 66 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date reached will be 1 Eb 0 Yaxkin. The day
part of this date is very clearly recorded in A8, the coefficient 1 being
expressed by one dot, and the day sign itself having the hook surrounded by
dots, and the prominent teeth, both of which are characteristic of the
grotesque head which denotes the day Eb. See figure 16, _s-u_.
The month glyph appears in A9a, the lower half of which unmistakably
records the month Yaxkin. (See fig. 19, _k, l_.) Note the _yax_ and _kin_
elements in each. The only difficulty here seems to be the fact that a bar
(5) is attached to this glyph. The writer believes, however, that the
unexplained element () is the month coefficient in this text, and that it
is an archaic form for 0. He would explain the bar as being merely
ornamental. The whole Initial Series reads: 8.14.3.1.12 1 Eb 0 Yaxkin.
The fact that there are some few irregularities in this text confirms
rather than invalidates the antiquity which has been ascribed to it by the
writer. Dating from the period when the Maya were just emerging from
savagery to the arts and practices of a semicivilized state, it is not at
all surprising that this inscription should reflect the crudities and
uncertainties of its time. Indeed, it is quite possible that at the very
early period from which it probably dates (8.14.3.1.12 1 Eb 0 Yaxkin) the
period glyphs had not yet become sufficiently conventionalized to show
individual peculiarities, and their identity may have been determined
solely by their position with reference to the introducing glyph, as
seemingly is the case in some of the period glyphs of this text.
The Initial Series on the Leyden Plate precedes the Initial Series on Stela
3 at Tikal, the earliest contemporaneous date from the monuments, by more
than 160 years, and with the possible exception of the Tuxtla Statuette
above described, probably records the earliest date of Maya history. It
should be noted here that Cycle-8 Initial Series are occasionally found in
the Dresden Codex, though none are quite so early as the Initial Series
from the Tuxtla Statuette. {199}
Passing over the Initial Series whose cycle coefficient is 9, many of which
have already been described, we come next to the consideration of Initial
Series whose cycle coefficient is 10, a very limited number indeed. As
explained in Chapter I, the southern cities did not long survive the
opening of Cycle 10, and since Initial-series dating did not prevail
extensively in the later cities of the north, Initial Series showing 10
cycles are very unusual.
In figure 75, _B_, is shown the Initial Series from the Temple of the
Initial Series at Chichen Itza, the great metropolis of northern Yucatan.
This inscription is not found on a stela but on the under side of a lintel
over a doorway leading into a small and comparatively insignificant temple.
The introducing glyph appears in A1-B2 and is followed by the
Initial-series number in A3-A5. The student will have little difficulty in
deciphering all of the coefficients except that belonging to the kin in A5,
which is a head-variant numeral, and the whole number will be found to read
10.2.9.1.?. The coefficient of the day of the terminal date is very clearly
9 (see B5) and the month part, 7 Zac (see A6). We may now read this Initial
Series as 10.2.9.1.? 9? 7 Zac; in other words, the kin coefficient and the
day sign are still indeterminate. First substituting 0 as the missing value
of the kin coefficient, the terminal date reached will be 10.2.9.1.0 13
Ahau 18 Yax. But according to Table XV, position 18 Yax is just 9 days
earlier than position 7 Zac, the month part recorded in A6. Consequently,
in order to reach 7 Zac from 10.2.9.1.0 13 Ahau 18 Yax, 9 more days are
necessary. Counting these forward from 10.2.9.1.0 13 Ahau 18 Yax, the date
reached will be 10.2.9.1.9 9 Muluc 7 Zac, which is the date recorded on
this lintel. Compare the day sign with figure 16, _m, n_, and the month
sign with figure 19, _s, t_. {200}
[Illustration: FIG. 76. The Cycle-10 Initial Series from Quen Santo (from
drawings): _A_, Stela 1; _B_, Stela 2. There is less than a year's
difference in time between the Chichen Itza Initial Series and the Initial
Series in _B_.]
Two other Initial Series whose cycle coefficient is 10 yet remain to be
considered, namely, Stelæ 1 and 2 at Quen Santo.[171] The first of these is
shown in figure 76, A, but unfortunately only a fragment of this monument
has been recovered. In A1-B2 appears a perfectly regular form of the
introducing glyph (see fig. 24), and this is followed in A3-B4 by the
Initial-series number itself, with the exception of the kin, the glyph
representing which has been broken off. The student will readily identify
A3 as 10 cycles, noting the clasped hand on the head-variant period glyph,
and B3 as 2 katuns. The glyph in A4 has very clearly the coefficient 5, and
even though it does not seem to have the fleshless lower jaw of the tun
head, from its position alone--after the unmistakable katun sign in B3 we
are perfectly justified in assuming that 5 tuns are recorded here. Both the
coefficient and the glyph in B4 are unfamiliar. However, as the former must
be one of the numerals 0 to 19, inclusive, since it is not one of the
numerals 1 to 19, inclusive, it is clear that it must be a new form for 0.
The sign to which it is attached bears no resemblance to either the normal
form for the uinal or the head variant; but since it occupies the 4th
position after the introducing glyph, B4, we are justified in assuming that
0 uinals are recorded here. Beyond this we can not proceed with certainty,
though the values for the missing parts suggested below are probably those
recorded on the lost fragments of the monument. As recorded in A3-B4 this
number reads 10.2.5.0.?. Now, if we assume that the missing term is filled
with 0, we shall have recorded the end of an even hotun in the Long Count,
and this monument becomes a regular hotun-marker. That this monument was a
hotun-marker is corroborated by the fact that Stela 2 from Quen Santo very
clearly records the close of the hotun next after 10.2.5.0.0, which the
writer believes this monument marks. For {201} this reason it seems
probable that the glyph which stood in A5 recorded 0 kins.
Reducing this number to units of the first order by means of Table XIII, we
obtain:
A3 = 10 × 144,000 = 1,440,000
B3 = 2 × 7,200 = 14,400
A4 = 5 × 360 = 1,800
B4 = 0 × 20 = 0
A5[172] = 0 × 1 = 0
---------
1,456,200
Deducting from this number all the Calendar Rounds possible, 76 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date reached will be 9 Ahau 18 Yax, and the
whole Initial Series originally recorded on this monument was probably
10.2.5.0.0 9 Ahau 18 Yax.
In figure 76, _B_, is shown Stela 2 from Quen Santo. The workmanship on
this monument is somewhat better than on Stela 1 and, moreover, its Initial
Series is complete. The introducing glyph appears in A1-B2 and is followed
by the Initial-series number in A3-A5. Again, 10 cycles are very clearly
recorded in A3, the clasped hand of the cycle head still appearing in spite
of the weathering of this glyph. The katun sign in B3 is almost entirely
effaced, though sufficient traces of its coefficient remain to enable us to
identify it as 2. Note the position of the uneffaced dot with reference to
the horizontal axis of the glyph. Another dot the same distance above the
axis would come as near the upper left-hand corner of the glyph-block as
the uneffaced dot does to the lower left-hand corner. Moreover, if 3 had
been recorded here the uneffaced dot would have been nearer the bottom. It
is clear that 1 and 4 are quite out of the question and that 2 remains the
only possible value of the numeral here. We are justified in assuming that
the effaced period glyph was the katun sign. In A4 10 tuns are very clearly
recorded; note the fleshless lower jaw of the tun head. The uinal head with
its characteristic mouth curl appears in B4. The coefficient of this latter
glyph is identical with the uinal coefficient in the preceding text (see
fig. 76, _A_) in B4, which we there identified as a form for 0. Therefore
we must make the same identification here, and B4 then becomes 0 uinals.
From its position, if not from its appearance, we are justified in
designating the glyph in A5 the head for the kin period; since the
coefficient attached to this head is the same as the one in the preceding
glyph (B4), we may therefore conclude that 0 kins are recorded here. The
whole number expressed in A3-A5 is {202} therefore 10.2.10.0.0. Reducing
this to units of the first order by means of Table XIII, we have:
A3 = 10 × 144,000 = 1,440,000
B3 = 2 × 7,200 = 14,400
A4 = 10 × 360 = 3,600
B4 = 0 × 20 = 0
A5 = 0 × 1 = 0
---------
1,458,000
Deducting from this number all the Calendar Rounds possible, 76 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date reached will be 2 Ahau 13 Chen.
Although the day sign in B5 is effaced, the coefficient 2 appears quite
clearly. The month glyph is recorded in A6. The student will have little
difficulty in restoring the coefficient as 13, and the month glyph is
certainly either Chen, Yax, Zac, or Ceh (compare fig. 19, _o_ and _p_, _q_
and _r_, _s_ and _t_, and _u_ and _v_, respectively). Moreover, since the
month coefficient is 13, the day sign in B5 can have been only Chicchan,
Oc, Men, or Ahau (see Table VII); since the kin coefficient in A5 is 0, the
effaced day sign must have been Ahau. Therefore the Initial Series on Stela
2 at Quen Santo reads 10.2.10.0.0 2 Ahau 13 Chen and marked the hotun
immediately following the hotun commemorated by Stela 1 at the same site.
The student will note also that the date on Stela 2 at Quen Santo is less
than a year later than the date recorded by the Initial Series on the
Temple lintel from Chichen Itza (see fig. 75, _B_). And a glance at the map
in plate 1 will show, further, that Chichen Itza and Quen Santo are
separated from each other by almost the entire length (north and south) of
the Maya territory, the former being in the extreme northern part of
Yucatan and the latter considerably to the south of the central Maya
cities. The presence of two monuments so close together chronologically and
yet so far apart geographically is difficult to explain. Moreover, the
problem is further complicated by the fact that not one of the many cities
lying between has yielded thus far a date as late as either of these.[173]
The most logical explanation of this interesting phenomenon seems to be
that while the main body of the Maya moved northward into Yucatan after the
collapse of the southern cities others retreated southward into the
highlands of Guatemala; that while the northern emigrants {203} were
colonizing Yucatan the southern branch was laying the foundation of the
civilization which was to flourish later under the name of the Quiche and
other allied peoples; and finally, that as Chichen Itza was a later
northern city, so Quen Santo was a later southern site, the two being at
one period of their existence at least approximately contemporaneous, as
these two Initial Series show.
It should be noted in this connection that Cycle-10 Initial Series are
occasionally recorded in the Dresden Codex, though the dates in these cases
are all later than those recorded on the Chichen Itza lintel and the Quen
Santo stelæ. Before closing the presentation of Initial-series texts it is
first necessary to discuss two very unusual and highly irregular examples
of this method of dating, namely, the Initial Series from the east side of
Stela C at Quirigua and the Initial Series from the tablet in the Temple of
the Cross at Palenque. The dates recorded in these two texts, so far as
known,[174] are the only ones which are not counted from the starting point
of Maya chronology, the date 4 Ahau 8 Cumhu.
In figure 77, _A_, is shown the Initial Series on the east side of Stela C
at Quirigua.[175] The introducing glyph appears in A1-B2, and is followed
by the Initial-series number in A3-A5. The student will easily read this as
13.0.0.0.0. Reducing this number to units of the first order by means of
Table XIII, we have:
A3 = 13 × 144,000 = 1,872,000
B3 = 0 × 7,200 = 0
A4 = 0 × 360 = 0
B4 = 0 × 20 = 0
A5 = 0 × 1 = 0
---------
1,872,000
Deducting from this number all the Calendar Rounds possible, 98[176] (see
Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141),
respectively, to the remainder, the terminal date reached should be, under
ordinary circumstances, 4 Ahau 3 Kankin. An inspection of our text,
however, will show that the terminal date recorded in B5-A6 is unmistakably
4 Ahau 8 Cumhu, and not 4 Ahau 3 Kankin. The month part in A6 is unusually
clear, and there can be no doubt {204} that it is 8 Cumhu. Compare A6 with
figure 19, _g', h'_. If we have made no mistake in calculations, then it is
evident that 13.0.0.0.0 counted forward from the starting point of Maya
chronology, 4 Ahau 8 Cumhu, will not reach the terminal date recorded.
Further, since the count in Initial Series has never been known to be
backward,[177] we are forced to accept one of two conclusions: Either the
starting point is not 4 Ahau 8 Cumhu, or there is some error in the
original text. However, there is one way by means of which we can ascertain
the date from which the number 13.0.0.0.0 is counted. The terminal date
reached by the count is recorded very clearly as 4 Ahau 8 Cumhu. Now, if we
reverse our operation and count the given number, 13.0.0.0.0, _backward_
from the known terminal date, 4 Ahau 8 Cumhu, we reach the starting point
from which the count proceeds.
[Illustration: FIG. 77. Initial Series which proceed from a date prior to 4
Ahau 8 Cumhu, the starting point of Maya chronology: _A_, Stela C (east
side) at Quirigua; _B_, Temple of the Cross at Palenque.]
Deducting from this number, as before, all the Calendar Rounds possible, 98
(see p. 203, footnote 3), and applying rules 1, 2, and 3 (pp. 139, 140,
141, respectively) to the remainder, remembering that in each operation the
direction of the count is _backward_, not forward,--the starting point will
be found to be 4 Ahau 8 Zotz. This is the first Initial Series yet
encountered which has not proceeded from the date 4 Ahau 8 Cumhu, and until
the new starting point here indicated can be substantiated it will be well
to accept the correctness of this text only with a reservation. The most we
can say at present is that if the number recorded in A3-A5, 13.0.0.0.0, be
counted forward from 4 Ahau 8 Zotz as a starting point, the terminal date
reached by calculation will agree with the terminal date as recorded in
B5-A6, 4 Ahau 8 Cumhu. {205}
Let us next examine the Initial Series on the tablet from the Temple of the
Cross at Palenque, which is shown in figure 77, _B_.[178] The introducing
glyph appears in A1-B2, and is followed by the Initial-series number in
A3-B7. The period glyphs in B3, B4, B5, B6, and B7 are all expressed by
their corresponding normal forms, which will be readily recognized. Passing
over the cycle coefficient in A3 for the present, it is clear that the
katun coefficient in A4 is 19. Note the dots around the mouth,
characteristic of the head for 9 (fig. 52, _g-l_), and the fleshless lower
jaw, the essential element of the head for 10 (fig. 52, _m-r_). The
combination of the two gives the head in A4 the value of 19. The tun
coefficient in A5 is equally clear as 13. Note the banded headdress,
characteristic of the head for 3 (fig. 51, _h, i_), and the fleshless lower
jaw of the 10 head, the combination of the two giving the head for 13 (fig.
52, _w_).[179] The head for 4 and the hand zero sign appear as the
coefficient of the uinal and kin signs in A6 and A7, respectively. The
number will read, therefore, ?.19.13.4.0. Let us examine the cycle
coefficient in A3 again. The natural assumption, of course, is that it is
9. But the dots characteristic of the head for 9 are not to be found here.
As this head has no fleshless lower jaw, it can not be 10 or any number
above 13, and as there is no clasped hand associated with it, it can not
signify 0, so we are limited to the numbers, 1, 2, 3, 4, 5,[180] 6, 7, 8,
11, 12, and 13, as the numeral here recorded. Comparing this form with
these numerals in figures 51 and 52, it is evident that it can not be 1, 3,
4, 5, 6, 7, 8, or 13, and that it must therefore be 2, 11, or 12.
Substituting these three values in turn, we have 2.19.13.4.0, 11.19.13.4.0,
and 12.19.13.4.0 as the possible numbers recorded in A3-B7, and reducing
these numbers to units of the first order and deducting the highest number
of Calendar Rounds possible from each, and applying rules 1, 2, and 3 (pp.
139, 140, and 141, respectively) to their remainders, the terminal dates
reached will be:
2.19.13.4.0 5 Ahau 3 Pax
11.19.13.4.0 9 Ahau 8 Yax
12.19.13.4.0 8 Ahau 13 Pop
If this text is perfectly regular and our calculations are correct, one of
these three terminal dates will be found recorded, and the value of the
cycle coefficient in A3 can be determined.
The terminal date of this Initial Series is recorded in A8-B9 and the
student will easily read it as 8 Ahau 18 Tzec. The only difference {206}
between the day coefficient and the month coefficient is that the latter
has a fleshless lower jaw, increasing its value by 10. Moreover, comparison
of the month sign in B9 with _g_ and _h_, figure 19, shows unmistakably
that the month here recorded is Tzec. But the terminal date as recorded
does not agree with any one of the three above terminal dates as reached by
calculation and we are forced to accept one of the two conclusions which
confronted us in the preceding text (fig. 77, A): Either the starting point
of this Initial Series is not the date 4 Ahau 8 Cumhu, or there is some
error in the original text.[181]
Assuming that the ancient scribes made no mistakes in this inscription, let
us count backward from the recorded terminal date, 8 Ahau 18 Tzec, each of
the three numbers 2.19.13.4.0, 11.19.13.4.0, and 12.19.13.4.0, one of
which, we have seen, is recorded in A3-B7.
Reducing these numbers to units of the first order by means of Table XIII,
and deducting all the Calendar Rounds possible from each (see Table XVI),
and, finally, applying rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively), to the remainders, the starting points will be found to be:
7 Ahau 3 Mol for 2.19.13.4.0
3 Ahau 18 Mac for 11.19.13.4.0
4 Ahau 8 Zotz for 12.19.13.4.0
Which of these starting points are we to accept as the one from which this
number is counted? The correct answer to this question will give at the
same time the value of the cycle coefficient, which, as we have seen, must
be 2, 11, or 12. Most Maya students have accepted as the starting point of
this Initial-series number the last of the three dates above given, 4 Ahau
8 Zotz, which involves also the identification of the cycle coefficient in
A3 as 12. The writer has reached the same conclusion from the following
points:
1. The cycle coefficient in A3, except for its very unusual headdress, is
almost identical with the other two head-variant numerals, whose values are
known to be 12. These three head numerals are shown side by side in figure
52, _t-v, t_ being the form in A3 above, inserted in this figure for the
sake of comparison. Although these three heads show no single element or
characteristic that is present in all (see p. 100), each is very similar to
the other two and at the same time is dissimilar from all other
head-variant numerals. This fact warrants the conclusion that the head in
A3 represents the numeral 12, and if this is so the starting point of the
Initial Series under discussion is 4 Ahau 8 Zotz.
2. Aside from the fact that 12 seems to be the best reading of the head in
A3, and consequently that the starting point of this number is 4 Ahau 8
Zotz, the writer believes that 4 Ahau 8 Zotz should be selected, if for no
other reason than that another Initial Series has been found which proceeds
from this same date, while no other Initial Series known is counted from
either 7 Ahau 3 Mol or 3 Ahau 18 Mac.
[Illustration: INITIAL SERIES AND SECONDARY SERIES ON LINTEL 21,
YAXCHILAN]
{207}
As we have seen in discussing the preceding text, from the east side of
Stela C at Quirigua (fig. 77, _A_), the Initial Series there recorded was
counted from the same starting point, 4 Ahau 8 Zotz, as the Initial Series
from the Temple of the Cross at Palenque, if we read the latter as
12.19.13.4.0. This coincidence, the writer believes, is sufficient to
warrant the identification of the head in A3 (fig. 77, _B_) as the head
numeral 12 and the acceptance of this Initial Series as proceeding from the
same starting point as the Quirigua text just described, namely, the date 4
Ahau 8 Zotz. With these two examples the discussion of Initial-series texts
will be closed.
TEXTS RECORDING INITIAL SERIES AND SECONDARY SERIES
It has been explained (see pp. 74-76) that in addition to Initial-series
dating the Maya had another method of expressing their dates, known as
Secondary Series, which was used when more than one date had to be recorded
on the same monument. It was stated, further, that the accuracy of
Secondary-series dating depended solely on the question whether or not the
Secondary Series was referred to some date whose position in the Long Count
was fixed either by the record of its Initial Series or in some other way.
The next class of texts to be presented will be those showing the use of
Secondary Series in connection with an Initial Series, by means of which
the Initial-series values of the Secondary-series dates, that is, their
proper positions in the Long Count, may be worked out even though they are
not recorded in the text.
The first example presented will be the inscription on Lintel 21 at
Yaxchilan, which is figured in plate 16.[182] As usual, when an Initial
Series is recorded, the introducing glyph opens the text and this sign
appears in A1, being followed by the Initial-series number itself in B1-B3.
This the student will readily decipher as 9.0.19.2.4, recording apparently
a very early date in Maya history, within 20 years of 9.0.0.0.0 8 Ahau 13
Ceh, the date arbitrarily fixed by the writer as the opening of the first
great period.
Reducing this number by means of Table XIII to units of the first
order[183] and deducting all the Calendar Rounds possible, 68 (see Table
XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively)
to the remainder, the terminal date reached will be 2 Kan 2 Yax. This date
the student will find recorded in A4 and A7a, glyph B6b being the
month-sign "indicator," or the closing glyph of the {208} Supplementary
Series, here shown with the coefficient 9. Compare the day sign in A4a with
the sign for Kan in figure 16, _f_, and the month sign in A7a with the sign
for Yax in figure 19, _q, r_. We have then recorded in A1-A4[184], and A7a
the Initial-series date 9.0.19.2.4 2 Kan 2 Yax. At first sight it would
appear that this early date indicates the time at or near which this lintel
was inscribed, but a closer examination reveals a different condition.
Following along through the glyphs of this text, there is reached in C3-C4
still another number in which the normal forms of the katun, tun, and uinal
signs clearly appear in connection with bar and dot coefficients. The
question at once arises, Has the number recorded here anything to do with
the Initial Series, which precedes it at the beginning of this text?
Let us first examine this number before attempting to answer the above
question. It is apparent at the outset that it differs from the
Initial-series numbers previously encountered in several respects:
1. There is no introducing glyph, a fact which at once eliminates the
possibility that it might be an Initial Series.
2. There is no kin period glyph, the uinal sign in C3 having two
coefficients instead of one.
3. The order of the period glyphs is reversed, the highest period, here the
katun, closing the series instead of commencing it as heretofore.
It has been explained (see p. 129) that in Secondary Series the order of
the period glyphs is almost invariably the reverse of that shown by the
period glyphs in Initial Series; and further, that the former are usually
presented as ascending series, that is, with the lowest units first, and
the latter invariably as descending series, with the highest units first.
It has been explained also (see p. 128) that in Secondary Series the kin
period glyph is usually omitted, the kin coefficient being attached to the
left of the uinal sign. Since both of these points (see 2 and 3, above) are
characteristic of the number in C3-C4, it is probable that a Secondary
Series is recorded here, and that it expresses 5 kins, 16 uinals, 1 tun,
and 15 katuns. Reversing this, and writing it according to the notation
followed by most Maya students (see p. 138, footnote 1), we have as the
number recorded by C3-C4, 15.1.16.5.
Reducing this number to units of the first order by means of Table XIII, we
have:
C4 = 15 × 7,200 = 108,000
D3 = 1 × 360 = 360
C3 = 16 × 20 = 320
C3 = 5 × 1 = 5
-------
108,685
Since all the Calendar Rounds which this number contains, 5 (see {209}
Table XVI) may be deducted from it without affecting its value, we can
further reduce it to 13,785 (108,685 - 94,900), and this will be the number
used in the following calculations.
It was stated (on p. 135) in describing the direction of the count that
numbers are usually counted forward from the dates next preceding them in a
text, although this is not invariably true. Applying this rule to the
present case, it is probable that the Secondary-series number 15.1.16.5,
which we have reduced to 13,785 units of the first order, is counted
_forward_ from the date 2 Kan 2 Yax, the one next preceding it in our text,
a date, moreover, the Initial-series value of which is known.
Remembering that this date 2 Kan 2 Yax is our new starting point, and that
the count is forward, by applying rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively), to 13,785, the new terminal date reached will be 7 Muluc 17
Tzec; and this date is recorded in C5-D5. Compare C5 with the sign for the
day Muluc in figure 16, _m, n_, and D5 with the sign for the month Tzec in
figure 19, _g, h_. Furthermore, by adding the Secondary-series number
15.1.16.5 to 9.0.19.2.4 (the Initial-series number which fixes the position
of the date 2 Kan 2 Yax in the Long Count), the Initial-series value of the
terminal date of the Secondary Series (calculated and identified above as 7
Muluc 17 Tzec) can also be determined as follows:
9. 0.19. 2.4 2 Kan 2 Yax Initial Series
15. 1.16.5 Secondary-series number
9.16. 1. 0.9 7 Muluc 17 Tzec Initial Series of the
Secondary-series
terminal date 7 Muluc
17 Tzec
The student may verify the above calculations by treating 9.16.1.0.9 as a
new Initial-series number, and counting it forward from 4 Ahau 8 Cumhu, the
starting point of Maya chronology. The terminal date reached will be found
to be the same date as the one recorded in C5-D5, namely, 7 Muluc 17 Tzec.
What is the meaning then of this text, which records two dates nearly 300
years apart?[185] It must be admitted at the outset that the nature of the
events which occurred on these two dates, a matter probably set forth in
the glyphs of unknown meaning in the text, is totally unknown. It is
possible to gather from other sources, however, some little data concerning
their significance. In the first place, 9.16.1.0.9 7 Muluc 17 Tzec is
almost surely the "contemporaneous date" of this lintel, the date
indicating the time at or near which it was formally dedicated or put into
use. This point is established almost to a certainty by the fact that all
the other dates known at Yaxchilan are very much nearer to 9.16.1.0.9 7
Muluc 17 Tzec in point {210} of time than to 9.0.19.2.4 2 Kan 2 Yax, the
Initial-series date recorded on this lintel. Indeed, while they range from
9 days[186] to 75 years from the former, the one nearest the latter is more
than 200 years later. This practically proves that 9.16.1.0.9 7 Muluc 17
Tzec indicates the "contemporaneous time" of this lintel and that
9.0.19.2.4 2 Kan 2 Yax referred to some earlier event which took place
perhaps even before the founding of the city. And finally, since this
inscription is on a lintel, we may perhaps go a step further and hazard the
conclusion that 9.16.1.0.9 7 Muluc 17 Tzec records the date of the erection
of the structure of which this lintel is a part.
We may draw from this inscription a conclusion which will be found to hold
good in almost all cases, namely, that the last date in a text almost
always indicates the "contemporaneous time" of the monument upon which it
appears. In the present text, for example, the Secondary-series date 7
Muluc 17 Tzec, the Initial-series value of which was found to be
9.16.1.0.9, is in all probability its contemporaneous date, or very near
thereto. It will be well to remember this important point, since it enables
us to assign monuments upon which several different dates are recorded to
their proper periods in the Long Count.
The next example illustrating the use of Secondary Series with an Initial
Series is the inscription from Stela 1 at Piedras Negras, figured in plate
17.[187] The order of the glyphs in this text is somewhat irregular. It
will be noted that there is an uneven number of glyph columns, so that one
column will have to be read by itself. The natural assumption would be that
A and B, C and D, and E and F are read together, leaving G, the last
column, to be read by itself. This is not the case, however, for A,
presenting the Initial Series, is read first, and then B C, D E, and F G,
in pairs. The introducing glyph of the Initial Series appears in A1 and is
followed by the Initial-series number 9.12.2.0.16 in A2-A6. The student
should be perfectly familiar by this time with the processes involved in
counting this number from its starting point, and should have no difficulty
in determing by calculation the terminal date recorded in A7, C2, namely, 5
Cib 14 Yaxkin.[188] Compare A7 with the sign for Cib in figure 16, _z_, and
C2 with the sign for Yaxkin in figure 19, _k, l_. The Initial Series
recorded in A1-A7, C2 is 9.12.2.0.16 5 Cib 14 Yaxkin.
[Illustration: INITIAL SERIES AND SECONDARY SERIES ON STELA 1,
PIEDRAS NEGRAS]
{211}
Passing over the glyphs in B3-E1, the meanings of which are unknown, we
reach in D2 E2 a number showing very clearly the tun and uinal signs, the
latter having two coefficients instead of one. Moreover, the order of these
period glyphs is reversed, the lower standing first in the series. As
explained in connection with the preceding text, these points are both
characteristic of Secondary-series numbers, and we may conclude therefore
that D2 E2 records a number of this kind. Finally, since the kin
coefficient in Secondary Series usually appears on the left of the uinal
sign, we may express this number in the commonly accepted notation as
follows: 12.9.15. Reducing this to units of the first order, we have:
E2 = 12 × 360 = 4,320
D2 = 9 × 20 = 180
D2 = 15 × 1 = 15
-----
4,515
Remembering that Secondary-series numbers are usually counted from the
dates next preceding them in the texts, in this case 5 Cib 14 Yaxkin, and
proceeding according to rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively), the terminal date of the Secondary Series reached will be 9
Chuen 9 Kankin, which is recorded in F1 G1, though unfortunately these
glyphs are somewhat effaced. Moreover, since the position of 5 Cib 14
Yaxkin in the Long Count is known, that is, its Initial-series value, it is
possible to determine the Initial-series value of this new date, 9 Chuen 9
Kankin:
9.12. 2. 0.16 5 Cib 14 Yaxkin
12. 9.15
9.12.14.10.11 9 Chuen 9 Kankin
But the end of this text has not been reached with the date 9 Chuen 9
Kankin in F1 G1. Passing over F2 G2, the meanings of which are unknown, we
reach in F3 an inverted Ahau with the coefficient 5 above it. As explained
on page 72, this probably signifies 5 kins, the inversion of the glyph
changing its meaning from that of a particular day sign, Ahau, to a general
sign for the kin day period (see fig. 34, _d_). The writer recalls but one
other instance in which the inverted Ahau stands for the kin sign--on the
north side of Stela C at Quirigua.
We have then another Secondary-series number consisting of 5 kins, which is
to be counted from some date, and since Secondary-series numbers are
usually counted from the date next preceding them in the text, we are
justified in assuming that 9 Chuen 9 Kankin is our new starting point.
Counting 5 forward from this date, according to rules 1, 2, and 3 (pp. 139,
140, and 141, respectively), the terminal date reached will be 1 Cib 14
Kankin, and this latter date is recorded in G3-G4. Compare G3 with the sign
for Cib in A7 and in figure 16, _z_, and G4 with the sign for Kankin in
figure 19, _y, z_. Moreover, since the Initial-series value of 9 Chuen 9
Kankin was calculated above as 9.12.14.10.11, {212} the Initial-series
value of this new date, 1 Cib 14 Kankin, also can be calculated from it:
9.12.14.10.11 9 Chuen 9 Kankin
5
9.12.14.10.16 1 Cib 14 Kankin
Passing over G5 as unknown, we reach in G6-G7 another Secondary-series
number. The student will have little difficulty in identifying G6 as 2
uinals, 5 kins, and G7 as 1 katun. It will be noted that no tun sign
appears in this number, which is a very unusual condition. By far the
commoner practice in such cases in which 0 units of some period are
involved is to record the period with a coefficient 0. However, this was
not done in the present case, and since no tuns are recorded, we may
conclude that none were involved, and G6-G7 may be written 1.(0).2.5.
Reducing this number to units of the first order, we have:
G7 = 1 × 7,200 = 7,200
([189]) 0 × 360 = 0
G6 = 2 × 20 = 40
G6 = 5 × 1 = 5
-----
7,245
Remembering that the starting point from which this number is counted is
the date next preceding it, 1 Cib 14 Kankin, and applying rules 1, 2, and 3
(pp. 139, 140, and 141, respectively), the terminal date reached will be 5
Imix 19 Zac; this latter date is recorded in G8-G9. Compare G8 with the
sign for Imix in figure 16, _a, b_, and G9 with the sign for Zac in figure
19, _s, t_. Moreover, since the Initial Series of 1 Cib 14 Kankin was
obtained by calculation from the date next preceding it, the Initial Series
of 5 Imix 19 Zac may be determined in the same way.
9.12. 14. 10.16 1 Cib 14 Kankin
1. 0.[189] 2. 5
9.13. 14. 13. 1 5 Imix 19 Zac
With the above date closes the known part of this text, the remaining
glyphs, G10-G12, being of unknown meaning.
Assembling all the glyphs deciphered above, the known part of this text
reads as follows:
9.12. 2. 0.16 A1-A7, C2 5 Cib 14 Yaxkin
12. 9.15 D2 E2
9.12. 14. 10.11 F1 G1 9 Chuen 9 Kankin
5 F3
9.12. 14. 10.16 G3 G4 1 Cib 14 Kankin
1. 0.[189] 2. 5 G6 G7
9.13. 14. 13. 1 G8 G9 5 Imix 19 Zac
[Illustration: INITIAL SERIES (_A_) AND SECONDARY SERIES (_B_) ON STELA
K, QUIRIGUA]
{213} We have recorded here four different dates, of which the last,
9.13.14.13.1 5 Imix 19 Zac, probably represents the actual date, or very
near thereto, of this monument.[190] The period covered between the first
and last of these dates is about 32 years, within the range of a single
lifetime or, indeed, of the tenure of some important office by a single
individual. The unknown glyphs again probably set forth the nature of the
events which occurred on the dates recorded.
In the two preceding texts the Secondary Series given are regular in every
way. Not only was the count forward each time, but it also started in every
case from the date immediately preceding the number counted. This
regularity, however, is far from universal in Secondary-series texts, and
the following examples comprise some of the more common departures from the
usual practice.
In plate 18 is figured the Initial Series from Stela K at Quirigua.[191]
The text opens on the north side of this monument (see pl. 18, _A_) with
the introducing glyph in A1-B2. This is followed by the Initial-series
number 9.18.15.0.0 in A3-B4, which leads to the terminal date 3 Ahau 3 Yax.
The day part of this date the student will find recorded in its regular
position, A5a. Passing over A5b and B5, the meanings of which are unknown,
we reach in A6 a Secondary-series number composed very clearly of 10 uinals
and 10 kins (10.10), which reduces to the following number of units of the
first order:
A6 = 10 × 20 = 200
A6 = 10 × 1 = 10
---
210
The first assumption is that this number is counted forward from the
terminal date of the Initial Series, 3 Ahau 3 Yax, and performing the
operations indicated in rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively) the terminal date reached will be 5 Oc 8 Uo. Now, although
the day sign in B6b is clearly Oc (see fig. 16, _o-q_), its coefficient is
very clearly 1, not 5, and, moreover, the month in A7a is unmistakably 18
Kayab (see fig. 19, _d'-f'_). Here then instead of finding the date
determined by calculation, 5 Oc 8 Uo, the date recorded is 1 Oc 18 Kayab,
and consequently there is some departure from the practices heretofore
encountered.
Since the association of the number 10.10 is so close with (1) the terminal
date of the Initial Series, 3 Ahau 3 Yax, and (2) the date 1 Oc 18 Kayab
almost immediately following it, it would almost seem as though these two
dates must be the starting point and terminal date, respectively, of this
number. If the count is forward, we have just proved that this can not be
the case; so let us next count the {214} number backward and see whether we
can reach the date recorded in B6b-A7a (1 Oc 18 Kayab) in this way.
Counting 210 _backward_ from 3 Ahau 3 Yax, according to rules 1, 2, and 3
(pp. 139, 140, and 141, respectively), the terminal date reached will be 1
Oc 18 Kayab, as recorded in B6b-A7. In other words, the Secondary Series in
this text is counted backward from the Initial Series, and therefore
precedes it in point of time. This will appear from the Initial-series
value of 1 Oc 18 Kayab, which may be determined by calculation:
9.18.15. 0. 0 3 Ahau 3 Yax
10.10
9.18.14. 7.10 1 Oc 18 Kayab
This text closes on the south side of the monument in a very unusual manner
(see pl. 18, _B_). In B3a appears the month-sign indicator, here recorded
as a head variant with a coefficient 10, and following immediately in B3b a
Secondary-series number composed of 0 uinals and 0 kins, or, in other
words, nothing. It is obvious that in counting this number 0.0, or nothing,
either backward or forward from the date next preceding it in the text, 1
Oc 18 Kayab in B6b-A7a on the north side of the stela, the same date 1 Oc
18 Kayab will remain. But this date is not repeated in A4, where the
terminal date of this Secondary Series, 0.0, seems to be recorded. However,
if we count 0.0 from the terminal date of the Initial Series, 3 Ahau 3 Yax,
we reach the date recorded in A4, 3 Ahau 3 Yax,[192] and this whole text so
far as deciphered will read:
9.18.15. 0. 0 3 Ahau 3 Yax
10.10 backward
9.18.14. 7.10 1 Oc 18 Kayab
0. 0 forward from Initial Series
9.18.15. 0. 0 3 Ahau 3 Yax
The reason for recording a Secondary-series number equal to zero, the
writer believes, was because the first Secondary-series date 1 Oc 18 Kayab
precedes the Initial-series date, which in this case marks the time at
which this monument was erected. Hence, in order to have the closing date
on the monument record the contemporaneous time of the monument, it was
necessary to repeat the Initial-series date; this was accomplished by
adding to it a Secondary-series date denoting zero. Stela K is the next to
the latest hotun-marker at Quirigua following immediately Stela I, the
Initial series of which marks the hotun ending 9.18.10.0.0 10 Ahau 8 Zac
(see pl. 6, _C_).
Mr. Bowditch (1910: p. 208) has advanced a very plausible explanation to
account for the presence of the date 9.18.14.7.10 1 Oc 18 Kayab {215} on
this monument. He shows that at the time when Stela K was erected, namely,
9.18.15.0.0 3 Ahau 3 Yax, the official calendar had outrun the seasons by
just 210 days, or exactly the number of days recorded in A6, plate 18, A
(north side); and further, that instead of being the day 3 Yax, which
occurred at Quirigua about the beginning of the dry season,[193] in reality
the season was 210 days behind, or at 18 Kayab, about the beginning of the
rainy season. This very great discrepancy between calendar and season could
not have escaped the notice of the priests, and the 210 days recorded in A6
may well represent the days actually needed on the date 9.18.15.0.0 3 Ahau
3 Yax to bring the calendar into harmony with the current season. If this
be true, then the date 9.18.14.7.0 1 Oc 18 Kayab represented the day
indicated by the sun when the calendar showed that the 3d hotun in Katun 18
of Cycle 9 had been completed. Mr. Bowditch suggests the following free
interpretation of this passage: "The sun has just set at its northern
point[194] and we are counting the day 3 Yax--210 days from 18 Kayab--which
is the true date in the calendar according to our traditions and records
for the sun to set at this point on his course." As stated above, the
writer believes this to be the true explanation of the record of 210 days
on this monument.
[Illustration: FIG. 78. The Initial Series on Stela J, Quirigua.]
In figures 78 and 79 are illustrated the Initial Series and Secondary
Series from Stela J at Quirigua.[195] For lack of space the introducing
glyph in this text has been omitted; it occupies the position of six
glyph-blocks, however, A1-B3, after which the Initial-series number
9.16.5.0.0 follows in A4-B8. This leads to the terminal date 8 Ahau 8 Zotz,
which is recorded in A9, B9, B13, the glyph in A13 being the month-sign
indicator here shown with the coefficient 9. Compare B9 with the second
variant for Ahau in figure 16 _h', i'_, and B13 with the sign for Zotz in
figure 19, _e, f_. The {216} Initial-series part of this text therefore in
A1-B9, B13, is perfectly regular and reads as follows: 9.16.5.0.0 8 Ahau 8
Zotz. The Secondary Series, however, are unusual and differ in several
respects from the ones heretofore presented.
[Illustration: FIG. 79. The Secondary Series on Stela J, Quirigua.]
The first Secondary Series inscribed on this monument (see fig. 79, _A_) is
at B1-B2. This series the student should readily decipher as 3 kins, 13
uinals, 11 tuns, and 0 katuns, which we may write 0.11.13.3. This number
presents one feature, which, so far as the writer knows, is unique in the
whole range of Maya texts. The highest order of units actually involved in
this number is the tun, but for some unknown reason the ancient scribe saw
fit to add the katun sign also, B2, which, however, he proceeded to nullify
at once by attaching to it the coefficient 0. For in so far as the
numerical value is concerned, 11.13.3 and 0.11.13.3 are equal. The next
peculiarity is that the date which follows this number in B3-A4 is not its
terminal date, as we have every reason to expect, but, on the contrary, its
starting point. In other words, in this Secondary Series the starting point
follows instead of precedes the number counted from it. This date is very
clearly 12 Caban 5 Kayab; compare B3 with the sign for Caban in figure 16,
_a', b'_, and A4 with the sign for Kayab in figure 19, _d'-f'_. So far as
Stela J is concerned there is no record of the position which this date
occupied in the Long Count; that is, there are no data by means of which
its Initial Series may be calculated. Elsewhere at Quirigua, however, this
date is recorded twice as an Initial Series and in each place it has the
same value, 9.14.13.4.17. We may safely conclude, therefore, that the date
in A3-B4 is 9.14.13.4.17 12 Caban 5 Kayab, and use it in our calculations
as such. Reducing 0.11.13.3 to units of the first order, we have:
B2 = 0 × 7,200 = 0
A2 = 11 × 360 = 3,960
B1 = 13 × 20 = 260
B1 = 3 × 1 = 3
-----
4,223
{217} Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to
this number, the terminal date reached will be 10 Ahau 8 Chen, which is
nowhere recorded in the text (see fig. 79, A).
The Initial Series corresponding to this date, however, may be calculated
from the Initial Series which we have assigned to the date 12 Caban 5
Kayab:
9.14.13. 4.17 12 Caban 5 Kayab
0.11.13. 3
9.15. 5. 0. 0 10 Ahau 8 Chen
Although the date 9.15.5.0.0 10 Ahau 8 Chen is not actually recorded at
Quirigua, it is reached on another monument by calculation just as here. It
has a peculiar fitness here on Stela J in that it is just one katun earlier
than the Initial Series on this monument (see fig. 78), 9.16.5.0.0 8 Ahau 8
Zotz.
The other Secondary Series on this monument (see fig. 79, _B_) appears at
B1-A2, and records 18 tuns, 3 uinals, and 14 kins, which we may write thus:
18.3.14. As in the preceding case, the date following this number in B2-A3
is its starting point, not its terminal date, a very unusual feature, as
has been explained. This date is 6 Cimi 4 Tzec--compare B2 with the sign
for Cimi in figure 16, _h, i_, and A3 with the sign for Tzec in figure 19,
_g, h_--and as far as Stela J is concerned it is not fixed in the Long
Count. However, elsewhere at Quirigua this date is recorded in a Secondary
Series, which is referred back to an Initial Series, and from this passage
its corresponding Initial Series is found to be 9.15.6.14.6 6 Cimi 4 Tzec.
Reducing the number recorded in B1-A2, 18.3.14, to units of the first
order, we have:
A2 = 18 × 360 = 6,480
B2 = 3 × 20 = 60
B2 = 14 × 1 = 14
-----
6,554
Applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to the
number, the terminal date reached will be 8 Ahau 8 Zotz, which does not
appear in figure 79, _B_. The Initial Series corresponding to this date may
be calculated as follows:
9.15. 6.14. 6 6 Cimi 4 Tzec
18. 3.14
9.16. 5. 0. 0 8 Ahau 8 Zotz
But this was the Initial Series recorded on the reverse of this monument,
consequently the Secondary-series dates, both of which have {218} preceded
the Initial-series date in point of time, bring this count up to the
contemporaneous time of this monument, which was 9.16.5.0.0 8 Ahau 8 Zotz.
In view of the fact that the Secondary Series on Stela J are both earlier
than the Initial Series, the chronological sequence of the several dates is
better preserved by regarding the Initial Series as being at the close of
the inscription instead of at the beginning, thus:
9.14.13. 4.17 12 Caban 5 Kayab Figure 79, _A_, B3-A4
0.11.13. 3 B1-B2
[9.15. 5. 0. 0] [10 Ahau 8 Chen][196]
[1.14. 6][197]
9.15. 6.14. 6 6 Cimi 4 Tzec Figure 79, _B_, B2-A3
18. 3.14 B1-A2
9.16. 5. 0. 0 8 Ahau 8 Zotz Figure 78, A1-B9, B13
By the above arrangement all the dates present in the text lead up to
9.16.5.0.0 8 Ahau 8 Zotz as the most important date, because it alone
records the particular hotun-ending which Stela J marks. The importance of
this date over the others is further emphasized by the fact that it alone
appears as an Initial Series.
The text of Stela J illustrates two points in connection with Secondary
Series which the student will do well to bear in mind: (1) The starting
points of Secondary-series numbers do not always precede the numbers
counted from them, and (2) the terminal dates and starting points are not
always both recorded.
The former point will be illustrated in the following example:
In plate 19, _A_, is figured the Initial Series from the west side of Stela
F at Quirigua.[198] The introducing glyph appears in A1-B2 and is followed
by the Initial-series number in A3-A5. This is expressed by head variants
and reads as follows: 9.14.13.4.17. The terminal date reached by this
number is 12 Caban 5 Kayab, which is recorded in B5-A6. The student will
readily identify the numerals as above by comparing them with the forms in
figures 51-53, and the day and month signs by comparing them with figures
16, _a', b'_, and 19, _d'-f'_, respectively. The Initial Series therefore
reads 9.14.13.4.17 12 Caban 5 Kayab.[199]
[Illustration: INITIAL SERIES (_A_) AND SECONDARY SERIES (_B_) ON STELA F
(WEST SIDE), QUIRIGUA]
{219}
Passing over B6-A10, the meanings of which are unknown, we reach in B10 the
Secondary-series number 13.9.9. Reducing this to units of the first order,
we have:
B10b = 13 × 360 = 4,680
B10a = 9 × 20 = 180
B10a = 9 × 1 = 9
-----
4,869
Assuming that our starting point is the date next preceding this number in
the text, that is, the Initial-series terminal date 12 Caban 5 Kayab in
B5-A6, and applying rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively), the terminal day reached will be 6 Cimi 4 Tzec. This date
the student will find recorded in plate 19, _B_, B11b-A12a. Compare B11b
with the sign for Cimi in figure 16, _h, i_, and A12a with the sign for
Tzec in figure 19, _g, h_. Moreover, since the Initial-series value of the
starting point 12 Caban 5 Kayab is known, the Initial-series value of the
terminal date 6 Cimi 4 Tzec may be calculated from it:
9.14.13. 4.17 12 Caban 5 Kayab
13. 9. 9
9.15. 6.14. 6 6 Cimi 4 Tzec[200]
In A15 is recorded the date 3 Ahau 3 Mol (compare A15a with fig. 16, _k',
i'_, and A15b with fig. 19, _m, n_) and in A17 the date 4 Ahau 13 Yax
(compare A17a with fig. 16, _e'-g'_ and A17b with fig. 19, _q, r_). This
latter date, 4 Ahau 13 Yax, is recorded elsewhere at Quirigua in a
Secondary Series attached to an Initial Series, where it has the
Initial-series value 9.15.0.0.0. This value we may assume, therefore,
belongs to it in the present case, giving us the full date 9.15.0.0.0 4
Ahau 13 Yax. For the present let us pass over the first of these two dates,
namely, 3 Ahau 3 Mol, the Initial Series of which as well as the reason for
its record here will better appear later.
In B17-A18a is recorded another Secondary-series number composed of 3 kins,
13 uinals, 16 tuns, and 1 katun, which we may write thus: 1.16.13.3. The
student will note that the katun coefficient in A18a is expressed by an
unusual form, the thumb. As explained on page 103, this has a numerical
value of 1. Again, our text presents another irregular feature. Instead of
being counted either forward or backward from the date next preceding it in
the text; that is, 4 Ahau 13 Yax in A17, this number is counted from the
date following it in the text, like the two Secondary-series numbers in
Stela J, just discussed. This starting date recorded in A18b B18a is 12
Caban 5 Kayab, which, as we have seen, is also the date recorded by the
Initial Series in plate 19, _A_, A1-A6. We are perfectly justified in {220}
assuming, therefore, that the 12 Caban 5 Kayab in A18b-B18a had the same
Initial-series value as the 12 Caban 5 Kayab in plate 19, _A_, B5-A6,
namely, 9.14.13.4.17. Reducing the number in B17-A18a, namely, 1.16.13.3,
to units of the first order, we have:
A18a = 1 × 7,200 = 7,200
B17b = 16 × 360 = 5,760
B17a = 13 × 20 = 260
B17a = 3 × 1 = 3
------
13,223
Remembering that this number is to be counted forward from the date 12
Caban 5 Kayab, and applying rules 1, 2, and 3 (pp. 139, 140, and 141,
respectively), the terminal date reached will be 1 Ahau 3 Zip, which is
recorded in A19. Compare the coefficient of the day sign in A19a with the
coefficient of the katun sign in A18a, and the day sign itself with the
profile variant for Ahau in figure 16, _h', i'_. For the month sign,
compare A19b with figure 19, d. But since the Initial-series value of the
starting point is known, we may calculate from it the Initial-series value
of the new terminal date:
9.14.13. 4.17 12 Caban 5 Kayab
1.16.13. 3
9.16.10. 0. 0 1 Ahau 3 Zip
Passing over to the east side of this monument, the student will find
recorded there the continuation of this inscription (see pl. 20).[201] This
side, like the other, opens with an introducing glyph A1-B2, which is
followed by an Initial Series in A3-A5. Although this number is expressed
by head variants, the forms are all familiar, and the student will have
little difficulty in reading it as 9.16.10.0.0. The terminal date which
this number reaches is recorded in B5-B8; that is, 1[202] Ahau 3 Zip, the
"month indicator" appearing as a head variant in A8 with the head-variant
coefficient 10. But this date is identical with the date determined by
calculation and actually recorded at the close of the inscription on the
other side of this monument, and since no later date is recorded elsewhere
in this text, we may conclude that 9.16.10.0.0 1 Ahau 3 Zip represents the
contemporaneous time of Stela F, and hence that it was a regular
hotun-marker. Here again, as in the case of Stela J at Quirigua, the
importance of the "contemporaneous date" is emphasized not only by the fact
that all the other dates lead up to it, but also by the fact that it is
expressed as an Initial Series.
[Illustration: INITIAL SERIES ON STELA F (EAST SIDE), QUIRIGUA]
{221}
[Illustration: FIG. 80. Glyphs which may disclose the nature of the events
that happened at Quirigua on the dates: _a_, 9. 14. 13. 4. 17 12 Caban 5
Kayab; _b_, 9. 15. 6. 14. 6 6 Cimi 4 Tzec.]
We have explained all the dates figured except 3 Ahau 3 Mol in plate 19,
_B_, A15, the discussion of which was deferred until after the rest of the
inscription had been considered. It will be remembered in connection with
Stela J (figs. 78, 79) that one of the dates reached in the course of the
calculations was just 1 katun earlier than the date recorded by the Initial
Series on the same monument. Now, one of the Initial-series values
corresponding to the date 3 Ahau 3 Mol here under discussion is
9.15.10.0.0, exactly 1 katun earlier than the Initial-series date on Stela
F. In other words, if we give to the date 3 Ahau 3 Mol in A15 the value
9.15.10.0.0, the cases are exactly parallel. While it is impossible to
prove that this particular Initial Series was the one which the ancient
scribes had in mind when they recorded this date 3 Ahau 3 Mol, the writer
believes that the coincidence and parallel here presented are sufficient to
warrant the assumption that this is the case. The whole text reads as
follows:
9.14.13. 4.17 12 Caban 5 Kayab Plate 19, _A_, A1-A6
13. 9. 9 Plate 19, _A_, A10
9.15. 6.14. 6 6 Cimi 4 Tzec Plate 19, _B_, B11b-A12a
[9.15.10. 0. 0] 3 Ahau 3 Mol Plate 19, _B_, A15
[9.15. 0. 0. 0] 4 Ahau 13 Yax Plate 19, _B_, A17
9.14.13. 4.17 12 Caban 5 Kayab Plate 19, _B_, A18b B18a
1.16.13. 3 Plate 19, _B_, B17 A18a
9.16.10. 0. 0 1 Ahau 3 Zip Plate 19, _B_, A19
(repeated as Initial Series on east side of monument)
9.16.10. 0. 0 1 Ahau 3 Zip Plate 20, A1-B5-B8
The student will note the close similarity between this inscription and
that on Stela J (figured in figs. 78 and 79), a summary of which appears on
page 239. Both commence with the same date, 9.14.13.4.17 12 Caban 5 Kayab;
both show the date 9.15.6.14.6 6 Cimi 4 Tzec; both have dates which are
just 1 katun in advance of the hotuns which they mark; and finally, both
are hotun-markers, Stela J preceding Stela F by just 1 hotun. The date from
which both proceed, 9.14.13.4.17 12 Caban 5 Kayab, is an important one at
Quirigua, being the earliest date there. It appears on four monuments,
namely, Stelæ J, F, and E, and Zoömorph G. Although the writer has not been
able to prove the point, he is of the opinion that the glyph shown in
figure 80, _a_, tells the meaning of the event which happened on this date,
which is, moreover, the earliest date at Quirigua which {222} it is
possible to regard as being contemporaneous. Hence, it is not improbable
that it might refer to the founding of the city or some similar event,
though this is of course a matter of speculation. The fact, however, that
9.14.13.4.17 12 Caban 5 Kayab is the earliest date on four different
hotun-markers shows that it was of supreme importance in the history of
Quirigua. This concludes the discussion of texts showing the use of
Secondary Series with Initial Series.
TEXTS RECORDING PERIOD ENDINGS
It was explained in Chapter III (p. 77) that in addition to Initial-series
dating and Secondary-series dating, the Maya used still another method in
fixing events, which was designated Period-ending dating. It was explained
further that, although Period-ending dating was less exact than the other
two methods, it served equally well for all practical purposes, since dates
fixed by it could not recur until after a lapse of more than 18,000 years,
a considerably longer period than that covered by the recorded history of
mankind. Finally, the student will recall that the katun was said to be the
period most commonly used in this method of dating.
The reason for this is near at hand. Practically all of the great southern
cities rose, flourished, and fell within the period called Cycle 9 of Maya
chronology. There could have been no doubt throughout the southern area
which particular cycle was meant when the "current cycle" was spoken of.
After the date 9.0.0.0.0 8 Ahau 13 Ceh had ushered in a new cycle there
could be no change in the cycle coefficient until after a lapse of very
nearly 400 (394.250 +) years. Consequently, after Cycle 9 had commenced
many succeeding generations of men knew no other, and in time the term
"current cycle" came to mean as much on a monument as "Cycle 9." Indeed, in
Period-ending dating the Cycle 9 was taken for granted and scarcely ever
recorded. The same practice obtains very generally to-day in regard to
writing the current century, such expressions as July 4, '12, December 25,
'13, being frequently seen in place of the full forms July 4, 1912, A. D.,
December 25, 1913, A. D.; or again, even more briefly, 7/4/12 and 12/25/13
to express the same dates, respectively. The desire for brevity, as has
been explained, probably gave rise to Period-ending dating in the first
place, and in this method the cycle was the first period to be eliminated
as superfluous for all practical purposes. No one could have forgotten the
number of the current cycle.
When we come to the next lower period, however, the katun, we find a
different state of affairs. The numbers belonging to this period were
changing every 20 (exactly, 19.71 +) years; that is, three or four times in
the lifetime of many individuals; hence, there was plenty of opportunity
for confusion about the number of the katun in which a particular event
occurred. Consequently, in order to insure accuracy the katun is almost
always the unit used in Period-ending dating.
[Illustration: EXAMPLES OF PERIOD-ENDING DATES IN CYCLE 9]
{223}
In plate 21 are figured a number of Period-ending dates, the glyphs of
which have been ranged in horizontal lines, and are numbered from left to
right for convenience in reference. The true positions of these glyphs in
the texts from which they have been taken are given in the footnotes in
each case. In plate 21, _A_, is figured a Period-ending date from Stela 2
at Copan.[203] The date 12 Ahau 8 Ceh appears very clearly in glyphs 1 and
2. Compare the month sign with figure 19, _u, v_. There follows in 3 a
glyph the upper part of which probably represents the "ending sign" of this
date. By comparing this form with the ending signs in figure 37 its
resemblance to figure 37, _o_, will be evident. Indeed, figure 37, _o_, has
precisely the same lower element as glyph 3. In glyph 4 follows the
particular katun, 11, whose end fell on the date recorded in glyphs 1 and
2. The student can readily prove this for himself by reducing the
Period-ending date here recorded to its corresponding Initial Series and
counting the resulting number forward from the common starting point, 4
Ahau 8 Cumhu, as follows: Since the cycle glyph is not expressed, we may
fill this omission as the Maya themselves filled it, by supplying Cycle 9.
Moreover, since the _end_ of a katun is recorded here, it is clear that all
the lower periods--the tuns, uinals, and kins--will have to appear with the
coefficient 0, as they are all brought to their respective ends with the
ending of any katun. Therefore we may write the Initial-series number
corresponding to the end of Katun 11, as 9.11.0.0.0. Treating this number
as an Initial Series, that is, first reducing it to units of the first
order, then deducting from it all the Calendar Rounds possible, and finally
applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to the
remainder, the student will find that the terminal date reached will be the
same as the date recorded in glyphs 1 and 2, namely, 12 Ahau 8 Ceh. In
other words, the Katun 11, which ended on the date 12 Ahau 8 Ceh, was
9.11.0.0.0 12 Ahau 8 Ceh, and both indicate exactly the same position in
the Long Count. The next example (pl. 21, _B_) is taken from the tablet in
the Temple of the Foliated Cross at Palenque.[204] In glyph 1 appears the
date 8 Ahau 8 Uo (compare the month form with fig. 19, _b, c_) and in glyph
3 the "ending" of Katun 13. The ending sign here is the variant shown in
figure 37, _a-h_, and it occurs just above the coefficient 13. These two
glyphs therefore record the fact that Katun 13 ended with the day 8 Ahau 8
Uo. The student may again test the accuracy of the record by changing this
Period-ending date to its {224} corresponding Initial-series number,
9.13.0.0.0, and performing the various operations indicated in such cases.
The resulting Initial-series terminal date will be the same as the date
recorded in glyphs 1 and 2, 8 Ahau 8 Uo.
In plate 21, _C_, is figured a Period-ending date taken from Stela 23 at
Naranjo.[205] The date 6 Ahau 13 Muan appears very clearly in glyphs 1 and
2 (compare the month form with fig. 19, _a', b'_). Glyph 3 is the ending
sign, here showing three common "ending elements," (1) the clasped hand;
(2) the element with the curl infix; (3) the tassel-like postfix. Compare
this form with the ending signs in figure 37, _l-q_, and with the zero
signs in figure 54. In glyph 4 is recorded the particular katun, 14, which
came to its end on the date recorded in 1 and 2. The element prefixed to
the Katun 14 in glyph 4 is also an ending sign, though it always occurs as
a prefix or superfix attached to the sign of the period whose close is
recorded. Examples illustrating its use are shown in figure 37, _a-h_, with
which the ending element in glyph 4 should be compared. The glyphs 1 to 4
in plate 21, _C_, therefore record that Katun 14 came to an end on the date
6 Ahau 13 Muan. As we have seen above, this could be shown to correspond
with the Initial Series 9.14.0.0.0 6 Ahau 13 Muan.
This same date, 6 Ahau 13 Muan ending Katun 14, is also recorded on Stela
16 at Tikal (see pl. 21, _D_).[206] The date itself appears in glyphs 1 and
2 and is followed in 3 by a sign which is almost exactly like the ending
sign in glyph 3 just discussed (see pl. 21, _C_). The subfixes are
identical in both cases, and it is possible to distinguish the lines of the
hand element in the weathered upper part of the glyph in 3. Compare glyph 3
with the ending signs in figure 37, _l-q_, and with the zero signs in
figure 54. As in the preceding example, glyph 4 shows the particular katun
whose end is recorded here--Katun 14. The period glyph itself appears as a
head variant to which is prefixed the same ending prefix or superfix shown
with the period glyph in the preceding example. See also figure 37, _a-h_.
As above stated, the Initial Series corresponding to this date is
9.14.0.0.0 6 Ahau 13 Muan.
One more example will suffice to illustrate the use of katun Period-ending
dates. In plate 21, _E_, is figured a Period-ending date from Stela 4 at
Copan.[207] In glyphs 1 and 2 appears the date 4 Ahau 13 Yax (compare the
month in glyph 2 with fig. 19, _q, r_), which is followed by the ending
sign in 3. This is composed of the hand, a very common "ending" element
(see fig. 37, _j, k_) with a grotesque head superfix, also another "ending
sign" (see _i, r, u, v_ of the plate just named). In glyph 4 follows the
particular katun (Katun 15) whose {225} end is here recorded. This date
corresponds to the Initial Series 9.15.0.0.0 4 Ahau 13 Yax.
Cases where tun endings are recorded are exceedingly rare. The bare
statement that a certain tun, as Tun 10, for example, had come to its end
left much to be desired in the way of accuracy, since there was a Tun 10 in
every katun, and consequently any given tun recurred after an interval of
20 years; in other words, there were three or four different Tun 10's to be
distinguished from one another in the average lifetime. Indeed, to keep
them apart at all it was necessary either to add the particular katun in
which each fell or to add the date on which each closed. The former was a
step away from the brevity which probably prompted the use of Period-ending
dating in the first place, and the latter imposed too great a task on the
memory, that is, keeping in mind the 60 or 70 various tun endings which the
average lifetime included. For these reasons tun-ending dates occur but
rarely, only when there was little or no doubt concerning the particular
katun in which they fell.
In plate 21, _F_, is figured a tun-ending date from the tablet in the
Temple of the Inscription at Palenque.[208] In glyph 1 appears an ending
sign showing the hand element and the grotesque flattened head (for the
latter see fig. 37, _i, r, u, v_), both common ending signs. The remaining
element, another grotesque head with a flaring postfix, is an unusual
variant of the tun head found only at Palenque (see fig. 29, _h_). The
presence of the tun sign with these two ending signs indicates probably
that some tun ending follows. Glyphs 2 and 3 record the date 5 Ahau 18
Tzec, and glyph 4 records Tun 13. We have here then the record of a Tun 13,
which ended on the date 5 Ahau 18 Tzec. But which of the many Tun 13s in
the Long Count was the one that ended on this particular date? To begin
with, we are perfectly justified in assuming that this particular tun
occurred somewhere in Cycle 9, but this assumption does not aid us greatly,
since there were twenty different Tun 13s in Cycle 9, one for each of the
twenty katuns. However, in the full text of the inscription from which this
example is taken, 5 Ahau 3 Chen is the date next preceding, and although
the fact is not recorded, this latter date closed Katun 8 of Cycle 9.
Moreover, shortly after the tun-ending date here under discussion, the date
"3 Ahau 3 Zotz, end of Katun 9," is recorded. It seems likely, therefore,
that this particular Tun 13, which ended on the date 5 Ahau 18 Tzec, was
9.8.13.0.0 of the Long Count, after 9.8.0.0.0 but before 9.9.0.0.0.
Reducing this number to units of the first order, and applying the several
rules given for solving Initial Series, the terminal date of 9.8.13.0.0
will be found to agree with the terminal date recorded in glyphs 2 and 3,
namely, 5 Ahau 18 Tzec, {226} and this tun ending corresponded, therefore,
to the Initial Series 9.8.13.0.0 5 Ahau 18 Tzec.
Another tun-ending date from Stela 5 at Tikal is figured in plate 21,
_G_.[209] In glyphs 1 and 2 the date 4 Ahau 8 Yaxkin appears, the month
sign being represented as a head variant, which has the essential elements
of the sign for Yaxkin (see fig. 19, _k, l_). Following this in glyph 3 is
Tun 13, to which is prefixed the same ending-sign variant as the prefixial
or superfixial elements in figure 37, _i, r, u, v_. We have recorded here
then "Tun 13 ending on 4 Ahau 8 Yaxkin," though there seems to be no
mention elsewhere in this inscription of the number of the katun in which
this particular tun fell. By referring to Great Cycle 54 of Goodman's
Tables (Goodman, 1897), however, it appears that Tun 13 of Katun 15 of
Cycle 9 closed with this date 4 Ahau 8 Yaxkin, and we may assume,
therefore, that this is the correct position in the Long Count of the
tun-ending date here recorded. This date corresponds to the Initial Series
9.15.13.0.0 4 Ahau 8 Yaxkin.
There is a very unusual Period-ending date on the west side of Stela C at
Quirigua[210] (see pl. 21, _H_). In glyphs 1 and 2 appears the number 0
kins, 0 uinals, 5 tuns, and 17 katuns, which we may write 17.5.0.0 and
following this in glyphs 3 and 4 is the date 6 Ahau 13 Kayab. At first
sight this would appear to be a Secondary Series, the number 17.5.0.0 being
counted forward from some preceding date to reach the date 6 Ahau 13 Kayab
recorded just after it. The next date preceding this on the west side of
Stela C at Quirigua is the Initial-series terminal date 6 Ahau 13 Yaxkin,
illustrated together with its corresponding Initial-series number in figure
68, _A_. However, all attempts to reach the date 6 Ahau 13 Kayab by
counting either forward or backward the number 17.5.0.0 from the date 6
Ahau 13 Yaxkin will prove unsuccessful, and we must seek another
explanation for the four glyphs here under discussion. If this were a
Period-ending date it would mean that Tun 5 of Katun 17 came to an end on
the date 6 Ahau 13 Kayab. Let us see whether this is true. Assuming that
our cycle coefficient is 9, as we have done in all the other Period-ending
dates presented, we may express glyphs 1 and 2 as the following
Initial-series number, provided they represent a period ending, not a
Secondary-series number: 9.17.5.0.0. Reducing this number to units of the
1st order, and applying the rules previously given for solving Initial
Series, the terminal date reached will be 6 Ahau 13 Kayab, identical with
the date recorded in glyphs 3 and 4. We may conclude, therefore, that this
example records the fact that "Tun 5 of Katun 17 ended on the date 6 Ahau
13 Kayab," this being identical with the Initial Series 9.17.5.0.0 6 Ahau
13 Kayab.
[Illustration: EXAMPLES OF PERIOD-ENDING DATES IN CYCLES OTHER THAN CYCLE
9]
{227}
The foregoing Period-ending dates have all been in Cycle 9, even though
this fact has not been recorded in any of the above examples. We come next
to the consideration of Period-ending dates which occurred in cycles other
than Cycle 9.
In plate 22, _A_, is figured a Period-ending date from the tablet in the
Temple of the Cross at Palenque.[211] In glyphs 1 and 2 appears the date 4
Ahau 8 Cumhu (compare the month form in glyph 2 with fig. 19, _g', h'_),
and in glyph 3 an ending sign (compare glyph 3 with the ending signs in
fig. 37, _l-q_, and with the zero signs in fig. 54). There follows in glyph
4, Cycle 13. These four glyphs record the fact, therefore, that Cycle 13
closed on the date 4 Ahau 8 Cumhu, the starting point of Maya chronology.
This same date is again recorded on a round altar at Piedras Negras (see
pl. 22, _B_).[212] In glyphs 1 and 2 appears the date 4 Ahau 8 Cumhu, and
in glyph 3a the ending sign, which is identical with the ending sign in the
preceding example, both having the clasped hand, the subfix showing a curl
infix, and the tassel-like postfix. Compare also figure 37, _l-q_, and
figure 54. Glyph 3b clearly records Cycle 13. The dates in plate 22, _A,
B_, are therefore identical. In both cases the cycle is expressed by its
normal form.
In plate 22, _C_, is figured a Period-ending date from the tablet in the
Temple of the Foliated Cross at Palenque.[213] In glyph 1 appears an ending
sign in which the hand element and tassel-like postfix show clearly. This
is followed in glyph 2 by Cycle 2, the clasped hand on the head variant
unmistakably indicating the cycle head. Finally, in glyphs 3 and 4 appears
the date 2 Ahau 3 Uayeb (compare the month form with fig. 19, _i'_).[214]
The glyphs in plate 22, _C_, record, therefore, the fact that Cycle 2
closed on the date 2 Ahau 3 Uayeb, a fact which the student may prove for
himself by converting this Period-ending date into its corresponding
Initial Series and solving the same. Since the end of a cycle is recorded
here, it is evident that the katun, tun, uinal, and kin coefficients must
all be 0, and our Initial-series number will be, therefore, 2.0.0.0.0.
Reducing this to units of the 1st order and proceeding as in the case of
Initial Series, the terminal date reached will be 2 Ahau 3 Uayeb, just as
recorded in glyphs 3 and 4. The Initial Series corresponding to this
Period-ending date will be 2.0.0.0.0 2 Ahau 3 Uayeb.
These three Period-ending dates (pl. 22, _A-C_) are not to be considered as
referring to times contemporaneous with the erection of the monuments upon
which they are severally inscribed, since they {228} precede the opening of
Cycle 9, the first historic epoch of the Maya civilization, by periods
ranging from 2,700 to 3,500 years. As explained elsewhere, they probably
referred to mythological events. There is a date, however, on a tablet in
the Temple of the Cross at Palenque which falls in Cycle 8, being fixed
therein by an adjoining Period-ending date that may have been historical.
This case is figured in plate 22, _G_.[215] In glyphs 4 and 5 appears the
date 8 Ahau 13 Ceh (compare the month form in glyph 5 with fig. 16, _u,
v_). This is followed in glyph 6 by a sign which shows the same ending
element as the forms in figure 37, _i, r, u, v_, and this in turn is
followed by Cycle 9 in glyph 7. The date recorded in this case is Cycle 9
ending on the date 8 Ahau 13 Ceh, which corresponds to the Initial Series
9.0.0.0.0 8 Ahau 13 Ceh.
Now, in glyphs 1 and 2 is recorded the date 2 Caban 10 Xul (compare the day
sign with fig. 16, _a', b'_, and the month sign with fig. 19, _i, j_), and
following this date in glyph 3 is the number 3 kins, 6 uinals, or 6.3. This
looks so much like a Secondary Series that we are justified in treating it
as such until it proves to be otherwise. As the record stands, it seems
probable that if we count this number 6.3 in glyph 3 forward from the date
2 Caban 10 Xul in glyphs 1 and 2, the terminal date reached will be the
date recorded in glyphs 4 and 5; that is, the next date following the
number. Reducing 6.3 to units of the first order, we have:
Glyph 3 = 6 × 20 = 120
Glyph 3 = 3 × 1 = 3
---
123
Counting this number forward from 2 Caban 10 Xul according to the rules
which apply in such cases, the terminal day reached will be 8 Ahau 13 Ceh,
exactly the date which is recorded in glyphs 4 and 5. But this latter date,
we have just seen, is declared by the text to have closed Cycle 9, and
therefore corresponded with the Initial Series 9.0.0.0.0 8 Ahau 13 Ceh.
Hence, from this known Initial Series we may calculate the Initial Series
of the date 2 Caban 10 Xul by subtracting from 9.0.0.0.0 the number 6.3, by
which the date 2 Caban 10 Xul precedes the date 9.0.0.0.0 8 Ahau 13 Ceh:
9. 0. 0. 0. 0 8 Ahau 13 Ceh
6. 3
8.19.19.11.17 2 Caban 10 Xul
This latter date fell in Cycle 8, as its Initial Series indicates. It is
quite possible, as stated above, that this date may have referred to some
actual historic event in the annals of Palenque, or at least of {229} the
southern Maya, though the monument upon which it is recorded probably dates
from an epoch at least 200 years later.
In a few cases Cycle-10 ending dates have been found. Some of these are
surely "contemporaneous," that is, the monuments upon which they appear
really date from Cycle 10, while others are as surely "prophetic," that is,
the monuments upon which they are found antedate Cycle 10. Examples of both
kinds follow.
In plate 22, _E_, is figured a Period-ending date from Stela 8 at
Copan.[216] Glyphs 1 and 2 declare the date 7 Ahau 18 ?, the month sign in
glyph 2 being effaced. In glyph 3 is recorded Cycle 10, the cycle sign
being expressed by its corresponding head variant. Note the clasped hand,
the essential characteristic of the cycle head. Above this appears the same
ending sign as that shown in figure 37, _a-h_, and it would seem probable,
therefore, that these three glyphs record the end of Cycle 10. Let us test
this by changing the Period-ending date in glyph 3 into its corresponding
Initial-series number and then solving this for the resulting terminal
date. Since the end of a cycle is here indicated, the katun, tun, uinal,
and kin coefficients must be 0 and the Initial-series number will be,
therefore, 10.0.0.0.0. Reducing this to units of the first order and
applying the rules indicated in such cases, the resulting terminal date
will be found to be 7 Ahau 18 Zip. But this agrees exactly with the date
recorded in glyphs 1 and 2 so far as the latter go, and since the two agree
so far as they go, we may conclude that glyphs 1-3 in plate 22, _E_,
express "Cycle 10 ending on the date 7 Ahau 18 Zip." Although this is a
comparatively late date for Copan, the writer is inclined to believe that
it was "contemporaneous" rather than "prophetic."
The same can not be said, however, for the Cycle-10 ending date on Zoömorph
G at Quirigua (see pl. 22, _F_). Indeed, this date, as will appear below,
is almost surely "prophetic" in character. Glyphs 1 and 2 record the date 7
Ahau 18 Zip (compare the month form in glyph 2 with fig. 19, _d_) and glyph
3 shows very clearly "the end of Cycle 10." Compare the ending prefix in
glyph 4 with the same element in fig. 37, _a-h_. Hence we have recorded
here the fact that "Cycle 10 ended on the date 7 Ahau 18 Zip," a fact
proved also by calculation in connection with the preceding example. Does
this date represent, therefore, the contemporaneous time of Zoömorph G, the
time at which it was erected, or at least dedicated? Before answering this
question, let us consider the rest of the text from which this example is
taken. The Initial Series on Zoömorph G at Quirigua has already been shown
in figure 70, and, according to page 187, it records the date 9.17.15.0.0 5
Ahau 3 Muan. On the grounds of antecedent probability, we are justified in
assuming at the outset that this date {230} therefore indicates the epoch
or position of Zoömorph G in the Long Count, because it alone appears as an
Initial Series. In the case of all the other monuments at Quirigua,[217]
where there is but one Initial Series in the inscription, that Initial
Series marks the position of the monument in the Long Count. It seems
likely, therefore, judging from the general practice at Quirigua, that
9.17.15.0.0 5 Ahau 3 Muan was the contemporaneous date of Zoömorph G, not
10.0.0.0.0 7 Ahau 18 Zip, that is, the Initial Series corresponding to the
Period-ending date here under discussion (see pl. 22, _F_).[218]
Other features of this text point to the same conclusion. In addition to
the Initial Series on this monument there are upward of a dozen
Secondary-series dates, all of which except _one_ lead to 9.17.15.0.0 5
Ahau 3 Muan. Moreover, this latter date is recorded thrice in the text, a
fact which points to the conclusion that it was the contemporaneous date of
this monument.
There is still another, perhaps the strongest reason of all, for believing
that Zoömorph G dates from 9.17.15.0.0 5 Ahau 3 Muan rather than from
10.0.0.0.0 7 Ahau 18 Zip. If assigned to the former date, every hotun from
9.15.15.0.0 9 Ahau 18 Xul to 9.19.0.0.0 9 Ahau 18 Mol has its corresponding
marker or period-stone at Quirigua, there being not a single break in the
sequence of the fourteen monuments necessary to mark the thirteen hotun
endings between these two dates. If, on the other hand, the date 10.0.0.0.0
7 Ahau 18 Zip is assigned to this monument, the hotun ending 9.17.15.0.0 5
Ahau 3 Muan is left without its corresponding monument at this city, as are
also all the hotuns after 9.19.0.0.0 9 Ahau 18 Mol up to 10.0.0.0.0 7 Ahau
18 Zip, a total of four in all. The perfect sequence of the monuments at
Quirigua developed by regarding Zoömorph G as dating from 9.17.15.0.0 5
Ahau 3 Muan, and the very fragmentary sequence which arises if it is
regarded as dating from 10.0.0.0.0 7 Ahau 18 Zip, is of itself practically
sufficient to prove that the former is the correct date, and when taken
into consideration with the other points above mentioned leaves no room for
doubt.
If this is true, as the writer believes, the date "Cycle 10 ending on 7
Ahau 18 Zip" on Zoömorph G is "prophetic" in character, since it did not
occur until nearly 45 years after the erection of the monument upon which
it was recorded, at which time the city of Quirigua had probably been
abandoned, or at least had lost her prestige.
Another Cycle-10 ending date, which differs from the preceding in that it
is almost surely contemporaneous, is that on Stela 11 at Seibal, {231} the
latest of the great southern sites.[219] This is figured in plate 22, _D_.
Glyphs 1 and 2 show very clearly the date 7 Ahau 18 Zip, and glyph 3
declares this to be "at the end of Cycle 10."[220] Compare the ending-sign
superfix in glyph 3 with figure 37, _a-h_. This glyph is followed by 1
katun in 4, which in turn is followed by the date 5 Ahau 3 Kayab in 5 and
6. Finally, glyph 7 declares "The end of Katun 1." Counting forward 1 katun
from 10.0.0.0.0 7 Ahau 18 Zip, the date reached will be 5 Ahau 3 Kayab, as
recorded by 5 and 6, and the Initial Series corresponding to this date will
be 10.1.0.0.0 5 Ahau 3 Kayab, as declared by glyph 7. See below:
10.0.0.0.0 7 Ahau 18 Zip
1.0.0.0
10.1.0.0.0 5 Ahau 3 Kayab
End of Katun 1.
This latter date is found also on Stelæ 8, 9, and 10, at the same city.
Another Cycle-10 ending date which was probably "prophetic", like the one
on Zoömorph G at Quirigua, is figured on Altar S at Copan (see fig. 81). In
the first glyph on the left appears an Initial-series introducing glyph;
this is followed in glyphs 1-3 by the Initial-series number 9.15.0.0.0,
which the student will find leads to the terminal date 4 Ahau 13 Yax
recorded in glyph 4. This whole Initial Series reads, therefore, 9.15.0.0.0
4 Ahau 13 Yax. In glyph 6a is recorded 5 katuns and in glyph 7 the date 7
Ahau 18 Zip, in other words, a Secondary Series.[221] Reducing the number
in glyph 6a to units of the first order, we have:
6a = 5 × 7,200 = 36,000
{0 × 360 = 0
Not recorded {0 × 20 = 0
{0 × 1 = 0
------
36,000
{232}
[Illustration: FIG. 81. The Initial Series, Secondary Series, and
Period-ending date on Altar S, Copan.]
Counting this number forward from the date 4 Ahau 13 Yax, the terminal date
reached will be found to agree with the date recorded in glyph 7, 7 Ahau 18
Zip. But turning to our text again, we find that this date is declared by
glyph 8a to be at the end of Cycle 10. Compare the ending sign, which
appears as the superfix in glyph 8a, with figure 37, _a-h_. Therefore the
Secondary-series date 7 Ahau 18 Zip, there recorded, closed Cycle 10. The
same fact could have been determined by adding the Secondary-series number
in glyph 6a to the Initial-series number of the starting point 4 Ahau 13
Yax in glyphs 1-3:
9.15. 0.0.0 4 Ahau 13 Yax
5.(0.0.0)
10.0. 0.0.0 7 Ahau 18 Zip
[Illustration: INITIAL SERIES, SECONDARY SERIES, AND
PERIOD-ENDING DATES ON STELA 3, PIEDRAS NEGRAS]
{233} The "end of Cycle 10" in glyph 8a is merely redundancy. The writer
believes that 9.15.0.0.0 4 Ahau 13 Yax indicates the present time of Altar
S rather than 10.0.0.0.0 7 Ahau 18 Zip, and that consequently the latter
date was "prophetic" in character, as was the same date on Zoömorph G at
Quirigua. One reason which renders this probable is that the sculpture on
Altar S very closely resembles the sculpture on Stelæ A and B at Copan,
both of which date from 9.15.0.0.0 4 Ahau 13 Yax. A possible explanation of
the record of Cycle 10 on this monument is the following: On the date of
this monument, 9.15.0.0.0 4 Ahau 13 Yax, just three-fourths of Cycle 9 had
elapsed. This important fact would hardly have escaped the attention of the
old astronomer-priests, and they may have used this monument to point out
that only a quarter cycle, 5 katuns, was left in Cycle 9. This concludes
the discussion of Cycle-10 Period-ending dates.
The student will note in the preceding example (fig. 81) that
Initial-series, Secondary-series, and Period-ending dating have all been
used together in the same text, glyphs 1-4 recording an Initial-series
date, glyphs 6a and 7, a Secondary-series date, and glyphs 7 and 8a, a
Period-ending date. This practice is not at all unusual in the inscriptions
and several texts illustrating it are figured below.
TEXTS RECORDING INITIAL SERIES, SECONDARY SERIES, AND PERIOD ENDINGS
In plate 23 is shown the inscription on Stela 3 at Piedras Negras. The
introducing glyph appears in A1 and is followed by the Initial-series
number 9.12.2.0.16 in B1-B3. This number reduced to units of the first
order and counted forward from its starting point will be found to reach
the terminal date 5 Cib 14 Yaxkin, which the student will readily recognize
in A4-B7; the "month-sign indicator" appearing very clearly in A7, with the
coefficient 9 affixed to it. Compare the day sign in A4 with figure 16,
_z_, and the month sign in B7 with figure 19, _k, l_. The Initial Series
recorded in A1-A4, B7 reads, therefore, 9.12.2.0.16 5 Cib 14 Yaxkin. In C1
D1 is recorded the number 0 kins, 10 uinals, and 12 tuns; that is, 12.10.0,
the first of several Secondary Series in this text. Reducing this to units
of the first order and counting it forward from the terminal date of the
Initial Series, 5 Cib 14 Yaxkin, the terminal date of the Secondary Series
will be found to be 1 Cib 14 Kankin, which the student will find recorded
in C2b D2a. The Initial-series value of this latter date may be calculated
as follows:
9.12. 2. 0.16 5 Cib 14 Yaxkin
12.10. 0
9.12.14.10.16 1 Cib 14 Kankin
Following along the text, the next Secondary-series number appears in
D4-C5a and consists of 10 kins,[222] 11 uinals, 1 tun, and 1 katun; that
{234} is, 1.1.11.10. Reducing this number to units of the first order and
counting it forward from the date next preceding it in the text, that is, 1
Cib 14 Kankin in C2b D2a, the new terminal date reached will be 4 Cimi 14
Uo, which the student will find recorded in D5-C6. Compare the day sign in
D5 with figure 16, _h, i_, and the month sign in C6 with figure 19, _b, c_.
The Initial-series value of this new date may be calculated from the known
Initial-series value of the preceding date:
9.12.14.10.16 1 Cib 14 Kankin
1. 1.11.10
9.13.16. 4. 6 4 Cimi 14 Uo
The third Secondary Series appears in E1 and consists of 15 kins,[223] 8
uinals, and 3 tuns, or 3.8.15. Reducing this number to units of the first
order and counting it forward from the date next preceding it in the text,
4 Cimi 14 Uo, in D5-C6, the new terminal date reached will be 11 Imix 14
Yax, which the student will find recorded in E2 F2. The day sign in E2
appears, as is very unusual, as a head variant of which only the headdress
seems to show the essential element of the day sign Imix. Compare E2 with
figure 16, _a, b_, also the month sign in F2 with figure 19, _q, r_. The
Initial Series of this new terminal date may be calculated as above:
9.13.16. 4. 6 4 Cimi 14 Uo
3. 8.15
9.13.19.13. 1 11 Imix 14 Yax
The fourth and last Secondary Series in this text follows in F6 and
consists of 19 kins and 4 uinals, that is, 4.19. Reducing this number to
units of the first order and counting it forward from the date next
preceding it in the text, 11 Imix 14 Yax in E2 F2, the new terminal date
reached will be 6 Ahau 13 Muan, which the student will find recorded in
F7-F8. Compare the month sign in F8 with figure 19, _a' b'_. But the glyph
following this date in F9 is very clearly an ending sign; note the hand,
tassel-like postfix, and subfixial element showing the curl infix, all of
which are characteristic ending elements (see figs. 37, _l-q_, and 54).
Moreover, in F10 is recorded "the end of Katun 14." Compare the ending
prefix in this glyph with figure 37, _a-h_. This would seem to indicate
that the date in F7-F8, 6 Ahau 13 Muan, closed Katun 14 of Cycle 9 of the
Long Count. Whether this be true or not may be tested by finding the
Initial-series value corresponding to 6 Ahau 13 Muan, as above:
9.13.19.13. 1 11 Imix 14 Yax
4.19
9.14. 0. 0. 0 6 Ahau 13 Muan
[Illustration: INITIAL SERIES, SECONDARY SERIES, AND
PERIOD-ENDING DATES ON STELA E (WEST SIDE), QUIRIGUA]
{235} This shows that the date 6 Ahau 13 Muan closed Katun 14, as glyphs
F9-F10 declare. This may also be verified by changing "the end of Katun 14"
recorded in F9-F10 into its corresponding Initial-series value, 9.14.0.0.0,
and solving for the terminal date. The day reached by these calculations
will be 6 Ahau 13 Muan, as above. This text, in so far as it has been
deciphered, therefore reads:
9.12. 2. 0.16 5 Cib 14 Yaxkin A1-A4, B7
12.10. 0 C1 D1
9.12.14.10.16 1 Cib 14 Kankin C2b D2a
1. 1.11.10 D4-C5a
9.13.16. 4. 6 4 Cimi 14 Uo D5-C6
3. 8.15 E1
9.13.19.13. 1 11 Imix 14 Yax E2 F2
4.19 F6
9.14. 0. 0. 0 6 Ahau 13 Muan F7-F8
End of Katun 14 F9-F10
The inscription just deciphered is worthy of special note for several
reasons. In the first place, all its dates and numbers are not only
exceedingly clear, thus facilitating their identification, but also
unusually regular, the numbers being counted forward from the dates next
preceding them to reach the dates next following them in every case; all
these features make this text particularly well adapted for study by the
beginner. In the second place, this inscription shows the three principal
methods employed by the Maya in recording dates, that is, Initial-series
dating, Secondary-series dating, and Period-ending dating, all combined in
the same text, the example of each one being, moreover, unusually good.
Finally, the Initial Series of this inscription records identically the
same date as Stela 1 at Piedras Negras, namely, 9.12.2.0.16 5 Cib 14
Yaxkin. Compare plate 23 with plate 17. Indeed, these two monuments, Stelæ
1 and 3, stand in front of the same building. All things considered, the
inscription on Stela 3 at Piedras Negras is one of the most satisfactory
texts that has been found in the whole Maya territory.