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.
Another example showing the use of these three methods of dating in one and the same text is the inscription on Stela E at Quirigua, illustrated in plate 24 and figure 82.[224] This text begins with the Initial Series on the west side. The introducing glyph appears in A1-B3 and is followed by the Initial-series number 9.14.13[225].4.17 in A4-A6. Reducing this number to units of the first order, remembering the correction in the tun coefficient in A5 noted below, and applying the rules previously given for solving Initial Series, the terminal date {236} reached will be 12 Caban 5 Kayab. This the student will readily recognize in B6-B8b, the form in B8a being the "month sign indicator," here shown with a head-variant coefficient 10. Compare B6 with figure 16, _a', b'_, and B8b with figure 19, _d'-f'_. This Initial Series therefore should read as follows: 9.14.13.4.17 12 Caban 5 Kayab. Following down the text, there is reached in B10b-A11a, a Secondary-series number consisting of 3 kins, 13 uinals, and 6 tuns, that is, 6.13.3. Counting this number forward from the date next preceding it in the text, 12 Caban 5 Kayab, the date reached will be 4 Ahau 13 Yax, which the student will find recorded in B11. Compare the month form in B11b with figure 19, _q, r_. But since the Initial-series value of 12 Caban 5 Kayab is known, the Initial-series value of 4 Ahau 13 Yax may be calculated from it as follows:
9.14.13. 4.17 12 Caban 5 Kayab 6.13. 3 9.15. 0. 0. 0 4 Ahau 13 Yax
[Illustration: FIG. 82. The Initial Series on Stela E (east side), Quirigua.]
The next Secondary-series number appears in B12, plate 24, _B_, and consists of 6 kins, 14 uinals, and 1 tun, that is, 1.14.6.[226] The student will find that all efforts to reach the next date recorded in the text, 6 Cimi 4 Tzec in A13b B13a, by counting forward 1.14.6 from 4 Ahau 13 Yax in B11, the date next preceding this number, will prove unsuccessful. However, by counting _backward_ 1.14.6 from 6 Cimi 4 Tzec, he will find the date from which the count proceeds is 10 Ahau 8 Chen, though this latter date is nowhere recorded in this text. We have seen elsewhere, on Stela F for example (pl. 19, _A, B_), that the date 6 Cimi 4 Tzec corresponded to the Initial-series number 9.15.6.14.6; consequently, we may calculate the position of the unrecorded {237} date 10 Ahau 8 Chen in the Long Count from this known Initial Series, by subtracting[227] 1.14.6 from it:
9.15.6.14.6 6 Cimi 4 Tzec 1.14.6 9.15.5. 0.0 10 Ahau 8 Chen
We now see that there are 5 tuns, that is, 1 hotun, not recorded here, namely, the hotun from 9.15.0.0.0 4 Ahau 13 Yax, to 9.15.5.0.0 10 Ahau 8 Chen, and further, that the Secondary-series number 1.14.6 in B12 is counted from the unexpressed date 10 Ahau 8 Chen to reach the terminal date 6 Cimi 4 Tzec recorded in A13b B13a.
The next Secondary-series number appears in A14b B14 and consists of 15 kins, 16 uinals, 1 tun, and 1 katun, that is, 1.1.16.15. As in the preceding case, however, all efforts to reach the date following this number, 11 Imix 19 Muan in A15b B15a, by counting it forward from 6 Cimi 4 Tzec, the date next preceding it in the text, will prove unavailing. As before, it is necessary to count it _backward_ from 11 Imix 19 Muan to determine the starting point. Performing this operation, the starting point will be found to be the date 7 Cimi 9 Zotz. Since neither of these two dates, 11 Imix 19 Muan and 7 Cimi 9 Zotz, occurs elsewhere at Quirigua, we must leave their corresponding Initial-series values indeterminate for the present.
The last Secondary Series in this text is recorded in A17b B17a and consists of 19 kins,[228] 4 uinals, and 8 tuns. Reducing this number to units of the first order and counting it forward from the date next preceding it in the text, 11 Imix 19 Muan in A15b B15a, the terminal date reached will be 13 Ahau 18 Cumhu, which the student will find recorded in A18. Compare the month sign with figure 19, _g', h'_. But immediately following this date in B18a is Katun 17 and in the upper part of B18b the hand-denoting ending. These glyphs A18 and B18 would seem to indicate, therefore, that Katun 17 came to an end on the date 13 Ahau 18 Cumhu. That they do, may be proved beyond all doubt by changing this period ending into its corresponding Initial-series number 9.17.0.0.0 and solving for the terminal date. This will be found to be 13 Ahau 18 Cumhu, which is recorded in A18. This latter date, therefore, had the following position in the Long Count: 9.17.0.0.0 13 Ahau 18 Cumhu. But having determined the position of this latter date in the Long Count, that is, its Initial-series value, it is now possible to fix the positions of the two dates 11 Imix 19 Muan and 7 Cimi 9 Zotz, which we were obliged to leave indeterminate above. Since the date 13 Ahau 18 Cumhu was derived {238} by counting forward 8.4.19 from 11 Imix 19 Muan, the Initial-series value of the latter may be calculated by subtracting 8.4.19 from the Initial-series value of the former:
9.17. 0. 0. 0 13 Ahau 18 Cumhu 8. 4.19 9.16.11.13. 1 11 Imix 19 Muan
And since the date 11 Imix 19 Muan was reached by counting forward 1.1.16.15 from 7 Cimi 9 Zotz, the Initial-series value of the latter may be calculated by subtracting 1.1.16.15 from the now known Initial-series value of the former:
9.16.11.13. 1 11 Imix 19 Muan 1. 1.16.15 9.15. 9.14. 6 7 Cimi 9 Zotz
Although this latter date is not recorded in the text, the date next preceding the number 1.1.16.15 is 6 Cimi 4 Tzec, which corresponded to the Initial Series 9.15.6.14.6 6 Cimi 4 Tzec, as we have seen, a date which was exactly 3 tuns earlier than 7 Cimi 9 Zotz, 9.15.9.14.6 - 9.15.6.14.6 = 3.0.0.
The inscription on the west side closes then in A18 B18 with the record that Katun 17 ended on the date 13 Ahau 18 Cumhu. The inscription on the east side of this same monument opens with this same date expressed as an Initial Series, 9.17.0.0.0 13 Ahau 18 Cumhu. See figure 82, A1-A6, A7,[229] and A10.
The reiteration of this date as an Initial Series, when its position in the Long Count had been fixed unmistakably on the other side of the same monument by its record as a Period-ending date, together with the fact that it is the latest date recorded in this inscription, very clearly indicates that it alone designated the contemporaneous time of Stela E, and hence determines the fact that Stela E was a hotun-marker. This whole text, in so far as deciphered, reads as follows:
West side: 9.14.13.[230]4.17 12 Caban 5 Kayab Plate 24, _A_, A1-B5, B8b 6. 13. 3 Plate 24, _A_, B10b-A11a 9.15. 0. 0. 0 4 Ahau 13 Yax Plate 25, _A_, B11 [5. 0. 0] Undeclared 9.15. 5. 0. 0 10 Ahau 8 Chen " 1. 14. 6 Plate 24, _B_, B12 9.15. 6. 14. 6 6 Cimi 4 Tzec Plate 24, _B_, A13b, B13a [3. 0. 0] Undeclared {239} 9.15. 9. 14. 6 7 Cimi 9 Zotz " 1. 1. 16.15 Plate 24, _B_, A14b B14 9.16.11. 13. 1 11 Imix 19 Muan Plate 24, _B_, A15b B15a 8. 4.19 Plate 24, _B_, A17b B17a 9.17. 0. 0. 0 13 Ahau 18 Cumhu Plate 24, _B_, A18 End of Katun 17 Plate 24, _B_, B18 East side: 9.17. 0. 0. 0 13 Ahau 18 Cumhu Figure 82, A1-A6, A7, A10
Comparing the summary of the inscription on Stela E at Quirigua, just given, with the summaries of the inscriptions on Stelæ J and F, and Zoömorph G, at the same city, all four of which are shown side by side in Table XVII,[231] the interrelationship of these four monuments appears very clearly.
TABLE XVII. INTERRELATIONSHIP OF DATES ON STELÆ E, F, AND J AND ZOÖMORPH G, QUIRIGUA
Date Stela J Stela F Stela E Zoömorph G 9.14.13. 4.17 12 Caban 5 Kayab X X X X 9.15. 0. 0. 0 4 Ahau 13 Yax - X X - 9.15. 5. 0. 0 10 Ahau 8 Chen X - X - 9.15. 6.14. 6 6 Cimi 4 Tzec X X X X 9.15. 9.14. 6 7 Cimi 9 Zotz - - X - 9.15.10. 0. 0 3 Ahau 3 Mol - X - - 9.16. 5. 0. 0 8 AHAU 8 ZOTZ X - - - 9.16.10. 0. 0 1 AHAU 8 ZIP - X - - 9.16.11.13. 1 11 Imix 19 Muan - - X - 9.17. 0. 0. 0 13 AHAU 18 CUMHU - - X - 9.17.15. 0. 0 5 AHAU 3 MUAN - - - X
In spite of the fact that each one of these four monuments marks a different hotun in the Long Count, and consequently dates from a different period, all of them go back to the same date, 9.14.13.4.17 12 Caban 5 Kayab, as their original starting point (see above). This date would almost certainly seem, therefore, to indicate some very important event in the annals of Quirigua. Moreover, since it is the earliest date found at this city which can reasonably be regarded as having occurred during the actual occupancy of the site, it is not improbable that it may represent, as explained elsewhere, the time at which Quirigua was founded.[232] It is necessary, however, to {240} caution the student that the above explanation of the date 9.14.13.4.17 12 Caban 5 Kayab, or indeed any other for that matter, is in the present state of our knowledge entirely a matter of conjecture.
Passing on, it will be seen from Table XVII that two of the monuments, namely, Stelæ E and F, bear the date 9.15.0.0.0 4 Ahau 3 Yax, and two others, Stelæ E and J, the date 9.15.5.0.0 10 Ahau 8 Chen, one hotun later. All four come together again, however, with the date 9.15.6.14.6 6 Cimi 4 Tzec, which is recorded on each. This date, like 9.14.13.4.17 12 Caban 5 Kayab, designates probably another important event in Quirigua history, the nature of which, however, again escapes us. After the date 9.15.6.14.6 6 Cimi 4 Tzec, these monuments show no further correspondences, and we may pass over the intervening time to their respective closing dates with but scant notice, with the exception of Zoömorph G, which records a half dozen dates in the hotun that it marks, 9.17.15.0.0 5 Ahau 3 Muan. (These latter are omitted from Table XVII.)
This concludes the presentation of Initial-series, Secondary-series, and Period-ending, dating, with which the student should be sufficiently familiar by this time to continue his researches independently.
It was explained (see p. 76) that, when a Secondary-series date could not be referred ultimately to either an Initial-series date or a Period-ending date, its position in the Long Count could not be determined with certainty, and furthermore that such a date became merely one of the 18,980 dates of the Calendar Round and could be fixed only within a period of 52 years. A few examples of Calendar-round dating are given in figure 83 and plate 25. In figure 83, A, is shown a part of the inscription on Altar M at Quirigua.[233] In A1 B1 appears a number consisting of 0 kins, 2 uinals, and 3 tuns, that is, 3.2.0, and following this in A2b B2, the date 4 Ahau 13 Yax, and in A3b B3 the date 6 Ahau 18 Zac. Compare the month glyphs in B2 and B3 with _q_ and _r_, and _s_ and _t_, respectively, of figure 19. This has every appearance of being a Secondary Series, one of the two dates being the starting point of the number 3.2.0, and the other its terminal date. Reducing 3.2.0 to units of the first order, we have:
B1 = 3 × 360 = 1,080 A1 = 2 × 20 = 40 A1 = 0 × 1 = 0 ----- 1,120
[Illustration: CALENDAR-ROUND DATES ON ALTAR 5, TIKAL]
{241}
Counting this number forward from 4 Ahau 13 Yax, the nearest date to it in the text, the terminal date reached will be found to be 6 Ahau 18 Zac, the date which, we have seen, was recorded in A3b B3. It is clear, therefore, that this text records the fact that 3.2.0 has been counted forward from the date 4 Ahau 13 Yax and the date 6 Ahau 18 Zac has been reached, but there is nothing given by means of which the position of either of these dates in the Long Count can be determined; consequently either of these dates will be found recurring like any other Calendar-round date, at intervals of every 52 years. In such cases the first assumption to be made is that one of the dates recorded the close of a hotun, or at least of a tun, in Cycle 9 of the Long Count. The reasons for this assumption are quite obvious.
[Illustration: FIG. 83. Calendar-round dates: _A_, Altar M, Quirigua; _B_, Altar Z, Copan.]
The overwhelming majority of Maya dates fall in Cycle 9, and nearly all inscriptions have at least one date which closed some hotun or tun of that cycle. Referring to Goodman's Tables, in which the tun endings of Cycle 9 are given, the student will find that the date 4 Ahau 13 Yax occurred as a tun ending in Cycle 9, at 9.15.0.0.0 4 Ahau 13 Yax, in which position it closed not only a hotun but also a katun. Hence, it is probable, although the fact is not actually recorded, that the Initial-series value of the date 4 Ahau 13 Yax in this text is 9.15.0.0.0 4 Ahau 13 Yax, and if this is so the Initial-series value of the date 6 Ahau 18 Zac will be:
9.15.0.0.0 4 Ahau 13 Yax 3.2.0 9.15.3.2.0 6 Ahau 18 Zac
{242} In the case of this particular text the Initial-series value 9.15.0.0.0 might have been assigned to the date 4 Ahau 13 Yax on the ground that this Initial-series value appears on two other monuments at Quirigua, namely, Stelæ E and F, with this same date.
In figure 83, _B_, is shown a part of the inscription from Altar Z at Copan.[234] In A1 B1 appears a number consisting of 1 kin, 8 uinals, and 1 tun, that is, 1.8.1, and following this in B2-A3 is the date 13 Ahau 18 Cumhu, but no record of its position in the Long Count. If 13 Ahau 18 Cumhu is the terminal date of the number 1.8.1, the starting point can be calculated by counting this number backward, giving the date 12 Cauac 2 Zac. On the other hand, if 13 Ahau 18 Cumhu is the starting point, the terminal date reached by counting 1.8.1 forward will be 1 Imix 9 Mol. However, since an ending prefix appears just before the date 13 Ahau 18 Cumhu in A2 (compare fig. 37, _a-h_), and since another, though it must be admitted a very unusual ending sign, appears just after this date in A3 (compare the prefix of B3 with the prefix of fig. 37, _o_, and the subfix with the subfixes of _l-n_ and _q_ of the same figure), it seems probable that 13 Ahau 18 Cumhu is the terminal date and also a Period-ending date. Referring to Goodman's Tables, it will be found that the only tun in Cycle 9 which ended with the date 13 Ahau 18 Cumhu was 9.17.0.0.0 13 Ahau 18 Cumhu, which not only ended a hotun but a katun as well.[235] If this is true, the unrecorded starting point 12 Cauac 2 Zac can be shown to have the following Initial-series value:
9.17. 0.0. 0 13 Ahau 18 Cumhu 1.8. 1 Backward 9.16.18.9.19 12 Cauac 2 Zac
In each of the above examples, as we have seen, there was a date which ended one of the katuns of Cycle 9, although this fact was not recorded in connection with either. Because of this fact, however, we were able to date both of these monuments with a degree of probability amounting almost to certainty. In some texts the student will find that the dates recorded did not end any katun, hotun, or even tun, in Cycle 9, or in any other cycle, and consequently such dates can not be assigned to their proper positions in the Long Count by the above method.
The inscription from Altar 5 at Tikal figured in plate 25 is a case in point. This text opens with the date 1 Muluc 2 Muan in glyphs 1 and 2 (the first glyph or starting point is indicated by the star). {243} Compare glyph 1 with figure 16, _m_, _n_, and glyph 2 with figure 19, _a', b'_. In glyphs 8 and 9 appears a Secondary-series number consisting of 18 kins, 11 uinals, and 11 tuns (11.11.18). Reducing this number to units of the first order and counting it forward from the date next preceding it in the text, 1 Muluc 2 Muan in glyphs 1 and 2, the terminal date reached will be 13 Manik 0 Xul, which the student will find recorded in glyphs 10 and 11. Compare glyph 10 with figure 16, _j_, and glyph 11 with figure 19, _i, j_. The next Secondary-series number appears in glyphs 22 and 23, and consists of 19 kins, 9 uinals, and 8 tuns (8.9.19). Reducing this to units of the first order and counting forward from the date next preceding it in the text, 13 Manik 0 Xul in glyphs 10 and 11, the terminal date reached will be 11 Cimi 19 Mac, which the student will find recorded in glyphs 24 and 25. Compare glyph 24 with figure 16, _h, i_, and glyph 25 with figure 19, _w_, _x_. Although no number appears in glyph 26, there follows in glyphs 27 and 28 the date 1 Muluc 2 Kankin, which the student will find is just three days later than 11 Cimi 19 Mac, that is, one day 12 Manik 0 Kankin, two days 13 Lamat 1 Kankin, and three days 1 Muluc 2 Kankin.
In spite of the fact that all these numbers are counted regularly from the dates next preceding them to reach the dates next following them, there is apparently no glyph in this text which will fix the position of any one of the above dates in the Long Count. Moreover, since none of the day parts show the day sign Ahau, it is evident that none of these dates can end any uinal, tun, katun, or cycle in the Long Count, hence their positions can not be determined by the method used in fixing the dates in figure 83, _A_ and _B_.
There is, however, another method by means of which Calendar-round dates may sometimes be referred to their proper positions in the Long Count. A monument which shows only Calendar-round dates may be associated with another monument or a building, the dates of which are fixed in the Long Count. In such cases the fixed dates usually will show the positions to which the Calendar-round dates are to be referred.
Taking any one of the dates given on Altar 5 in plate 25, as the last, 1 Muluc 2 Kankin, for example, the positions at which this date occurred in Cycle 9 may be determined from Goodman's Tables to be as follows:
9. 0.16. 5.9 1 Muluc 2 Kankin 9. 3. 9. 0.9 1 Muluc 2 Kankin 9. 6. 1.13.9 1 Muluc 2 Kankin 9. 8.14. 8.9 1 Muluc 2 Kankin 9.11. 7. 3.9 1 Muluc 2 Kankin 9.13.19.16.9 1 Muluc 2 Kankin 9.16.12.11.9 1 Muluc 2 Kankin 9.19. 5. 6.9 1 Muluc 2 Kankin
{244} Next let us ascertain whether or not Altar 5 was associated with any other monument or building at Tikal, the date of which is fixed unmistakably in the Long Count. Says Mr. Teobert Maler, the discoverer of this monument:[236] "A little to the north, fronting the north side of this second temple and very near it, is a masonry quadrangle once, no doubt, containing small chambers and having an entrance to the south. In the middle of this quadrangle stands Stela 16 in all its glory, still unharmed, _and in front of it, deeply buried in the earth, we found Circular Altar 5_, which was destined to become so widely renowned." It is evident from the foregoing that the altar we are considering here, called by Mr. Maler "Circular Altar 5," was found in connection with another monument at Tikal, namely, Stela 16. But the date on this latter monument has already been deciphered as "6 Ahau 13 Muan ending Katun 14" (see pl. 21, _D_; also p. 224), and this date, as we have seen, corresponded to the Initial Series 9.14.0.0.0 6 Ahau 13 Muan.
Our next step is to ascertain whether or not any of the Initial-series values determined above as belonging to the date 1 Muluc 2 Kankin on Altar 5 are near the Initial Series 9.14.0.0.0 6 Ahau 13 Muan, which is the Initial-series date corresponding to the Period-ending date on Stela 16. By comparing 9.14.0.0.0 with the Initial-series values of 1 Muluc 2 Kankin given above the student will find that the fifth value, 9.13.19.16.9, corresponds with a date 1 Muluc 2 Kankin, which was only 31 days (1 uinal and 11 kins) earlier than 9.14.0.0.0 6 Ahau 13 Muan. Consequently it may be concluded that 9.13.19.16.9 was the particular day 1 Muluc 2 Kankin which the ancient scribes had in mind when they engraved this text. From this known Initial-series value the Initial-series values of the other dates on Altar 5 may be obtained by calculation. The texts on Altar 5 and Stela 16 are given below to show their close connection:
_Altar 5_
9.12.19.12. 9 1 Muluc 2 Muan glyphs 1 and 2 11.11.18 glyphs 8 and 9 9.13.11. 6. 7 13 Manik 0 Xul glyphs 10 and 11 8. 9.19 glyphs 22 and 23 9.13.19.16. 6 11 Cimi 19 Mac glyphs 24 and 25 (3) undeclared 9.13.19.16. 9 1 Muluc 2 Kankin glyphs 27 and 28 (1.11) (Time between the two monuments, 31 days.)
_Stela 16_
9.14.0.0.0 6 Ahau 13 Muan A1-A4
Sometimes, however, monuments showing Calendar-round dates stand {245} alone, and in such cases it is almost impossible to fix their dates in the Long Count. At Yaxchilan in particular Calendar-round dating seems to have been extensively employed, and for this reason less progress has been made there than elsewhere in deciphering the inscriptions.
ERRORS IN THE ORIGINALS
Before closing the presentation of the subject of the Maya inscriptions the writer has thought it best to insert a few texts which show actual errors in the originals, mistakes due to the carelessness or oversight of the ancient scribes.
[Illustration: FIG. 84. Texts showing actual errors in the originals: _A_, Lintel, Yaxchilan; _B_, Altar Q, Copan; _C_, Stela 23, Naranjo.]
Errors in the original texts may be divided into two general classes: (1) Those which are revealed by inspection, and (2) those which do not appear until after the indicated calculations have been made and the results fail to agree with the glyphs recorded.
An example of the first class is illustrated in figure 84, _A_. A very cursory inspection of this text--an Initial Series from a lintel at Yaxchilan--will show that the uinal coefficient in C1 represents an impossible condition from the Maya point of view. This glyph as it stands {246} unmistakably records 19 uinals, a number which had no existence in the Maya system of numeration, since 19 uinals are always recorded as 1 tun and 1 uinal.[237] Therefore the coefficient in C1 is incorrect on its face, a fact we have been able to determine before proceeding with the calculation indicated. If not 19, what then was the coefficient the ancient scribe should have engraved in its place? Fortunately the rest of this text is unusually clear, the Initial-series number 9.15.6.?.1 appearing in B1-D1, and the terminal date which it reaches, 7 Imix 19 Zip, appearing in C2 D2. Compare C2 with figure 16, _a, b_, and D2 with figure 19, d. We know to begin with that the uinal coefficient must be one of the eighteen numerals 0 to 17, inclusive. Trying 0 first, the number will be 9.15.6.0.1, which the student will find leads to the date 7 Imix 4 Chen. Our first trial, therefore, has proved unsuccessful, since the date recorded is 7 Imix 19 Zip. The day parts agree, but the month parts are not the same. This month part 4 Chen is useful, however, for one thing, it shows us how far distant we are from the month part 19 Zip, which is recorded. It appears from Table XV that in counting forward from position 4 Chen just 260 days are required to reach position 19 Zip. Consequently, our first trial number 9.15.6.0.1 falls short of the number necessary by just 260 days. But 260 days are equal to 13 uinals; therefore we must increase 9.15.6.0.1 by 13 uinals. This gives us the number 9.15.6.13.1. Reducing this to units of the first order and solving for the terminal date, the date reached will be 7 Imix 19 Zip, which agrees with the date recorded, in C2 D2. We may conclude, therefore, that the uinal coefficient in C1 should have been 13, instead of 19 as recorded.
Another error of the same kind--that is, one which may be detected by inspection--is shown in figure 84, _B_. Passing over glyphs 1, 2, and 3, we reach in glyph 4 the date 5 Kan 13 Uo. Compare the upper half of 4 with figure 16, _f_, and the lower half with figure 19, _b, c_. The coefficient of the month sign is very clearly 13, which represents an impossible condition when used to indicate the position of a day whose name is Kan; for, according to Table VII, the only positions which the day Kan can ever occupy in any division of the year are 2, 7, 12, and 17. Hence, it is evident that we have detected an error in this text before proceeding with the calculations indicated. Let us endeavor to ascertain the coefficient which should have been used with the month sign in glyph 4 instead of the 13 actually recorded. These glyphs present seemingly a regular Secondary Series, the starting point being given in 1 and 2, the number in 3, and the terminal date in 4. Counting this number 3.4 forward from the starting point, 6 Ahau 13 Kayab, the terminal date reached will be 5 Kan 12 Uo. Comparing this with the terminal date actually recorded, we find that the two agree except for the month coefficient. But since the date recorded represents an impossible condition, as we {247} have shown, we are justified in assuming that the month coefficient which should have been used in glyph 4 was 12, instead of 13. In other words, the craftsman to whom the sculpturing of this inscription was intrusted engraved here 3 dots instead of 2 dots, and 1 ornamental crescent, which, together with the 2 bars present, would have given the month coefficient determined by calculation, 12. An error of this kind might occur very easily and indeed in many cases may be apparent rather than real, being due to weathering rather than to a mistake in the original text.
Some errors in the inscriptions, however, can not be detected by inspection, and develop only after the calculations indicated have been performed, and the results are found to disagree with the glyphs recorded. Errors of this kind constitute the second class mentioned above. A case in point is the Initial Series on the west side of Stela E at Quirigua, figured in plate 24, _A_. In this text the Initial-series number recorded in A4-A6 is very clearly 9.14.12.4.17, and the terminal date in B6-B8b is equally clearly 12 Caban 5 Kayab. Now, if this number 9.14.12.4.17 is reduced to units of the first order and is counted forward from the same starting point as practically all other Initial Series, the terminal date reached will be 3 Caban 10 Kayab, not 12 Caban 5 Kayab, as recorded. Moreover, if the same number is counted forward from the date 4 Ahau 8 Zotz, which may have been another starting point for Initial Series, as we have seen, the terminal date reached will be 3 Caban 10 Zip, not 12 Caban 5 Kayab, as recorded. The inference is obvious, therefore, that there is some error in this text, since the number recorded can not be made to reach the date recorded. An error of this kind is difficult to detect, because there is no indication in the text as to which glyph is the one at fault. The first assumption the writer makes in such cases is that the date is correct and that the error is in one of the period-glyph coefficients. Referring to Goodman's Table, it will be found that the date 12 Caban 5 Kayab occurred at the following positions in Cycle 9 of the Long Count:
9. 1. 9.11.17 12 Caban 5 Kayab 9. 4. 2. 6.17 12 Caban 5 Kayab 9. 6.15. 1.17 12 Caban 5 Kayab 9. 9. 7.14.17 12 Caban 5 Kayab 9.12. 0. 9.17 12 Caban 5 Kayab 9.14.13. 4.17 12 Caban 5 Kayab 9.17. 5.17.17 12 Caban 5 Kayab 9.19.18.12.17 12 Caban 5 Kayab
An examination of these values will show that the sixth in the list, 9.14.13.4.17, is very close to the number recorded in our text, 9.14.12.4.17. Indeed, the only difference between the two is that the former has 13 tuns while the latter has only 12. The similarity between these two numbers is otherwise so close and the error in this {248} event would be so slight--the record of 2 dots and 1 ornamental crescent instead of 3 dots--that the conclusion is almost inevitable that the error here is in the tun coefficient, 12 having been recorded instead of 13. In this
## particular case the Secondary Series and the Period-ending date, which
follow the Initial-series number 9.14.12.4.17, prove that the above reading of 13 tuns for the 12 actually recorded is the one correction needed to rectify the error in this text.
Another example indicating an error which can not be detected by inspection is shown in figure 84, _C_. In glyphs 1 and 2 appears the date 8 Eznab 16 Uo (compare glyph 1 with fig. 16, _c'_, and glyph 2 with fig. 19, _b, c_). In glyph 3 follows a number consisting of 17 kins and 4 uinals (4.17). Finally, in glyphs 4 and 5 is recorded the date 2 Men 13 Yaxkin (compare glyph 4 with fig. 16, _y_, and glyph 5 with fig. 19, _k, l_). This has every appearance of being a Secondary Series, of which 8 Eznab 16 Uo is the starting point, 4.17, the number to be counted, and 2 Men 13 Yaxkin the terminal date. Reducing 4.17 to units of the first order and counting it forward from the starting point indicated, the terminal date reached will be 1 Men 13 Yaxkin. This differs from the terminal date recorded in glyphs 4 and 5 in having a day coefficient of 1 instead of 2. Since this involves but a very slight change in the original text, we are probably justified in assuming; that the day coefficient in glyph 4 should have been 1 instead of 2 as recorded.
One more example will suffice to show the kind of errors usually encountered in the inscriptions. In plate 26 is figured the Initial Series from Stela N at Copan. The introducing glyph appears in A1 and is followed by the Initial-series number 9.16.10.0.0 in A2-A6, all the coefficients of which are unusually clear. Reducing this to units of the first order and solving for the terminal date, the date reached will be 1 Ahau 3 Zip. This agrees with the terminal date recorded in A7-A15 except for the month coefficient, which is 8 in the text instead of 3, as determined by calculation. Assuming that the date recorded is correct and that the error is in the coefficient of the period glyphs the next step is to find the positions in Cycle 9 at which the date 1 Ahau 8 Zip occurred. Referring to Goodman's Tables, these will be found to be:
9. 0. 8.11.0 1 Ahau 8 Zip 9. 3. 1. 6.0 1 Ahau 8 Zip 9. 5.14. 1.0 1 Ahau 8 Zip 9. 8. 6.14.0 1 Ahau 8 Zip 9.10.19. 9.0 1 Ahau 8 Zip 9.13.12. 4.0 1 Ahau 8 Zip 9.16. 4.17.0 1 Ahau 8 Zip 9.18.17.12.0 1 Ahau 8 Zip
[Illustration: INITIAL SERIES ON STELA N, COPAN, SHOWING ERROR IN MONTH COEFFICIENT]
{249} The number in the above list coming nearest to the number recorded in this text (9.16.10.0.0) is the next to the last, 9.16.4.17.0. But in order to reach this value of the date 1 Ahau 8 Zip (9.16.4.17.0) with the number actually recorded, two considerable changes in it are first necessary, (1) replacing the 10 tuns in A4 by 4 tuns, that is, changing 2 bars to 4 dots, and (2) replacing 0 uinals in A5 by 17 uinals, that is, changing the 0 sign to 3 bars and 2 dots. But these changes involve a very considerable alteration of the original, and it seems highly improbable, therefore, that the date here _intended_ was 9.16.4.17.0 1 Ahau 8 Zip. Moreover, as any other number in the above list involves at least three changes of the number recorded in order to reach 1 Ahau 8 Zip, we are forced to the conclusion that the error must be in the terminal date, not in one of the coefficients of the period glyphs. Let us therefore assume in our next trial that the Initial-series number is correct as it stands, and that the error lies somewhere in the terminal date. But the terminal date reached in counting 9.16.10.0.0 forward in the Long Count will be 1 Ahau 3 Zip, as we have seen on the preceding page, and this date differs from the terminal date recorded by 5--1 bar in the month coefficient. It would seem probable, therefore, that the bar to the left of the month sign in A15 should have been omitted, in which case the text would correctly record the date 9.16.10.0.0 1 Ahau 3 Zip.
The student will note that in all the examples above given the errors have been in the numerical coefficients, and not in the signs to which they are attached; in other words, that although the numerals are sometimes incorrectly recorded, the period, day, and month glyphs never are.
Throughout the inscriptions, the exceptions to this rule are so very rare that the beginner is strongly advised to disregard them altogether, and to assume when he finds an incorrect text that the error is in one of the numerical coefficients. It should be remembered also in this connection that errors in the inscriptions are exceedingly rare, and a glyph must not be condemned as incorrect until every effort has been made to explain it in some other way.
This concludes the presentation of texts from the inscriptions. The student will have noted in the foregoing examples, as was stated in