Front matter (continued 6)
Reading edition
A3 = 9 × 144,000 = 1,296,000
B3 = 17 × 7,200 = 122,400
A4 = 5 × 360 = 4,680
B4 = 0 × 20 = 1,800
A5 = 0 × 1 = 0
————
1,420,200
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 day reached will be found to be 6 Ahau 13 Kayab.
In B5 the profile variant of the day sign, Ahau, is clearly recorded (fig. 16, h', i'), and to it is attached a head-variant numeral. Comparing this with the head-variant numerals in figures 51-53, the student will have little difficulty in identifying it as the head for 6 (see fig. 51, t-v). Note the so-called "hatchet eye" in A5, which is the determining characteristic of the head for 6 (see p. 99). Passing over A6 B6, A7 B7, A8 B8, we reach in A9 the closing glyph of the Supplementary Series, here showing the head-variant coefficient 10 (see fig. 52, m-r). In B9, the next glyph, is recorded the month 13 Kayab (see fig. 19, d'-f'). The whole Initial Series therefore reads 9.17.5.0.0 6 Ahau 13 Kayab.
All the Initial Series heretofore presented have had normal-form numerals with the exception of an incidental head-variant number here and there. By this time the student should have become thoroughly familiar with the use of bar and dot numerals in the inscriptions and should be ready for the presentation of texts showing head-variant numerals, a more difficult group of glyphs to identify.
In plate 12, A, is figured the Initial Series on the tablet from the Temple of the Foliated Cross at Palenque.[151] The introducing glyph appears in A1 B2, and is followed by the Initial-series number in A3-B7. The student will have little difficulty in identifying the heads in B3, B4, B5, B6, and B7 as the head variants for the cycle, katun, tun, uinal, and kin, respectively. The head in A3 prefixed to the cycle glyph in B3 has for its determining characteristic the forehead ornament composed of more than one part (here, of two parts). As explained on page 97, this is the essential element of the head for 1. Compare A3 with figure 51, a-e, and the two glyphs will be found to be identical. We may conclude, therefore, that in place of the usual 9 cycles heretofore encountered in Initial Series, we have recorded in A3-B3 1 cycle.[152] The katun coefficient in A4 resembles closely the cycle coefficient except that its forehead ornament is composed of but a single part, a large curl. As explained on page 97, the heads for 1 and 8 are very similar, and are to be distinguished from each other only by their forehead ornaments, the former having a forehead ornament composed of more than one part, as in A3, and the latter a forehead ornament composed of but one part, as here in A4. This head, moreover, is very similar to the head for 8 in figure 52, a-f; indeed, the only difference is that the former has a fleshless lower jaw. This is the essential element of the head for 10 (see p. 100); when applied to the head for any other numeral it increases the value of the resulting head by 10. Therefore we have recorded in A4 B4, 18 (8 + 10) katuns. The tun coefficient in A5 has for its determining characteristic the tun headdress, which, as explained on page 99, is the essential element of the head for 5 (see fig. 51, n-s). Therefore A5 represents 5, and A5 B5, 5 tuns. The uinal coefficient in A6 has for its essential elements the large bulging eye, square irid, and snaglike front tooth. As stated on page 98, these characterize the head for 4, examples of which are given in figure 51, j-m. Consequently, A6 B6 records 4 uinals. The kin coefficient in A7 is quite clearly 0. The student will readily recognize the clasped hand, which is the determining characteristic of the 0 head (see p. 101 and fig. 53, s-w). The number recorded in A3-B7 is, therefore, 1.18.5.4.0. Reducing this number to units of the 1st order by means of Table XIII, we obtain:
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 12
GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF HEAD-VARIANT NUMERALS AND PERIOD GLYPHS
A3B3 = 1 × 144,000 = 144,000
A4B4 = 18 × 7,200 = 129,600
A5B5 = 5 × 360 = 1,800
A6B6 = 4 × 20 = 80
A7B7 = 0 × 1 = 0
————
275,480
Deducting from this number all the Calendar Rounds possible, 14 (see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), the terminal date reached will be 1 Ahau 13 Mac. Of this date, the day part, 1 Ahau, is recorded very clearly in A8 B8. Compare the head in A8 with the head in A3, which, we have seen, stood for 1 and also with figure 51, a-e, and the head in B8 with figure 16, h', i', the profile head for the day sign Ahau. This text is irregular in that the month glyph follows immediately the day glyph, i.e., in A9. The glyph in A9 has a coefficient 13, which agrees with the month coefficient determined by calculation, and a comparison of B9 with the forms for the months in figure 19 shows that the month Mac (fig. 19, w, x) is here recorded. The whole Initial Series therefore reads 1.18.5.4.0 1 Ahau 13 Mac.
In plate 12, B, is figured the Initial Series on the tablet from the Temple of the Sun at Palenque.[153] The introducing glyph appears in A1-B2 and is followed by the Initial-series number in A3-B7. The student will have no difficulty in identifying the period glyphs in B3, B4, B5, B6, and B7; and the cycle, katun, and tun coefficients in A3, A4, and A5, respectively, will be found to be exactly like the corresponding coefficients in the preceding Initial Series (pl. 12, A, A3, A4, A5), which, as we have seen, record the numbers 1, 18, and 5, respectively. The uinal coefficient in A6, however, presents a new form. Here the determining characteristic is the banded headdress, or fillet, which distinguishes the head for 3, as explained on page 98 (see fig. 51 h, i). We have then in A6 B6 record of 3 uinals. The kin coefficient in A7 is very clearly 6. Note the "hatchet eye," which, as explained on page 99, is the essential element of this head numeral, and also compare it with figure 51, t-v. The number recorded in A3-B7 therefore is 1.18.5.3.6. Reducing this to units of the first order by means of Table XIII, we obtain:
A3B3 = 1 × 144,000 = 144,000
A4B4 = 18 × 7,200 = 129,600
A5B5 = 5 × 360 = 1,800
A6B6 = 3 × 20 = 60
A7B7 = 6 × 1 = 6
————
275,466
Deducting from this number all the Calendar Rounds possible, 14 (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 13 Cimi 19 Ceh. If this inscription is regular, the day part of the above date should follow in A8 B8, the former expressing the coefficient and the latter the day sign. Comparing A8 with the head numerals in figures 51-53, it will be found to be like the second variant for 13 in figure 52, x-b', the essential element of which seems to be the pendulous nose surmounted by a curl, the protruding mouth fang, and the large bulging eye. Comparing the glyph in B8 with the day signs in figure 16, it will be seen that the form here recorded is the day sign Cimi (fig. 16, h, i). Therefore A8 B8 expresses the day 13 Cimi. The month glyph is recorded very irregularly in this text, since it occurs neither immediately after the Supplementary Series or the day sign, but the second glyph after the day sign, in B9. A comparison of this form with figure 19, u-v, shows that the month Ceh is recorded here. The coefficient is 19. Why the glyph in A9 should stand between the day and its month glyph is unknown; this case constitutes one of the many unsolved problems in the study of the Maya glyphs. This whole Initial Series reads 1.18.5.3.6 13 Cimi 19 Ceh.
The student will note that this Initial Series records a date 14 days earlier than the preceding Initial Series (pl. 12, A). That two dates should be recorded which were within 14 days of each other, and yet were more than 3,000 years earlier than practically all other Maya dates, is a puzzling problem. These two Initial Series from the Temple of the Sun and that of the Foliated Cross at Palenque, together with a Secondary-series date from the Temple of the Cross in the same city, have been thoroughly reviewed by Mr. Bowditch (1906). The conclusions he reaches and the explanation he offers to account for the occurrence of three dates so remote as these are very reasonable, and, the writer believes, will be generally accepted by Maya students.
Fig. 69. Initial Series showing head-variant numerals and period glyphs: A, House C of the Palace Group at Palenque; B, Stela P at Copan.
In figure 69, A, is shown the Initial Series inscribed on the rises and treads of the stairway leading to House C in the Palace at Palenque.[154] The introducing glyph is recorded in A1, and the Initial-series number follows in B1-B3. The student will readily recognize the period glyphs in B1b, A2b, B2b, A3b, and B3b. The head expressing the cycle coefficient in B1a has for its essential element the dots centering around the corner of the mouth. As explained on page 100, this characterizes the head for 9 (see fig. 52, g-l, where variants for the 9 head are figured). In B1, therefore, we have recorded 9 cycles, the number almost always found in Initial Series as the cycle coefficient. The essential element of the katun coefficient in A2a is the forehead ornament composed of a single part. This denotes the head for 8 (see p. 100, and fig. 52, a-f; also compare A2a with the heads denoting 18 in the two preceding examples, pl. 12, A, A4, and pl. 12, B, A4, each of which shows the same forehead ornament). The tun coefficient in B2a is exactly like the cycle coefficient just above it in B1a; that is, 9, having the same dotting of the face near the corner of the mouth. The uinal coefficient in A3a is 13. Compare this head numeral with A8, plate 12, B, which also denotes 13, and also with figure 52, x-b'. The essential elements (see p. 101) are the large pendulous nose surmounted by a curl, the bulging eye, and the mouth fang, the last mentioned not appearing in this case. Since the kin coefficient in B3a is somewhat effaced, let us call it 0 for the present[155] and proceed to reduce our number 9.8.9.13.0 to units of the first order by means of Table XIII:
B1 = 9 × 144,000 = 1,296,000
A2 = 8 × 7,200 = 57,600
B2 = 9 × 360 = 3,240
A3 = 13 × 20 = 260
B3 = 0 × 1 = 0
————
1,357,100
Deducting from this number all the Calendar Rounds possible, 71 (see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to the remainder, we reach as the terminal date 8 Ahau 13 Pop. Now let us examine the text and see what is the terminal date actually recorded. In A4b the student will have little difficulty in recognizing the profile variant of the day sign Ahau (see fig. 16, h', i'). This at once gives us the missing value for the kin coefficient in B3, for the day Ahau can never be reached in an Initial Series if the kin coefficient is other than 0. Similarly, the day Imix can never be reached in Initial Series if the kin coefficient is other than 1, etc. Every one of the 20 possible kin coefficients, 0 to 19, has a corresponding day to which it will always lead, that is, Ahau to Cauac, respectively (see Table I). Thus, if the kin coefficient in an Initial-series number were 5, for example, the day sign of the resulting terminal date must be Chicchan, since Chicchan is the fifth name after Ahau in Table I. Thus the day sign in Initial-series terminal dates may be determined by inspection of the kin coefficient as well as by rule 2 (p. 140), though, as the student will see, both are applications of the same principle, that is, deducting all of the 20s possible and counting forward only the remainder. Returning to our text, we can now say without hesitation that our number is 9.8.9.13.0 and that the day sign in A4b is Ahau. The day coefficient in A4a is just like the katun coefficient in A2a, having the same determining characteristic, namely, the forehead ornament composed of one part. A comparison of this ornament with the ornament on the head for 8 in A2a will show that the two forms are identical. The bifurcate ornament surmounting the head in A4a is a part of the headdress, and as such should not be confused with the forehead ornament. The failure to recognize this point might cause the student to identify A4a as the head for 1, that is, having a forehead ornament composed of more than one part, instead of the head for 8. The month glyph, which follows in B4b, is unfortunately effaced, though its coefficient in B4a is clearly the head for 13. Compare B4a with the uinal coefficient in A3a and with the heads for 13 in figure 52, x-b'. As recorded, therefore, the terminal date reads 8 Ahau 13 ?, thus agreeing in every particular so far as it goes with the terminal date reached by calculation, 8 Ahau 13 Pop. In all probability the effaced sign in B4b originally was the month Pop. The whole Initial Series therefore reads 9.8.9.13.0 8 Ahau 13 Pop.
In figure 69, B, is shown the Initial Series from Stela P at Copan.[156] The introducing glyph appears in A1-B2 and is followed by the Initial-series number in A3-B4. The student will readily identify A3, B3, and A4 as 9 cycles, 9 katuns, and 10 tuns, respectively. Note the beard on the head representing the number 9 in both A3a and B3a. As explained on page 100, this characteristic of the head for 9 is not always present (see fig. 52, g-i). The uinal and kin glyphs have been crowded together into one glyph-block, B4, the uinal appearing in B4a and the kin in B4b. Both their coefficients are 0, which is expressed in each case by the form shown in figure 47. The whole number recorded is 9.9.10.0.0; reducing this to units of the first order by means of Table XIII, we obtain:
A3 = 9 × 144,000 = 1,296,000
B3 = 9 × 7,200 = 64,800
A4 = 10 × 360 = 3,600
B4a = 0 × 20 = 0
B4b = 0 × 1 = 0
————
1,364,400
Deducting from this number all of the Calendar Rounds possible, 71 (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 Pop. In A5a the day 2 Ahau is very clearly recorded, the day sign being expressed by the profile variant and the 2 by two dots (incorrectly shown as one dot in the accompanying drawing).[157] Passing over A5b, B5, and A6 we reach in B6a the closing glyph of the Supplementary Series, and in the following glyph, B6b, the month part of this terminal date. The coefficient is 13, and comparing the sign itself with the month signs in figure 19, it will be seen that the form in a (Pop) is the month recorded here. The whole Initial Series therefore reads 9.9.10.0.0 2 Ahau 13 Pop.
Fig. 70. Initial Series, showing head-variant numerals and period glyphs, from Zoömorph G at Quirigua.
In figure 70 is illustrated the Initial Series from Zoömorph G at Quirigua.[158] The introducing glyph appears in A1-B2 and is followed in C1-H1 by the Initial-series number. Glyphs C1 D1 record 9 cycles. The dots on the head for 9 in C1 are partially effaced. In C2 is the katun coefficient and in D2 the katun sign. The determining characteristic of the head for 7 appears in C2, namely, the scroll passing under the eye and projecting upward and in front of the forehead. See page 100 and figure 51, w. It would seem, then, at first sight that 7 katuns were recorded in C2 D2. That this was not the case, however, a closer examination of C2 will show. Although the lower part of this glyph is somewhat weathered, enough still remains to show that this head originally had a fleshless lower jaw, a character increasing its value by 10. Consequently, instead of having 7 katuns in C2 D2 we have 17 (7 + 10) katuns. Compare C2 with figure 53, j-m. In E1 F1, 15 tuns are recorded. The tun headdress in E1 gives the value 5 to the head there depicted (see fig. 51, n-s) and the fleshless lower jaw adds 10, making the value of E1 15. Compare figure 53, b-e, where examples of the head for 15 are given. Glyphs E2 and F2 represent 0 uinals and G1 H1 0 kins; note the clasped hand in E2 and G1, which denotes the 0 in each case. This whole number therefore reads 9.17.15.0.0. Reducing this to units of the first order by means of Table XIII, we have:
C1 D1 = 9 × 144,000 = 1,296,000
C2 D2 = 17 × 7,200 = 122,400
E1 F1 = 15 × 360 = 5,400
E2 F2 = 0 × 20 = 0
G1 H1 = 0 × 1 = 0
————
1,423,800
Deducting from this number all the Calendar Rounds possible, 75 (see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively), to the remainder, the terminal day reached will be 5 Ahau 3 Muan. The day is recorded in G2 H2. The day sign in H2 is quite clearly the grotesque head variant for Ahau in figure 16, j'-k'. The presence of the tun headdress in G2 indicates that the coefficient here recorded must have been either 5 or 15, depending on whether or not the lower part of the head originally had a fleshless lower jaw or not. In this particular case there is no room for doubt, since the numeral in G2 is a day coefficient, and day coefficients as stated in Chapter III, can never rise above 13. Consequently the number 15 can not be recorded in G2, and this form must stand for the number 5.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 13
OLDEST INITIAL SERIES AT COPAN—STELA 15
Passing over I1 J1, I2 J2, K1 Ll, K2 L2, we reach in M1 the closing glyph of the Supplementary Series, here shown with a coefficient of 10, the head having a fleshless lower jaw. The month sign follows in N1. The coefficient is 3 and by comparing the sign itself with the month glyphs in figure 19, it will be apparent that the sign for Muan in a' or b' is recorded here. The Initial Series of this monument therefore is 9.17.15.0.0 5 Ahau 3 Muan.
In closing the presentation of Initial-series texts which show both head-variant numerals and period glyphs, the writer has thought best to figure the Initial Series on Stela 15 at Copan, because it is not only the oldest Initial Series at Copan, but also the oldest one known in which head-variant numerals are used[159] (see pl. 13). The introducing glyph appears at A1-B2. There follows in A3 a number too much effaced to read, but which, on the basis of all our previous experience, we are justified in calling 9. Similarly B3 must be the head variant of the cycle sign. The numeral 4 is clearly recorded in A4. Note the square irid, protruding fang, and mouth curl. Compare A4 with figure 51, j-m. Although the glyph in B4 is too much effaced to read, we are justified in assuming that it is the head variant of the katun sign. The glyph in A5 is the numeral 10. Note the fleshless lower jaw and other characteristics of the death's-head. Again we are justified in assuming that B5 must be the head variant of the tun sign. The glyphs A6, B6 clearly record 0 uinals. Note the clasped hand denoting zero in A6, and the curling mouth fang of the uinal period glyph in B6. This latter glyph is the full-figure form of the uinal sign[160] (a frog). Compare B6 with figure 33, which shows the uinal sign on Stela D at Copan. The stela is broken off just below the uinal sign and its coefficient; and therefore the kin coefficient and sign, the day coefficient and sign, and the month coefficient and sign, are missing. Assembling the four periods present, we have 9.4.10.0.?. Calling the missing kin coefficient 0, and reducing this number to units of the first order by means of Table XIII, we have:
A3 B3 = 9 × 144,000 = 1,296,000
A4 B4 = 4 × 7,200 = 28,800
A5 B5 = 10 × 360 = 3,600
A6 B6 = 0 × 20 = 0
0 × 1 = 0
————
1,328,400
Deducting from this number all the Calendar Rounds possible, 69 (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 12 Ahau 8 Mol. This date is reached on the assumption that the missing kin coefficient was zero. This is a fairly safe assumption, since when the tun coefficient is either 0, 5, 10, or 15 (as here) and the uinal coefficient is 0 (as here), the kin coefficient is almost invariably zero. That is, the close of an even hotun in the Long Count is recorded.
While at Copan in May, 1912, the writer was shown a fragment of a stela 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]
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 14
INITIAL SERIES ON STELA D, COPAN, SHOWING FULL-FIGURE NUMERAL GLYPHS AND PERIOD GLYPHS
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 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.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 15
INITIAL SERIES ON STELA J, COPAN
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 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 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.
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.
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 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.
Fig. 73. The Initial Series on the Tuxtla Statuette, the oldest Initial Series known (in the early part of Cycle 8).
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.
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]
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 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.
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.
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.
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 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 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 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 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.
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.
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 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 02.19.13.4.0
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.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 16
INITIAL SERIES AND SECONDARY SERIES ON LINTEL 21, YAXCHILAN
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 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 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 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.
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 17
INITIAL SERIES AND SECONDARY SERIES ON STELA 1, PIEDRAS NEGRAS
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, 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
BUREAU OF AMERICAN ETHNOLOGYBULLETIN 57 PLATE 18
INITIAL SERIES (A) AND SECONDARY SERIES (B) ON STELA K, QUIRIGUA
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 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 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.
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 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.
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
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: