n from monuments, a process which consists briefly in the application t

he method of designating p

r example, in figure 66 the glyph-blocks in columns A and B are read together from left to right and top to bottom, thus, A1 B1, A2 B2, A3 B3, etc. When glyph-block B10 is reached the next in order is C1, which is followed by D1, C2 D2, C3 D3, etc. Again, when D10 is reached the next in order is E1, which is followed by F1, E2 F2, E3 F3, etc. In this way the order of reading proceeds from left to right and from top to bottom, in pairs of columns, that is, G H, I J, K L, and M N throughout the inscription, and usually closes with the glyph-block in the lower right-hand corner, as N10 in figure 66. By this simple

CAN ETHNOLOGYBU

S, SHOWING USE OF BAR AND DOT NUM

rding Init

method of dating. Moreover, since the normal forms for the numerals and the period glyphs will be more easily recognised by the beginner than the

, without which Initial Series never seem to have been recorded in the inscriptions. These elements are: (1) the trinal superfix, (2) the pair of comblike lateral appendages, (3) the normal form of the tun sign, (4) the trinal subfix, and (5) the variable central element. As stated above, all these appear in the large glyph A1-B2. Moreover, a comparison of A1-B2 with the introducing glyphs given in figure 24 shows that these fo

omparison of it with figure 27, a, b, the normal form for the katun, will show. It has the normal-form numeral 18 (3 bars and 3 dots) prefixed to it, and this whole glyph therefore signifies 18 katuns. The next glyph should record the tuns, and a comparison of the glyph in A4 with the normal form of the tun sign in figure 29, a, b, shows this to be the case. The numeral 5 (1 bar prefixed to the tun sign) shows that this period is to be used 5 times; that is, multiplied by 5. The next glyph (B4) should be the uinal sign, and a comparison of B4 with figure 31, a-c, the normal form of the uinal sign, shows the identity of these two glyphs. The coefficient of the uinal sign contains as its most conspicuous element the clas

case 9.18.5.0.0, to units of the first order; this may be done by multiplying the recorded coefficients by the numerical values of the periods to which they are respectively attached

144,000 =

× 7,200

× 360

0 × 2

0 ×

-

27,

be the number used in t

al Series the starting point, although never recorded, is practically always the date 4 Ahau 8 Cumhu. Exceptions to this rule are so very rare that they may be dis

rd, and that the student should always proceed upon this assumption. However, in the present case there is no room for uncertainty, since the direction of the count in an Initial Series

s in the present case, and we may therefore subtract from 1,427,400 all the Calendar Rounds possible before proceeding to count it from the starting point. By referring to Table XVI, it appears that 1,427,400 contains 75 complete Calendar Rounds, or 1,423,500; hence, the latter

3; 3,900 ÷ 13 = 300. Now since there is no fractional part in the resulting quotient, the numerator of an assumed fractional part will be 0; counting for

ent, the numerator of an assumed fractional part will be 0; counting forward 0 in Table I, from Ahau, the day sign of the starting point (4 Ahau 8 Cumhu), we reach Ahau as the day sign of the terminal date. In other wor

rs from Table XV, in which the 365 positions of the year are given, that after position 8 Cumhu there are only 16 positions in the year-11 more in Cumhu and 5 in Uayeb. These must be subtracted, therefore, from 250 in order to bring the count to the end of the year; 250 - 16 = 234, so 234 is the number of positions we must count forward in the new year. It is clear that the first 11 uinals in the year will use up exactly 220 of our 234 positions (11 × 20 = 220), and that

are only 365 positions in the year, and having reached 13 Ceh in counting forward 250 from 8 Cumhu, counting the remaining 115 days forward from day reached by 250, that is, 13 Ceh, we should reach our starting point (8 Cumhu) again. Another good check in the present case would be to count backward 250 from 13 Ceh; if our calculations have been correct, the start

rminal date-the day and its corresponding position in the year. If we have made no arithmetical errors in calculations and if the text i

hould appear in B5. The glyph in B5 quite clearly records the day 4 Ahau by means of 4 dots prefixed to the sign shown in figure 16, e'-g', which is the form for the day name Ahau, thereby agreeing with the value of the day part of the terminal date as determined by calculation. So far then we have read our text correctly. Following along the next six or seven glyphs, A6-C1a, which record the Supplementary Series,[120] we reach in C1a a sign similar to the forms shown in figure 65. This glyph, which alwa

rmore, that it records a date, 4 Ahau 13 Ceh, which was distant 9.18.5.0.0 from the starting point of Maya chronology. The writer interprets this text as signifying that 9.18.5.0.0 4 Ahau 13 Ceh was the date on which Zo?morph P at Quirig

ntroducing glyph, which is followed in B1 B3 by the Initial-series number 9.12.15.13.7. The five period glyphs are all expressed by t

which form it may be more conveniently used. This reduction, which forms the f

144,000 =

× 7,200

× 360

3 × 20

7 ×

-

88,

the number used in the

p. 135). Since this number is an Initial Series, in all probability its starting point wi

step 3, p. 136); since our number is an Initial Series,

which the count commences, and the direction of the count, we may

e preliminary rule, page 143). According to Table XVI it appears that 1,388,067 contains 73 Calendar Rounds, or 1,385,540; after ded

, the numerator of the fractional part of the quotient, from 4, the day coefficient of t

e fractional part of the quotient, from Ahau, the day sign of our starting point, 4 Ahau 8 Cumhu, in Table I,

the terminal date. The calculations by means of which 0 Kayab is reached are as follows: After 8 Cumhu there are 16 positions in the year, which we must subtract from 337; 337 - 16 = 321, which is to be counted forward in the new year. This number contains just 1 more than

ntical. Moreover, A4 has the bar and dot coefficient 9 attached to it, that is, 4 dots and 1 bar; consequently it is clear that in A4 we have recorded the day 9 Manik, the same day as reached by calculation. For some unknown reason, at Naranjo the month glyphs of the Initial-series terminal dates do not regularly follow the closing glyphs of the Supplementary Series; indeed, in the text here under discussion, so far as we can judge from the badly effaced glyphs, no Supplementary Series seems to have been recorde

f'; that is, 0 Kayab. However, in A6 such a glyph is reached, and the student will have no difficulty in identifying the month sign with d'-f' in the above figure. Consequently, we have recorded in A4,

.0.0, all the period glyphs and coefficients of which are expressed by normal forms. The student's attention is called to the form for 0 used with the uinal and kin signs in A4a and A4b, respectively, which differs from the form for 0 recorded with the uinal and kin signs

units of the 1st order by m

144,000 =

× 7,200

0 × 360

0 ×

0 ×

-

29,

sible, 75 (see Table XVI), it may be reduced to 5,700

ind this date in the text. The regular position for the day in Initial-series terminal dates is immediately following the last period glyph, which, as we have seen above, was in A4b. Therefore the day glyph should be B4a. An inspection of this latter glyph will show that it records the day 10 Ahau, both the day sign and the coefficient being u

at the day, 10 Ahau, was recorded in B4a; hence, since the month glyph was not recorded in its regular position, it must be in B4b, immediately following the day glyph. By comparing the glyph in B4b with the month signs in figure 19, it will be found exactly like the month sign for Zac (s-t), and we may therefore conclude that

resenting the hotu

the close of the 5-tun period ending 9.18.5.0.0 4 Ahau 13 Ceh, and Stela I, the 5-tun period next following, that ending 9.18.10.0.0 10 Ahau 8 Zac. In other words, Zo?morph P and Stela I were two successive time-markers, or "period stones," in the chronological record at Quirigua. For this 5-tun period so conspicuously recorded in the inscriptions from the older Maya cities the writer would suggest the name hotun, ho meaning 5 in Maya and tun being the name of the 360-day period. This word has an etymological parallel in the Maya word for the 20-tun period, katun, which we have seen may hav

in the other Naranjo text (pl. 6, B) at A1. Then follows regularly in B1-B3 the number 9.12.10.5.12, the numbers and period glyphs of which are all expressed by normal forms. By this time

144,000 =

× 7,200

× 360

5 × 2

12 ×

-

86,

he present calculations are concerned (1,386,112 - 1,385,540). First applying rule 1, page 139, and next rule 2, page 140, to this number (572), the student will find the day reached

CAN ETHNOLOGYBU

, SHOWING USE OF BAR AND DOT NUMER

accept Eb as the day sign recorded in A4. The 4 dots prefixed to this sign show that the day 4 Eb is here indicated. The month sign, as stated on page 152, usually follows the last glyph of the Supplementary Series; passing over B4, A5, B5, and A6, we reach the latter glyph in B6. Compare the left half of B6 with the forms given in figure 65. The coefficient 9 or 10 is expressed by a considerably effaced head numeral. Immediately following the month-sign "indicator" is the month sign itself in A7. The student will have little

ns may be as easy as possible. By this time, however, the student should be sufficiently familiar with the normal forms of the period glyphs to be a

s. The next glyph, A3, should be the katun sign, and a comparison of this form with the head variant for katun in e-h, figure 27, shows this to be the case. The determining characteristic (see p. 69) is probably the oval in the top of the head, which appears in both of these forms for the katun. The katun coefficient is 15 (3 bars). The next glyph, A4, should record the tuns, and by comparing this form with the head variant for the tun sign in e-g, figure 29, this also is found to be the case. Both heads show the same essential characteristic-the fleshless lower jaw (see p. 70). The coefficient is 0 (compare fig. 47). The uinal head in A5 is equally unmistakable. Note the large cu

and normal-form numerals in A2-A6 is therefore 9.15.

144,000 =

× 7,200

0 × 3

0 × 2

0 ×

-

04,

ber rules 1 and 2 (pp. 139 and 140, respectively), the day reached will be found to be 4 Ahau. Applying rule 3 (p. 141), the posit

ing this glyph with the second variant for the day sign Ahau in figure 16, h'-i', the two forms will be found to be identical, and we may accept A7 as recording the day 4 Ahau. Immediately following in A8 is the month sign, again out of its usual place as in plate 6, C. Comparing it with the month signs in figure 19, it will be fou

, the oval in the top of the head in B2, the fleshless lower jaw in A3, the large mouth curl in B3, and the flaring subfix in A4, which are the essential elements of the head variants for the cycle, katun, tun, uinal, and kin, respectively.

f Table XIII to units of

144,000 =

× 7,200

× 360

8 × 2

0 ×

-

03,

for Ahau previously encountered in plate 6, A, B5 and C, B4b, and in plate 7, A, A7. Turning now to the forms for the day sign Ahau in figure 16, it is seen that the form in A4 resembles the third variant j' or k', the grotesque head, and it is clear that the day 12 Ahau is here recorded. At first sight the student might think that the month glyph follows in A5, but a closer inspection of this form shows that this is not the case. In the first place, since the day sign is Ahau the month coefficient must be eith

t of the month-glyph "indicator";[134] and consequently that the month glyph itself follows, as we have seen, in B9. In other words, the terminal date recorded, 12 Ahau 18 Cumhu, agrees with the terminal date reached by calculation, a

stakable, as it has the same superfix as in the normal form for the katun. At first sight the student might read the bar and dot coefficient as 14, but the two middle crescents are purely decorative and have no numerical value, and the numeral recorded here is 12 (see pp. 88-91). Although the tun and uinal period glyphs in A4a and A4b,[136] respectively, are effaced, their coefficients may

CAN ETHNOLOGYBU

, SHOWING USE OF BAR AND DOT NUMER

f the 1st order by means

144,000 =

× 7,200

0 × 360

0 ×

0 ×

-

86,

pplementary Series is reached in B6a. Compare this glyph with the forms in figure 65. The coefficient of B6a is again a head-variant numeral, as in the case of the kin period glyph in B4a, above. The fleshless lower jaw and other skull-like characteristics indicate that the numeral 10 is here recorded. Compare B6a with figure 52, m-r. Since B6a is the last glyph of the Supplementary Series, the next glyph B6b should represent the month sign. By comparing the latter form with the month signs in figure 19 the student wil

it is reasonable to assume that 4 dots originally occupied the effaced part of this glyph. If the use of 9 cycles in this number gives a terminal date which agrees with the terminal date recorded, the above assumption becomes a certainty. In B3 six katuns are recorded. Note the ornamental dotted ovals on each side of the dot in the numeral 6. Although the head for the tun in A4 is partially effaced, we are warranted in assuming that this was the period originally recorded here. The coefficient 10 appears clearly. The uinal head in B4 is totally unfamiliar

le coefficient

aced glyph in A

gular head in B4

aced glyph in A

must have been the tun, uinal, and kin signs, respectively. Indeed, the only important assumption consisted in arbitrarily designating the cycle coefficient 9, when, so far as the appearance of A3 is concerned, it might have been either 6, 7, 8, 9, or 10. The reason for choosing 9 rests on the overwhelming evide

144,000 =

× 7,200

× 360

0 × 2

0 ×

-

42,

lement standing between the numeral and the day sign is unknown. Following along through A6, B6, A7, B7, the closing glyph of the Supplementary Series is reached in A8. The glyph itself is on the left and the coefficient, here expressed by a head variant, is on the right. The student will have no difficulty in recognizing the glyph and its coefficient by comparing the former with figure 65, and the latter with the head variant for 10 in figure 52, m-r. Note the fleshless lower jaw in the head numeral in both places

t ways. The bars denoting 5 have square ends and all show considerable ornamentation. This type of bar was an early manifestation and gave way in later times to more rounded forms. The dots also show this greater ornamentation, which is reflected, too, by the signs themselves. The head forms show greater att

umerals and head-variant period glyphs: A, St

ve no difficulty in reading except for the head-variant numeral attached to the kin sign in A5. The clasped hand in this glyph, however, suggests that 0 kins are recorded here, and a co

144,000 =

× 7,200

0 × 3

0 × 2

0 ×

-

03,

coefficient. These several points indicate that the day sign is not the glyph in B5, also that the day sign is, therefore, out of its regular position. The next glyph in the text, A6, instead of being one of the Supplementary Series is the day glyph 6 Ahau, which should have been recorded in B5. The student will readily make the same identification after comparing A6 with figure 16, e'-g'. A glance at the remainder of the text, will show that no Supplementary Series is recorded, and consequ

the use of both normal-form and head-variant period glyphs in this text, the cycle, tun, and uinal in B1a, A2a, and A2b, respectively, being expressed by the latter, and t

144,000

× 7,200

× 360

0 ×

0 ×

-

13,

8 Zotz. Turning to our text, the student will have no difficulty in recognizing in B2b the day 8 Ahau. The month glyph in this inscription irregularly follows immediately the day glyph. Compare the form in A3a with the month signs in figur

s or the originals themselves. However, in order to familiarize the student with photographic reproductions of Maya texts a few will be inserted here illust

A3, 0 uinals in B3, and 0 kins in B4. The student will note the clasped hand in the cycle head, the oval in the top of the katun head, the large mouth curl in the uinal head, and the flar

144,000 =

× 7,200

× 360

0 × 2

0 ×

-

11,

ize the day 11 Ahau in this form. Following along the glyphs of the Supplementary Series in C1 D1, C2 D2, the closing glyph is reached in C3b. It is very clear and has a coefficient of 9. The glyph following (D3) should record the month sign. A comparison of this form with the several month signs in figure 19 shows that Tzec is the month here recorded. Compare D3 with figure 19,

CAN ETHNOLOGYBU

, SHOWING USE OF BAR AND DOT NUMER

and the coefficients as bar and dot numerals. Excepting the kin coefficient in A4, the number is quite easily read as 9.12.8.14.? An inspection of our text shows that the coefficient must be 0, 1, 2, or 3. Let us work out the termina

144,000 =

× 7,200

× 360

4 × 20

0 ×

-

85,

ctively), to the remainder, the terminal day reached will be 11 Ahau 3 Pop. Therefore the Initial-series numbers 9.12.8.14.1, 9.12.8.14.2, an

4.0 11 A

.1 12 Imi

14.2 13

4.3 1 Ak

two of the above four possible terminal dates, and reduces the possible values for the kin coefficient in A4 to 0 or 1. Comparing the glyph in B4 with the day signs in figure 16, the form here recorded will be found to be identical with the sign for Imix in figure 16, a. This eliminates the first terminal date above and leaves the second, the day part of which we have just seen appears in B4. This further proves that the kin coefficient in A4 is 1. The final confirmation of this identification will come from the month glyph, which must be 4 Pop if we have correctly identified the d

ppears clearly, and their identification rests on their relative positions with reference to the introducing glyph. The reliability of this basis of identification for the period glyphs of Initial Series has been thoroughly tested in the texts already presented and is further confirmed in this very inscription by the uinal head. Even if the large mouth c

ns of Table XIII to units o

144,000 =

× 7,200

× 360

0 × 2

0 ×

-

15,

he human head may yet be traced, thus enabling us to identify this form as the day sign Ahau. Compare figure 16, h', i'. The coefficient of A4 is very clearly 4 dots, that is, 4, and consequently this glyph agrees with the day as determined by calculation, 4 Ahau. Passing over B4, A5, B5, and A6, we reach in B6 the closing glyph of the Supplementary Series, h

AN ETHNOLOGYBULL

WING USE OF BAR AND DOT NUMERALS AND HE

AN ETHNOLOGYBULL

USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT

it records the earliest contemporaneous[148] date

n picking out the clasped hand in A3, the oval in the top of the head in B3, the fleshless lower jaw in A4, the mouth curl in B4, as the essential characteristic of the cycle, katun, tun, and uinal heads, respe

144,000 =

× 7,200

× 360

× 20

0 ×

-

20,

VI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to

y 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

ere and there. By this time the student should have become thoroughly familiar with the use of bar and dot numerals in the inscript

n 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

AN ETHNOLOGYBULL

RIES, SHOWING USE OF HEAD-VARI

× 144,000

× 7,200

5 × 360

4 × 2

= 0 ×

-

5,

ead 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

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 (s

× 144,000

× 7,200

5 × 360

3 × 2

= 6 ×

-

5,

ike 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 neit

actically 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 thor

numerals and period glyphs: A, House C of the

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, hav

144,000 =

× 7,200

× 360

3 × 20

0 ×

-

57,

in 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

ely. 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

144,000 =

× 7,200

× 360

0 ×

0 ×

-

64,

ed, 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, B

ead-variant numerals and period gl

e 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 tun

× 144,000

7 × 7,200

15 × 360

= 0 ×

= 0

-

23,

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

AN ETHNOLOGYBULL

L SERIES AT C

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,

le 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 m

× 144,000

4 × 7,20

10 × 360

= 0 ×

1

-

28,

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 eit

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 write

n 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

igure 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 a

s recorded in A1. The variable central element in keeping with the other glyphs of the inscri

AN ETHNOLOGYBULL

OPAN, SHOWING FULL-FIGURE NU

n 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 wil

dentification 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 a

ntial 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 anthr

head in B2 without the former but with the latter represents the numeral 5. Compare the head of the a

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

nting 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 i

15.5.0.0; reducing this by means of Table

144,000 =

× 7,200

× 360

0 × 2

0 ×

-

05,

le XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141 respectiv

iliar 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,

rs 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

AN ETHNOLOGYBULL

RIES ON ST

eye of the grotesque head, and the element (**) on the left-hand side about where the ear lobe should be. The whole glyph un

than the Initial Series on Stela B at Copan (pl. 7, A). According to the write

nusual or irregular in some respect, examples of which it is necessar

tudent 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 anoth

by means of Table XIII to unit

44,000 =

× 7,200

× 360

0 ×

0 ×

-

93,

2 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 c

he same interlacing scheme, though in this case the glyph ba

o 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 genera

irigua: a, Mat pattern of glyph sequen

f the first order by mea

44,000 =

7,200 =

× 36

0 ×

0 ×

-

11,

le XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respecti

Quirigua: a, Tun coefficient; b, suggested restoration o

h 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 t

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 w

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

tla Statuette, the oldest Initial Seri

yph (?) of the Initial Seri

s 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

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 resemb

,000 =

200 =

360

20

× 1

-

96,

racter 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

o the Tuxtla Statuette Initial Series, is the earliest known. B, On a lintel from the Temple of the Ini

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 disting

ts of the first order by me

144,000 =

× 7,200

× 360

1 × 2

12 ×

-

53,

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 sig

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 coefficie

ivilized 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

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

eries 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 C

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 1

A, Stela 1; B, Stela 2. There is less than a year's difference in ti

ot 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 t

ts of the first order by me

144,000

× 7,200

× 360

0 × 2

] = 0

-

56,

nd 3 (pp. 139, 140, and 141, respectively) to the remainder, the terminal date reached will be 9 Ahau 18 Ya

her 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 latt

144,000

× 7,200

× 360

0 × 2

0 ×

-

58,

yph 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 bee

ntral 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

ore 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 I

g glyph appears in A1-B2, and is followed by the Initial-series number in A3-A5. The student will easily

144,000

× 7,2

0 × 3

0 × 2

0 ×

-

72,

nd 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

Ahau 8 Cumhu, the starting point of Maya chronology: A, Stela

tarting 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 on

. 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 assoc

4.0 5 Ah

.4.0 9 A

.4.0 8 A

ect, one of these three terminal dates will be found recorded,

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

ckward from the recorded terminal date, 8 Ahau 18 Tzec, each of the three numbers 2.19.

Calendar Rounds possible from each (see Table XVI), and, finally, applying rules 1, 2, and 3 (p

Mol for 2

Mac for 11

otz for 12

ycle 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 date

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

s 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

AN ETHNOLOGYBULL

SECONDARY SERIES ON

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 a

nitial Series and

curacy 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 w

g 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, recordi

upplementary 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 clo

ove question. It is apparent at the outset that it differs from the

t which at once eliminates the possibil

, the uinal sign in C3 having t

the highest period, here the katun, closing the

nvariably 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

ts of the first order by me

× 7,200

× 360

6 × 20

5 ×

-

8,

deducted from it without affecting its value, we can further reduce it to 13,785

is 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 o

s 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

4 2 Kan 2 Yax

Secondary-s

17 Tzec Initial Series

date 7 Mu

, and counting it forward from 4 Ahau 8 Cumhu, the starting point of Maya chronology. The terminal

te" 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 2

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 d

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

AN ETHNOLOGYBULL

ECONDARY SERIES ON S

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 kin

× 360

9 × 2

15 ×

,

, 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. More

0. 16 5 Ci

9.

10. 11 9 Ch

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 gener

some date, and since Secondary-series numbers are usually counted from the date next preceding

tter 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 Ini

10. 11 9 Ch

10. 16 1 Ci

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,

× 7,200

) 0 ×

2 × 2

5 ×

,

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,

10. 16 1 Ci

[189]

13. 1 5 I

part of this text, the remaining glyp

iphered above, the known part

16 A1-A7, C2

. 15

. 11 F1 G1 9

. 16 G3 G4 1

89] 2.

3. 1 G8 G9 5

AN ETHNOLOGYBULL

D SECONDARY SERIES (B

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 tenu

t also started in every case from the date immediately preceding the number counted. This regularity, however, is far from univ

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 B

0 × 20

10 ×

1

y) 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 (

ollowing 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

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 th

. 0. 0 3

.

7. 10 1 O

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 r

. 0. 0 3

0 bac

7. 10 1 O

rd from In

. 0. 0 3

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

93] 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 cal

tial Series on S

er 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 th

ndary Series on S

ng 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 i

× 7,2

× 360

3 × 20

3 ×

,

y) to this number, the terminal date reached will be 10 Ahau 8

ever, may be calculated from the Initial Series wh

4. 17 12 Ca

1. 1

0. 0 10

other monument by calculation just as here. It has a peculiar fitness here on Stela J in that it is j

ry 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

× 360

3 × 2

14 ×

,

he terminal date reached will be 8 Ahau 8 Zotz, which does not appear in figure 7

14. 6 6

3.

0. 0 8 A

ing this count up to the contemporaneous time of this monument, which was 9.16.5.0.0 8 Ahau 8 Zotz. In view of the fact that the Secondary Series on Stela J are both earlier than the Init

12 Caban 5 Kayab

13. 3

. 0] 10 Ahau

4. 6]

6 Cimi 4 Tzec Fi

. 14

Ahau 8 Zotz Fig

important date, because it alone records the particular hotun-ending which Stela J marks. The importance

do well to bear in mind: (1) The starting points of Secondary-series numbers do not always precede the

l be illustrated in

head variants and reads as follows: 9.14.13.4.17. The terminal date reached by this number is 12 Caban 5 Kayab, which is recorded in B5-A6. The student will readily identify the numerals as above by comparin

AN ETHNOLOGYBULL

CONDARY SERIES (B) ON STE

n, we reach in B10 the Secondary-series number 13.9.9

13 × 36

9 × 2

= 9 ×

,

respectively), the terminal day reached will be 6 Cimi 4 Tzec. This date the student will find recorded in plate 19, B, B11b-A12a. Compare B11b with the sign for Cimi in figure 16, h, i, and A12a with the si

4. 17 12 Ca

.

4. 6 6 Cimi

hau 13 Yax, is recorded elsewhere at Quirigua in a Secondary Series attached to an Initial Series, where it has the Initial-series value 9.15.0.0.0. This value we may assume, therefore, belongs to it in the present case, givi

ture. Instead of being counted either forward or backward from the date next preceding it in the text; that is, 4 Ahau 13 Yax in A17, this number is counted from the date following it in the text, like the two Secondary-series numbers in Stela J, just discussed. This starting date recorded in A18b B18a is 12 Caban 5 Kayab, which, as we have seen, is

× 7,200

16 × 36

13 ×

= 3 ×

-

,2

ip, which is recorded in A19. Compare the coefficient of the day sign in A19a with the coefficient of the katun sign in A18a, and the day sign itself with the profile variant for Ahau in figure 16, h'

4. 17 12 Ca

6. 1

. 0. 0 1

9.16.10.0.0. The terminal date which this number reaches is recorded in B5-B8; that is, 1[202] Ahau 3 Zip, the "month indicator" appearing as a head variant in A8 with the head-variant coefficient 10. But this date is identical with the date determined by calculation and actually recorded at the close of the inscription on the other side of this monument, and since no later date is recorded e

AN ETHNOLOGYBULL

ON STELA F (EAS

ts that happened at Quirigua on the dates: a, 9. 14. 13.

e date recorded by the Initial Series on the same monument. Now, one of the Initial-series values corresponding to the date 3 Ahau 3 Mol here under discussion is 9.15.10.0.0, exactly 1 katun earlier than the Initial-series date on Stela F. In other words, if we give to the date 3 Ahau 3 Mol in A15 the value 9.15.10.0.0, the cases are exa

12 Caban 5 Kayab

Plate 1

Cimi 4 Tzec Plat

0] 3 Ahau 3 Mol

] 4 Ahau 13 Yax

2 Caban 5 Kayab Pl

3 Plate 19,

1 Ahau 3 Zip P

ial Series on eas

1 Ahau 3 Zip P

hich both proceed, 9.14.13.4.17 12 Caban 5 Kayab, is an important one at Quirigua, being the earliest date there. It appears on four monuments, namely, Stel? J, F, and E, and Zo?morph G. Although the writer has not been able to prove the point, he is of the opinion that the glyph shown in figure 80, a, tells the meaning of the event which happened on this date, which is, moreover, the earliest date at Quirigua which it is possible to regard

rding Peri

plained 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 th

(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

xactly, 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

AN ETHNOLOGYBULL

RIOD-ENDING DA

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 recorde

ompare 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 wh

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 re

mpare 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 a

e 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 Perio

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,

e 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

in, 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

AN ETHNOLOGYBULL

NDING DATES IN CYCLE

act has not been recorded in any of the above examples. We come next to the co

re 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, wh

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 katu

re, 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 mon

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

= 6 ×

3 = 3

2

d 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 Ini

0. 0 8 Ah

.

11. 17 2

this date may have referred to some actual historic event in the annals of Palenque, or at least of the south

is, the monuments upon which they appear really date from Cycle 10, while others are as surely "prophet

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 s

he preceding example. Does this date represent, therefore, the contemporaneous time of Zo?morph 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 Zo?morph 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 therefore indicates the epoch or position

rd 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

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 se

c" in character, since it did not occur until nearly 45 years after the erection of the monument upon which it

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 decla

0. 0 7 A

0.

0. 0 5 A

f Kat

nd also on Stel? 8, 9,

ing 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, theref

× 7,200

36

orded 0

1

-

,0

Secondary Series, and Period-

his 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,

0. 0 4 A

0. 0

0. 0 7 A

AN ETHNOLOGYBULL

RIES, AND PERIOD-ENDING DATE

which renders this probable is that the sculpture on Altar S very closely resembles the sculpture on Stel? 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

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

l Series, Secondary Se

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 o

0. 16 5 Ci

10

10. 16 1 Ci

nd 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. Comp

10. 16 1 Ci

. 11

. 4. 6 4

ext, 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 hea

. 4. 6 4

8

13. 1 11

t 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

13. 1 11

.

0. 0 6 A

AN ETHNOLOGYBULL

ES, AND PERIOD-ENDING DATES ON

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 da

16 5 Cib 14 Y

0. 0

. 16 1 Cib 14

11. 10

4 . 6 4 Cim

8.

3. 1 11 Imix

1

. 0 6 Ahau

Katun 1

ext 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 i

nd applying the rules previously given for solving Initial Series, the terminal date 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-

4. 17 12 Ca

1

0. 0 4 A

Series on Stela E (

ax 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

14. 6 6

1

0. 0 10

hau 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 cou

5a, 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

art 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

0. 0 13 Ah

4

13. 1 11

from 7 Cimi 9 Zotz, the Initial-series value of the latter may be calculated

13. 1 11

. 16

14. 6 7

is 6 Cimi 4 Tzec, which corresponded to the Initial Series 9.15.6.14.6 6 Cimi 4 Tzec, as we have s

te 13 Ahau 18 Cumhu. The inscription on the east side of this same monument opens with this same date

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

]4.17 12 Caban 5 Kayab

late 24, A

4 Ahau 13 Yax P

0] Un

0. 0 10 Ah

Plate 2

Cimi 4 Tzec Plat

0] Un

14. 6 7 Ci

5 Plate 24,

1 Imix 19 Muan Pla

late 24, B

3 Ahau 18 Cumhu

un 17 Plat

. 0 13 Ahau 18 Cumhu F

the inscriptions on Stel? J and F, and Zo?morph G, at the same city, all four of which are shown

P OF DATES ON STEL? E, F, AN

Stela F Ste

17 12 Caban

0 4 Ahau 13

0 10 Ahau 8

. 6 6 Cimi 4

. 6 7 Cimi 9

. 0 3 Ahau 3

0 8 AHAU 8

. 0 1 AHAU 8

. 1 11 Imix 1

0 13 AHAU 18

. 0 5 AHAU 3

tainly 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 exp

.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

and Period-ending, dating, with which the student should be suffici

d 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, an

× 360

2 × 2

0 ×

,

AN ETHNOLOGYBULL

ND DATES ON

een 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

dates: A, Altar M, Qui

e 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,

0. 0 4 A

2

2. 0 6 A

en assigned to the date 4 Ahau 13 Yax on the ground that this Initial-series value ap

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

0. 0 13 Ah

1 Ba

9. 19 12

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

t 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

is 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 t

Count. A monument which shows only Calendar-round dates may be associated with another monument or a building, the dates of which are fix

1 Muluc 2 Kankin, for example, the positions at which this date occur

5. 9 1 Mul

. 9 1 Mulu

3. 9 1 Mul

8. 9 1 Mul

3. 9 1 Mul

16. 9 1 Mul

11. 9 1 Mul

6. 9 1 Mul

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 consideri

.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

ta

9 1 Muluc 2 Mua

18 glyph

13 Manik 0 Xul

glyphs

11 Cimi 19 Mac

unde

1 Muluc 2 Kanki

tween the two mo

el

. 0 6 Ahau

to fix their dates in the Long Count. At Yaxchilan in particular Calendar-round dating seems to have been extensiv

in the

ter has thought it best to insert a few texts which show actual errors in the o

the originals: A, Lintel, Yaxchilan; B

are revealed by inspection, and (2) those which do not appear until after the indica

ately 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

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 record

ayab. 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, ther

1. 17 12 C

. 17 12 Ca

1. 17 12 C

4. 17 12 C

9. 17 12 C

4. 17 12 Ca

7. 17 12 Ca

12. 17 12 C

ween these two numbers is otherwise so close and the error in this 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 i

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,

cients 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

11. 0 1 A

6. 0 1

1. 0 1 A

14. 0 1 A

. 9. 0 1

. 4. 0 1

17. 0 1

. 12. 0 1

AN ETHNOLOGYBULL

A N, COPAN, SHOWING ER

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 correc

al coefficients, and not in the signs to which they are attached; in other words, that althoug

ume 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

aring it was erected, or at least formally dedicated. The writer has endeavored to show, moreover, that many, if indeed not most, of the monuments, were "time markers" or "period stones," in every way similar to the "period stones" which the northern Maya are known to[239] have erected at regularly recurring periods. That the period which was used as this chronological unit may have varied in different localities and at different epochs is not at all improbable. The northern Maya at the time of the Spa

mize the importance of that which is already gained. Thirty years ago the Maya inscriptions were a sealed book, yet to-day we read in the glyphic writing the rise and fall of the several cities in relation to one another, and follow the course of Maya development ev