Chapter II

(pp. 33-34), the interval between succeeding monuments at Quirigua is in every case 1,800 days, or 5 tuns. Therefore, it would seem probable that at Quirigua at least this period was the unit used for marking the lapse of time. As each 5-tun period was completed, its close was marked by the erection of a monument, on which was recorded its ending date. Thus the writer believes Zoömorph P marked 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 {166} 10 Ahau 8 Zac. In other words, Zoömorph 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 have been named directly from its numerical value, _kal_ being the word for 20 in Maya and _kaltun_ contracted to katun, thus meaning 20 tuns. Although no glyph for the _hotun_ has as yet been identified,[126] the writer is inclined to believe that the sign in figure 67, _a, b_, which is frequently encountered in the texts, will be found to represent this time period. The bar at the top in both _a_ and _b_, figure 67, surely signifies 5; therefore the glyph itself must mean "1 tun." This form recalls the very unusual variant of the tun from Palenque (see fig. 29, _h_). Both have the wing and the () element.

The next Initial Series presented (see pl. 6, _D_) is from Stela 24 at Naranjo.[127] The text opens with the introducing glyph, which is in the same relative position as the introducing glyph 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 the student should have no difficulty in recognizing these and in determining the number as given above. Reducing this according to rule 1, page 134, the following result should be obtained:

B1 = 9 × 144,000 = 1,296,000 A2 = 12 × 7,200 = 86,400 B2 = 10 × 360 = 3,600 A3 = 5 × 20 = 100 B3 = 12 × 1 = 12 --------- 1,386,112

Deducting[128] from this number all the Calendar Rounds possible, 73 (see preliminary rule, p. 143, and Table XVI), we may reduce it to 572 without affecting its value in so far as the 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 to be 4 Eb. And applying rule 3, page 141, he will find that the year position reached will be 10 Yax;[129] hence, the terminal date as determined by calculation will be 4 Eb 10 Yax.

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS]

{167}

Turning again to the text (pl. 6, _D_), the next step (see step 5, p. 151) is to find the glyphs representing the above terminal date. In this connection it should be remembered that the day part of an Initial-series terminal date usually follows immediately the last period glyph of the number. The glyph in A4, therefore, should record the day reached. Comparing this form with the several day signs in figure 16, it appears that A4 more closely resembles the sign for Eb (fig. 16, _s-u_) than any of the others, hence the student may 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 difficulty in tracing its resemblance to the month Yax in figure 19, _q, r_, although in A7 the Yax element itself appears as the prefix instead of as the superfix, as in _q_ and _r_, just cited. This difference, however, is immaterial. The month coefficient is quite clearly 10,[130] and the whole terminal date recorded will read 4 Eb 10 Yax, which corresponds exactly with the terminal date determined by calculation. We may accept this text, therefore, as recording the Initial-series date 9.12.10.5.12 4 Eb 10 Yax of Maya chronology.

In the foregoing examples nothing but normal-form period glyphs have been presented, in order that the first exercises in deciphering the inscriptions 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 able to recognize them when they are present in the text, and the next Initial Series figured will have its period glyphs expressed by head variants.

In A, plate 7, is figured the Initial Series from Stela B at Copan.[131] The introducing glyph appears at the head of the inscription in A1 {168} and is followed by a head-variant glyph in A2, to which is prefixed a bar and dot coefficient of 9. By its position, immediately following the introducing glyph, we are justified in assuming that A2 records 9 cycles, and after comparing it with _d-f_, figure 25, where the head variant of the cycle sign is shown, this assumption becomes a certainty. Both heads have the same clasped hand in the same position, across the lower part of the face, which, as explained on page 68, is the essential element of the cycle head; therefore, A2 records 9 cycles. 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 curl protruding from the back part of the mouth, which was said (p. 71) to be the essential element of this sign. Compare figure 31, _d-f_, where the head variant for the uinal is given. The coefficient of A5 is like the coefficient of A4 (0), and we have recorded, therefore, 0 uinals. The closing period glyph of the Initial Series in A6 is the head variant for the kin sign. Compare this form with figure 34, _e-g_, where the kin head is figured. The determining characteristic of this head is the subfixial element, which appears also in the normal form for the kin sign (see fig. 34, _a_). Again, the coefficient of A6 is like the coefficient of A4 and A5, hence we have recorded here 0 kins.

The number recorded by the head-variant period glyphs and normal-form numerals in A2-A6 is therefore 9.15.0.0.0; reducing this by means of Table XIII, we have:

A2 = 9 × 144,000 = 1,296,000 A3 = 15 × 7,200 = 108,000 A4 = 0 × 360 = 0 A5 = 0 × 20 = 0 A6 = 0 × 1 = 0 --------- 1,404,000

Deducting from this number all the Calendar Rounds possible, 73 (see Table XVI), it may be reduced to 18,460. Applying to this number 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 position of 4 Ahau in the year will be found to be 13 Yax. Therefore the terminal date determined by calculation will be 4 Ahau 13 Yax. {169}

According to step 5 (p. 151), the day reached should follow immediately the last period glyph, which in this case was in A6; hence the day should be recorded in A7. This glyph has a coefficient 4, but the glyph does not resemble either of the forms for Ahau shown in B5, plate 6, _A_, or in B4a, _C_ of the same plate. However, by comparing 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 found to exactly correspond with the sign for Yax in _q-r_. The coefficient is 13. Therefore the terminal date recorded, 4 Ahau 13 Yax, agrees with the terminal date reached by calculation, and the whole Initial Series reads 9.15.0.0.0 4 Ahau 13 Yax. This date marks the close not only of a hotun in the Long Count, but of a katun as well.

In _B_, plate 7, is figured the Initial Series from Stela A at Copan.[132] The introducing glyph appears in A1 B1, and is followed by the Initial-series number in A2-A4. The student will have no difficulty in picking out the clasped hand in A2, 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. Compare these glyphs with figures 25, _d-f_, 27, _e-h_, 29, _e-g_, 31, _d-f_, and 34, _e-g_, respectively. The coefficients of these period glyphs are all normal forms and the student will have no difficulty in reading this number as 9.14.19.8.0.[133]

Reducing this by means of Table XIII to units of the 1st order, we have:

A2 = 9 × 144,000 = 1,296,000 B2 = 14 × 7,200 = 100,800 A3 = 19 × 360 = 6,840 B3 = 8 × 20 = 160 A4 = 0 × 1 = 0 --------- 1,403,800

Deducting from this all the Calendar Rounds possible, 73 (see Table XVI), and applying rules 1 and 2 (pp. 139 and 140, respectively), to the remainder, the day reached will be 12 Ahau. And applying rule 3 (p. 141), the month reached will be 18 Cumhu, giving for the terminal date as reached by calculation 12 Ahau 18 Cumhu. The day should be recorded in B4, and an examination of this glyph shows that its coefficient is 12, the day coefficient reached by calculation. The glyph itself, however, is unlike the forms for Ahau previously encountered in plate 6, _A_, B5 and _C_, B4b, and in plate 7, _A_, A7. Turning {170} 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 either 3, 8, 13, or 18, not 7, as recorded (see Table VII), and, in the second place, the glyph itself in A5 bears no resemblance whatsoever to any of the month signs in figure 19. Consequently the month part of the Initial-series terminal date of this text should follow the closing glyph of the Supplementary Series. Following along the glyphs next in order, we reach in A9 a glyph with a coefficient 9, although the sign itself bears no resemblance to the month-glyph "indicators" heretofore encountered (see fig. 65).

The glyph following, however, in A9b is quite clearly 18 Cumhu (see fig. 19, _g'-h'_), which is the month part of the terminal date as reached by calculation. Therefore, since A9a has the coefficient 9 it is probable that it is a variant 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, and the whole text, so far as it can be deciphered, reads 9.14.19.8.0 12 Ahau 18 Cumhu. The student will note that this Initial Series precedes the Initial Series in plate 7, _A_ by exactly 10 uinals, or 200 days. Compare _A_ and _B_, plate 7.

In plate 8, _A_, is figured the Initial Series from Stela 6 at Copan.[135] The introducing glyph occupies the space of four glyph-blocks, A1-B2, and there follows in A3-B4a the Initial-series number 9.12.10.0.0. The cycle glyph in A3 is partially effaced; the clasped hand, however, the determining characteristic of the cycle head, may still be distinguished. The katun head in B3 is also unmistakable, 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 be distinguished as 10 and 0, respectively. In such a case the student is perfectly justified in assuming that the tun and uinal signs originally stood here. In B4a the kin period glyph is expressed by its normal form and the kin coefficient by a head-variant numeral, the clasped hand of which indicates that it stands for 0 (see fig. 53, _s-w_).[137] The number here recorded is 9.12.10.0.0.

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS]

{171}

Reducing this to units of the 1st order by means of Table XIII, we have:

A3 = 9 × 144,000 = 1,296,000 B3 = 12 × 7,200 = 86,400 A4a = 10 × 360 = 3,600 A4b = 0 × 20 = 0 B4a = 0 × 1 = 0 --------- 1,386,000

Deducting from this number all the Calendar Rounds possible, 73 (see Table XVI), and applying to the remainder rules 1, 2, and 3 (pp. 139-141), respectively, the date reached by the resulting calculations will be 9 Ahau 18 Zotz. Turning to our text again, the student will have little difficulty in identifying B4b as 9 Ahau, the day of the above terminal date. The form Ahau here recorded is the grotesque head, the third variant _j'_ or _k'_ in figure 16. Following the next glyphs in order, A5-A6, the closing glyph of the Supplementary 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 will readily recognize that the sign for Zotz in _e_ or _f_ is the month sign here recorded. The coefficient 18 stands above. Consequently, B4b and B6b represent the same terminal date, 9 Ahau 18 Zotz, as reached by calculation. This whole Initial Series reads 9.12.10.0.0 9 Ahau 18 Zotz, and according to the writer's view, the monument upon which it occurs (Stela 6 at Copan) was the period stone for the hotun which began with the day 9.12.5.0.1 4 Imix 4 Xul[138] and ended with the day 9.12.10.0.0 9 Ahau 18 Zotz, here recorded.

In plate 8, _B_, is figured the Initial Series from Stela 9 at Copan.[139] The introducing glyph stands in A1-B2 and is followed by the five period glyphs in A3-A5. The cycle is very clearly recorded in A3, the clasped hand being of a particularly realistic form. Although {172} the coefficient is

## partially effaced, enough remains to show that it was above 5, having had

originally more than the one bar which remains, and less than 11, there being space for only one more bar or row of dots. In all the previous Initial Series the cycle coefficient was 9, consequently 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 and seems to have the fleshless lower jaw properly belonging to the tun head; from its position, however, the 4th in the number, we are justified in calling this glyph the uinal sign. Its coefficient denotes that 0 uinals are recorded here. Although the period glyph in A5 is also entirely effaced, the coefficient appears clearly as 0, and from position again, 5th in the number, we are justified once more in assuming that 0 kins were originally recorded, here. It seems at first glance that the above reading of the number A3-A5 rests on several assumptions:

1. That the cycle coefficient was originally 9. 2. That the effaced glyph in A4 was a tun head. 3. That the irregular head in B4 is a uinal head. 4. That the effaced glyph in A5 was a kin sign.

The last three are really certainties, since the Maya practice in recording Initial Series demanded that the five period glyphs requisite--the cycle, katun, tun, uinal, and kin--should follow each other in this order, and in no other. Hence, although the 3d, 4th, and 5th glyphs are either irregular or effaced, they 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 evidence of antecedent probability. Moreover, as stated above, if the terminal date recorded agrees with the terminal date determined by calculation, using the cycle coefficient as 9, our assumption becomes a certainty. Designating the above number as 9.6.10.0.0 then and reducing this by means of Table XIII, we obtain:

A3 = 9 × 144,000 = 1,296,000 B3 = 6 × 7,200 = 43,200 A4 = 10 × 360 = 3,600 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,342,800

{173} Deducting from this number all the Calendar Rounds possible, 70 (see Table XVI), and applying rules 1, 2, and 3 (pp. 139, 140, and 141, respectively) to the remainder, the date determined by the resulting calculations will be 8 Ahau 13 Pax. Turning to our text again, the student will have little difficulty in recognizing the first part of this date, the day 8 Ahau, in B5. The numeral 8 appears clearly, and the day sign is the profile-head _h'_ or _i'_, the second variant for Ahau in figure 16. The significance of the element 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. The following glyph, B8, is one of the clearest in the entire text. The numeral is 13, and the month sign on comparison with figure 19 unmistakably proves itself to be the sign for Pax in _c'_. Therefore the terminal date recorded in B5, B8, namely, 8 Ahau 13 Pax, agrees with the terminal date determined by calculation; it follows, further, that the effaced cycle coefficient in A3 must have been 9, the value tentatively ascribed to it in the above calculations. The whole Initial Series reads 9.6.10.0.0 8 Ahau 13 Pax.

Some of the peculiarities of the numerals and signs in this text are doubtless due to its very great antiquity, for the monument presenting this inscription, Stela 9, records the next to earliest Initial Series[140] yet deciphered at Copan.[141] Evidences of antiquity appear in the glyphs in several different 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 attention to detail, giving the whole glyph a more ornate appearance. All this embellishment gave way in later times to more simplified forms, and we have represented in this text a stage in glyph morphology before conventionalization had worn down the different signs to little more than their essential elements. {174}

[Illustration: FIG. 68. Initial Series showing bar and dot numerals and head-variant period glyphs: _A_, Stela C (west side), Quirigua; _B_, Stela M, Copan.]

In figure 68, _A_, is figured the Initial Series on the west side of Stela C at Quirigua.[142] The introducing glyph in A1-B2 is followed by the number in A3-A5, which the student will have 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 comparison of this form with figure 53, _s-w_, confirms the suggestion. The number therefore reads 9.1.0.0.0. Reducing this number by means of Table XIII to units of the 1st order, we obtain:

A3 = 9 × 144,000 = 1,296,000 B3 = 1 × 7,200 = 7,200 A4 = 0 × 360 = 0 B4 = 0 × 20 = 0 A5 = 0 × 1 = 0 --------- 1,303,200

Deducting from this number 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, we reach for the terminal date 6 Ahau 13 Yaxkin. Looking for the day part of this date in B5, we find that the form there recorded bears no resemblance to 6 Ahau, the day determined by calculation. Moreover, comparison of it with the day signs in figure 16 shows that it is unlike all of them; further, there is {175} no bar and dot 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 consequently that the month glyph will be found immediately following the day glyph in B6. The form in B6 has a coefficient 13, one of the four (3, 8, 13, 18) which the month must have, since the day sign is Ahau (see Table VII). A comparison of the form in B6 with the month signs in figure 19 shows that the month Yaxkin in _k_ or _l_ is the form here recorded; therefore the terminal date recorded agrees with the terminal date reached by calculation, and the text reads 9.1.0.0.0 6 Ahau 13 Yaxkin.[143]

In figure 68, _B_, is shown the Initial Series on Stela M at Copan.[144] The introducing glyph appears in A1 and the Initial-series number in B1a-B2a. The student will note 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 the katun and kin in B1b and B2a, respectively, by the former. The number recorded is 9.16.5.0.0, and this reduces to units of the first order, as follows (see Table XIII):

B1a = 9 × 144,000 = 1,296,000 B1b = 16 × 7,200 = 115,200 A2a = 5 × 360 = 1,800 A2b = 0 × 20 = 0 B2a = 0 × 1 = 0 --------- 1,413,000

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 by the resulting calculations will be 8 Ahau 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 {176} the day glyph. Compare the form in A3a with the month signs in figure 19 and it will be found to be the sign for Zotz (see fig. 19, _e-f_). The coefficient is 8 and the whole glyph represents the month part 8 Zotz, the same as determined by calculation. This whole Initial Series reads 9.16.5.0.0 8 Ahau 8 Zotz.

The Maya texts presented up to this point have all been drawings of originals, which are somewhat easier to make out than either photographs of the originals or the originals themselves. However, in order to familiarize the student with photographic reproductions of Maya texts a few will be inserted here illustrating the use of bar and dot numerals with both normal-form and head-variant period glyphs, with which the student should be perfectly familiar by this time.

In plate 9, _A_, is figured a photograph of the Initial Series on the front of Stela 11 at Yaxchilan.[145] The introducing glyph appears in A1 B1; 9 cycles in A2; 16 katuns in B2, 1 tun in 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 flaring postfix in the kin head. The tun is expressed by its normal form. The number here recorded is 9.16.1.0.0, and reducing this to units of the first order by means of Table XIII, we have:

A2 = 9 × 144,000 = 1,296,000 B2 = 16 × 7,200 = 115,200 A3 = 1 × 360 = 360 B3 = 0 × 20 = 0 A4 = 0 × 1 = 0 --------- 1,411,560

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 by the resulting calculations will be 11 Ahau 8 Tzec. The day part of this date is very clearly recorded in B4 immediately after the last period glyph, and the student will readily recognize 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, _g-h_. The month coefficient is 8. The terminal date, therefore, recorded in B4 and D3 (11 Ahau 8 Tzec) agrees with the terminal date determined by calculation, and this whole text reads 9.16.1.0.0 11 Ahau 8 Tzec. The meaning of the element between the tun coefficient and the tun sign in A3, which is repeated again in D3 between the month coefficient and the month sign, is unknown.

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS]

{177}

In plate 9, _B_, is figured the Initial Series on an altar in front of Structure 44 at Yaxchilan.[146] The introducing glyph appears in A1 B1 and is followed by the number in A2-A4. The period glyphs are all expressed as head variants 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 terminal dates for all four of these values, commencing with 0, and then see which of the resulting terminal days is the one actually recorded in A4. Reducing the number 9.12.8.14.0 to units of the first order by means of Table XIII, we have:

A2 = 9 × 144,000 = 1,296,000 B2 = 12 × 7,200 = 86,400 A3= 8 × 360 = 2,880 B3 = 14 × 20 = 280 A4= 0 × 1 = 0 --------- 1,385,560

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 11 Ahau 3 Pop. Therefore the Initial-series numbers 9.12.8.14.1, 9.12.8.14.2, and 9.12.8.14.3 will lead to the three days immediately following 9.12.8.14.0 11 Ahau 3 Pop. Therefore our four possible terminal dates will be:

9.12.8.14.0 11 Ahau 3 Pop 9.12.8.14.1 12 Imix 4 Pop <------ 9.12.8.14.2 13 Ik 5 Pop 9.12.8.14.3 1 Akbal 6 Pop

Now let us look for one of these four terminal dates in the text. The day reached by an Initial Series is almost invariably recorded immediately after the last period glyph; therefore, if this inscription is regular, the day glyph should be B4. This glyph probably has the coefficient 12 (2 bars and 2 numerical dots), the oblong element between probably being ornamental only. This number must be either 11 or 12, since if it were 13 the 3 dots would all be of the same size, which is not the case. An inspection of the coefficient in B4 eliminates from consideration, therefore, the last 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 {178} 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 day as 12 Imix. If, on the other hand, the day were 11 Ahau, the month glyph would be 3 Pop. Passing over A5 B5, A6 B6, C1 D1, and C2, we, reach in D2a the closing glyph of the Supplementary Series, here showing the coefficient 9. Compare this form with figure 65. The month glyph, therefore, should appear in D2b. The coefficient of this glyph is very clearly 4, thus confirming our identification of B4 as 12 Imix. (See Table VII.) And finally, the month glyph itself is Pop. Compare D2b with figure 19, a. The whole Initial Series in plate 9, _B_, therefore reads 9.12.8.14.1 12 Imix 4 Pop.

In plate 10, is figured the Initial Series from Stela 3 at Tikal.[147] The introducing glyph, though somewhat effaced, may still be recognized in A1. The Initial-series number follows in B1-B3. The head-variant period glyphs are too badly weathered to show the determining characteristic in each case, except the uinal head in A3, the mouth curl of which appears 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 curl of the head in A3 had not proved that the uinal was recorded here, we should have assumed this to be the case because this glyph, A3, is the fourth from the introducing glyph. The presence of the mouth curl therefore confirms the identification based on position. The student will have no difficulty in reading the number recorded in B1-B3 as 9.2.13.0.0.

Reducing this number by means of Table XIII to units of the first order, we obtain:

B1 = 9 × 144,000 = 1,296,000 A2 = 2 × 7,200 = 14,400 B2 = 13 × 360 = 4,680 A3 = 0 × 20 = 0 B3 = 0 × 1 = 0 --------- 1,315,080

Deducting all the Calendar Rounds possible from this number, 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 4 Ahau 13 Kayab. It remains to find this date in the text. The glyph in A4, the proper position for the day glyph, is somewhat effaced, though the profile of the 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, here recorded with a coefficient of 9. Compare B6 with figure 65. The month glyph follows in A7 with the coefficient 13. Comparing this latter glyph with the month signs in figure 19, it is evident that the month Kayab (fig. 19, _d'-f'_) is recorded in A7, which reads, therefore, 13 Kayab. Hence the whole text records the Initial Series 9.2.13.0.0 4 Ahau 13 Kayab.

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS--STELA 3, TIKAL]

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF BAR AND DOT NUMERALS AND HEAD-VARIANT PERIOD GLYPHS--STELA A (EAST SIDE), QUIRIGUA]

{179}

This Initial Series is extremely important, because it records the earliest contemporaneous[148] date yet found on a monument[149] in the Maya territory.

In plate 11 is figured the Initial Series from the east side of Stela A at Quirigua.[150] The introducing glyph appears in A1-B2 and the Initial-series number in A3-A5. The student will have little difficulty in 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, respectively. The kin head in A5 is the banded-headdress variant (compare fig. 34, _i, j_), and this completes the number, which is 9.17.5.0.0. Reducing this by means of Table XIII to units of the first order, we have:

A3 = 9 × 144,000 = 1,296,000 B3 = 17 × 7,200 = 122,400 A4 = 5 × 360 = 1,800 B4 = 0 × 20 = 0 A5 = 0 × 0 = 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, {180} 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:

[Illustration: GLYPHS REPRESENTING INITIAL SERIES, SHOWING USE OF HEAD-VARIANT NUMERALS AND PERIOD GLYPHS]

{181}

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 {182} 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. {183}

[Illustration: 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) {184} 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 {185} 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. {186}

[Illustration: 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