Chapter VI: The Codices (3)

[39] This statement does not take account of the Tuxtla Statuette and the Holactun Initial Series, which extend the range of the dated monuments to ten centuries.

[40] For the discussion of the number of cycles in a great cycle, a question concerning which there are two different opinions, see pp. 107 et seq.

[41] There are only two known exceptions to this statement, namely, the Initial Series on the Temple of the Cross at Palenque and that on the east side of Stela C at Quirigua, already noted.

[42] Mr. Bowditch (1910: App. VIII, 310-18) discusses the possible meanings of this element.

[43] For explanation of the term "full-figure glyphs," see p. 67.

[44] See the discussion of Serpent numbers in Chapter VI.

[45] These three inscriptions are found on Stela N, west side, at Copan, the tablet of the Temple of the Inscriptions at Palenque, and Stela 10 at Tikal. For the discussion of these inscriptions, see pp. 114-127.

[46] The discussion of glyphs which may represent the great cycle or period of the 6th order will be presented on pp. 114-127 in connection with the discussion of numbers having six or more orders of units.

[47] The figure on Zoömorph B at Quirigua, however, has a normal human head without grotesque characteristics.

[48] The full-figure glyphs are included with the head variants in this proportion.

[49] Any system of counting time which describes a date in such a manner that it can not recur, satisfying all the necessary conditions, for 374,400 years, must be regarded as absolutely accurate in so far as the range of human life on this planet is concerned.

[50] There are a very few monuments which have two Initial Series instead of one. So far as the writer knows, only six monuments in the entire Maya area present this feature, namely, Stelæ F, D, E, and A at Quirigua, Stela 17 at Tikal, and Stela 11 at Yaxchilan.

[51] Refer to p. 64 and figure 23. It will be noted that the third tooth (i. e. day) after the one named 7 Akbal 11 Cumhu is 10 Cimi 14 Cumhu.

[52] This method of dating does not seem to have been used with either uinal or kin period endings, probably because of the comparative frequency with which any given date might occur at the end of either of these two periods.

[53] In Chapter IV it will be shown that two bars stand for the number 10. It will be necessary to anticipate the discussion of Maya numerals there presented to the extent of stating that a bar represented 5 and a dot or ball, 1. The varying combinations of these two elements gave the values up to 20.

[54] The u kahlay katunob on which the historical summary given in Chapter I is based shows an absolutely uninterrupted sequence of katuns for more than 1,100 years. See Brinton (1882 b: pp. 152-164). It is necessary to note here a correction on p. 153 of that work. Doctor Brinton has omitted a Katun 8 Ahau from this u kahlay katunob, which is present in the Berendt copy, and he has incorrectly assigned the abandonment of Chichen Itza to the preceding katun, Katun 10 Ahau, whereas the Berendt copy shows this event took place during the katun omitted, Katun 8 Ahau.

[55] There are, of course, a few exceptions to this rule--that is, there are some monuments which indicate an interval of more than 3,000 years between the extreme dates. In such cases, however, this interval is not divided into katuns, nor in fact into any regularly recurring smaller unit, with the single exception mentioned in footnote 1, p. 84.

[56] On one monument, the tablet from the Temple of the Inscriptions at Palenque, there seems to be recorded a kind of u kahlay katunob; at least, there is a sequence of ten consecutive katuns.

[57] The word "numeral," as used here, has been restricted to the first twenty numbers, 0 to 19, inclusive.

[58] See p. 96, footnote 1.

[59] In one case, on the west side of Stela E at Quirigua, the number 14 is also shown with an ornamental element (). This is very unusual and, so far as the writer knows, is the only example of its kind. The four dots in the numbers 4, 9, 14, and 19 never appear thus separated in any other text known.

[60] In the examples given the numerical coefficients are attached as prefixes to the katun sign. Frequently, however, they occur as superfixes. In such cases, however, the above observations apply equally well.

[61] Care should be taken to distinguish the number or figure 20 from any period which contained 20 periods of the order next below it; otherwise the uinal, katun, and cycle glyphs could all be construed as signs for 20, since each of these periods contains 20 units of the period next lower.

[62] The Maya numbered by relative position from bottom to top, as will be presently explained.

[63] This form of zero is always red and is used with black bar and dot numerals as well as with red in the codices.

[64] It is interesting to note in this connection that the Zapotec made use of the same outline in graphic representations of the tonalamatl. On page 1 of the Zapotec Codex Féjerváry-Mayer an outline formed by the 260 days of the tonalamatl exactly like the one in fig. 48, _a_, is shown.

[65] This form of zero has been found only in the Dresden Codex. Its absence from the other two codices is doubtless due to the fact that the month glyphs are recorded only a very few times in them--but once in the Codex Tro-Cortesiano and three times in the Codex Peresianus.

[66] The forms shown attached to these numerals are those of the day and month signs (see figs. 16, 17, and 19, 20, respectively), and of the period glyphs (see figs. 25-35, inclusive). Reference to these figures will explain the English translation in the case of any form which the student may not remember.

[67] The following possible exceptions, however, should be noted: In the Codex Peresianus the normal form of the tun sign sometimes occurs attached to varying heads, as (). Whether these heads denote numerals is unknown, but the construction of this glyph in such cases (a head attached to the sign of a time period) absolutely parallels the use of head-variant numerals with time-period glyphs in the inscriptions. A much stronger example of the possible use of head numerals with period glyphs in the codices, however, is found in the Dresden Codex. Here the accompanying head () is almost surely that for the number 16, the hatchet eye denoting 6 and the fleshless lower jaw 10. Compare (+) with fig. 53, _f-i_, where the head for 16 is shown. The glyph () here shown is the normal form for the kin sign. Compare fig. 34, b. The meaning of these two forms would thus seem to be 16 kins. In the passage in which these glyphs occur the glyph next preceding the head for 16 is "8 tuns," the numerical coefficient 8 being expressed by one bar and three dots. It seems reasonably clear here, therefore, that the form in question is a head numeral. However, these cases are so very rare and the context where they occur is so little understood, that they have been excluded in the general consideration of head-variant numerals presented above.

[68] It will appear presently that the number 13 could be expressed in two different ways: (1) by a special head meaning 13, and (2) by the essential characteristic of the head for 10 applied to the head for 3 (i. e., 10 + 3 = 13).

[69] For the discussion of Initial Series in cycles other than Cycle 9, see pp. 194-207.

[70] The subfixial element in the first three forms of fig. 54 does not seem to be essential, since it is wanting in the last.

[71] As previously explained, the number 20 is used only in the codices and there only in connection with tonalamatls.

[72] Whether the Maya used their numerical system in the inscriptions and codices for counting anything besides time is not known. As used in the texts, the numbers occur only in connection with calendric matters, at least in so far as they have been deciphered. It is true many numbers are found in both the inscriptions and codices which are attached to signs of unknown meaning, and it is possible that these may have nothing to do with the calendar. An enumeration of cities or towns, or of tribute rolls, for example, may be recorded in some of these places. Both of these subjects are treated of in the Aztec manuscripts and may well be present in Maya texts.

[73] The numerals and periods given in fig. 56 are expressed by their normal forms in every case, since these may be more readily recognized than the corresponding head variants, and consequently entail less work for the student. It should be borne in mind, however, that any bar and dot numeral or any period in fig. 56 could be expressed equally well by its corresponding head form without affecting in the least the values of the resulting numbers.

[74] There may be three other numbers in the inscriptions which are considerably higher (see pp. 114-127).

[75] These are: (1) The tablet from the Temple of the Cross at Palenque; (2) Altar 1 at Piedras Negras; and (3) The east side of Stela C at Quirigua.

[76] This case occurs on the tablet from the Temple of the Foliated Cross at Palenque.

[77] It seems probable that the number on the north side of Stela C at Copan was not counted from the date 4 Ahau 8 Cumhu. The writer has not been able to satisfy himself, however, that this number is an Initial Series.

[78] Mr. Bowditch (1910: pp. 41-42) notes a seeming exception to this, not in the inscription, however, but in the Dresden Codex, in which, in a series of numbers on pp. 71-73, the number 390 is written 19 uinals and 10 kins, instead of 1 tun, 1 uinal, and 10 kins.

[79] That it was a Cycle 13 is shown from the fact that it was just 13 cycles in advance of Cycle 13 ending on the date 4 Ahau 8 Cumhu.

[80] See p. 156 and fig. 66 for method of designating the individual glyphs in a text.

[81] The kins are missing from this number (see A9, fig. 60). At the maximum, however, they could increase this large number only by 19. They have been used here as at 0.

[82] As will be explained presently, the kin sign is frequently omitted and its coefficient attached to the uinal glyph. See p. 127.

[83] Glyph A9 is missing but undoubtedly was the kin sign and coefficient.

[84] The lowest period, the kin, is missing. See A9, fig. 60.

[85] The use of the word "generally" seems reasonable here; these three texts come from widely separated centers--Copan in the extreme southeast, Palenque in the extreme west, and Tikal in the central part of the area.

[86] A few exceptions to this have been noted on pp. 127, 128.

[87] The Books of Chilan Balam have been included here as they are also expressions of the native Maya mind.

[88] This excludes, of course, the use of the numerals 1 to 13, inclusive, in the day names, and in the numeration of the cycles; also the numerals 0 to 19, inclusive, when used to denote the positions of the days in the divisions of the year, and the position of any period in the division next higher.

[89] Various methods and tables have been devised to avoid the necessity of reducing the higher terms of Maya numbers to units of the first order. Of the former, that suggested by Mr. Bowditch (1910: pp. 302-309) is probably the most serviceable. Of the tables Mr. Goodman's Archæic Annual Calendar and Archæic Chronological Calendar (1897) are by far the best. By using either of the above the necessity of reducing the higher terms to units of the first order is obviated. On the other hand, the processes by means of which this is achieved in each case are far more complicated and less easy of comprehension than those of the method followed in this book, a method which from its simplicity might be termed perhaps the logical way, since it reduces all quantities to a primary unit, which is the same as the primary unit of the Maya calendar. This method was first devised by Prof. Ernst Förstemann, and has the advantage of being the most readily understood by the beginner, sufficient reason for its use in this book.

[90] This number is formed on the basis of 20 cycles to a great cycle (20×144,000=2,880,000). The writer assumes that he has established the fact that 20 cycles were required to make 1 great cycle, in the inscriptions as well as in the codices.

[91] This is true in spite of the fact that in the codices the starting points frequently appear to follow--that is, they stand below--the numbers which are counted from them. In reality such cases are perfectly regular and conform to this rule, because there the order is not from top to bottom but from bottom to top, and, therefore, when read in this direction the dates come first.

[92] These intervening glyphs the writer believes, as stated in Chapter II, are those which tell the real story of the inscriptions.

[93] Only two exceptions to this rule have been noted throughout the Maya territory: (1) The Initial Series on the east side of Stela C at Quirigua, and (2) the tablet from the Temple of the Cross at Palenque. It has been explained that both of these Initial Series are counted from the date 4 Ahau 8 Zotz.

[94] In the inscriptions an Initial Series may always be identified by the so-called introducing glyph (see fig. 24) which invariably precedes it.

[95] Professor Förstemann has pointed out a few cases in the Dresden Codex in which, although the count is backward, the special character indicating the fact is wanting (fig. 64). (See _Bulletin_ 28, p. 401.)

[96] There are a few cases in which the "backward sign" includes also the numeral in the second position.

[97] In the text wherein this number is found the date 4 Ahau 8 Camhu stands below the lowest term.

[98] It should be noted here that in the _u kahlay katunob_ also, from the Books of Chilan Balam, the count is always forward.

[99] For transcribing the Maya numerical notation into the characters of our own Arabic notation Maya students have adopted the practice of writing the various terms from left to right in a _descending_ series, as the units of our decimal system are written. For example, 4 katuns, 8 tuns, 3 uinals, and 1 kin are written 4.8.3.1; and 9 cycles, 16 katuns, 1 tun, 0 uinal, and 0 kins are written 9.16.1.0.0. According to this method, the highest term in each number is written on the left, the next lower on its right, the next lower on the right of that, and so on down through the units of the first, or lowest, order. This notation is very convenient for transcribing the Maya numbers and will be followed hereafter.

[100] The reason for rejecting all parts of the quotient except the numerator of the fractional part is that this part alone shows the actual number of units which have to be counted either forward or backward, as the count may be, in order to reach the number which exactly uses up or finishes the dividend--the last unit of the number which has to be counted.

[101] The student can prove this point for himself by turning to the tonalamatl wheel in pl. 5; after selecting any particular day, as 1 Ik for example, proceed to count 260 days from this day as a starting point, in either direction around the wheel. No matter in which direction he has counted, whether beginning with 13 Imix or 2 Akbal, the 260th day will be 1 Ik again.

[102] The student may prove this for himself by reducing 9.0.0.0.0 to days (1,296,000), and counting forward this number from the date 4 Ahau 8 Cumhu, as described in the rules on pages 138-143. The terminal date reached will be 8 Ahau 13 Ceh, as given above.

[103] Numbers may also be added to or subtracted from Period-ending dates, since the positions of such dates are also fixed in the Long Count, and consequently may be used as bases of reference for dates whose positions in the Long Count are not recorded.

[104] In adding two Maya numbers, for example 9.12.2.0.16 and 12.9.5, care should be taken first to arrange like units under like, as:

9.12. 2. 0.16
12. 9. 5
-------------
9.12.14.10. 1

Next, beginning at the right, the kins or units of the 1st place are added together, and after all the 20s (here 1) have been deducted from this sum, place the remainder (here 1) in the kin place. Next add the uinals, or units of the 2d place, adding to them 1 for each 20 which was carried forward from the 1st place. After all the 18s possible have been deducted from this sum (here 0) place the remainder (here 10) in the uinal place. Next add the tuns, or units of the 3d place, adding to them 1 for each 18 which was carried forward from the 2d place, and after deducting all the 20s possible (here 0) place the remainder (here 14) in the tun place. Proceed in this manner until the highest units present have been added and written below.

Subtraction is just the reverse of the preceding. Using the same numbers:

9.12. 2.0.16
12.9. 5
------------
9.11. 9.9.11

5 kins from 16 = 11; 9 uinals from 18 uinals (1 tun has to be borrowed) = 9; 12 tuns from 21 tuns (1 katun has to be borrowed, which, added to the 1 tun left in the minuend, makes 21 tuns) = 9 tuns; 0 katuns from 11 katuns (1 katun having been borrowed) = 11 katuns; and 0 cycles from 9 cycles = 9 cycles.

[105] The Supplementary Series present perhaps the most promising field for future study and investigation in the Maya texts. They clearly have to do with a numerical count of some kind, which of itself should greatly facilitate progress in their interpretation. Mr. Goodman (1897: p. 118) has suggested that in some way the Supplementary Series record the dates of the Initial Series they accompany according to some other and unknown method, though he offers no proof in support of this hypothesis. Mr. Bowditch (1910: p. 244) believes they probably relate to time, because the glyphs of which they are composed have numbers attached to them. He has suggested the name Supplementary Series by which they are known, implying in the designation that these Series in some way supplement or complete the meaning of the Initial Series with which they are so closely connected. The writer believes that they treat of some lunar count. It seems almost certain that the moon glyph occurs repeatedly in the Supplementary Series (see fig. 65).

[106] The word "closing" as used here means only that in reading from left to right and from top to bottom--that is, in the normal order--the sign shown in fig. 65 is always the last one in the Supplementary Series, usually standing immediately before the month glyph of the Initial-series terminal date. It does not signify, however, that the Supplementary Series were to be read in this direction, and, indeed, there are strong indications that they followed the reverse order, from right to left and bottom to top.

[107] In a few cases the sign shown in fig. 65 occurs elsewhere in the Supplementary Series than as its "closing" glyph. In such cases its coefficient is not restricted to the number 9 or 10.

[108] In the codices frequently the month parts of dates are omitted and starting points and terminal dates alike are expressed as days only; thus, 2 Ahau, 5 Imix, 7 Kan, etc. This is nearly always the case in tonalamatls and in certain series of numbers in the Dresden Codex.

[109] Only a very few month signs seem to be recorded in the Codex Tro-Cortesiano and the Codex Peresianus. The Tro-Cortesiano has only one (p. 73b), in which the date 13 Ahau 13 Cumhu is recorded thus (). Compare the month form in this date with fig. 20, _z-b'_. Mr. Gates (1910: p. 21) finds three month signs in the Codex Peresianus, on pp. 4, 7, and 18 at 4c7, 7c2, and 18b4, respectively. The first of these is 16 Zac (). Compare this form with fig. 20, _o_. The second is 1 Yaxkin (+). Compare this form with fig. 20, _i-j_. The third is 12 Cumhu (++); see fig. 20, _z-b'_.

[110] As used throughout this work, the word "inscriptions" is applied only to texts from the monuments.

[111] The term glyph-block has been used instead of glyph in this connection because in many inscriptions several different glyphs are included in one glyph-block. In such cases, however, the glyphs within the glyph-block follow precisely the same order as the glyph-blocks themselves follow in the pairs of columns, that is, from left to right and top to bottom.

[112] Initial Series which have all their period glyphs expressed by normal forms are comparatively rare; consequently the four examples presented in pl. 6, although they are the best of their kind, leave something to be desired in other ways. In pl. 6, _A_, for example, the month sign was partially effaced though it is restored in the accompanying reproduction; in _B_ of the same plate the closing glyph of the Supplementary Series (the month-sign indicator) is wanting, although the month sign itself is very clear. Again, in _D_ the details of the day glyph and month glyph are partially effaced (restored in the reproduction), and in _C_, although the entire text is very clear, the month sign of the terminal date irregularly follows immediately the day sign. However, in spite of these slight irregularities, it has seemed best to present these particular texts as the first examples of Initial Series, because their period glyphs are expressed by normal forms exclusively, which, as pointed out above, are more easily recognized on account of their greater differentiation than the corresponding head variants.

[113] In most of the examples presented in this chapter the full inscription is not shown, only that part of the text illustrating the particular point in question being given. For this reason reference will be made in each case to the publication in which the entire inscription has been reproduced. The full text on Zoömorph P at Quirigua will be found in Maudslay, 1889-1902: II, pls. 53, 54, 55, 56, 57, 59, 63, 64.

[114] All glyphs expressed in this way are to be understood as inclusive. Thus A1-B2 signifies 4 glyphs, namely, A1, B1, A2, B2,

[115] The introducing glyph, so far as the writer knows, always stands at the beginning of an inscription, or in the second glyph-block, that is, at the top. Hence an Initial Series can never precede it.

[116] The Initial Series on Stela 10 at Tikal is the only exception known. See pp. 123-127.

[117] As will appear in the following examples, nearly all Initial Series have 9 as their cycle coefficient.

[118] In the present case therefore so far as these calculations are concerned, 3,900 is the equivalent of 1,427,400.

[119] It should be remembered in this connection, as explained on pp. 47, 55, that the positions in the divisions of the year which the Maya called 3, 8, 13, and 18 correspond in our method of naming the positions of the days in the months to the 4th, 9th, 14th, and 19th positions, respectively.

[120] As stated in footnote 1, p. 152, the meaning of the Supplementary Series has not yet been worked out.

[121] The reasons which have led the writer to this conclusion are given at some length on pp. 33-36.

[122] For the full text of this inscription see Maler, 1908 b: pl. 36.

[123] Since nothing but Initial-series texts will be presented in the plates and figures immediately following, a fact which the student will readily detect by the presence of the introducing glyph at the head of each text, it is unnecessary to repeat for each new text step 2 (p. 135) and step 3 (p. 136), which explain how to determine the starting point of the count and the direction of the count, respectively; and the student may assume that the starting point of the several Initial Series hereinafter figured will always be the date 4 Ahau 8 Cumhu and that the direction of the count will always be forward.

[124] As will appear later, in connection with the discussion of the Secondary Series, the Initial-series date of a monument does not always correspond with the ending date of the period whose close the monument marks. In other words, the Initial-series date is not always the date contemporaneous with the formal dedication of the monument as a time-marker. This point will appear much more clearly when the function of Secondary Series has been explained.

[125] For the full text of this inscription see Hewett, 1911: pl. XXXV _C_.

[126] So far as the writer knows, the existence of a period containing 5 tuns has not been suggested heretofore. The very general practice of closing inscriptions with the end of some particular 5-tun period in the Long Count, as 9.18.5.0.0, or 9.18.10.0.0, or 9.18.15.0.0, or 9.19.0.0.0, for example, seems to indicate that this period was the unit used for measuring time in Maya chronological records, at least in the southern cities. Consequently, it seems likely that there was a special glyph to express this unit.

[127] For the full text of this inscription see Maler, 1908 b: pl. 39.

[128] The student should note that from this point steps 2 (p. 139) and 3 (p. 140) have been omitted in discussing each text (see p. 162, footnote 3).

[129] In each of the above cases--and, indeed, in all the examples following--the student should perform the various calculations by which the results are reached, in order to familiarize himself with the workings of the Maya chronological system.

[130] The student may apply a check at this point to his identification of the day sign in A4 as being that for the day Eb. Since the month coefficient in A7 is surely 10 (2 bars), it is clear from Table VII that the only days which can occupy this position in any division of the year are Ik, Manik, Eb, and Caban. Now, by comparing the sign in A4 with the signs for Ik, Manik, and Caban, _c, j_, and _a', b'_, respectively, of fig. 16, it is very evident that A4 bears no resemblance to any of them; hence, since Eb is the only one left which can occupy a position 10, the day sign in A4 must be Eb, a fact supported by the comparison of A4 with fig. 16, _s-u_, above.

[131] The full text of this inscription will be found in Maudslay, 1889-1901: I, pls. 35-37.

[132] The full text of this inscription is given in Maudslay, 1889-1902: I, pls. 27-30.

[133] Note the decoration on the numerical bar.

[134] So far as known to the writer, this very unusual variant for the closing glyph of the Supplementary Series occurs in but two other inscriptions in the Maya territory, namely, on Stela N at Copan. See pl. 26, Glyph A14, and Inscription 6 of the Hieroglyphic Stairway at Naranjo, Glyph A1 (?). (Maler, 1908 b: pl. 27.)

[135] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 105-107.

[136] In this glyph-block, A4, the order of reading is irregular; instead of passing over to B4a after reading A4a (the 10 tuns), the next glyph to be read is the sign below A4a, A4b, which records 0 uinals, and only after this has been read does B4a follow.

[137] Texts illustrating the head-variant numerals in full will be presented later.

[138] The preceding hotun ended with the day 9.12.5.0.0 3 Ahau 3 Xul and therefore the opening day of the next hotun, 1 day later, will be 9.12.5.0.1 4 Imix 4 Xul.

[139] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 109, 110.

[140] The oldest Initial Series at Copan is recorded on Stela 15, which is 40 years older than Stela 9. For a discussion of this text see pp. 187, 188.

[141] An exception to this statement should be noted in an Initial Series on the Hieroglyphic Stairway, which records the date 9.5.19.3.0 8 Ahau 3 Zotz. The above remark applies only to the large monuments, which, the writer believes, were period-markers. Stela 9 is therefore the next to the oldest "period stone" yet discovered at Copan. It is more than likely, however, that there are several older ones as yet undeciphered.

[142] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 17-19.

[143] Although this date is considerably older than that on Stela 9 at Copan, its several glyphs present none of the marks of antiquity noted in connection with the preceding example (pl. 8, _B_). For example, the ends of the bars denoting 5 are not square but round, and the head-variant period glyphs do not show the same elaborate and ornate treatment as in the Copan text. This apparent contradiction permits of an easy explanation. Although the Initial Series on the west side of Stela C at Quirigua undoubtedly refers to an earlier date than the Initial Series on the Copan monument, it does not follow that the Quirigua monument is the older of the two. This is true because on the other side of this same stela at Quirigua is recorded another date, 9.17.5.0.0 6 Ahau 13 Kayab, more than three hundred years later than the Initial Series 9.1.0.0.0 6 Ahau 13 Yaxkin on the west side, and this later date is doubtless the one which referred to present time when this monument was erected. Therefore the Initial Series 9.1.0.0.0 6 Ahau 13 Yaxkin does not represent the period which Stela C was erected to mark, but some far earlier date in Maya history.

[144] For the full text of this inscription see Maudslay, 1889-1902: I, pl. 74.

[145] For the full text of this inscription see Maler, 1903: II, No. 2, pls. 74, 75.

[146] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 79, 2.

[147] For the full text of this inscription see Maler, 1911: V, No. 1, pl. 15.

[148] As used throughout this book, the expression "the contemporaneous date" designates the time when the monument on which such a date is found was put into formal use, that is, the time of its erection. As will appear later in the discussion of the Secondary Series, many monuments present several dates between the extremes of which elapse long periods. Obviously, only one of the dates thus recorded can represent the time at which the monument was erected. In such inscriptions the final date is almost invariably the one designating contemporaneous time, and the earlier dates refer probably to historical, traditional, or even mythological events in the Maya past. Thus the Initial Series 9.0.19.2.4 2 Kan 2 Yax on Lintel 21 at Yaxchilan, 9.1.0.0.0 6 Ahau 13 Yazkin on the west side of Stela C at Quirigua, and 9.4.0.0.0 13 Ahau 18 Yax from the Temple of the Inscriptions at Palenque, all refer probably to earlier historical or traditional events in the past of these three cities, but they do not indicate the dates at which they were severally recorded. As Initial Series which refer to purely mythological events may be classed the Initial Series from the Temples of the Sun, Cross, and Foliated Cross at Palenque, and from the east side of Stela C at Quirigua, all of which are concerned with dates centering around or at the beginning of Maya chronology. Stela 3 at Tikal (the text here under discussion), on the other hand, has but one date, which probably refers to the time of its erection, and is therefore contemporaneous.

[149] There are one or two earlier Initial Series which probably record contemporaneous dates; these are not inscribed on large stone monuments but on smaller antiquities, namely, the Tuxtla Statuette and the Leyden Plate. For the discussion of these early contemporaneous Initial Series, see pp. 194-198.

[150] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 4-7.

[151] For the full text of this inscription see Maudslay, 1889-1902: IV, pls. 80-82.

[152] As explained on p. 179, footnote 1, this Initial Series refers probably to some mythological event rather than to any historical occurrence. The date here recorded precedes the historic period of the Maya civilization by upward of 3,000 years.

[153] For the full text of this inscription see Maudslay, 1889-1902; IV, pls. 87-89.

[154] For the full text of this inscription, see Maudslay, 1889-1902: IV, pl. 23.

[155] It is clear that if all the period coefficients above the kin have been correctly identified, even though the kin coefficient is unknown, by designating it 0 the date reached will be within 19 days of the date originally recorded. Even though its maximum value (19) had originally been recorded here, it could have carried the count only 19 days further. By using 0 as the kin coefficient, therefore, we can not be more than 19 days from the original date.

[156] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 88, 89.

[157] While at Copan the writer made a personal examination of this monument and found that Mr. Maudslay's drawing is incorrect as regards the coefficient of the day sign. The original has two numerical dots between two crescents, whereas the Maudslay drawing shows one numerical dot between two distinct pairs of crescents, each pair, however, of different shape.

[158] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 41-44.

[159] For the text of this monument see Spinden, 1913: VI, pl. 23, 2.

[160] For the discussion of full-figure glyphs, see pp. 65-73.

[161] The characteristics of the heads for 7, 14, 16, and 19 will be found in the heads for 17, 4, 6, and 9, respectively.

[162] For the full text of this inscription see Maudslay, 1889-1902: I, pls. 47, 48.

[163] The student will note also in connection with this glyph that the pair of comblike appendages usually found are here replaced by a pair of fishes. As explained on pp. 65-66, the fish represents probably the original form from which the comblike element was derived in the process of glyph conventionalization. The full original form of this element is therefore in keeping with the other full-figure forms in this text.

[164] For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 66-71.

[165] The student should remember that in this diagonal the direction of reading is from bottom to top. See pl. 15, _B_, glyphs 7, 8, 9, 10, 11, 12, etc. Consequently the upper half of 13 follows the lower half in this particular glyph.

[166] For the full text of this inscription see Hewett, 1911: pl. XXII _B_.

[167] A few monuments at Quirigua, namely, Stelæ F, D, E, and A, have two Initial Series each. In A both of the Initial Series have 0 for the coefficients of their uinal and kin glyphs, and in F, D, E, the Initial Series which shows the position of the monument in the Long Count, that is, the Initial Series showing the katun ending which it marks, has 0 for its uinal and kin coefficients.

[168] In 1913 Mr. M. D. Landry, superintendent of the Quirigua district, Guatemala division of the United Fruit Co., found a still earlier monument about half a mile west of the main group. This has been named Stela S. It records the katun ending prior to the one on Stela H, i. e., 9.15.15.0.0 9 Ahau 18 Xul.

[169] For the full text of this inscription see Holmes, 1907: pp. 691 et seq., and pls. 34-41.

[170] For a full discussion of the Tuxtla Statuette, including the opinions of several writers as to its inscription, see Holmes, 1907: pp. 691 et seq. The present writer gives therein at some length the reasons which have led him to accept this inscription as genuine and contemporaneous.

[171] For the full text of these inscriptions, see Seler, 1902-1908: II, 253, and 1901 c: I, 23, fig. 7. During his last visit to the Maya territory the writer discovered that Stela 11 at Tikal has a Cycle-10 Initial Series, namely, 10.2.0.0.0. 3 Ahau 3 Ceh.

[172] Missing.

[173] At Seibal a Period-ending date 10.1.0.0.0 5 Ahau 3 Kayab is clearly recorded, but this is some 30 years earlier than either of the Initial Series here under discussion, a significant period just at this particular epoch of Maya history, which we have every reason to believe was filled with stirring events and quickly shifting scenes. Tikal, with the Initial Series 10.2.0.0.0 3 Ahau 3 Ceh, and Seibal with the same date (not as an Initial Series, however) are the nearest, though even these fall 10 years short of the Quen Santo and Chichen Itza Initial Series.

[174] Up to the present time no successful interpretation of the inscription on Stela C at Copan has been advanced. The inscription on each side of this monument is headed by an introducing glyph, but in neither case is this followed by an Initial Series. A number consisting of 11.14.5.1.0 is recorded in connection with the date 6 Ahau 18 Kayab, but as this date does not appear to be fixed in the Long Count, there is no way of ascertaining whether it is earlier or later than the starting point of Maya chronology. Mr. Bowditch (1910: pp. 195-196) offers an interesting explanation of this monument, to which the student is referred for the possible explanation of this text. A personal inspection of this inscription failed to confirm, however, the assumption on which Mr. Bowditch's conclusions rest. For the full text of this inscription, see Maudslay, 1889-1902: I, pls. 39-41.

[175] For the full text of this inscription, see ibid.: II, pls. 16, 17, 19.

[176] Table XVI contains only 80 Calendar Rounds (1,518,400), but by adding 18 Calendar Rounds (341,640) the number to be subtracted, 98 Calendar Rounds (1,860,040), will be reached.

[177] Counting 13.0.0.0.0 backward from the starting point of Maya chronology, 4 Ahau 8 Cumhu, gives the date 4 Ahau 8 Zotz, which is no nearer the terminal date recorded in B5-A6 than the date 4 Ahau 3 Kankin reached by counting forward.

[178] For the full text of this inscription, see Maudslay, 1889-1902: IV, pls. 73-77.

[179] As noted in Chapter IV, this is one of the only two heads for 13 found in the inscriptions which is composed of the essential element of the 10 head applied to the 3 head, the combination of the two giving 13. Usually the head for 13 is represented by a form peculiar to this number alone and is not built up by the combination of lower numbers as in this case.

[180] Although at first sight the headdress resembles the tun sign, a closer examination shows that it is not this element.

[181] Similarly, it could be shown that the use of every other possible value of the cycle coefficient will not give the terminal date actually recorded.

[182] For the full text of this inscription see Maler, 1903: II, No. 2, pl. 56.

[183] From this point on this step will be omitted, but the student is urged to perform the calculations necessary in each case to reach the terminal dates recorded.

[184] Since the introducing glyph always accompanies an Initial Series, it has here been included as a part of it, though, as has been explained elsewhere, its function is unknown.

[185] The number 15.1.16.5 is equal to 108,685 days, or 297½ years.

[186] It is interesting to note in this connection that the date 9.16.1.0.0 11 Ahau 8 Tzec, which is within 9 days of 9.16.1.0.9 7 Muluc 17 Tzec, is recorded in four different inscriptions at Yaxchilan, one of which (see pl. 9, _A_) has already been figured.

[187] For the full text of this inscription see Maler, 1901: II, No. 1, pl. 12.

[188] The month-sign indicator appears in B2 with a coefficient 10.

[189] Not expressed.

[190] The writer has recently established the date of this monument as 9.13.15.0.0 13 Ahau 18 Pax, or 99 days later than the above date.

[191] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 47-49.

[192] Although the details of the day and month signs are somewhat effaced, the coefficient in each case is 3, agreeing with the coefficients in the Initial-series terminal date, and the outline of the month glyph suggests that it is probably Yax. See fig. 19, _q, r_.

[193] Since the Maya New Year's day, 0 Pop, always fell on the 16th of July, the day 3 Yax always fell on Jan. 15th, at the commencement of the dry season.

[194] Since 0 Pop fell on July 16th (Old Style), 18 Kayab fell on June 19th, which is very near the summer solstice, that is, the seeming northern limit of the sun, and roughly coincident with the beginning of the rainy season at Quirigua.

[195] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 46.

[196] Bracketed dates are those which are not actually recorded but which are reached by numbers appearing in the text.

[197] Although not recorded, the number 1.14.6 is the distance from the date 9.15.5.0.0 reached by the Secondary Series on one side to the starting point of the Secondary Series on the other side, that is, 9.15.6.14.6 6 Cimi 4 Tzec.

[198] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 37, 39, 40. For convenience in figuring, the lower parts of columns A and B are shown in _B_ instead of below the upper part. The numeration of the glyph-blocks, however, follows the arrangement in the original.

[199] This is one of the two Initial Series which justified the assumptions made in the previous text that the date 12 Caban 5 Kayab, which was recorded there, had the Initial-series value 9.14.13.4.17, as here.

[200] This is the text in which the Initial-series value 9.15.6.14.6 was found attached to the date 6 Cimi 4 Tzec.

[201] For the full text of this inscription see Maudslay, 1889-1902: II, pls. 38, 40.

[202] The frontlet seems to be composed of but one element, indicating for this head the value 8 instead of 1. However, as the calculations point to 1, it is probable there was originally another element to the frontlet.

[203] See Maudslay, 1889-1902: I, pl. 102, west side, glyphs A5b-A7a.

[204] See ibid.: IV, pl. 81, glyphs N15 O15.

[205] See Maler, 1908 b: IV, No. 2, pl. 38, east side, glyphs A17-B18.

[206] See ibid., 1911: V, pl. 26, glyphs A1-A4.

[207] See Maudslay, 1889-1902: I, pl. 104, glyphs A7, B7.

[208] See Maudslay, 1889-1902: IV, pl. 60, glyphs M1-N2.

[209] Maler, 1911: V, pl. 17, east side, glyphs A4-A5.

[210] See Maudslay, 1889-1902: II, pl. 19, west side, glyphs B10-A12.

[211] See Maudslay, 1889-1902: IV, pl. 75, glyphs D3-C5.

[212] See Maler, 1901: II, No. 1, pl. 8, glyphs A1-A2.

[213] See Maudslay, op. cit., pl. 81, glyphs C7-D8.

[214] It will be remembered that Uayeb was the name for the _xma kaba kin_, the 5 closing days of the year. Dates which fall in this period are exceedingly rare, and in the inscriptions, so far as the writer knows, have been found only at Palenque and Tikal.

[215] See Maudslay, 1889-1902: IV, pl. 77, glyphs P14-R2. Glyphs Q15-P17 are omitted from pl. 22, _G_, as they appear to be uncalendrical.

[216] See Maudslay, 1889-1902: I, pl. 100, glyphs C1 D1, A2.

[217] This excludes Stela C, which has two Initial Series (see figs. 68 and 77), though neither of them, as explained on p. 175, footnote 1, records the date of this monument. The true date of this monument is declared by the Period-ending date figured in pl. 21, _H_, which is 9.17.0.0.0 6 Ahau 13 Kayab. (See p. 226.)

[218] See Maudslay, 1889-1902: II, pl. 44, west side, glyphs G4 H4, F5.

[219] The dates 10.2.5.0.0 9 Ahau 18 Yax and 10.2.10.0.0 2 Ahau 13 Chen on Stelæ 1 and 2, respectively, at Quen Santo, are purposely excluded from this statement. Quen Santo is in the highlands of Guatemala (see pl. 1) and is well to the south of the Usamacintla region. It rose to prominence probably after the collapse of the great southern cities and is to be considered as inaugurating a new order of things, if not indeed a new civilization.

[220] See Maler, 1908 a: IV, No. 1, pl. 9, glyphs E2, F2, A3, and A4.

[221] The student will note that the lower periods (the tun, uinal, and kin signs) are omitted and consequently are to be considered as having the coefficient 0.

[222] The usual positions of the uinal and kin coefficients in D4a are reversed, the kin coefficient 10 standing above the uinal sign instead of at the left of it. The calculations show, however, that 10, not 11, is the kin coefficient.

[223] In this number also the positions of the uinal and kin coefficients are reversed.

[224] For the full text of this inscription, see Maudslay, 1889-1902: II, pls. 28-32.

[225] The student will note that 12, not 13, tuns are recorded in A5. As explained elsewhere (see pp. 247, 248), this is an error on the part of the ancient scribe who engraved this inscription. The correct tun coefficient is 13, as used above.

[226] This Secondary-series number is doubly irregular. In the first place, the kin and uinal coefficients are reversed, the latter standing to the left of its sign instead of above, and in the second place, the uinal coefficient, although it is 14, has an ornamental dot between the two middle dots.

[227] Since we counted _backward_ 1.14.6 from 6 Cimi 4 Tzec to reach 10 Ahau 8 Chen, we must _subtract_ 1.14.6 from the Initial-series value of 6 Cimi 4 Tzec to reach the Initial-series value of 10 Ahau 8 Chen.

[228] It is obvious that the kin and uinal coefficients are reversed in A17b since the coefficient above the uinal sign is very clearly 19, an impossible value for the uinal coefficient in the inscriptions, 19 uinals _always_ being written 1 tun, 1 uinal. Therefore the 19 must be the kin coefficient. See also p. 110, footnote 1.

[229] The first glyph of the Supplementary Series, B6a, very irregularly stands between the kin period glyph and the day part of the terminal date.

[230] Incorrectly recorded as 12. See pp. 247, 248.

[231] In this table the numbers showing the distances have been omitted and all dates are shown in terms of their corresponding Initial-series numbers, in order to facilitate their comparison. The contemporaneous date of each monument is given in bold-faced figures and capital letters, and the student will note also that this date not only ends a hotun in each case but is, further, the latest date in each text.

[232] The Initial Series on the west side of Stela D at Quirigua is 9.16.13.4.17 8 Caban 5 Yaxkin, which was just 2 katuns later than 9.14.13.4.17 12 Caban 5 Kayab, or, in other words, the second katun anniversary, if the term anniversary may be thus used, of the latter date.

[233] For the full text of this inscription, see Maudslay, 1889-1902: II, pl. 50.

[234] For the full text of this inscription, see Maudslay, 1889-1902: I, pl. 112.

[235] Every fourth hotun ending in the Long Count was a katun ending at the same time, namely:

9.16. 0.0.0 2 Ahau 13 Tzec
9.16. 5.0.0 8 Ahau 8 Zotz
9.16.10.0.0 1 Ahau 3 Zip
9.16.15.0.0 7 Ahau 18 Pop
9.17. 0.0.0 13 Ahau 18 Cumhu
etc.

[236] Maler, 1911: No. 1, p. 40.

[237] For a seeming exception to this statement, in the codices, see p. 110, footnote 1.

[238] That is, the age of one compared with the age of another, without reference to their actual age as expressed in terms of our own chronology.

[239] See Chapter II for the discussion of this point and the quotations from contemporary authorities, both Spanish and native, on which the above statement is based.

[240] As explained on p. 31, tonalamatls were probably used by the priests in making prophecies or divinations. This, however, is a matter apart from their composition, that is, length, divisions, dates, and method of counting, which more particularly concerns us here.

[241] The codices are folded like a screen or fan, and when opened form a continuous strip sometimes several yards in length. As will appear later, in many cases one tonalamatl runs across several pages of the manuscript.

[242] If there should be two or more columns of day signs the topmost sign of the left-hand column is to be read first.

[243] In the original this last red dot has disappeared. The writer has inserted it here to avoid confusing the beginner in his first acquaintance with a tonalamatl.

[244] This and similar outlines which follow are to be read down in columns.

[245] The fifth sign in the lower row is also a sign of the Death God (see fig. 3). Note the eyelashes, suggesting the closed eyes of the dead.

[246] The last sign Chuen, as mentioned above, is only a repetition of the first sign, indicating that the tonalamatl has re-entered itself.

[247] As previously stated, the order of reading the glyphs in columns is from left to right and top to bottom.

[248] The right-hand dot of the 13 is effaced.

[249] The manuscript has incorrectly 7.

[250] In the title of plate 30 the page number should read 102 instead of 113.

[251] The manuscript incorrectly has 24.

[252] Incorrectly recorded as 13 in the text.

[253] Incorrectly recorded as 15 in the text.

[254] _Bull. 28, Bur. Amer. Ethn._, p. 400.

[255] The terminal dates reached have been omitted, since for comparative work the Initial-series numbers alone are sufficient to show the relative positions in the Long Count.

[256] The manuscript incorrectly reads 10.13.3.13.2; that is, reversing the position of the tun and uinal coefficients.

[257] The manuscript incorrectly reads 10.8.3.16.4. The katun coefficient is changed to 13, above. These corrections are all suggested by Professor Förstemann and are necessary if the calculations he suggests are correct, as seems probable.

[258] The manuscript incorrectly reads 8.16.4.11.0. The uinal coefficient is changed to an 8, above.

[259] The manuscript incorrectly reads 10.19.6.0.8. The uinal coefficient is changed to 1, above.

[260] The manuscript incorrectly reads 9.16.4.10.18. The uinal coefficient is changed to 11, above.

[261] The manuscript incorrectly reads 9.19.8.7.8. The tun coefficient is changed to 5, above.

[262] Bowditch, 1909: p. 279.

[263] The manuscript has incorrectly 16 Uo. It is obvious this can not be correct, since from Table VII Kan can occupy only the 2d, 7th, 12th, or 17th position in the months. The correct reading here, as we shall see, is probably 17 Uo. This reading requires only the addition of a single dot.

[264] In the text the coefficient appears to be 8, but in reality it is 9, the lower dot having been covered by the marginal line at the bottom.

[265] Counting backward 8.2.0 (2,920) from 9 Ahau, 1 Ahau is reached.

[266] Professor Förstemann restored the top terms of the four numbers in this row, so as to make them read as given above.

[267] The manuscript reads 1.12.5.0, which Professor Förstemann corrects to 1.12.8.0; in other words, changing the uinal from 5 to 8. This correction is fully justified in the above calculations.