Fig. 23Fig.23. Diagram showing section of Calendar-round wheel.
Fig.23. Diagram showing section of Calendar-round wheel.
It is clear that after one complete revolution of A, 18,980 days will have passed the starting point B, and that after two revolutions 37,960 days will have passed, and after three, 56,940, and so on. Indeed, it is only a question of the number of revolutions of A until as many as 1,500,000, or any number of days in fact, will have passed the starting point B, or, in other words, will have elapsed since the initial date,4 Ahau 8 Cumhu. This is actually what happened according to the Maya conception of time.
For example, let us imagine that a certain Initial Series expresses in terms of cycles, katuns, tuns, uinals, and kins, the number 1,461,463, and that the date recorded by this number of days is7 Akbal 11 Cumhu. Referring to figure23, it is evident that 77 revolutions of the cogwheel A, that is, 77 Calendar Rounds, will use up 1,461,460 of the 1,461,463 days, since 77×18,980 = 1,461,460. Consequently, when 77 Calendar Rounds shall have passed we shall still have left 3 days (1,461,463-1,461,460 = 3), which must be carried forward into the next Calendar Round. The 1,461,461st day will be5 Imix 9 Cumhu, that is, the day following4 Ahau 8 Cumhu(see fig.23); the 1,461,462d day will be6 Ik 10 Cumhu, and the 1,461,463d day, the last of the days in our Initial Series,7 Akbal 11 Cumhu, the date recorded. Examples of this method of dating (by Initial Series) will be given in Chapter V, where this subject will be considered in greater detail.
THE INTRODUCING GLYPH
In the inscriptions an Initial Series is invariably preceded by the so-called "introducing glyph," the Maya name for which is unknown.Several examples of this glyph are shown in figure24. This sign is composed of four constant elements:
1. The trinal superfix.2. The pair of comblike lateral appendages.3. The tun sign (see fig.29,a,b).4. The trinal subfix.
1. The trinal superfix.2. The pair of comblike lateral appendages.3. The tun sign (see fig.29,a,b).4. The trinal subfix.
1. The trinal superfix.
2. The pair of comblike lateral appendages.
3. The tun sign (see fig.29,a,b).
4. The trinal subfix.
Fig. 24Fig.24. Initial-series "introducing glyph."
Fig.24. Initial-series "introducing glyph."
In addition to these four constant elements there is one variable element which is always found between the pair of comblike lateral appendages. In figure24,a,b,e, this is a grotesque head; inc, a natural head; and ind, one of the 20 day-signs,Ik. This element varies greatly throughout the inscriptions, and, judging from its central position in the "introducing glyph" (itself the most prominent character in every inscription in which it occurs), it must have had an exceedingly important meaning.[42]A variant of the comblike appendages is shown in figure24,c,e, in which these elements are replaced by a pair of fishes. However, in such cases, all of which occur at Copan, the treatment of the fins and tail of the fish strongly suggests the elements they replace, and it is not improbable, therefore, that the comblike appendages of the "introducing glyph" are nothing more nor less than conventionalized fish fins or tails; in other words, that they are a kind of glyphic synecdoche in which a part (the fin) stands for the whole (the fish). That the original form of this element was the fish and not its conventionalized fin (*) seems to be indicated by several facts: (1) On Stela D at Copan, where only full-figure glyphs are presented,[43]the two comblike appendages of the "introducing glyph" appear unmistakably as two fishes. (2) In some of the earliest stelæ at Copan, as Stelæ 15 and P, while these elements are not fish forms, a head (fish?) appears with the conventionalized comb element in each case. The writer believes the interpretation of this phenomenon to be, that at the early epoch in whichStelæ 15 and P were erected the conventionalization of the element in question had not been entirely accomplished, and that the head was added to indicate the form from which the element was derived. (3) If the fish was the original form of the comblike element in the "introducing glyph," it was also the original form of the same element in the katun glyph. (Compare the comb elements (†) in figures27,a,b,e, and24,a,b,dwith each other.) If this is true, a natural explanation for the use of the fish in the katun sign lies near at hand. As previously explained on page28, the comblike element stands for the soundca(chard); whilekalin Maya means 20. Also the element (**) stands for the soundtun. Thereforecatunorkatunmeans 20 tuns. But the Maya word for "fish,"cay(chard) is also a close phonetic approximation of the soundcaorkal. Consequently, the fish sign may have been the original element in the katun glyph, which expressed the concept 20, and which the conventionalization of glyphic forms gradually reduced to the element (††) without destroying, however, its phonetic value.
Without pressing this point further, it seems not unlikely that the comblike elements in the katun glyph, as well as in the "introducing glyph," may well have been derived from the fish sign.
Turning to the codices, it must be admitted that in spite of the fact that many Initial Series are found therein, the "introducing glyph" has not as yet been positively identified. It is possible, however, that the sign shown in figure24,f, may be a form of the "introducing glyph"; at least it precedes an Initial Series in four places in the Dresden Codex (see pl.32). It is composed of the trinal superfix and a conventionalized fish (?).
Mr. Goodman calls this glyph (fig.24,a-e) the sign for the great cycle or unit of the 6th place (see TableVIII). He bases this identification on the fact that in the codices units of the 6th place stand immediately above[44]units of the 5th place (cycles), and consequently since this glyph stands immediately above the units of the 5th place in the inscriptions it must stand for the units of the 6th place. While admitting that the analogy here is close, the writer nevertheless is inclined to reject Mr. Goodman's identification on the following grounds: (1) This glyphneveroccurs with a numerical coefficient, while units of all the other orders—that is, cycles, katuns, tuns, uinals, and kinsare neverwithout them. (2) Units of the 6th order in the codices invariably have a numerical coefficient, as do all the other orders. (3) In the only three places in the inscriptions[45]in which six periods are seemingly recorded, though not as Initial Series, the 6th period has a numerical coefficient just as have the other five, and,moreover, the glyph in the 6th position is unlike the forms in figure24. (4) Five periods, not six, in every Initial Series express the distance from the starting point,4 Ahau 8 Cumhu, to the date recorded at the end of the long numbers.
It is probable that when the meaning of the "introducing glyph" has been determined it will be found to be quite apart from the numerical side of the Initial Series, at least in so far as the distance of the terminal date from the starting point,4 Ahau 8 Cumhu, is concerned.
While an Initial Series in the inscriptions, as has been previously explained, is invariably preceded by an "introducing glyph," the opposite does not always obtain. Some of the very earliest monuments at Copan, notably Stelæ 15, 7, and P, have "introducing glyphs" inscribed on two or three of their four sides, although but one Initial Series is recorded on each of these monuments. Examples of this use of the "introducing glyph," that is, other than as standing at the head of an Initial Series, are confined to a few of the earliest monuments at Copan, and are so rare that the beginner will do well to disregard them altogether and to follow this general rule: That in the inscriptions a glyph of the form shown in figure24,a-e, will invariably be followed by an Initial Series.
Having reached the conclusion that the introducing glyph was not a sign for the period of the 6th order, let us next examine the signs for the remaining orders or periods of the chronological system (cycles, katuns, tuns, uinals, and kins), constantly bearing in mind that these five periods alone express the long numbers of an Initial Series.[46]
Each of the above periods has two entirely different glyphs which may express it. These have been called (1) The normal form; (2) The head variant. In the inscriptions examples of both these classes occur side by side in the same Initial Series, seemingly according to no fixed rule, some periods being expressed by their normal forms and others by their head variants. In the codices, on the other hand, no head-variant period glyphs have yet been identified, and although the normal forms of the period glyphs have been found, they do not occur as units in Initial Series.
As head variants also should be classified the so-called "full-figure glyphs," in which the periods given in TableVIIIare represented by full figures instead of by heads. In these forms, however, only the heads of the figures are essential, since they alone present the determining characteristics, by means of which in each case identification is possible. Moreover, the head part of any full-figure variant is characterized by precisely the same essential elements as thecorresponding head variant for the same period, or in other words, the addition of the body parts in full-figure glyphs in no way influences or changes their meanings. For this reason head-variant and full-figure forms have been treated together. These full-figure glyphs are exceedingly rare, having been found only in five Initial Series throughout the Maya area: (1) On Stela D at Copan; (2) on Zoömorph B at Quirigua; (3) on east side Stela D at Quirigua; (4) on west side Stela D at Quirigua; (5) on Hieroglyphic Stairway at Copan. A few full-figure glyphs have been found also on an oblong altar at Copan, though not as parts of an Initial Series, and on Stela 15 as a period glyph of an Initial Series.
THE CYCLE GLYPH
Fig. 25Fig.25. Signs for the cycle:a-c, Normal forms;d-f, head variants.
Fig.25. Signs for the cycle:a-c, Normal forms;d-f, head variants.
Fig. 26Fig.26. Full-figure variant of cycle sign.
Fig.26. Full-figure variant of cycle sign.
The Maya name for the period of the 5th order in TableVIIIis unknown. It has been called "the cycle," however, by Maya students, and in default of its true designation, this name has been generally adopted. The normal form of the cycle glyph is shown in figure25,a,b,c. It is composed of an element which appears twice over a knotted support. The repeated element occurs also in the signs for the monthsChen, Yax, Zac, andCeh(see figs.19,o-v,20,l-p). This has been called theCauacelement because it is similar to the sign for the dayCauacin the codices (fig.17,b'), though on rather inadequate grounds the writer is inclined to believe. The head variant of the cycle glyph is shown in figure25,d-f. The essential characteristic of this grotesque head with its long beak is the hand element (*), which forms the lower jaw, though in avery few instanceseven this is absent. In the full-figure forms this same head is joined to the body of a bird (see fig.26). The bird intended is clearly a parrot, the feet, claws, and beak being portrayed in a very realistic manner. No glyph for the cycle has yet been found in the codices.
THE KATUN GLYPH
Fig. 27Fig.27. Signs for the katun:a-d, Normal forms;e-h, head variants.
Fig.27. Signs for the katun:a-d, Normal forms;e-h, head variants.
Fig. 28Fig.28. Full-figure variant of katun sign.
Fig.28. Full-figure variant of katun sign.
The period of the 4th place or order was called by the Maya thekatun; that is to say, 20 tuns, since it contained 20 units of the 3dorder (see TableVIII). The normal form of the katun glyph is shown in figure27,a-d. It is composed of the normal form of the tun sign (fig.29,a,b) surmounted by the pair of comblike appendages, which we have elsewhere seen meant 20, and which were probably derived from the representation of a fish. The whole glyph thus graphically portrays the concept 20 tuns, which according to TableVIIIis equal to 1 katun. The normal form of the katun glyph in the codices (fig.27,c,d) is identical with the normal form in the inscriptions (fig.27,a,b). Several head variants are found. The most easily recognized, though not the most common, is shown in figure27,e, in which the superfix is the same as in the normal form; that is, the element (†), which probably signifies 20 in this connection. To be logical, therefore, the head element should be the same as the head variant of the tun glyph, but this is not the case (see fig.29,e-h). When this superfix is present, the identification of the head variant of the katun glyph is an easy matter, but when it is absent it is difficult to fix on any essential characteristic. The general shape of the head is like the head variant of the cycle glyph. Perhaps the oval (**) in the top of the head in figure27,f-h, and the small curling fang (††) represented as protruding from the back part of the mouth are as constant as any of the other elements. The head of the full-figure variant in figure28presents the same lack of essential characteristics as the head variant, though in this form the small curling fang is also found. Again, the body attached to this head is that of a bird which has been identified as an eagle.
THE TUN GLYPH
Fig. 29Fig.29. Signs for the tun:a-d, Normal forms;e-h, head variants.
Fig.29. Signs for the tun:a-d, Normal forms;e-h, head variants.
Fig. 30Fig.30. Full-figure variant of tun sign.
Fig.30. Full-figure variant of tun sign.
The period of the 3d place or order was called by the Maya thetun, which means "stone," possibly because a stone was set up every 360 days or each tun or some multiple thereof. Compare so-called hotun or katun stones described on page34. The normal sign for the tun in the inscriptions (see fig.29,a,b) is identical with the form found in the codices (see fig.29,c). The head variant, which bears a general resemblance to the head variant for the cycle and katun, has several forms. The one most readily recognized, because it has the normal sign for its superfix, is shown in figure29,d,e. The determining characteristic of the head variant of the tun glyph, however, is the fleshless lower jaw (‡), as shown in figure29f,g, though even this is lacking in some few cases. The form shown in figure29,h, is found at Palenque, where it seems to represent the tun period in several places. The head of the full-figure form (fig.30) has the same fleshless lower jaw for its essential characteristic as the head-variant forms in figure29. The body joined to this head is again that of a bird the identity of which has not yet been determined.
THE UINAL GLYPH
Fig. 31Fig.31. Signs for the uinal:a-c, Normal forms;d-f, head variants.
Fig.31. Signs for the uinal:a-c, Normal forms;d-f, head variants.
Fig. 32Fig.32. Full-figure variant of uinal sign on Zoömorph B, Quirigua.
Fig.32. Full-figure variant of uinal sign on Zoömorph B, Quirigua.
Fig. 33Fig.33. Full-figure variant of uinal sign on Stela D, Copan.
Fig.33. Full-figure variant of uinal sign on Stela D, Copan.
The period occupying the 2d place was called by the Mayauinaloru. This latter word means also "the moon" in Maya, and the fact that the moon is visible for just about 20 days in each lunation may account for the application of its name to the 20-day period. The normal form of the uinal glyph in the inscriptions (see fig.31,a,b) is practically identical with the form in the codices (see fig.31,c).Sometimes the subfixial element (‡‡) is omitted in the inscriptions, as in figure31,a. The head variant of the uinal glyph (fig.31,d-f) is the most constant of all of the head forms for the various periods. Its determining characteristic is the large curl emerging from the back part of the mouth. The sharp-pointed teeth in the upper jaw are also a fairly constant feature. In very rare cases both of these elements are wanting. In such cases the glyph seems to be without determining characteristics. The animal represented in the full-figure variants of the uinal is that of a frog (fig.32,) the head of which presents precisely the same characteristics as the head variants of the uinal, just described. That the head variant of the uinal-period glyph was originally derived from the representation of a frog can hardly be denied in the face of such striking confirmatory evidence as that afforded by the full-figure form of the uinal in figure33. Here the spotted body, flattened head, prominent mouth, and bulging eyes of the frog are so realistically portrayed that there is no doubt as to the identity of the figure intended. Mr. Bowditch (1910: p. 257) has pointed out in this connection an interesting phonetic coincidence, which can hardly be other than intentional. The Maya word for frog isuo, which is a fairly close phonetic approximation ofu, the Maya word for "moon" or "month." Consequently, the Maya may have selected the figure of the frog on phonetic grounds to represent their 20-day period. If this point could be established it would indicate an unmistakable use of the rebus form of writing employed by the Aztec. That is, the figure of a frog in the uinal-period glyph would not recall the object which it pictures, but the sound of that object's name,uo, approximating the sound ofu, which in turn expressed the intended idea, namely, the 20-day period. Mr. Bowditch has suggested also that the grotesque birds which stand for the cycle, katun, and tun periods in these full-figure forms may also have been chosen because of the phonetic similarity of their names to the names of these periods.
THE KIN GLYPH
Fig. 34Fig.34. Signs for the kin:a,b, Normal forms;c,d, miscellaneous;e-k, head variants.
Fig.34. Signs for the kin:a,b, Normal forms;c,d, miscellaneous;e-k, head variants.
The period of the 1st, or lowest, order was called by the Mayakin, which meant the "sun" and by association the "day." The kin, as has been explained, was the primary unit used by the Maya in counting time. The normal form of this period glyph in the inscriptions is shown in figure34,a, which is practically identical with the form in the codices (fig.34,b). In addition to the normal form of the kin sign, however, there are several other forms representing this period which can not be classified either as head variants or full-figure variants, as in figure34,c, for example, which bears no resemblance whatever to the normal form of the kin sign. It is difficult to understand how two characters as dissimilar as those shown inaandc, figure34, could ever be used to express the same idea, particularly since there seems to be no element common to both. Indeed, so dissimilar are they that one is almost forced to believe that they were derived from two entirely distinct glyphs. Still another and very unusual sign for the kin is shown in figure34,d; indeed, the writer recalls but two places where it occurs: Stela 1 at Piedras Negras, and Stela C (north side) at Quirigua. It is composed of the normal form of the sign for the dayAhau(fig.16,e') inverted and a subfixial element which varies in each of the two cases. These variants (fig.34,c,d) are found only in the inscriptions. The head variants of the kin period differ from each other as much as the various normal forms above given. The form shown in figure34,e, may be readily recognized by its subfixial element (*) and the element (†),both of which appear in the normal form, figure34,a. In some cases, as in figure34,f-h, this variant also has the square irid and the crooked, snag-like teeth projecting from the front of the mouth. Again, any one of these features, or even all, may be lacking. Another and usually more grotesque type of head (fig.34,i,j) has as its essential element the banded headdress. A very unusual head variant is that shown in figure34,k, the essential characteristic of which seems to be the crossbones in the eye. Mr. Bowditch has included also in his list of kin signs the form shown in figure34,l, from an inscription at Tikal. While this glyph in fact does stand between two dates which are separated by one day from each other, that is,6 Eb 0 Popand7 Ben 1 Pop, the writer believes, nevertheless, that only the element (‡)—an essential part of the normal form for the kin—here represents the period one day, and that the larger characters above and below have other meanings. In the full-figure variants of the kin sign the figure portrayed is that of a human being (fig.35), the head of which is similar to the one in figure34,i,j, having the same banded headdress.[47]
Fig. 35Fig.35. Full-figure variant of kin sign.
Fig.35. Full-figure variant of kin sign.
This concludes the presentation of the various forms which stand for the several periods of TableVIII. After an exhaustive study of these as found in Maya texts the writer has reached the following generalizations concerning them:
1.Prevalence.The periods in Initial Series are expressed far more frequently by head variants than by normal forms. The preponderance of the former over the latter in all Initial Series known is in the proportion of about 80 per cent of the total[48]against 12 per cent, the periods in the remaining 8 per cent being expressed by these two forms used side by side. In other words, four-fifths of all the Initial Series known have their periods expressed by head-variant glyphs.
2.Antiquity.Head-variant period glyphs seem to have been used very much earlier than the normal forms. Indeed, the first use of the former preceded the first use of the latter by about 300 years, while in Initial Series normal-form period glyphs do not occur until nearly 100 years later, or about 400 years after the first use of head variants for the same purpose.
3.Variation.Throughout the range of time covered by the Initial Series the normal forms for any given time-period differ but little from one another, all following very closely one fixed type. Althoughnearly 200 years apart in point of time, the early form of the tun sign in figure36,a, closely resembles the late form shown inbof the same figure, as to its essentials. Or again, although 375 years apart, the early form of the katun sign in figure36,c, is practically identical with the form in figure36,d. Instances of this kind could be multiplied indefinitely, but the foregoing are sufficient to demonstrate that in so far as the normal-form period glyphs are concerned but little variation occurred from first to last. Similarly, it may be said, the head variants for any given period, while differing greatly in appearance at different epochs, retained, nevertheless, the same essential characteristic throughout. For example, although the uinal sign in figure36,e, precedes the one in figure36,f, by some 800 years, the same essential element—the large mouth curl—appears in both. Again, although 300 years separate the cycle signs shown ingandh, figure36, the essential characteristic of the early form (fig.36,g), the hand, is still retained as the essential part of the late form (h).
Fig. 36Fig.36. Period glyphs, from widely separated sites and of different epochs, showing persistence of essential elements.
Fig.36. Period glyphs, from widely separated sites and of different epochs, showing persistence of essential elements.
4.Derivation.We have seen that the full-figure glyphs probably show the original life-forms from which the head variants were developed. And since from (2), above, it seems probable that the head variants are older than the so-called normal forms, we may reasonably infer that the full-figure glyphs represent the life-forms whose names the Maya originally applied to their periods, and further that the first signs for those periods were the heads of these life-forms. This develops a contradiction in our nomenclature, for if the forms which we have called head variants are the older signs for the periods and are by far the most prevalent, they should have been called the normal forms and not variants, and vice versa. However, the use of the term "normal forms" is so general that it would be unwise at this time to attempt to introduce any change in nomenclature.
Secondary Series
The Initial Series method of recording dates, although absolutely accurate,[49]was nevertheless somewhat lengthy, since in order to express a single date by means of it eight distinct glyphs were required, namely: (1) The Introducing glyph; (2) the Cycle glyph;(3) the Katun glyph; (4) the Tun glyph; (5) the Uinal glyph; (6) the Kin glyph; (7) the Day glyph; (8) the Month glyph. Moreover, its use in any inscription which contained more than one date would have resulted in needless repetition. For example, if all the dates on any given monument were expressed by Initial Series, every one would show the long distance (more than 3,000 years) which separated it from the common starting point of Maya chronology. It would be just like writing the legal holidays of the current year in this way: February 22d, 1913, A. D., May 30th, 1913, A. D., July 4th, 1913, A. D., December 25th, 1913, A. D.; or in other words, repeating in each case the designation of time elapsed from the starting point of Christian chronology.
The Maya obviated this needless repetition by recording but one Initial Series date on a monument;[50]and from this date as a new point of departure they proceeded to reckon the number of days to the next date recorded; from this date the numbers of days to the next; and so on throughout that inscription. By this device the position of any date in the Long Count (its Initial Series) could be calculated, since it could be referred back to a date, the Initial Series of which was expressed. For example, the terminal day of the Initial Series given on page64is7 Akbal 11 Cumhu, and its position in the Long Count is fixed by the statement in cycles, katuns, tuns, etc., that 1,461,463 days separate it from the starting point,4 Ahau 8 Cumhu. Now let us suppose we have the date10 Cimi 14 Cumhu, which is recorded as being 3 days later than the day7 Akbal 11 Cumhu,[51]the Initial Series of which is known to be 1,461,463. It is clear that the Initial Series corresponding to the date10 Cimi 14 Cumhu, although not actually expressed, will also be known since it must equal 1,461,463 (Initial Series of7 Akbal 11 Cumhu) + 3 (distance from7 Akbal 11 Cumhuto10 Cimi 14 Cumhu), or 1,461,466. Therefore it matters not whether we count three days forward from7 Akbal 11 Cumhu, or whether we count 1,461,466 days forward from the starting point of Maya chronology,4 Ahau 8 Cumhusince in each case the date reached will be the same, namely,10 Cimi 14 Cumhu. The former method, however, was used more frequently than all of the other methods of recording dates combined, since it insured all the accuracy of an Initial Series without repeating for each date so great a number of days.
Thus having one date on a monument the Initial Series of which was expressed, it was possible by referring subsequent dates to it, or to other dates which in turn had been referred to it, to fix accuratelythe positions of any number of dates in the Long Count without the use of their corresponding Initial Series. Dates thus recorded are known as "secondary dates," and the periods which express their distances from other dates of known position in the Long Count, as "distance numbers." A secondary date with its corresponding distance number has been designated a Secondary Series. In the example above given the distance number 3 kins and the date10 Cimi 14 Cumhuwould constitute a Secondary Series.
Here, then, in addition to the Initial Series is a second method, the Secondary Series, by means of which the Maya recorded their dates. The earliest use of a Secondary Series with which the writer is familiar (that on Stela 36 at Piedras Negras) does not occur until some 280 years after the first Initial Series. It seems to have been a later development, probably owing its origin to the desire to express more than one date on a single monument. Usually Secondary Series are to be counted from the dates next preceding them in the inscriptions in which they are found, though occasionally they are counted from other dates which may not even be expressed, and which can be ascertained only by counting backward the distance number from its corresponding terminal date. The accuracy of a Secondary series date depends entirely on the fact that it has been counted from an Initial Series, or at least from another Secondary series date, which in turn has been derived from an Initial Series. If either of these contingencies applies to any Secondary series date, it is as accurate a method of fixing a day in the Long Count as though its corresponding Initial Series were expressed in full. If, on the other hand, a Secondary series date can not be referred ultimately to an Initial Series or to a date the Initial Series of which is known though it may not be expressed, such a Secondary series date becomes only one of the 18,980 dates of the Calendar Round, and will recur at intervals of every 52 years. In other words, its position in the Long Count will be unknown.
Calendar-round Dates
Dates of the character just described may be called Calendar-round dates, since they are accurate only within the Calendar Round, or range of 52 years. While accurate enough for the purpose of distinguishing dates in the course of a single lifetime, this method breaks down when used to express dates covering a long period. Witness the chaotic condition of Aztec chronology. The Maya seem to have realized the limitations of this method of dating and did not employ it extensively. It was used chiefly at Yaxchilan on the Usamacintla River, and for this reason the chronology of that city is very much awry, and it is difficult to assign its various dates to their proper positions in the Long Count.
Period-ending Dates
The Maya made use of still another method of dating, which, although not so exact as the Initial Series or the Secondary Series, is, on the other hand, far more accurate than Calendar round dating. In this method a date was described as being at the end of some particular period in the Long Count; that is, closing a certain cycle, katun, or tun.[52]It is clear also that in this method only the nameAhauout of the 20 given in TableIcan be recorded, since it alone can stand at the end of periods higher than the kin. This is true, since:
1. The higher periods, as the uinal, tun, katun, and cycle are exactly divisible by 20 in every case (see TableVIII), and—
2. They are all counted from a day,Ahau, that is,4 Ahau 8 Cumhu. Consequently, all the periods of the Long Count, except the kin or primary unit, end with days the name parts of which are the signAhau.
This method of recording dates always involves the use of at least two factors, and usually three:
1. A particular period of the Long Count, as Cycle 9, or Katun 14, etc.
2. The date which ends the particular period recorded, as8 Ahau 13 Ceh, or6 Ahau 13 Muan, the closing dates respectively of Cycle 9 and Katun 14 of Cycle 9; and
3. A glyph or element which means "ending" or "is ended," or which indicates at least that the period to which it is attached has come to its close.
The first two of these factors are absolutely essential to this method of dating, while the third, the so-called "ending sign," is usually, though not invariably, present. The order in which these factors are usually found is first the date composed of the day glyph and month glyph, next the "ending sign," and last the glyph of the period whose closing day has just been recorded. Very rarely the period glyph and its ending sign precede the date.
The ending glyph has three distinct variants: (1) the element shown as the prefix or superfix in figure37,a-h,t, all of which are forms of the same variant; (2) the flattened grotesque head appearing either as the prefix or superfix ini,r,u,vof the same figure; and (3) the hand, which appears as the main element in the forms shown in figure37,j-q. The two first of these never stand by themselves but always modify some other sign. The first (fig.37,a-h,t) is always attached to the sign of the period whose end is recorded either as asuperfix (see fig.37,a, whereby the end of Cycle 10 is indicated[53]), or as a prefix (seet, whereby the end of Katun 14 is recorded). The second form is seen as a prefix inu, whereby the end of Katun 12 is recorded, and ini, whereby the end of Katun 11 is shown. This latter sign is found also as a superfix inr.