Fig. 19Fig.19. The month signs in the inscriptions.
Fig.19. The month signs in the inscriptions.
Fig. 20Fig.20. The month signs in the codices.
Fig.20. The month signs in the codices.
The sign for the monthYaxkinis identical in both figures19,k,l, and20,i,j. The sign for the monthMolin figures19,m,n, and20,kexhibits the same close similarity. The forms for the monthChenin figures19,o,p, and 20,l,m, on the other hand, bear only a slight resemblance to each other. The forms for the monthsYax(figs.19,q,r, and20,n),Zac(figs.19,s,t, and20,o), andCeh(figs.19,u,v, and20,p) are again identical in each case. The signs for the next month,Mac, however, are entirely dissimilar, the form commonly found in the inscriptions (fig.19,w) bearing absolutely no resemblance to that shown in figure20,q,r, the only form for this month in the codices. The very unusual variant (fig.19,x), from Stela 25 at Piedras Negras is perhaps a trifle nearer the form found in the codices. The flattened oval in the main part of the variant is somewhat like the upper part of the glyph in figure20,q. The essential element of the glyph for the monthMac, so far as the inscriptions are concerned, is the element (*) found as the superfix in bothwandx, figure19. The sign for the monthKankin(figs.19,y,z, and20,s,t) and the signs for the monthMuan(figs.19,a',b', and20,u,v) show only a general similarity. The signs for the last three months of the year,Pax(figs.19,c', and20,w),Kayab(figs.19,d'-f', and20,x,y), andCumhu(figs.19,g',h', and20,z,a',b') in the inscriptions and codices, respectively, are practically identical. The closing division of the year, the five days of the xma kaba kin, calledUayeb, is represented by essentially the same glyph in both the inscriptions and the codices. Compare figure19,i', with figure20,c'.
It will be seen from the foregoing comparison that on the whole the glyphs for the months in the inscriptions are similar to the corresponding forms in the codices, and that such variations as are found may readily be accounted for by the fact that the codices and the inscriptions probably not only emanate from different parts of the Maya territory but also date from different periods.
The student who wishes to decipher Maya writing is strongly urged to memorize the signs for the days and months given in figures16,17,19, and20, since his progress will depend largely on his ability to recognize these glyphs when he encounters them in the texts.
The Calendar Round, or 18980-day Period
Before taking up the study of the Calendar Round let us briefly summarize the principal points ascertained in the preceding pages concerning the Maya method of counting time. In the first place we learned from the tonalamatl (pl.5) three things: (1) The number of differently named days; (2) the names of these days; (3) the order in which they invariably followed one another. And in the second place we learned in the discussion of the Maya year, or haab, just concluded, four other things: (1) The length of the year; (2) the number, length, and names of the several periods into which it was divided; (3) the order in which these periods invariably followed one another; (4) the positions of the days in these periods.
The proper combination of these two, the tonalamatl, or "round of days," and the haab, or year of uinals, and the xma kaba kin, formed the Calendar Round, to which the tonalamatl contributed the namesof the days and the haab the positions of these days in the divisions of the year. TheCalendar Roundwas the most important period in Maya chronology, and a comprehension of its nature and of the principles which governed its composition is therefore absolutely essential to the understanding of the Maya system of counting time.
It has been explained (see p.41) that the complete designation or name of any day in the tonalamatl consisted of two equally essential parts: (1) The name glyph, and (2) the numerical coefficient. Disregarding the latter for the present, let us first seewhichof the twenty names in TableI, that is, the name parts of the days, can stand at the beginning of the Maya year.
In applying any sequence of names or numbers to another there are only three possibilities concerning the names or numbers which can stand at the head of the resulting sequence:
1. When the sums of the units in each of the two sequences contain no common factor, each one of the units in turn will stand at the head of the resulting sequence.
2. When the sum of the units in one of the two sequences is a multiple of the sum of the units in the other, only the first unit can stand at the head of the resulting sequence.
3. When the sums of the units in the two sequences contain a common factor (except in those cases which fall under (2), that is, in which one is a multiple of the other) only certain units can stand at the head of the sequence.
Now, since our two numbers (the 20 names in TableIand the 365 days of the year) contain a common factor, and since neither is a multiple of the other, it is clear that only the last of the three contingencies just mentioned concerns us here; and we may therefore dismiss the first two from further consideration.
The Maya year, then, could begin only with certain of the days in TableI, and the next task is to find out which of these twenty names invariably stood at the beginnings of the years.
When there is a sequence of 20 names in endless repetition, it is evident that the 361st will be the same as the 1st, since 360 = 20 × 18. Therefore the 362d will be the same as the 2d, the 363d as the 3d, the 364th as the 4th, and the 365 as the 5th. But the 365th, or 5th, name is the name of the last day of the year, consequently the 1st day of the following year (the 366th from the beginning) will have the 6th name in the sequence. Following out this same idea, it appears that the 361st day of thesecond yearwill have the same name as that with which it began, that is, the 6th name in the sequence, the 362d day the 7th name, the 363d the 8th, the 364th the 9th, and the 365th, or last day of thesecond year, the 10th name. Therefore the 1st day of thethird year(the 731st from the beginning) will have the 11th name in the sequence. Similarly it could be shownthat thethird year, beginning with the 11th name, would necessarily end with the 15th name; and thefourth year, beginning with the 16th name (the 1096th from the beginning) would necessarily end with the 20th, or last name, in the sequence. It results, therefore, from the foregoing progression that thefifth yearwill have to begin with the 1st name (the 1461st from the beginning), or the same name with which thefirst yearalso began.
This is capable of mathematical proof, since the 1st day of thefifth yearhas the 1461st name from the beginning of the sequence, for 1461 = 4×365+1 = 73×20+1. The1in the second term of this equation indicates that the beginning day of thefifth yearhas been reached; and the1in the third term indicates that the name-part of this day is the 1st name in the sequence of twenty. In other words, every fifth year began with a day, the name part of which was the same, and consequently only four of the names in TableIcould stand at the beginnings of the Maya years.
The four names which successively occupied this, the most important position of the year, were:Ik, Manik, Eb, and Caban(see TableV, in which these four names are shown in their relation to the sequence of twenty). Beginning with any one of these,Ikfor example, the next in order,Manik, is 5 days distant, the next,Eb, another five days, the next,Caban, another 5 days, and the next,Ik, the name with which the Table started, another 5 days.
Table V.RELATIVE POSITIONS OF DAYS BEGINNING MAYA YEARS
Since one of the four names just given invariably began the Maya year, it follows that in any given year, all of its nineteen divisions, the 18 uinals and the xma kaba kin, also began with the same name, which was the name of the first day of the first uinal. This is necessarily true because these 19 divisions of the year, with the exception of the last, each contained 20 days, and consequently the name of the first day of the first division determined the names of the first days of all the succeeding divisions of that particular year. Furthermore, since the xma kaba kin, the closing division of the year, contained but 5 days, the name of the first day of the following year; as well asthe names of the first days of all of its divisions, was shifted forward in the sequence another 5 days, as shown above.
This leads directly to another important conclusion: Since the first days of all the divisions of any given year always had the same name-part, it follows that the second days of all the divisions of that year had the same name, that is, the next succeeding in the sequence of twenty. The third days in each division of that year must have had the same name, the fourth days the same name, and so on, throughout the 20 days of the month. For example, if a year began with the day-nameIk, all of the divisions in that year also began with the same name, and the second days of all its divisions had the day-nameAkbal, the third days the nameKan, the fourth days the nameChicchan, and so forth. This enables us to formulate the following—
Rule.The 20 day-names always occupy the same positions in all the divisions of any given year.
But since the year and its divisions must begin with one of four names, it is clear that the second positions also must be filled with one of another group of four names, and the third positions with one of another group of four names, and so on, through all the positions of the month. This enables us to formulate a second—
Rule.Only four of the twenty day-names can ever occupy any given position in the divisions of the years.
But since, in the years whenIkis the 1st name,Manikwill be the 6th,Ebthe 11th, andCabanthe 16th, and in the years whenManikis the 1st,Ebwill be the 6th,Cabanthe 11th, andIkthe 16th, and in the years whenEbis the 1st,Cabanwill be the 6th,Ikthe 11th, andManikthe 16th, and in the years whenCabanis the 1st,Ikwill be the 6th,Manikthe 11th, andEbthe 16th, it is clear that any one of this group which begins the year may occupy also three other positions in the divisions of the year, these positions being 5 days distant from each other. Consequently, it follows thatAkbal, Lamat, Ben, andEznabin TableV, the names which occupy the second positions in the divisions of the year, will fill the 7th, 12th, and 17th positions as well. SimilarlyKan, Muluc, Ix, andCauacwill fill the 3d, 8th, 13th, and 18th positions, and so on. This enables us to formulate a third—
Rule.The 20 day-names are divided into five groups of four names each, any name in any group being five days distant from the name next preceding it in the same group, and furthermore, the names of any one group will occupy four different positions in the divisions of successive years, these positions being five days apart in each case. This is expressed in TableVI, in which these groups are shown as well as the positions in the divisions of the years which the names of each group may occupy. A comparison with TableVwill demonstrate that this arrangement is inevitable.
Table VI.POSITIONS OF DAYS IN DIVISIONS OF MAYA YEAR
But we have seen on page47and in TableIVthat the Maya did not designate the first days of the several divisions of the years according to our system. It was shown there that the first day ofPopwas not written1 Pop, but0 Pop, and similarly the second day of Pop was written not2 Pop, but1 Pop, and the last day, not20 Pop, but19 Pop. Consequently, before we can use the names in TableVIas the Maya used them, we must make this shift, keeping in mind, however, thatIk,Manik,Eb, andCaban(the only four of the twenty names which could begin the year and which were written0 Pop,5 Pop,10 Pop, or15 Pop) would be written in our notation1st Pop,6th Pop,11th Pop, and16th Pop, respectively. This difference, as has been previously explained, results from the Maya method of counting time by elapsed periods.
TableVIIshows the positions of the days in the divisions of the year according to the Maya conception, that is, with the shift in the month coefficient made necessary by this practice of recording their days as elapsed time.
The student will find TableVIIvery useful in deciphering the texts, since it shows at a glance the only positions which any given day can occupy in the divisions of the year. Therefore when the sign for a day has been recognized in the texts, from TableVIIcan be ascertained the only four positions which this day can hold in the month, thus reducing the number of possible month coefficients for which search need be made, from twenty to four.
Table VII.POSITIONS OF DAYS IN DIVISIONS OF MAYA YEAR ACCORDING TO MAYA NOTATION
Now let us summarize the points which we have successively established as resulting from the combination of the tonalamatl and haab, remembering always that as yet we have been dealing only withthe name parts of the days and not their complete designations. Bearing this in mind, we may state the following facts concerning the 20 day-names and their positions in the divisions of the year:
1. The Maya year and its several divisions could begin only with one of these four day-names:Ik,Manik,Eb, andCaban.
2. Consequently, any particular position in the divisions of the year could be occupied only by one of four day-names.
3. Consequently, every fifth year any particular day-name returned to the same position in the divisions of the year.
4. Consequently, any particular day-name could occupy only one of four positions in the divisions of the year, each of which it held in successive years, returning to the same position every fifth year.
5. Consequently, the twenty day-names were divided into five groups of four day-names each, any day-name of any group being five days distant from the day-name of the same group next preceding it.
6. Finally, in any given year any particular day-name occupied the same relative position throughout the divisions of that year.
Up to this point, however, as above stated, we have not been dealing with the complete designations of the Maya days, but only theirname partsor name glyphs, the positions of which in the several divisions of the year we have ascertained.
It now remains to join the tonalamatl, which gives the complete names of the 260 Maya days, to the haab, which gives the positions of the days in the divisions of the year, in such a way that any one of the days whose name-part isIk,Manik,Eb, orCabanshall occupy the first position of the first division of the year; that is,0 Pop, or, as we should write it, the first day ofPop. It matters little which one of these four name parts we choose first, since in four years each one of them in succession will have appeared in the position0 Pop.
Perhaps the easiest way to visualize the combination of the tonalamatl and the haab is to conceive these two periods as two cogwheels revolving in contact with each other. Let us imagine that the first of these,A(fig.21), has 260 teeth, or cogs, each one of which is named after one of the 260 days of the tonalamatl and follows the sequence shown in plate5. The second wheel,B(fig.21), is somewhat larger, having 365 cogs. Each of the spaces or sockets between these represents one of the 365 positions of the days in the divisions of the year, beginning with0 Popand ending with4 Uayeb. See TableIVfor the positions of the days at the end of one year and the commencement of the next. Finally, let us imagine that these two wheels are brought into contact with each other in such a way that the tooth or cog named2 IkinAshall fit into the socket named0 PopinB, after which both wheels start to revolve in the directions indicated by the arrows.
Fig. 21Fig.21. Diagram showing engagement of tonalamatl wheel of 260 days (A), and haab wheel of 365 positions (B); the combination of the two giving the Calendar Round, or 52-year period.
Fig.21. Diagram showing engagement of tonalamatl wheel of 260 days (A), and haab wheel of 365 positions (B); the combination of the two giving the Calendar Round, or 52-year period.
The first day of the year whose beginning is shown at the point of contact of the two wheels in figure21is2 Ik 0 Pop, that is, the day2 Ikwhich occupies the first position in the monthPop. The next day in succession will be3 Akbal 1 Pop, the next4 Kan 2 Pop, the next5 Chicchan 3 Pop, the next6 Cimi 4 Pop, and so on. As the wheels revolve in the directions indicated, the days of the tonalamatl successively fall into their appropriate positions in the divisions of the year. Since the number of cogs in A is smaller than the number in B, it is clear that the former will have returned to its starting point,2 Ik(that is, made one complete revolution), before the latter will have made one complete revolution; and, further, that when the latter (B) has returned to its starting point,0 Pop, the corresponding cog in B will not be2 Ik, but another day (3 Manik), since by that time the smaller wheel will have progressed 105 cogs, or days, farther, to the cog3 Manik.
The question now arises, how many revolutions will each wheel have to make before the day2 Ikwill return to the position0 Pop. The solution of this problem depends on the application of one sequence to another, and the possibilities concerning the numbers or names which stand at the head of the resulting sequence, a subject already discussed on page52. In the present case the numbers in question, 260 and 365, contain a common factor, therefore our problem falls under the third contingency there presented. Consequently, only certain of the 260 days can occupy the position0 Pop, or, in other words, cog2 Ikin A will return to the position0 Popin B in fewer than 260 revolutions of A. The actual solution of the problemis a simple question of arithmetic. Since the day2 Ikcan not return to its original position in A until after 260 days shall have passed, and since the day0 Popcan not return to its original position in B until after 365 days shall have passed, it is clear that the day2 Ik 0 Popcan not recur until after a number of days shall have passed equal to the least common multiple of these numbers, which is (260/5)×(365/5)×5, or 52×73×5 = 18,980 days. But 18,980 days = 52×365 = 73×260; in other words the day2 Ik 0 Popcan not recur until after 52 revolutions of B, or 52 years of 365 days each, and 73 revolutions of A, or 73 tonalamatls of 260 days each. The Maya name for this 52-year period is unknown; it has been called the Calendar Round by modern students because it was only after this interval of time had elapsed that any given day could return to the same position in the year. The Aztec name for this period wasxiuhmolpilliortoxiuhmolpia.[34]
The Calendar Round was the real basis of Maya chronology, since its 18,980 dates included all the possible combinations of the 260 days with the 365 positions of the year. Although the Maya developed a much more elaborate system of counting time, wherein any date of the Calendar Round could be fixed with absolute certainty within a period of 374,400 years, this truly remarkable feat was accomplished only by using a sequence of Calendar Rounds, or 52-year periods, in endless repetition from a fixed point of departure.
In the development of their chronological system the Aztec probably never progressed beyond the Calendar Round. At least no greater period of time than the round of 52 years has been found in their texts. The failure of the Aztec to develop some device which would distinguish any given day in one Calendar Round from a day of the same name in another has led to hopeless confusion in regard to various events of their history. Since the same date occurred at intervals of every 52 years, it is often difficult to determine the particular Calendar Round to which any given date with its corresponding event is to be referred; consequently, the true sequence of events in Aztec history still remains uncertain.
Professor Seler says in this connection:[35]
Anyone who has ever taken the trouble to collect the dates in old Mexican history from the various sources must speedily have discovered that the chronology is very much awry, that it is almost hopeless to look for an exact chronology. The date of the fall of Mexico is definitely fixed according to both the Indian and the Christian chronology ... but in regard to all that precedes this date, even to events tolerably near the time of the Spanish conquest, the statements differ widely.
Anyone who has ever taken the trouble to collect the dates in old Mexican history from the various sources must speedily have discovered that the chronology is very much awry, that it is almost hopeless to look for an exact chronology. The date of the fall of Mexico is definitely fixed according to both the Indian and the Christian chronology ... but in regard to all that precedes this date, even to events tolerably near the time of the Spanish conquest, the statements differ widely.
Such confusion indeed is only to be expected from a system of counting time and recording events which was so loose as to permit the occurrence of the same date twice, or even thrice, within the span of a single life; and when a system so inexact was used to regulate the lapse of any considerable number of years, the possibilities for error and misunderstanding are infinite. Thus it was with Aztec chronology.
On the other hand, by conceiving the Calendar Rounds to be in endless repetition from a fixed point of departure, and measuring time by an accurate system, the Maya were able to secure precision in dating their events which is not surpassed even by our own system of counting time.
Fig. 22Fig.22. Signs for the Calendar Round:a, According to Goodman;b, according to Förstemann.
Fig.22. Signs for the Calendar Round:a, According to Goodman;b, according to Förstemann.
The glyph which stood for the Calendar Round has not been determined with any degree of certainty. Mr. Goodman believes the form shown in figure22,a, to be the sign for this period, while Professor Förstemann is equally sure that the form represented bybof this figure expressed the same idea. This difference of opinion between two authorities so eminent well illustrates the prevailing doubt as to just what glyph actually represented the 52-year period among the Maya. The sign in figure22,a, as the writer will endeavor to show later, is in all probability the sign for the great cycle.
As will be seen in the discussion of the Long Count, the Maya, although they conceived time to be an endless succession of Calendar Rounds, did not reckon its passage by the lapse of successive Calendar Rounds; consequently, the need for a distinctive glyph which should represent this period was not acute. The contribution of the Calendar Round to Maya chronology was its 18,980 dates, and the glyphs which composed these are found repeatedly in both the codices and the inscriptions (see figs.16,17,19,20). No signs have been found as yet, however, for either the haab or the tonalamatl, probably because, like the Calendar Round, these periods were not used as units in recording long stretches of time.
It will greatly aid the student in his comprehension of the discussion to follow if he will constantly bear in mind the fact that one Calendar Round followed another without interruption or the interpolation of a single day; and further, that the Calendar Round may be likened to a large cogwheel having 18,980 teeth, each one of which represented one of the dates of this period, and that this wheel revolved forever, each cog passing a fixed point once every 52 years.
The Long Count
We have seen:
1. How the Maya distinguished 1 day from the 259 others in the tonalamatl;
2. How they distinguished the position of 1 day from the 364 others in the haab, or year; and, finally,
3. How by combining (1) and (2) they distinguished 1 day from the other 18,979 of the Calendar Round.
It remains to explain how the Maya insured absolute accuracy in fixing a day within a period of 374,400 years, as stated above, or how they distinguished 1 day from 136,655,999 others.
The Calendar Round, as we have seen, determined the position of a given day within a period of only 52 years. Consequently, in order to prevent confusion of days of the same name in successive Calendar Rounds or, in other words, to secure absolute accuracy in dating events, it was necessary to use additional data in the description of any date.
In nearly all systems of chronology that presume to deal with really long periods the reckoning of years proceeds from fixed starting points. Thus in Christian chronology the starting point is the Birth of Christ, and our years are reckoned as B. C. or A. D. according as they precede or follow this event. The Greeks reckoned time from the earliest Olympic Festival of which the winner's name was known, that is, the games held in 776 B. C., which were won by a certain Coroebus. The Romans took as their starting point the supposed date of the foundation of Rome, 753 B. C. The Babylonians counted time as beginning with the Era of Nabonassar, 747 B. C. The death of Alexander the Great, in 325 B. C., ushered in the Era of Alexander. With the occupation of Babylon in 311 B. C. by Seleucus Nicator began the so-called Era of Seleucidæ. The conquest of Spain by Augustus Cæsar in 38 B. C. marked the beginning of a chronology which endured for more than fourteen centuries. The Mohammedans selected as their starting point the flight of their prophet Mohammed from Mecca in 622 A. D., and events in this chronology are described as having occurred so many years after the Hegira (The Flight). The Persian Era began with the date 632 A. D., in which year Yezdegird III ascended the throne of Persia.
It will be noted that each of the above-named systems of chronology has for its starting point some actual historic event, the occurrence, if not the date of which, is indubitable. Some chronologies, however, commence with an event of an altogether different character, the date of which from its very nature must always remain hypothetical. In this class should be mentioned such chronologies as reckon time from the Creation of the World. For example, the Era of Constantinople, the chronological system used in the Greek Church,commences with that event, supposed to have occurred in 5509 B. C. The Jews reckoned the same event as having taken place in 3761 B. C. and begin the counting of time from this point. A more familiar chronology, having for its starting point the Creation of the World, is that of Archbishop Usher, in the Old Testament, which assigns this event to the year 4004 B. C.
In common with these other civilized peoples of antiquity the ancient Maya had realized in the development of their chronological system the need for a fixed starting point, from which all subsequent events could be reckoned, and for this purpose they selected one of the dates of their Calendar Round. This was a certain date,4 Ahau 8 Cumhu,[36]that is, a day named4 Ahau, which occupied the 9th position in the monthCumhu, the next to last division of the Maya year (see TableIII).
While the nature of the event which took place on this date[37]is unknown, its selection as the point from which time was subsequently reckoned alone indicates that it must have been of exceedingly great importance to the native mind. In attempting to approximate its real character, however, we are not without some assistance from the codices and the inscriptions. For instance, it is clear that all Maya dates which it is possible to regard as contemporaneous[38]refer to a time fully 3,000 years later than the starting point (4 Ahau 8 Cumhu) from which each is reckoned. In other words, Maya history is a blank for more than 3,000 years after the initial date of the Maya chronological system, during which time no events were recorded.
This interesting condition strongly suggests that the starting point of Maya chronology was not an actual historical event, as the founding of Rome, the death of Alexander, the birth of Christ, or the flight of Mohammed from Mecca, but that on the contrary it was a purely hypothetical occurrence, as the Creation of the World or the birth of the gods; and further, that the date4 Ahau 8 Cumhuwas not chosen as the starting point until long after the time it designates. This, or some similar assumption, is necessary to account satisfactorily for the observed facts:
1. That, as stated, after the starting point of Maya chronology there is a silence of more than 3,000 years, unbroken by a single contemporaneous record, and
2. That after this long period had elapsed all the dated monuments[39]had their origin in the comparatively short period of four centuries.
Consequently, it is safe to conclude that no matter what the Maya may have believed took place on this date4 Ahau 8 Cumhu, in reality when this day was present time they had not developed their distinctive civilization or even achieved a social organization.
It is clear from the foregoing that in addition to the Calendar Round, the Maya made use of a fixed starting point in describing their dates. The next question is, Did they record the lapse of more than 3,000 years simply by using so unwieldy a unit as the 52-year period or its multiples? A numerical system based on 52 as its primary unit immediately gives rise to exceedingly awkward numbers for its higher terms; that is, 52, 104, 156, 208, 260, 312, etc. Indeed, the expression of really large numbers in terms of 52 involves the use of comparatively large multipliers and hence of more or less intricate multiplications, since the unit of progression is not decimal or even a multiple thereof. The Maya were far too clever mathematicians to have been satisfied with a numerical system which employed units so inconvenient as 52 or its multiples, and which involved processes so clumsy, and we may therefore dismiss the possibility of its use without further consideration.
In order to keep an accurate account of the large numbers used in recording dates more than 3,000 years distant from the starting point, a numerical system was necessary whose terms could be easily handled, like the units, tens, hundreds, and thousands of our own decimal system. Whether the desire to measure accurately the passage of time actually gave rise to their numerical system, or vice versa, is not known, but the fact remains that the several periods of Maya chronology (except the tonalamatl, haab, and Calendar Round, previously discussed) are the exact terms of a vigesimal system of numeration, with but a single exception. (See Table VIII.)
Table VIII.THE MAYA TIME-PERIODS
TableVIIIshows the several periods of Maya chronology by means of which the passage of time was measured. All are the exact terms of a vigesimal system of numeration, except in the 2d place (uinals),in which 18 units instead of 20 make 1 unit of the 3d place, or order next higher (tuns). The break in the regularity of the vigesimal progression in the 3d place was due probably to the desire to bring the unit of this order (the tun) into agreement with the solar year of 365 days, the number 360 being much closer to 365 than 400, the third term of a constant vigesimal progression. We have seen on page45that the 18 uinals of the haab were equivalent to 360 days or kins, precisely the number contained in the third term of the above table, the tun. The fact that the haab, or solar year, was composed of 5 days more than the tun, thus causing a discrepancy of 5 days as compared with the third place of the chronological system, may have given to these 5 closing days of the haab—that is, the xma kaba kin—the unlucky character they were reputed to possess.
The periods were numbered from 0 to 19, inclusive, 20 units of any order (except the 2d) always appearing as 1 unit of the order next higher. For example, a number involving the use of 20 kins was written 1 uinal instead.
We are now in possession of all the different factors which the Maya utilized in recording their dates and in counting time:
1. The names of their dates, of which there could be only 18,980 (the number of dates in the Calendar Round).
2. The date, or starting point,4 Ahau 8 Cumhu, from which time was reckoned.
3. The counters, that is, the units, used in measuring the passage of time.
It remains to explain how these factors were combined to express the various dates of Maya chronology.
Initial Series
The usual manner in which dates are written in both the codices and the inscriptions is as follows: First, there is set down a number composed of five periods, that is, a certain number of cycles, katuns, tuns, uinals, and kins, which generally aggregate between 1,300,000 and 1,500,000 days; and this number is followed by one of the 18,980 dates of the Calendar Round. As we shall see in the next chapter, if this large number of days expressed as above be counted forward from the fixed starting point of Maya chronology,4 Ahau 8 Cumhu, the date invariably[41]reached will be found to be the date written at the end of the long number. This method of dating has been called theInitial Series, because when inscribed on a monument it invariably standsat the headof the inscription.
The student will better comprehend this Initial-series method of dating if he will imagine the Calendar Round represented by a large cogwheel A, figure23, having 18,980 teeth, each one of which isnamed after one of the dates of the calendar. Furthermore, let him suppose that the arrow B in the same figure points to the tooth, or cog, named4 Ahau 8 Cumhu; and finally that from this as its original position the wheel commences to revolve in the direction indicated by the arrow in A.