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diff --git a/.gitattributes b/.gitattributes new file mode 100644 index 0000000..6833f05 --- /dev/null +++ b/.gitattributes @@ -0,0 +1,3 @@ +* text=auto +*.txt text +*.md text diff --git a/39683-8.txt b/39683-8.txt new file mode 100644 index 0000000..780370b --- /dev/null +++ b/39683-8.txt @@ -0,0 +1,809 @@ +The Project Gutenberg EBook of Memoranda on the Maya Calendars Used in the +Books of Chilan Balam, by Charles P. Bowditch + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org/license + + +Title: Memoranda on the Maya Calendars Used in the Books of Chilan Balam + +Author: Charles P. Bowditch + +Release Date: May 12, 2012 [EBook #39683] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK MEMORANDA ON THE MAYA *** + + + + +Produced by Julia Miller, Paula Franzini and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + + + + + MEMORANDA ON THE MAYA CALENDARS + USED IN THE BOOKS OF + CHILAN BALAM + + BY + CHARLES P. BOWDITCH + + (From the American Anthropologist (N. S.), Vol. 3, January-March, 1901) + + NEW YORK + G. P. PUTNAM'S SONS + 1901 + + + + + MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM + + BY CHARLES P. BOWDITCH + + +Dr Brinton, in his _Maya Chronicles_, has translated the following +passages from the Book of Chilan Balam of Mani: + + ... in the thirteenth Ahau Ahpula died; for six years the count of + the thirteenth Ahau will not be ended; the count of the year was + toward the East, the month Pop began with (the day) fourth Kan; the + eighteenth day of the month Zip (that is) 9 Ymix, was the day on + which Ahpula died; and that the count may be known in numbers and + years, it was the year 1536. + +And again from the Book of Chilan Balam of Tizimin: + + The thirteenth Ahau; the death of Ahpulha took place; it was the + sixth year when ended the count of the thirteenth Ahau,--the count + of the year was from the east (the month) Pop passed on the fourth + Kan; on the eighteenth of (the month) Zip, 9 Imix was the day + Ahpulha died; it was the year 1536. + +In his remarks on these books Dr Brinton says: + + According to the reckoning as it now stands, six complete great + cycles were counted, and parts of two others, so that the native at + the time of the Conquest would have had eight great cycles to + distinguish apart. + + I have not found any clear explanation how this was accomplished. + We do not even know what name was given to this great cycle,[1] nor + whether the calendar was sufficiently perfected to prevent + confusion in dates in the remote past. + + [1] It should be noted that the grand cycle, which Dr Brinton refers + to, is the period of 13 × 7200 days = 93,600 days or 260 periods of + 360 days; while the grand cycle according to Goodman's method is 13 + × 144,000 days or 5200 periods of 360 days. + +It would seem, however, as if the reckoning of time as given in these +books is very accurate, fixing a date which would not be duplicated +within a limit of thirty-five hundred or four thousand years. + +The Books of Chilan Balam number the katuns on a different principle +from that used on the inscriptions or in the Dresden Codex, but the two +methods can be readily and usefully brought together, as the katun +itself remains the same in both methods. In the inscriptions the katuns +are numbered from 0 to 19, using Goodman's method though not his exact +nomenclature, and twenty of them equal one cycle. In the Chilan Balam +books, the katuns are named as Katun 13 Ahau, Katun 11 Ahau, etc., these +being the days with which they begin or with which the previous katun +ended; and as after thirteen katuns the same name is again given, this +nomenclature fixes a date within a period which equals 13 multiplied by +the number of days in a katun. There has been a difference of opinion as +to this number of days in a katun, but it is clear from the Books of +Chilan Balam that their reckoning was by terms of 20 × 360 days. The +followers of Perez, however, insist that the length of the katun was 24 +× 365 days. Sr Perez has indeed made this assertion,[2] but he rests his +opinion to a great degree on the fact that the naming of the katuns +proceeded in the following order, taking their names from the day Ahau +with which they began, viz.: + + Katun 13 Ahau, + Katun 11 Ahau, + Katun 9 Ahau, + Katun 7 Ahau, etc., + +and that by starting with a katun which begins with 13 Ahau and counting +forward a period of 24 × 365 days, we should reach another katun +beginning with 11 Ahau. But the same result is brought about by +considering the katun as a period of 20 × 360 days, as has been shown by +Dr Seler, among others; and since the Books of Chilan Balam state +distinctly that they reckon by so many scores of so-called years, and +as the initial dates of the inscriptions all reckon in the same way, it +is now generally considered that the katun consisted of 20 × 360 or 7200 +days. An objection to considering a katun as 20 × 360 days may be raised +in that the Books of Chilan Balam use the word "ańo" or year, but this +can be easily explained by the fact that the Spanish "year" was the +period which most nearly agreed with their tun or 360-day period, and +that the Books did not pretend to speak with scientific accuracy. + + [2] Stephens, _Incidents of Travel in Yucatan_, p. 441 et seq. + +Besides the above count, it is well known that the Mayas had a +year-and-month count. This consisted in naming each one of the twenty +days and in attaching to each of these days one of the numbers 1 to 13. +Besides this, each day so numbered was declared to be a given day of a +given month and to occur in a year marked by one of the year bearers--as +for instance in the Book of Chilan Balam, already quoted, where the day +is given as 9 Ymix 18 Zip in the year 4 Kan. Now this day and this year +could recur only after the lapse of fifty-two years or 18,980 days. + +It should be noted here that in the inscriptions and in the Dresden +Codex, the day Ymix was always the day 4, 9, 14, or 19 of any month, +showing that the day 1 of the month was Eznab, Akbal, Lamat, or Ben; +while in Landa and the Books of Chilan Balam the day Ymix was the day 3, +8, 13, or 18, showing that the day 1 of the month was Cauac, Kan, Muluc, +or Ix. That is, the months in modern times began with the day which +followed the day with which the months began in more ancient times. As +the tables are calculated for the inscriptions, it will be well, in +order to facilitate our calculations, to call the day on which Ahpula +died the nineteenth of the month Zip, instead of the eighteenth of that +month. + +Given that the katun consisted of 7200 days, a Katun 13 Ahau could not +recur until after the lapse of 13 × 7200 or 93,600 days, and the +recurrence of any day marked by the year-and-month count, and occupying +any particular place in a given katun, could not occur until after the +lapse of a period which is found by finding the least common multiple of +the two numbers 93,600 and 18,980. This is 6,832,800 days, which is a +period of 360 calendar rounds of 18,980 days or of 52 years each. This +is equal to 18,720 years, and, in the method of reckoning shown in the +initial dates of the inscriptions, would equal 3 grand cycles, 8 cycles, +and 9 katuns, or, to use the method of Goodman, 3.8.9.0.0.0. + +I have said that a day marked by the year-and-month count, and occupying +any particular place in a given katun, could not recur until the lapse +of this long period. This would be true if the day was specified as +being a given day in a given tun in a given katun, or even if the day +was stated as falling in a given uinal of a given tun in a given katun. +But in the case before us the death of Ahpula is said to have taken +place in the Katun 13 Ahau when six tuns or years of that katun remained +unexpired. Even with this rather loose designation such a day would not +recur within a period of 3500 or 4000 years. + +The day 4 Ahau 8 Cumhu seems to have been regarded as the beginning day +of the beginning cycle of some grand cycle. From this day all the +initial series of the inscriptions of Copan and Quirigua, of Piedras +Negras and Tikal, so far as we know them, count, except one where this +day 4 Ahau 8 Cumhu is itself given. In this place (on Stela C of +Quirigua) 4 Ahau 8 Cumhu is reckoned thus: "Grand cycle glyph +.13.0.0.0.0.", while in the Temple of the Cross it is declared to be a +thirteenth cycle. As this was the beginning date, there is reason to +believe that the beginning cycle of a great cycle received the number +13. + +I give here the first and last terms of a list of the beginning days of +the Katuns 13 Ahau in a complete round of 18,720 years occurring after +the beginning of the grand cycle called by Goodman Grand Cycle 54, which +began with 4 Ahau 8 Cumhu. It is of little consequence what particular +number is given to the grand cycle, as the whole series forms a +continuous count, and I shall therefore follow Goodman, who gives the +number 54 to the grand cycle glyphs common to Copan, Quirigua, etc. + +If 54.13.0.0.0.0. or the beginning of the grand cycle, called Grand +Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Katun 13 Ahau will +appear two katuns after this or with the count of + + 54.13.2.0.0.0. 13 Ahau 8 Mol Year 10 Ix, + +and other Katuns 13 Ahau will follow at intervals of 13 katuns as here +given: + + 54.13.15.0.0.0. 13 Ahau 8 Pax Year 6 Ix. + 1. 8. " 3 Xul 3 Cauac. + 2. 1. " 3 Kankin 12 " + + . . . . . . . . . . . + + 57.5.19.0.0.0. 13 Ahau 18 Ceh 11 Kan. + 6.12 13 Uo 8 Muluc. + 7. 5. 13 Yax 4 " + 18. 13 Cumhu 13 " + 57.8.11.0.0.0. 13 Ahau 8 Mol 10 Ix. + +But we are seeking a Katun 13 Ahau in which 14 tuns have elapsed and of +which 6 tuns still remain unexpired. We must, therefore, add 14 tuns or +14 × 360 days = 5040 days to each of the dates given and we shall then +have the following complete list of the beginning days of Tun 14 of +Katun 13 Ahau for the term of 18,720 years: + + 54.13. 2.14.0.0. 9 Ahau 18 Zotz 11 Kan. + 15. 18 Ceh 7 Kan. + 1. 8. 13 Uo 4 Muluc. + 2. 1. 13 Yax 13 Muluc. + 14. 13 Cumhu 9 Muluc. + 3. 7. 8 Mol 6 Ix. + 4. 0. 8 Pax 2 Ix. + 13. 3 Xul 12 Cauac. + 5. 6. 3 Kankin 8 Cauac. + 19. 18 Zip 5 Kan. + 6.12. 18 Zac 1 Kan. + 7. 5. 13 Pop 11 Muluc. + 18. 13 Chen 7 Muluc. + 54. 8.11.14.0.0. 13 Kayab 3 Muluc. + 9. 4. 8 Yaxkin 13 Ix. + 17. 8 Muan 9 Ix. + 10.10. 3 Tzec 6 Cauac. + 11. 3. 3 Mac 2 Cauac. + 16. 18 Uo 12 Kan. + 12. 9. 18 Yax 8 Kan. + 55.13. 2.14.0.0. 18 Cumhu 4 Kan. + -------- + 15. 13 Mol 1 Muluc. + 1. 8. 13 Pax 10 Muluc. + 2. 1. 8 Xul 7 Ix. + 14. 8 Kankin 3 Ix. + 3. 7. 3 Zotz 13 Cauac. + 4. 0. 3 Ceh 9 Cauac. + 13. 18 Pop 6 Kan. + 5. 6. 18 Chen 2 Kan. + 5.19. 18 Kayab 11 Kan. + 6.12. 13 Yaxkin 8 Muluc. + 7. 5. 13 Muan 4 Muluc. + 18. 8 Tzec 1 Ix. + 8.11. 8 Mac 10 Ix. + 9. 4. 3 Zip 7 Cauac. + 17. 3 Zac 3 Cauac. + -------- + 10.10. 3 Uayeb 12 Cauac. + 11.03. 18 Mol 9 Kan. + 16. 18 Pax 5 Kan. + 12. 9. 13 Xul 2 Muluc. + 56.13. 2.14.0.0. 13 Kankin 11 Muluc. + 15. 8 Zotz 8 Ix. + 1. 8. 8 Ceh 4 Ix. + 2. 1. 3 Uo 1 Cauac. + 14. 3 Yax 10 Cauac. + 3. 7. 3 Cumhu 6 Cauac. + 4. 0. 18 Yaxkin 3 Kan. + 13. 18 Muan 12 Kan. + 5. 6. 13 Tzec 9 Muluc. + 5.19. 13 Mac 5 Muluc. + 6.12. 8 Zip 2 Ix. + 7.5. 8 Zac 11 Ix. + 18. 3 Pop 8 Cauac. + 8.11. 3 Chen 4 Cauac. + 9. 4. 3 Kayab 13 Cauac. + 17. 18 Xul 10 Kan. + 10.10. 18 Kankin 6 Kan. + 11.03. 13 Zotz 3 Muluc. + 16. 13 Ceh 12 Muluc. + 12. 9. 8 Uo 9 Ix. + 57.13. 2.14.0.0. 8 Yax 5 Ix. + 15. 8 Cumhu 1 Ix. + 1. 8. 3 Mol 11 Cauac. + 2. 1. 3 Pax 7 Cauac. + 14. 18 Tzec 4 Kan. + -------- + 3. 7. 18 Mac 13 Kan. + 4. 0. 13 Zip 10 Muluc. + 4.13. 13 Zac 6 Muluc. + 5. 6. 8 Pop 3 Ix. + 5.19. 8 Chen 12 Ix. + 6.12. 8 Kayab 8 Ix. + 7. 5. 3 Yaxkin 5 Cauac. + 18. 3 Muan 1 Cauac. + 8.11. 18 Zotz 11 Kan. + +The only places where a year 4 Kan appears are at the dates + + 55.13. 2.14.0.0.[3] 9 Ahau 18 Cumhu Year 4 Kan, and + 57. 2.14.14.0.0. 9 Ahau 18 Tzec Year 4 Kan. + +But as the words used are that 6 years (or tuns) remained before the end +of the katun, and as a slightly longer time than just 6 tuns may have +remained, and as the month Zip in which the death of Ahpula occurred is +the third month of the year and so is near the beginning of the year 4 +Kan, it is quite possible that the beginning of the Tun 14 may have been +in the latter part of the preceding year, in which case, in addition to +the preceding dates, the following date might be the one which we are +seeking: + + 55. 9.17.14.0.0. 9 Ahau 3 Zac Year 3 Cauac. + + [3] It is necessary to remember that, by Goodman's methods, these + figures represent periods of past time. Thus the number 2 of the katun + means that 2 katuns have passed, and that the current katun is what we + should call the third; and that 0.0 means that a full count of uinals + and kins has occurred and that the current uinal and kin are what we + should call the first. + +As 9 Ymix 19 Zip is said to be in the year 4 Kan, we shall find this +date before the dates of the beginning of Tun 14 in the first two cases +and after the beginning of Tun 14 in the last case. This date of 9 Ymix +19 Zip will then be numbered thus, placing the three dates in +consecutive order: + + 1) 55.13. 2.13. 3. 1. 6 tuns 299 days to end of Katun 13 Ahau. + 2) 55. 9.17.14.11. 1. 5 " 139 " " " " + 3) 57. 2.14.13.16. 1. 6 " 39 " " " " + +In no one of the cases is the date 9 Ymix 19 Zip exactly 6 tuns before +the end of the Katun 13 Ahau, but it is possible that the annalist took +no account of fractions of tuns, either in excess of the 6 tuns or +otherwise. Thus in the first and last cases of the three, as first +given, he may have said to himself, "There are but 6 whole tuns +remaining of the katun and I will call it 6," or in the second case he +may have said: "There are 5 tuns remaining and 139 days besides; I will +call it 6 tuns." Whichever was the plan he followed, we can have at +present no means of ascertaining except from the results which we obtain +by calculation. + +The date found on Stela 9 of Copan, which is the earliest date of these +stelę of that place, in which the numbers preceding the period glyphs +are given by the line-and-dot method, is 54.9.6.10.0.0. This precedes +the above dates by the following periods: + + 1) 0.3.16.3. 3.1. = 548,341 days = 1,502 years 111 days. + 2) 1.0.11.4.11.1 = 1,952,861 " = 5,350 " 14 " + 3) 2.6. 8.3.16.1 = 4,667,001 " = 12,786 " 111 " + +If, now, we accept the first date of 55.13.2.13.3.1. as the date of +Ahpula's death, we shall have the date of Stela 9 of Copan as A.D. 34, +since the death occurred in 1536. If we accept the second date, +55.9.17.14.11.1., as the true one, Stela 9 must represent a date of B.C. +3814, and in the case of the third date, 57.2.14.13.16.1. in which the +period to elapse to the end of Katun 13 Ahau is the nearest to an exact +6 tuns, we should throw back Copan to B.C. 11,250. It is not probable, +however, that either of the last two dates is correct, both because of +the immense time which would have elapsed and because the monuments show +signs of no such age. We are therefore left to the date A.D. 34 as the +probable date of the earliest stela of Copan which we know of at +present. + +The following table gives the earliest and latest dates in Copan and +Quirigua as far as we know them, together with the dates of our calendar +corresponding thereto, on the supposition that the above date is rightly +deciphered: + + Copan: Stela 9, 9. 6.10.0.0 A.D. 34. + " N, 9.16.10.0.0 = 197 years later than A.D. 34 A.D. 231. + Quirigua: " C, 9. 1. 0.0.0 = 108 + " earlier " " say B.C. 75. + " K, 9.18.15.0.0 = 241 + " later " " A.D. 275. + +If this is correct, Copan lasted, so far as the erection of stelę is +concerned, for about 200 years, and Quirigua for about 350 years, though +of course this may be only a small part of the period of their +existence. + +The above calculations have been made on the supposition that the +initial dates record the date of the erection of the stelę, and on the +further supposition, as has been stated, that the same principle of +calculating time has been continued from the earliest ages. There is, +however, some evidence that a change has been made, at least in detail. +It has already been seen that the beginning day of the month has been +shifted from the Eznab, Akbal series to the Cauac, Kan series of days. +What difference this would have made in the relation of the +year-and-month count with the long count it is impossible to say without +knowing the means used to effect the change; but it is quite likely that +this relation was not affected. In the Book of Chilan Balam of Mani is +the entry: "The Thirteenth Ahau; then Pop was counted in order." And in +the Book of Chilan Balam of Chumayel we find, "The Thirteenth Ahau; Pop +was set in order." This statement occurs in the early part of the +chronicle, and the calculation of the Ahaus goes on after it in exactly +the same way as before it. This setting in order of Pop would not then +seem to have made any difference in the long count. At least it is very +probable that it means merely that the seasons and the calendar were +made to agree. + +Dr Brinton (_Maya Chronicles_, p. 85) also gives a translation of a part +of the Codice Perez, which refers to the "Doubling of the Katuns." The +statement is very obscure, but only tends to show that while the +counting of the katuns was carried on as in the Books of Chilan Balam, +the first of the series was called Katun 8 Ahau instead of Katun 13 +Ahau, while the last of the series was Katun 10 Ahau. This would not +necessarily change the consecutive order of the katuns, but might merely +give a new starting-point. + +While, therefore, it is impossible to say what change, if any, was made +in the reckoning of time, it may be said that there is no evidence at +present to show that the old relation of the long count to the +year-and-month count and to the count of the Books of Chilan Balam did +not continue to the time of the arrival of the Spaniards. Moreover, the +date of A.D. 34 for the monuments of Copan and Quirigua is by no means +unlikely to be the true one. At all events the above discussion of the +reckoning will not be useless if it succeeds in bringing out new facts, +and no one will be more ready to recognize any new evidence than I shall +be, even if the above deductions shall be shown to be erroneous. + + + + + * * * * * + + + + +Transcriber's note: + +In general every effort has been made to replicate the original text as +faithfully as possible, including some instances of inconsistencies of +spelling (Ahpula/Ahpulha; Ymix/Imix) and possible irregularities in the +use of commas and periods in Mayan dates. + + + + + +End of the Project Gutenberg EBook of Memoranda on the Maya Calendars Used +in the Books of Chilan Balam, by Charles P. 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Bowditch + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org/license + + +Title: Memoranda on the Maya Calendars Used in the Books of Chilan Balam + +Author: Charles P. Bowditch + +Release Date: May 12, 2012 [EBook #39683] + +Language: English + +Character set encoding: ISO-8859-1 + +*** START OF THIS PROJECT GUTENBERG EBOOK MEMORANDA ON THE MAYA *** + + + + +Produced by Julia Miller, Paula Franzini and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + +</pre> + + + + +<hr class="chap" /> + +<h1>MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM</h1> +<p> </p> +<p class="likeh4">BY</p> +<p class="author">CHARLES P. BOWDITCH</p> + +<p> </p> +<p class="likeh4">(From the American Anthropologist (<span class="smcap lowercase">N. S.</span>), Vol. 3, January-March, 1901)</p> + +<p> </p> +<p class="likeh4">NEW YORK<br /> +<big>G. P. PUTNAM'S SONS</big><br /> +<small>1901</small><br /> +</p> +<hr class="chap" /> +<p><span class="pagenum"><a name="Page_129" id="Page_129">[129]</a></span></p> + + +<p class="likeh2">MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM</p> + +<p class="likeh3"><span class="smcap">By</span> CHARLES P. BOWDITCH</p> + + +<p>Dr Brinton, in his <i>Maya Chronicles</i>, has translated the following +passages from the Book of Chilan Balam of Mani:</p> + +<blockquote><p> +... in the thirteenth Ahau Ahpula died; for six years the count of +the thirteenth Ahau will not be ended; the count of the year was +toward the East, the month Pop began with (the day) fourth Kan; the +eighteenth day of the month Zip (that is) 9 Ymix, was the day on +which Ahpula died; and that the count may be known in numbers and +years, it was the year 1536.</p></blockquote> + +<p>And again from the Book of Chilan Balam of Tizimin:</p> + +<blockquote><p> +The thirteenth Ahau; the death of Ahpulha took place; it was the +sixth year when ended the count of the thirteenth Ahau,—the count +of the year was from the east (the month) Pop passed on the fourth +Kan; on the eighteenth of (the month) Zip, 9 Imix was the day +Ahpulha died; it was the year 1536.</p></blockquote> + +<p>In his remarks on these books Dr Brinton says:</p> + +<blockquote><p> +According to the reckoning as it now stands, six complete great +cycles were counted, and parts of two others, so that the native at +the time of the Conquest would have had eight great cycles to +distinguish apart.</p> + +<p>I have not found any clear explanation how this was accomplished. +We do not even know what name was given to this great cycle,<a name="fnanchor_1_1" id="fnanchor_1_1"></a><a href="#footnote_1_1" class="fnanchor">[1]</a> nor +whether the calendar was sufficiently perfected to prevent +confusion in dates in the remote past.</p></blockquote> + +<p>It would seem, however, as if the reckoning of time as given in these +books is very accurate, fixing a date which would not b<span class="pagenum"><a name="page_130" id="page_130">[130]</a></span>e duplicated +within a limit of thirty-five hundred or four thousand years.</p> + +<p>The Books of Chilan Balam number the katuns on a different principle +from that used on the inscriptions or in the Dresden Codex, but the two +methods can be readily and usefully brought together, as the katun +itself remains the same in both methods. In the inscriptions the katuns +are numbered from 0 to 19, using Goodman's method though not his exact +nomenclature, and twenty of them equal one cycle. In the Chilan Balam +books, the katuns are named as Katun 13 Ahau, Katun 11 Ahau, etc., these +being the days with which they begin or with which the previous katun +ended; and as after thirteen katuns the same name is again given, this +nomenclature fixes a date within a period which equals 13 multiplied by +the number of days in a katun. There has been a difference of opinion as +to this number of days in a katun, but it is clear from the Books of +Chilan Balam that their reckoning was by terms of 20 × 360 days. The +followers of Perez, however, insist that the length of the katun was 24 +× 365 days. Sr Perez has indeed made this assertion,<a name="fnanchor_2_2" id="fnanchor_2_2"></a><a href="#footnote_2_2" class="fnanchor">[2]</a> but he rests his +opinion to a great degree on the fact that the naming of the katuns +proceeded in the following order, taking their names from the day Ahau +with which they began, viz.:</p> + +<div class='center'> +<table border="0" cellpadding="0" cellspacing="0" summary="katun Ahau"> + <tbody> + <tr> + <td class="tdleftpad">Katun</td> + <td class="tdrightpad">13</td> + <td class="tdleftpad">Ahau,</td> + </tr> + <tr> + <td class="tdleftpad">Katun</td> + <td class="tdrightpad">11</td> + <td class="tdleftpad">Ahau,</td> + </tr> + <tr> + <td class="tdleftpad">Katun</td> + <td class="tdrightpad">9</td> + <td class="tdleftpad">Ahau,</td> + </tr> + <tr> + <td class="tdleftpad">Katun</td> + <td class="tdrightpad">7</td> + <td class="tdleftpad">Ahau, etc.,</td> + </tr> + </tbody> + </table> +</div> + +<p>and that by starting with a katun which begins with 13 Ahau and counting +forward a period of 24 × 365 days, we should reach another katun +beginning with 11 Ahau. But the same result is brought about by +considering the katun as a period of 20 × 360 days, as has been shown by +Dr Seler, among others; and since the Books of Chilan Balam state +distinctly that they reckon by so<span class="pagenum"><a name="page_131" id="page_131">[131]</a></span> many scores of so-called years, and +as the initial dates of the inscriptions all reckon in the same way, it +is now generally considered that the katun consisted of 20 × 360 or 7200 +days. An objection to considering a katun as 20 × 360 days may be raised +in that the Books of Chilan Balam use the word "ańo" or year, but this +can be easily explained by the fact that the Spanish "year" was the +period which most nearly agreed with their tun or 360-day period, and +that the Books did not pretend to speak with scientific accuracy.</p> + +<p>Besides the above count, it is well known that the Mayas had a +year-and-month count. This consisted in naming each one of the twenty +days and in attaching to each of these days one of the numbers 1 to 13. +Besides this, each day so numbered was declared to be a given day of a +given month and to occur in a year marked by one of the year bearers—as +for instance in the Book of Chilan Balam, already quoted, where the day +is given as 9 Ymix 18 Zip in the year 4 Kan. Now this day and this year +could recur only after the lapse of fifty-two years or 18,980 days.</p> + +<p>It should be noted here that in the inscriptions and in the Dresden +Codex, the day Ymix was always the day 4, 9, 14, or 19 of any month, +showing that the day 1 of the month was Eznab, Akbal, Lamat, or Ben; +while in Landa and the Books of Chilan Balam the day Ymix was the day 3, +8, 13, or 18, showing that the day 1 of the month was Cauac, Kan, Muluc, +or Ix. That is, the months in modern times began with the day which +followed the day with which the months began in more ancient times. As +the tables are calculated for the inscriptions, it will be well, in +order to facilitate our calculations, to call the day on which Ahpula +died the nineteenth of the month Zip, instead of the eighteenth of that +month.</p> + +<p>Given that the katun consisted of 7200 days, a Katun 13 Ahau could not +recur until after the lapse of 13 × 7200 or 93,600 days, and the +recurrence of any day marked by the year-and-month count, and occupying +any particular place in a given katun, could<span class="pagenum"><a name="page_132" id="page_132">[132]</a></span> not occur until after the +lapse of a period which is found by finding the least common multiple of +the two numbers 93,600 and 18,980. This is 6,832,800 days, which is a +period of 360 calendar rounds of 18,980 days or of 52 years each. This +is equal to 18,720 years, and, in the method of reckoning shown in the +initial dates of the inscriptions, would equal 3 grand cycles, 8 cycles, +and 9 katuns, or, to use the method of Goodman, 3.8.9.0.0.0.</p> + +<p>I have said that a day marked by the year-and-month count, and occupying +any particular place in a given katun, could not recur until the lapse +of this long period. This would be true if the day was specified as +being a given day in a given tun in a given katun, or even if the day +was stated as falling in a given uinal of a given tun in a given katun. +But in the case before us the death of Ahpula is said to have taken +place in the Katun 13 Ahau when six tuns or years of that katun remained +unexpired. Even with this rather loose designation such a day would not +recur within a period of 3500 or 4000 years.</p> + +<p>The day 4 Ahau 8 Cumhu seems to have been regarded as the beginning day +of the beginning cycle of some grand cycle. From this day all the +initial series of the inscriptions of Copan and Quirigua, of Piedras +Negras and Tikal, so far as we know them, count, except one where this +day 4 Ahau 8 Cumhu is itself given. In this place (on Stela C of +Quirigua) 4 Ahau 8 Cumhu is reckoned thus: "Grand cycle glyph +.13.0.0.0.0.", while in the Temple of the Cross it is declared to be a +thirteenth cycle. As this was the beginning date, there is reason to +believe that the beginning cycle of a great cycle received the number +13.</p> + +<p>I give here the first and last terms of a list of the beginning days of +the Katuns 13 Ahau in a complete round of 18,720 years occurring after +the beginning of the grand cycle called by Goodman Grand Cycle 54, which +began with 4 Ahau 8 Cumhu. It is of little consequence what particular +number is given to the grand cycle, as the whole series forms a +continuous count, and I<span class="pagenum"><a name="page_133" id="page_133">[133]</a></span> shall therefore follow Goodman, who gives the +number 54 to the grand cycle glyphs common to Copan, Quirigua, etc.</p> + +<p>If 54.13.0.0.0.0. or the beginning of the grand cycle, called Grand +Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Katun 13 Ahau will +appear two katuns after this or with the count of</p> + +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates2"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"> <tr><td class="tdcenter"> 54.13.2.0.0.0.</td></tr></table></td> + <td class="tdleft"> + <table summary="col2"> <tr><td class="tdcenter"> 13 Ahau</td> <td class="tdleftpad"> 8 Mol </td></tr></table></td> + <td class="tdleft"> + <table summary="col3"> <tr><td class="tdcenter">Year</td> <td class="tdleftpad">10 Ix, </td></tr></table></td> + </tr> + </tbody> + </table> +</div> + +<p>and other Katuns 13 Ahau will follow at intervals of 13 katuns as here +given:</p> +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates2"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"> <tr><td class="tdcenter"> 54.13.15.0.0.0. </td></tr> + <tr><td class="tdcenter">1. 8.</td></tr> + <tr><td class="tdcenter">2. 1.</td></tr> </table></td> + <td class="tdleft"> + <table summary="col2"> <tr><td class="tdcenter"> 13 Ahau</td> <td class="tdleftpad"> 8 Pax</td></tr> + <tr><td class="tdcenter">"</td> <td class="tdleftpad"> 3 Xul</td></tr> + <tr><td class="tdcenter">"</td> <td class="tdleftpad"> 3 Kankin</td></tr></table></td> + <td class="tdleft"> + <table summary="col3"> <tr><td class="tdcenter">Year</td><td class="tdleftpad"> 6 Ix.</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Cauac.</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad">12 "</td></tr></table></td> + </tr> + </tbody> + </table> +</div> +<div class='center'> +<table summary="dots for time passes" style="width: 80%"> + <tbody> + <tr><td class="tdcenter"> . </td><td class="tdcenter"> . </td> + <td class="tdcenter"> . </td><td class="tdcenter"> . </td> + <td class="tdcenter"> . </td><td class="tdcenter"> . </td> + <td class="tdcenter"> . </td><td class="tdcenter"> . </td> + <td class="tdcenter"> . </td><td class="tdcenter"> . </td> + <td class="tdcenter"> . </td><td class="tdcenter"> . </td> + </tr> + </tbody> + </table> +</div> +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates3"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"> <tr><td class="tdcenter"> 57.5.19.0.0.0. </td></tr> + <tr><td class="tdcenter">6.12</td></tr> + <tr><td class="tdcenter">7. 5.</td></tr> + <tr><td class="tdcenter"> 18.</td></tr> + <tr><td class="tdcenter"> 57.8.11.0.0.0. </td></tr> </table></td> + <td class="tdleft"> + <table summary="col2"> <tr><td class="tdcenter">13 Ahau</td> <td class="tdleftpad">18 Ceh</td></tr> + <tr><td class="tdcenter">"</td> <td class="tdleftpad">13 Uo</td></tr> + <tr><td class="tdcenter">"</td> <td class="tdleftpad">13 Yax</td></tr> + <tr><td class="tdcenter">"</td> <td class="tdleftpad">13 Cumhu </td></tr> + <tr><td class="tdcenter">13 Ahau</td> <td class="tdleftpad"> 8 Mol</td></tr> +</table></td> + <td class="tdleft"> + <table summary="col3"> <tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Kan.</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Muluc.</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 "</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad">13 "</td></tr> + <tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Ix.</td></tr></table></td> + </tr> + </tbody> + </table> +</div> + +<p>But we are seeking a Katun 13 Ahau in which 14 tuns have elapsed and of +which 6 tuns still remain unexpired. We must, therefore, add 14 tuns or +14 × 360 days = 5040 days to each of the dates given and we shall then +have the following complete list of the beginning days of Tun 14 of +Katun 13 Ahau for the term of 18,720 years:</p> +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates4"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"><tr><td class="tdcenter">54.13. 2.14.0.0.</td></tr> +<tr><td class="tdcenter"> 15.</td></tr> +<tr><td class="tdcenter">1. 8.</td></tr> +<tr><td class="tdcenter">2. 1.</td></tr> +<tr><td class="tdcenter"> 14.</td></tr> +<tr><td class="tdcenter">3. 7.</td></tr> +<tr><td class="tdcenter">4. 0.</td></tr> +<tr><td class="tdcenter"> 13.</td></tr> +<tr><td class="tdcenter">5. 6.</td></tr> +<tr><td class="tdcenter"> 19.</td></tr> +<tr><td class="tdcenter">6.12.</td></tr> +<tr><td class="tdcenter">7. 5.</td></tr> +<tr><td class="tdcenter"> 18.</td></tr> +<tr><td class="tdcenter">54. 8.11.14.0.0.</td></tr> +<tr><td class="tdcenter">9. 4.</td></tr> +<tr><td class="tdcenter"> 17.</td></tr> +<tr><td class="tdcenter">10.10. </td></tr> +<tr><td class="tdcenter">11. 3. </td></tr> +<tr><td class="tdcenter"> 16.</td></tr> +<tr><td class="tdcenter">12. 9. </td></tr> +<tr><td class="tdcenter">55.13. 2.14.0.0.</td></tr> +<tr><td class="tdcenter"> </td></tr> +<tr><td class="tdcenter"> 15.</td></tr> +<tr><td class="tdcenter">1. 8.</td></tr> +<tr><td class="tdcenter">2. 1.</td></tr> +<tr><td class="tdcenter"> 14.</td></tr> +<tr><td class="tdcenter">3. 7.</td></tr> +<tr><td class="tdcenter">4. 0.</td></tr> +<tr><td class="tdcenter"> 13.</td></tr> +<tr><td class="tdcenter">5. 6.</td></tr> +<tr><td class="tdcenter">5.19.</td></tr> +<tr><td class="tdcenter">6.12.</td></tr> +<tr><td class="tdcenter">7. 5.</td></tr> +<tr><td class="tdcenter"> 18.</td></tr> +<tr><td class="tdcenter">8.11.</td></tr> +<tr><td class="tdcenter">9. 4.</td></tr> +<tr><td class="tdcenter"> 17.</td></tr> +<tr><td class="tdcenter"> </td></tr> +<tr><td class="tdcenter">10.10. </td></tr> +<tr><td class="tdcenter">11.03. </td></tr> +<tr><td class="tdcenter"> 16.</td></tr> +<tr><td class="tdcenter">12. 9. </td></tr> +<tr><td class="tdcenter">56.13. 2.14.0.0.</td></tr> +<tr><td class="tdcenter"> 15.</td></tr> +<tr><td class="tdcenter">1. 8.</td></tr> +<tr><td class="tdcenter">2. 1.</td></tr> +<tr><td class="tdcenter"> 14.</td></tr> +<tr><td class="tdcenter">3. 7.</td></tr> +<tr><td class="tdcenter">4. 0.</td></tr> +<tr><td class="tdcenter"> 13.</td></tr> +<tr><td class="tdcenter">5. 6.</td></tr> +<tr><td class="tdcenter">5.19.</td></tr> +<tr><td class="tdcenter">6.12.</td></tr> +<tr><td class="tdcenter">7.5.</td></tr> +<tr><td class="tdcenter"> 18.</td></tr> +<tr><td class="tdcenter">8.11.</td></tr> +<tr><td class="tdcenter">9. 4.</td></tr> +<tr><td class="tdcenter"> 17.</td></tr> +<tr><td class="tdcenter">10.10. </td></tr> +<tr><td class="tdcenter">11.03. </td></tr> +<tr><td class="tdcenter"> 16.</td></tr> +<tr><td class="tdcenter">12. 9. </td></tr> +<tr><td class="tdcenter">57.13. 2.14.0.0.</td></tr> +<tr><td class="tdcenter"> 15.</td></tr> +<tr><td class="tdcenter">1. 8.</td></tr> +<tr><td class="tdcenter">2. 1.</td></tr> +<tr><td class="tdcenter"> 14.</td></tr> +<tr><td class="tdcenter"> </td></tr> +<tr><td class="tdcenter">3. 7.</td></tr> +<tr><td class="tdcenter">4. 0.</td></tr> +<tr><td class="tdcenter">4.13.</td></tr> +<tr><td class="tdcenter">5. 6.</td></tr> +<tr><td class="tdcenter">5.19.</td></tr> +<tr><td class="tdcenter">6.12.</td></tr> +<tr><td class="tdcenter">7. 5.</td></tr> +<tr><td class="tdcenter"> 18.</td></tr> +<tr><td class="tdcenter">8.11.</td></tr> + </table></td> + <td class="tdleft"> + <table summary="col2"> +<tr><td class="tdcenter"> 9 Ahau</td> <td class="tdleftpad">18 Zotz</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Ceh</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Uo</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Yax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Cumhu</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Mol</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Pax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Xul</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Kankin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Zip</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Zac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Pop</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Chen</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Kayab</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Yaxkin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Muan</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Tzec</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Mac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Uo</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Yax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Cumhu</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"></td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Mol</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Pax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Xul</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Kankin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Zotz</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Ceh</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Pop</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Chen</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Kayab</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Yaxkin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Muan</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Tzec</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Mac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Zip</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Zac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"></td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Uayeb</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Mol</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Pax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Xul</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Kankin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Zotz</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Ceh</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Uo</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Yax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Cumhu</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Yaxkin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Muan</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Tzec</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Mac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Zip</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Zac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Pop</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Chen</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Kayab</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Xul</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Kankin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Zotz</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Ceh</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Uo</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Yax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Cumhu</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Mol</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Pax</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Tzec</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"></td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Mac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Zip</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Zac</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Pop</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Chen</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Kayab</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Yaxkin</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Muan</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">18 Zotz</td></tr> +</table></td> + <td class="tdleft"> + <table summary="col3"> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 7 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 2 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">12 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 5 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 7 Muluc.<span class="pagenum"><a name="page_134" id="page_134">[134]</a></span></td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 2 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">12 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">--------</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 7 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 2 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 7 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">--------</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">12 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 5 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 2 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">12 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 5 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 2 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Ix.<span class="pagenum"><a name="page_135" id="page_135">[135]</a></span></td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 12 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 9 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 5 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 7 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 4 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">--------</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">13 Kan.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">10 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 6 Muluc.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 3 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">12 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 8 Ix.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 5 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad"> 1 Cauac.</td></tr> +<tr><td class="tdcenter"> </td> <td class="tdleftpad">11 Kan.</td></tr> +</table></td> + </tr> + </tbody> + </table> +</div> + + +<p>The only places where a year 4 Kan appears are at the dates</p> +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates3"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"> <tr><td class="tdcenter"> 55.13. 2.14.0.0.<a name="fnanchor_3_3" id="fnanchor_3_3"></a><a href="#footnote_3_3" class="fnanchor">[3]</a> </td></tr> + <tr><td class="tdcenter"> 57. 2.14.14.0.0. </td></tr> </table></td> + <td class="tdleft"> + <table summary="col2"> <tr><td class="tdcenter"> 9 Ahau</td> <td class="tdleftpad">18 Cumhu </td></tr> + <tr><td class="tdcenter"> 9 Ahau </td> <td class="tdleftpad">18 Tzec</td></tr> +</table></td> + <td class="tdleft"> + <table summary="col3"> <tr><td class="tdcenter">Year</td> <td class="tdleftpad"> 4 Kan, and</td></tr> + <tr><td class="tdcenter">Year</td> <td class="tdleftpad"> 4 Kan.</td></tr></table></td> + </tr> + </tbody> + </table> +</div> + +<p>But as the words used are that 6 years (or tuns) remained before the end +of the katun, and as a slightly longer time than just 6 tuns may have +remained, and as the month Zip in which the death of Ahpula occurred is +the third month of the year and so is near the beginning of the year 4 +Kan, it is quite possible that the beginning of the Tun 14 may have been +in the latter part of<span class="pagenum"><a name="page_136" id="page_136">[136]</a></span> the preceding year, in which case, in addition to +the preceding dates, the following date might be the one which we are +seeking:</p> +<div class='center'> +<table style="width: 90%" border="0" cellpadding="0" cellspacing="0" summary="dates3"> + <tbody> + <tr> + <td class="tdleft"> + <table summary="col1"> + <tr><td class="tdcenter"> 55. 9.17.14.0.0. </td></tr> </table></td> + <td class="tdleft"> + <table summary="col2"> + <tr><td class="tdcenter"> 9 Ahau </td> <td class="tdleftpad">3 Zac </td></tr> +</table></td> + <td class="tdleft"> + <table summary="col3"> + <tr><td class="tdcenter"> Year</td> <td class="tdleftpad"> 3 Cauac. </td></tr></table></td> + </tr> + </tbody> + </table> +</div> + +<p>As 9 Ymix 19 Zip is said to be in the year 4 Kan, we shall find this +date before the dates of the beginning of Tun 14 in the first two cases +and after the beginning of Tun 14 in the last case. This date of 9 Ymix +19 Zip will then be numbered thus, placing the three dates in +consecutive order:</p> +<div class='center'> +<table border="0" cellpadding="0" cellspacing="0" summary="dates4"> + <tbody> + <tr> +<td class="tdleftpad2"> 1) 55.13. 2.13. 3. 1. </td> +<td class="tdleftpad3"> 6 tuns 299 days to end of Katun 13 Ahau.</td></tr> +<tr><td class="tdleftpad2">2) 55. 9.17.14.11. 1. </td> +<td class="tdleftpad3">5 " 139 " " " "</td></tr> +<tr><td class="tdleftpad2">3) 57. 2.14.13.16. 1.</td> +<td class="tdleftpad3">6 " 39 " " " "</td></tr> + </tbody> + </table> +</div> + +<p>In no one of the cases is the date 9 Ymix 19 Zip exactly 6 tuns before +the end of the Katun 13 Ahau, but it is possible that the annalist took +no account of fractions of tuns, either in excess of the 6 tuns or +otherwise. Thus in the first and last cases of the three, as first +given, he may have said to himself, "There are but 6 whole tuns +remaining of the katun and I will call it 6," or in the second case he +may have said: "There are 5 tuns remaining and 139 days besides; I will +call it 6 tuns." Whichever was the plan he followed, we can have at +present no means of ascertaining except from the results which we obtain +by calculation.</p> + +<p>The date found on Stela 9 of Copan, which is the earliest date of these +stelę of that place, in which the numbers preceding the period glyphs +are given by the line-and-dot method, is 54.9.6.10.0.0. This precedes +the above dates by the following periods:</p> +<div class='center'> +<table border="0" cellpadding="0" cellspacing="0" summary="dates4"> + <tbody> + <tr> +<td class="tdleftpad2">1) 0.3.16.3. 3.1. </td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 548,341</td> <td class="tdcenter">days</td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 1,502</td> <td class="tdcenter"> years</td> <td class="tdrightpad2">111</td> <td class="tdcenter"> days.</td> +</tr> + <tr> +<td class="tdleftpad2">2) 1.0.11.4.11.1 </td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 1,952,861 </td> <td class="tdcenter"> "</td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 5,350</td> <td class="tdcenter"> "</td> <td class="tdrightpad2">14</td> <td class="tdcenter"> "</td> +</tr> + <tr> +<td class="tdleftpad2">3) 2.6. 8.3.16.1 </td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 4,667,001</td> <td class="tdcenter"> " </td> <td class="tdleftpad2"> =</td> +<td class="tdrightpad2"> 12,786</td> <td class="tdcenter"> " </td> <td class="tdrightpad2">111</td> <td class="tdcenter"> "</td> +</tr> + </tbody> + </table> +</div> + +<p>If, now, we accept the first date of 55.13.2.13.3.1. as the date of +Ahpula's death, we shall have the date of Stela 9 of Copan as <span class="smcap lowercase">A.D.</span> 34, +since the death occurred in 1536. If we accept the second<span class="pagenum"><a name="page_137" id="page_137">[137]</a></span> date, +55.9.17.14.11.1., as the true one, Stela 9 must represent a date of <span class="smcap lowercase">B.C.</span> +3814, and in the case of the third date, 57.2.14.13.16.1. in which the +period to elapse to the end of Katun 13 Ahau is the nearest to an exact +6 tuns, we should throw back Copan to <span class="smcap lowercase">B.C.</span> 11,250. It is not probable, +however, that either of the last two dates is correct, both because of +the immense time which would have elapsed and because the monuments show +signs of no such age. We are therefore left to the date <span class="smcap lowercase">A.D.</span> 34 as the +probable date of the earliest stela of Copan which we know of at +present.</p> + +<p>The following table gives the earliest and latest dates in Copan and +Quirigua as far as we know them, together with the dates of our calendar +corresponding thereto, on the supposition that the above date is rightly +deciphered:</p> + +<div class='center'> +<table border="0" cellpadding="0" cellspacing="0" summary="dates5"> + <tbody> + <tr> + <td class="tdleftpad">Copan:</td><td class="tdcenter">Stela</td><td class="tdrightpad2"> 9,</td> + <td class="tdleftpad"> 9. 6.10.0.0 </td> + <td class="tdleftpad"></td> + <td class="tdleftpad"><span class="smcap lowercase">A.D.</span> 34.</td> </tr> <tr> + + <td class="tdleftpad"> </td><td class="tdcenter">"</td><td class="tdrightpad2"> N,</td> + <td class="tdleftpad"> 9.16.10.0.0 </td> + <td class="tdleftpad"> = 197 years later than <span class="smcap lowercase">A.D.</span> 34 </td> + <td class="tdleftpad"><span class="smcap lowercase">A.D.</span> 231.</td></tr> <tr> + + <td class="tdleftpad">Quirigua:</td><td class="tdcenter">"</td><td class="tdrightpad2"> C,</td> + <td class="tdleftpad">9. 1. 0.0.0 </td> + <td class="tdleftpad">= 108 + " earlier " " say </td> + <td class="tdleftpad"><span class="smcap lowercase">B.C.</span> 75.</td></tr> <tr> + + <td class="tdleftpad"> </td><td class="tdcenter">"</td><td class="tdrightpad2"> K,</td> + <td class="tdleftpad"> 9.18.15.0.0 </td> + <td class="tdleftpad"> = 241 + " later " "</td> + <td class="tdleftpad"><span class="smcap lowercase">A.D.</span> 275.</td> +</tr> + + </tbody> + </table> +</div> + + +<p>If this is correct, Copan lasted, so far as the erection of stelę is +concerned, for about 200 years, and Quirigua for about 350 years, though +of course this may be only a small part of the period of their +existence.</p> + +<p>The above calculations have been made on the supposition that the +initial dates record the date of the erection of the stelę, and on the +further supposition, as has been stated, that the same principle of +calculating time has been continued from the earliest ages. There is, +however, some evidence that a change has been made, at least in detail. +It has already been seen that the beginning day of the month has been +shifted from the Eznab, Akbal series to the Cauac, Kan series of days. +What difference this would have made in the relation of the +year-and-month count with the long count it is impossible to say without +knowing the means used to effect the change; but it is quite likely that +this relation was not affected. In the Book of Chilan Balam of Mani<span class="pagenum"><a name="page_138" id="page_138">[138]</a></span> is +the entry: "The Thirteenth Ahau; then Pop was counted in order." And in +the Book of Chilan Balam of Chumayel we find, "The Thirteenth Ahau; Pop +was set in order." This statement occurs in the early part of the +chronicle, and the calculation of the Ahaus goes on after it in exactly +the same way as before it. This setting in order of Pop would not then +seem to have made any difference in the long count. At least it is very +probable that it means merely that the seasons and the calendar were +made to agree.</p> + +<p>Dr Brinton (<i>Maya Chronicles</i>, p. 85) also gives a translation of a part +of the Codice Perez, which refers to the "Doubling of the Katuns." The +statement is very obscure, but only tends to show that while the +counting of the katuns was carried on as in the Books of Chilan Balam, +the first of the series was called Katun 8 Ahau instead of Katun 13 +Ahau, while the last of the series was Katun 10 Ahau. This would not +necessarily change the consecutive order of the katuns, but might merely +give a new starting-point.</p> + +<p>While, therefore, it is impossible to say what change, if any, was made +in the reckoning of time, it may be said that there is no evidence at +present to show that the old relation of the long count to the +year-and-month count and to the count of the Books of Chilan Balam did +not continue to the time of the arrival of the Spaniards. Moreover, the +date of <span class="smcap lowercase">A.D.</span> 34 for the monuments of Copan and Quirigua is by no means +unlikely to be the true one. At all events the above discussion of the +reckoning will not be useless if it succeeds in bringing out new facts, +and no one will be more ready to recognize any new evidence than I shall +be, even if the above deductions shall be shown to be erroneous.</p> + +<hr class="chap" /> +<p> </p> +<div class="footnotes"><h2>FOOTNOTES:</h2> +<div class="footnote"><p><a name="footnote_1_1" id="footnote_1_1"></a><a href="#fnanchor_1_1"><span class="label">[1]</span></a> It should be noted that the grand cycle, which Dr Brinton +refers to, is the period of 13 × 7200 days = 93,600 days or 260 periods +of 360 days; while the grand cycle according to Goodman's method is 13 × +144,000 days or 5200 periods of 360 days.</p></div> + +<div class="footnote"><p><a name="footnote_2_2" id="footnote_2_2"></a><a href="#fnanchor_2_2"><span class="label">[2]</span></a> Stephens, <i>Incidents of Travel in Yucatan</i>, p. 441 et seq.</p></div> + +<div class="footnote"><p><a name="footnote_3_3" id="footnote_3_3"></a><a href="#fnanchor_3_3"><span class="label">[3]</span></a> It is necessary to remember that, by Goodman's methods, +these figures represent periods of past time. Thus the number 2 of the +katun means that 2 katuns have passed, and that the current katun is +what we should call the third; and that 0.0 means that a full count of +uinals and kins has occurred and that the current uinal and kin are what +we should call the first.</p></div> +</div> +<hr class="chap" /> +<div class='tnote'> +<h2><a name="Transcribers_note" id="Transcribers_note">Transcriber's note:</a></h2> + +<p>In general every effort has been made to replicate the original text as +faithfully as possible, including some instances of inconsistencies of +spelling (Ahpula/Ahpulha; Ymix/Imix) and possible irregularities in the +use of commas and periods in Mayan dates.</p> +</div> + + + + + + + + +<pre> + + + + + +End of the Project Gutenberg EBook of Memoranda on the Maya Calendars Used +in the Books of Chilan Balam, by Charles P. 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Bowditch + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org/license + + +Title: Memoranda on the Maya Calendars Used in the Books of Chilan Balam + +Author: Charles P. Bowditch + +Release Date: May 12, 2012 [EBook #39683] + +Language: English + +Character set encoding: ASCII + +*** START OF THIS PROJECT GUTENBERG EBOOK MEMORANDA ON THE MAYA *** + + + + +Produced by Julia Miller, Paula Franzini and the Online +Distributed Proofreading Team at http://www.pgdp.net (This +file was produced from images generously made available +by The Internet Archive) + + + + + + + + + + MEMORANDA ON THE MAYA CALENDARS + USED IN THE BOOKS OF + CHILAN BALAM + + BY + CHARLES P. BOWDITCH + + (From the American Anthropologist (N. S.), Vol. 3, January-March, 1901) + + NEW YORK + G. P. PUTNAM'S SONS + 1901 + + + + + MEMORANDA ON THE MAYA CALENDARS USED IN THE BOOKS OF CHILAN BALAM + + BY CHARLES P. BOWDITCH + + +Dr Brinton, in his _Maya Chronicles_, has translated the following +passages from the Book of Chilan Balam of Mani: + + ... in the thirteenth Ahau Ahpula died; for six years the count of + the thirteenth Ahau will not be ended; the count of the year was + toward the East, the month Pop began with (the day) fourth Kan; the + eighteenth day of the month Zip (that is) 9 Ymix, was the day on + which Ahpula died; and that the count may be known in numbers and + years, it was the year 1536. + +And again from the Book of Chilan Balam of Tizimin: + + The thirteenth Ahau; the death of Ahpulha took place; it was the + sixth year when ended the count of the thirteenth Ahau,--the count + of the year was from the east (the month) Pop passed on the fourth + Kan; on the eighteenth of (the month) Zip, 9 Imix was the day + Ahpulha died; it was the year 1536. + +In his remarks on these books Dr Brinton says: + + According to the reckoning as it now stands, six complete great + cycles were counted, and parts of two others, so that the native at + the time of the Conquest would have had eight great cycles to + distinguish apart. + + I have not found any clear explanation how this was accomplished. + We do not even know what name was given to this great cycle,[1] nor + whether the calendar was sufficiently perfected to prevent + confusion in dates in the remote past. + + [1] It should be noted that the grand cycle, which Dr Brinton refers + to, is the period of 13 x 7200 days = 93,600 days or 260 periods of + 360 days; while the grand cycle according to Goodman's method is 13 + x 144,000 days or 5200 periods of 360 days. + +It would seem, however, as if the reckoning of time as given in these +books is very accurate, fixing a date which would not be duplicated +within a limit of thirty-five hundred or four thousand years. + +The Books of Chilan Balam number the katuns on a different principle +from that used on the inscriptions or in the Dresden Codex, but the two +methods can be readily and usefully brought together, as the katun +itself remains the same in both methods. In the inscriptions the katuns +are numbered from 0 to 19, using Goodman's method though not his exact +nomenclature, and twenty of them equal one cycle. In the Chilan Balam +books, the katuns are named as Katun 13 Ahau, Katun 11 Ahau, etc., these +being the days with which they begin or with which the previous katun +ended; and as after thirteen katuns the same name is again given, this +nomenclature fixes a date within a period which equals 13 multiplied by +the number of days in a katun. There has been a difference of opinion as +to this number of days in a katun, but it is clear from the Books of +Chilan Balam that their reckoning was by terms of 20 x 360 days. The +followers of Perez, however, insist that the length of the katun was 24 +x 365 days. Sr Perez has indeed made this assertion,[2] but he rests his +opinion to a great degree on the fact that the naming of the katuns +proceeded in the following order, taking their names from the day Ahau +with which they began, viz.: + + Katun 13 Ahau, + Katun 11 Ahau, + Katun 9 Ahau, + Katun 7 Ahau, etc., + +and that by starting with a katun which begins with 13 Ahau and counting +forward a period of 24 x 365 days, we should reach another katun +beginning with 11 Ahau. But the same result is brought about by +considering the katun as a period of 20 x 360 days, as has been shown by +Dr Seler, among others; and since the Books of Chilan Balam state +distinctly that they reckon by so many scores of so-called years, and +as the initial dates of the inscriptions all reckon in the same way, it +is now generally considered that the katun consisted of 20 x 360 or 7200 +days. An objection to considering a katun as 20 x 360 days may be raised +in that the Books of Chilan Balam use the word "ano" or year, but this +can be easily explained by the fact that the Spanish "year" was the +period which most nearly agreed with their tun or 360-day period, and +that the Books did not pretend to speak with scientific accuracy. + + [2] Stephens, _Incidents of Travel in Yucatan_, p. 441 et seq. + +Besides the above count, it is well known that the Mayas had a +year-and-month count. This consisted in naming each one of the twenty +days and in attaching to each of these days one of the numbers 1 to 13. +Besides this, each day so numbered was declared to be a given day of a +given month and to occur in a year marked by one of the year bearers--as +for instance in the Book of Chilan Balam, already quoted, where the day +is given as 9 Ymix 18 Zip in the year 4 Kan. Now this day and this year +could recur only after the lapse of fifty-two years or 18,980 days. + +It should be noted here that in the inscriptions and in the Dresden +Codex, the day Ymix was always the day 4, 9, 14, or 19 of any month, +showing that the day 1 of the month was Eznab, Akbal, Lamat, or Ben; +while in Landa and the Books of Chilan Balam the day Ymix was the day 3, +8, 13, or 18, showing that the day 1 of the month was Cauac, Kan, Muluc, +or Ix. That is, the months in modern times began with the day which +followed the day with which the months began in more ancient times. As +the tables are calculated for the inscriptions, it will be well, in +order to facilitate our calculations, to call the day on which Ahpula +died the nineteenth of the month Zip, instead of the eighteenth of that +month. + +Given that the katun consisted of 7200 days, a Katun 13 Ahau could not +recur until after the lapse of 13 x 7200 or 93,600 days, and the +recurrence of any day marked by the year-and-month count, and occupying +any particular place in a given katun, could not occur until after the +lapse of a period which is found by finding the least common multiple of +the two numbers 93,600 and 18,980. This is 6,832,800 days, which is a +period of 360 calendar rounds of 18,980 days or of 52 years each. This +is equal to 18,720 years, and, in the method of reckoning shown in the +initial dates of the inscriptions, would equal 3 grand cycles, 8 cycles, +and 9 katuns, or, to use the method of Goodman, 3.8.9.0.0.0. + +I have said that a day marked by the year-and-month count, and occupying +any particular place in a given katun, could not recur until the lapse +of this long period. This would be true if the day was specified as +being a given day in a given tun in a given katun, or even if the day +was stated as falling in a given uinal of a given tun in a given katun. +But in the case before us the death of Ahpula is said to have taken +place in the Katun 13 Ahau when six tuns or years of that katun remained +unexpired. Even with this rather loose designation such a day would not +recur within a period of 3500 or 4000 years. + +The day 4 Ahau 8 Cumhu seems to have been regarded as the beginning day +of the beginning cycle of some grand cycle. From this day all the +initial series of the inscriptions of Copan and Quirigua, of Piedras +Negras and Tikal, so far as we know them, count, except one where this +day 4 Ahau 8 Cumhu is itself given. In this place (on Stela C of +Quirigua) 4 Ahau 8 Cumhu is reckoned thus: "Grand cycle glyph +.13.0.0.0.0.", while in the Temple of the Cross it is declared to be a +thirteenth cycle. As this was the beginning date, there is reason to +believe that the beginning cycle of a great cycle received the number +13. + +I give here the first and last terms of a list of the beginning days of +the Katuns 13 Ahau in a complete round of 18,720 years occurring after +the beginning of the grand cycle called by Goodman Grand Cycle 54, which +began with 4 Ahau 8 Cumhu. It is of little consequence what particular +number is given to the grand cycle, as the whole series forms a +continuous count, and I shall therefore follow Goodman, who gives the +number 54 to the grand cycle glyphs common to Copan, Quirigua, etc. + +If 54.13.0.0.0.0. or the beginning of the grand cycle, called Grand +Cycle 54 by Goodman, begins with 4 Ahau 8 Cumhu, a Katun 13 Ahau will +appear two katuns after this or with the count of + + 54.13.2.0.0.0. 13 Ahau 8 Mol Year 10 Ix, + +and other Katuns 13 Ahau will follow at intervals of 13 katuns as here +given: + + 54.13.15.0.0.0. 13 Ahau 8 Pax Year 6 Ix. + 1. 8. " 3 Xul 3 Cauac. + 2. 1. " 3 Kankin 12 " + + . . . . . . . . . . . + + 57.5.19.0.0.0. 13 Ahau 18 Ceh 11 Kan. + 6.12 13 Uo 8 Muluc. + 7. 5. 13 Yax 4 " + 18. 13 Cumhu 13 " + 57.8.11.0.0.0. 13 Ahau 8 Mol 10 Ix. + +But we are seeking a Katun 13 Ahau in which 14 tuns have elapsed and of +which 6 tuns still remain unexpired. We must, therefore, add 14 tuns or +14 x 360 days = 5040 days to each of the dates given and we shall then +have the following complete list of the beginning days of Tun 14 of +Katun 13 Ahau for the term of 18,720 years: + + 54.13. 2.14.0.0. 9 Ahau 18 Zotz 11 Kan. + 15. 18 Ceh 7 Kan. + 1. 8. 13 Uo 4 Muluc. + 2. 1. 13 Yax 13 Muluc. + 14. 13 Cumhu 9 Muluc. + 3. 7. 8 Mol 6 Ix. + 4. 0. 8 Pax 2 Ix. + 13. 3 Xul 12 Cauac. + 5. 6. 3 Kankin 8 Cauac. + 19. 18 Zip 5 Kan. + 6.12. 18 Zac 1 Kan. + 7. 5. 13 Pop 11 Muluc. + 18. 13 Chen 7 Muluc. + 54. 8.11.14.0.0. 13 Kayab 3 Muluc. + 9. 4. 8 Yaxkin 13 Ix. + 17. 8 Muan 9 Ix. + 10.10. 3 Tzec 6 Cauac. + 11. 3. 3 Mac 2 Cauac. + 16. 18 Uo 12 Kan. + 12. 9. 18 Yax 8 Kan. + 55.13. 2.14.0.0. 18 Cumhu 4 Kan. + -------- + 15. 13 Mol 1 Muluc. + 1. 8. 13 Pax 10 Muluc. + 2. 1. 8 Xul 7 Ix. + 14. 8 Kankin 3 Ix. + 3. 7. 3 Zotz 13 Cauac. + 4. 0. 3 Ceh 9 Cauac. + 13. 18 Pop 6 Kan. + 5. 6. 18 Chen 2 Kan. + 5.19. 18 Kayab 11 Kan. + 6.12. 13 Yaxkin 8 Muluc. + 7. 5. 13 Muan 4 Muluc. + 18. 8 Tzec 1 Ix. + 8.11. 8 Mac 10 Ix. + 9. 4. 3 Zip 7 Cauac. + 17. 3 Zac 3 Cauac. + -------- + 10.10. 3 Uayeb 12 Cauac. + 11.03. 18 Mol 9 Kan. + 16. 18 Pax 5 Kan. + 12. 9. 13 Xul 2 Muluc. + 56.13. 2.14.0.0. 13 Kankin 11 Muluc. + 15. 8 Zotz 8 Ix. + 1. 8. 8 Ceh 4 Ix. + 2. 1. 3 Uo 1 Cauac. + 14. 3 Yax 10 Cauac. + 3. 7. 3 Cumhu 6 Cauac. + 4. 0. 18 Yaxkin 3 Kan. + 13. 18 Muan 12 Kan. + 5. 6. 13 Tzec 9 Muluc. + 5.19. 13 Mac 5 Muluc. + 6.12. 8 Zip 2 Ix. + 7.5. 8 Zac 11 Ix. + 18. 3 Pop 8 Cauac. + 8.11. 3 Chen 4 Cauac. + 9. 4. 3 Kayab 13 Cauac. + 17. 18 Xul 10 Kan. + 10.10. 18 Kankin 6 Kan. + 11.03. 13 Zotz 3 Muluc. + 16. 13 Ceh 12 Muluc. + 12. 9. 8 Uo 9 Ix. + 57.13. 2.14.0.0. 8 Yax 5 Ix. + 15. 8 Cumhu 1 Ix. + 1. 8. 3 Mol 11 Cauac. + 2. 1. 3 Pax 7 Cauac. + 14. 18 Tzec 4 Kan. + -------- + 3. 7. 18 Mac 13 Kan. + 4. 0. 13 Zip 10 Muluc. + 4.13. 13 Zac 6 Muluc. + 5. 6. 8 Pop 3 Ix. + 5.19. 8 Chen 12 Ix. + 6.12. 8 Kayab 8 Ix. + 7. 5. 3 Yaxkin 5 Cauac. + 18. 3 Muan 1 Cauac. + 8.11. 18 Zotz 11 Kan. + +The only places where a year 4 Kan appears are at the dates + + 55.13. 2.14.0.0.[3] 9 Ahau 18 Cumhu Year 4 Kan, and + 57. 2.14.14.0.0. 9 Ahau 18 Tzec Year 4 Kan. + +But as the words used are that 6 years (or tuns) remained before the end +of the katun, and as a slightly longer time than just 6 tuns may have +remained, and as the month Zip in which the death of Ahpula occurred is +the third month of the year and so is near the beginning of the year 4 +Kan, it is quite possible that the beginning of the Tun 14 may have been +in the latter part of the preceding year, in which case, in addition to +the preceding dates, the following date might be the one which we are +seeking: + + 55. 9.17.14.0.0. 9 Ahau 3 Zac Year 3 Cauac. + + [3] It is necessary to remember that, by Goodman's methods, these + figures represent periods of past time. Thus the number 2 of the katun + means that 2 katuns have passed, and that the current katun is what we + should call the third; and that 0.0 means that a full count of uinals + and kins has occurred and that the current uinal and kin are what we + should call the first. + +As 9 Ymix 19 Zip is said to be in the year 4 Kan, we shall find this +date before the dates of the beginning of Tun 14 in the first two cases +and after the beginning of Tun 14 in the last case. This date of 9 Ymix +19 Zip will then be numbered thus, placing the three dates in +consecutive order: + + 1) 55.13. 2.13. 3. 1. 6 tuns 299 days to end of Katun 13 Ahau. + 2) 55. 9.17.14.11. 1. 5 " 139 " " " " + 3) 57. 2.14.13.16. 1. 6 " 39 " " " " + +In no one of the cases is the date 9 Ymix 19 Zip exactly 6 tuns before +the end of the Katun 13 Ahau, but it is possible that the annalist took +no account of fractions of tuns, either in excess of the 6 tuns or +otherwise. Thus in the first and last cases of the three, as first +given, he may have said to himself, "There are but 6 whole tuns +remaining of the katun and I will call it 6," or in the second case he +may have said: "There are 5 tuns remaining and 139 days besides; I will +call it 6 tuns." Whichever was the plan he followed, we can have at +present no means of ascertaining except from the results which we obtain +by calculation. + +The date found on Stela 9 of Copan, which is the earliest date of these +stelae of that place, in which the numbers preceding the period glyphs +are given by the line-and-dot method, is 54.9.6.10.0.0. This precedes +the above dates by the following periods: + + 1) 0.3.16.3. 3.1. = 548,341 days = 1,502 years 111 days. + 2) 1.0.11.4.11.1 = 1,952,861 " = 5,350 " 14 " + 3) 2.6. 8.3.16.1 = 4,667,001 " = 12,786 " 111 " + +If, now, we accept the first date of 55.13.2.13.3.1. as the date of +Ahpula's death, we shall have the date of Stela 9 of Copan as A.D. 34, +since the death occurred in 1536. If we accept the second date, +55.9.17.14.11.1., as the true one, Stela 9 must represent a date of B.C. +3814, and in the case of the third date, 57.2.14.13.16.1. in which the +period to elapse to the end of Katun 13 Ahau is the nearest to an exact +6 tuns, we should throw back Copan to B.C. 11,250. It is not probable, +however, that either of the last two dates is correct, both because of +the immense time which would have elapsed and because the monuments show +signs of no such age. We are therefore left to the date A.D. 34 as the +probable date of the earliest stela of Copan which we know of at +present. + +The following table gives the earliest and latest dates in Copan and +Quirigua as far as we know them, together with the dates of our calendar +corresponding thereto, on the supposition that the above date is rightly +deciphered: + + Copan: Stela 9, 9. 6.10.0.0 A.D. 34. + " N, 9.16.10.0.0 = 197 years later than A.D. 34 A.D. 231. + Quirigua: " C, 9. 1. 0.0.0 = 108 + " earlier " " say B.C. 75. + " K, 9.18.15.0.0 = 241 + " later " " A.D. 275. + +If this is correct, Copan lasted, so far as the erection of stelae is +concerned, for about 200 years, and Quirigua for about 350 years, though +of course this may be only a small part of the period of their +existence. + +The above calculations have been made on the supposition that the +initial dates record the date of the erection of the stelae, and on the +further supposition, as has been stated, that the same principle of +calculating time has been continued from the earliest ages. There is, +however, some evidence that a change has been made, at least in detail. +It has already been seen that the beginning day of the month has been +shifted from the Eznab, Akbal series to the Cauac, Kan series of days. +What difference this would have made in the relation of the +year-and-month count with the long count it is impossible to say without +knowing the means used to effect the change; but it is quite likely that +this relation was not affected. In the Book of Chilan Balam of Mani is +the entry: "The Thirteenth Ahau; then Pop was counted in order." And in +the Book of Chilan Balam of Chumayel we find, "The Thirteenth Ahau; Pop +was set in order." This statement occurs in the early part of the +chronicle, and the calculation of the Ahaus goes on after it in exactly +the same way as before it. This setting in order of Pop would not then +seem to have made any difference in the long count. At least it is very +probable that it means merely that the seasons and the calendar were +made to agree. + +Dr Brinton (_Maya Chronicles_, p. 85) also gives a translation of a part +of the Codice Perez, which refers to the "Doubling of the Katuns." The +statement is very obscure, but only tends to show that while the +counting of the katuns was carried on as in the Books of Chilan Balam, +the first of the series was called Katun 8 Ahau instead of Katun 13 +Ahau, while the last of the series was Katun 10 Ahau. This would not +necessarily change the consecutive order of the katuns, but might merely +give a new starting-point. + +While, therefore, it is impossible to say what change, if any, was made +in the reckoning of time, it may be said that there is no evidence at +present to show that the old relation of the long count to the +year-and-month count and to the count of the Books of Chilan Balam did +not continue to the time of the arrival of the Spaniards. Moreover, the +date of A.D. 34 for the monuments of Copan and Quirigua is by no means +unlikely to be the true one. At all events the above discussion of the +reckoning will not be useless if it succeeds in bringing out new facts, +and no one will be more ready to recognize any new evidence than I shall +be, even if the above deductions shall be shown to be erroneous. + + + + + * * * * * + + + + +Transcriber's note: + +In general every effort has been made to replicate the original text as +faithfully as possible, including some instances of inconsistencies of +spelling (Ahpula/Ahpulha; Ymix/Imix) and possible irregularities in the +use of commas and periods in Mayan dates. + + + + + +End of the Project Gutenberg EBook of Memoranda on the Maya Calendars Used +in the Books of Chilan Balam, by Charles P. 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