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-The Project Gutenberg eBook of Mayan Nomenclature, by Charles P.
-Bowditch
-
-This eBook is for the use of anyone anywhere in the United States and
-most other parts of the world 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. If you are not located in the United States, you
-will have to check the laws of the country where you are located before
-using this eBook.
-
-Title: Mayan Nomenclature
-
-Author: Charles P. Bowditch
-
-Release Date: April 19, 2022 [eBook #67879]
-
-Language: English
-
-Produced by: The Online Distributed Proofreading Team at
-             https://www.pgdp.net (This file was produced from images
-             generously made available by The Internet Archive)
-
-*** START OF THE PROJECT GUTENBERG EBOOK MAYAN NOMENCLATURE ***
-
-
-
-
-
-  MAYAN NOMENCLATURE
-
-
-  BY
-  CHARLES P. BOWDITCH
-
-
-  _Privately Printed_
-
-
-  CAMBRIDGE
-  THE UNIVERSITY PRESS
-  1906
-
-
-It has long been well known that the Mexican numeration is vigesimal,
-and, as far as I know, there is no proof that it was ever used in the
-calculation of long reaches of time. The Cakchiquel numeration is also
-vigesimal, and Brinton states (Maya Chronicles, p. 44) that the Maya
-numeration is also vigesimal, giving
-
-  20 units = one kal   = 20
-  20 kal   = one bak   = 400
-  20 bak   = one pic   = 8000
-  20 pic   = one calab = 160000, etc.
-
-But this Maya system is never used in connection with days. Wherever a
-long number of days is referred to, we find invariably the following
-system in use:
-
-  20 units              = one of the second term
-  18 of the second term = one of the third term
-  20 of the third term  = one of the fourth term
-  20 of the fourth term = one of the fifth term.
-
-And this system is, as far as we know, used for nothing else but for
-reckoning days. The only difference between the first system and the
-second is that in the first system twenty of the second term equal one
-of the third, while in the second system eighteen of the second equal
-one of the third. This difference is, of course, essential, and it
-seems most probable that the change was introduced in order to bring
-the third term as near the length of the year as possible, and to
-conform the day numeration to the number of days and months in the year.
-
-Professor Cyrus Thomas is unwilling to see in this anything more than
-the counters by which to count the days, and denies to it the name of
-a calendar; but as the system of day numeration is different from
-the usual system, and is used only for counting days, and as this
-system counts forward in almost every case in the inscriptions, and in
-a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
-8 Cumhu, it seems impossible to see any difference between it and a
-calendar system.
-
-It was certainly to be hoped that the designations which Dr. Seler
-gave to these Maya periods of time in his “Die Monumente von Copan,
-etc.,”[1] would have been accepted by Americanists, especially since
-very good reasons were given by Seler for their adoption. But this
-view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
-latter in his “Maya Calendar, Part II.,” published in the “Report of
-the Bureau of American Ethnology,” still calls the period of 20 days
-a chuen and that of 360 days an ahau, while the former in his article
-on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
-1904 issue of the “Zeitschrift für Ethnologie,” makes the following
-statement: “The katun has also been supposed to be 24 × 365 = 8760 days
-long (and I held this view for a long time), indeed the long period
-of 52 × 365 = 18,980 days is also occasionally designated with the
-word, while the sixth multiple of this member or 113,800 is called
-an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
-periods of 1, 20, and 7200 days respectively.
-
-[1] See Seler, “Gesammelte Abhandlungen zur Amerikanischen Sprach- und
-Alterthumskunde,” Vol. I. p. 722.
-
-Such statements from such learned scholars must attract attention,
-especially as it is not the first time that they have made similar
-statements. If they give a correct statement of facts, it shows that
-the system of the Maya numeration or calendar was in a woful condition,
-as far as its nomenclature was concerned. It will be well, therefore,
-to take up this question of nomenclature anew. In all matters of this
-kind it is wise, while giving due value to the views of later writers,
-to place the most dependence for the solution of such questions upon
-contemporary or nearly contemporary evidence.
-
-And where is such evidence to be found? Though there are several
-Spanish writers who lived in the sixteenth century who have written
-on the Nahuas, Bishop Landa is the earliest Spanish authority who has
-dealt with Maya customs and history. And the only Maya authorities of
-an early date that the student has access to are the papers contained
-in Brinton’s Maya Chronicles, the principal of which are the Books
-of Chilan Balam, which Dr. Brinton declares “to constitute about all
-that remains to us ... of the ancient history of the peninsula” as
-far as he knows. Yet, in making objection to certain views of Dr.
-Seler, Dr. Förstemann says, “It is based on certain statements in the
-Books of Chilan Balam, a very dubious source according to Seler’s own
-assertion.” I am at a loss to know why such sweeping condemnation
-should be made of these books, for though the copies from which Dr.
-Brinton quotes may not be very old, these copies hand down to us
-records which must be of very great age. Dr. Förstemann himself quotes
-from them with approval, and it is certain that whatever may be their
-historical value, the evidence which they give incidentally cannot fail
-to be of great value. This evidence will, I think, prove--
-
-First, that the period of 20 times 360 days was called a katun and not
-an ahau.
-
-Second, that each of the constituent parts of a katun was called a tun.
-
-Third, that no such period of time as an ahaukatun is mentioned in the
-Books of Chilan Balam.
-
-The first assertion may seem difficult to prove when in far the larger
-number of cases where a separate katun is mentioned in the Books of
-Chilan Balam the word “ahau” seems to be substituted for “katun.”
-This is true in all five of the Books of Chilan Balam published by
-Brinton. But the reason of this is very evident, for it will be seen by
-a careful perusal that the word “ahaus” is never used when katuns in
-general are spoken of, and that whenever the word “ahau” is apparently
-given as a synonym of “katun,” it is merely the name of a particular
-katun and it always has a number attached to it and this number is the
-number of the day ahau with which a given katun ended. Further, this
-number is never an ordinal number, as translated by Brinton, but a
-cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
-in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
-the quotations from Brinton this substitution is made.
-
-It may be here stated that the inscriptions all show that where an
-even uinal is given (and therefore where an even tun, katun, or cycle
-is given) the day is Ahau. If then it was desirable to distinguish the
-katuns from each other, two methods could be used: either count them
-numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
-which the preceding katun had ended. The former method is found in the
-inscriptions and the Dresden Codex, the latter in the Books of Chilan
-Balam. The second method would not be possible if each katun ended
-with the same numbered ahau. But 7200 is not divisible by 13 without a
-remainder, but equals 13 × 553 + 11. If then a particular katun ended
-with 13 Ahau, the next would end with Ahau, but the number attached
-to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
-would end with 9, the next with 7, and so on. The katuns then would be
-known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
-Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.
-
-Taking up, therefore, No. I. of the Books of Chilan Balam, published by
-Brinton--that of Mani--we find in the paragraph numbered 1 by Brinton
-“This is the arrangement of the katuns” not “of the ahaus,” and in
-paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
-This is followed by the statement “When they set out for this country,
-it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
-2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
-etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
-and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
-are called fourscore years is equally clear. In paragraph 4 we have “4
-Ahau, 2 Ahau, 13 Ahau--threescore years they ruled Ziyan caan, etc.”
-Here three katuns are called threescore years.
-
-This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
-were each equal to a score of years of 365 days each. When, however,
-we try to account for the numbering of the katuns on this basis, we
-find that the numbers of the ahaus ending each katun would come in the
-following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
-while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
-10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”[2]
-which occurs in paragraph 3, is taken literally, there would seem to be
-no explanation of this difficulty; but if we consider that these books
-used these words as we often use them now as meaning approximately
-“years,” and if we substitute the third term of the numeral series
-as found in the codices for the word “years”--in other words, if we
-substitute 360 for 365--we find then that the katuns or scores of 360
-days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
-10, etc., as has been said and as given in the Books of Chilan Balam.
-This has been shown by Seler, Goodman, and others.
-
-[2] It is very probable that “años” is merely a gloss--and an erroneous
-one at that.
-
-It will then be a good working theory that the score of 360 days is
-called a katun, and that each katun is distinguished by the name of
-an ahau with its proper number, with which a katun ended. That the
-ahau and its number are merely the name of the katun and not the katun
-itself is shown in No. 5 of Brinton’s Books of Chilan Balam,--the
-Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
-the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
-paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
-was a synonym for “katun” would be as foolish as to say of a family
-containing John Smith, Mary Smith, and James Smith, that John and Mary
-and James were all synonyms of Smith, when they were merely names to
-distinguish one Smith from another.
-
-This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
-“Maya Chronicles”), where
-
-  Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”
-   ”   9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”
-   ”  10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”
-   ”  12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”
-   ”  15 says “u katunil ho ahau,” “In the katun 5 Ahau.”
-
-Also in the Book of Tizimin (pp. 139 et seq. of Brinton):
-
-  Par. 6, “Uaxac ahau--lay u katunil,” “8 Ahau--in this katun.”
-   ”   14, “Bolon ahau--lai--u katunil,” “9 Ahau--in this katun.”
-   ”   15, “Vuc ahau--u katunil,” “7 Ahau--in this katun.”
-
-Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):
-
-  Par. 2, “Uaxac ahau--layli u katunil,” “8 Ahau--in this katun.”
-   ”   8, “Bolon ahau--u katunil,” “9 Ahau--in this katun.”
-
-Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):
-
-  Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”
-            “laix u katunil,” “in this katun.”
-   ”   5, “Hun ahau--lay u katunil,” “1 Ahau--in this katun.”
-   ”   8, “Buluc ahau--laix u katunil,” “11 Ahau--in this katun.”
-          “Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”
-   ”   9, “Bolon ahau--lay katun,” “9 Ahau--in this katun.”
-          “Uac Ahau--lay u katunil,” “6 Ahau--in this katun.”
-
-I can find no excuse for considering “ahau” as a synonym for “katun” in
-these Books of Chilan Balam. And _a priori_ it is difficult to conceive
-of a numeral system being made up by a nation as cultivated as the
-Mayas, by which the name of a day should be taken to mean a period of
-time, with all the chances of error which might arise from such use.
-Moreover, if this were the case, it would be natural to suppose that in
-the inscriptions and codices the day sign ahau might be found meaning
-7200 days, and yet I am unaware that a single instance of this exists
-on the monuments or in the codices. There are one or two cases in the
-inscriptions where this has been suggested as being possible, but it is
-very far from being proved or from even having strong evidence in favor
-of such an explanation.
-
-Dr. Förstemann says that at times the name “katun” was given to the
-period of 18,980 days; but the only authority for this use is, as
-far as I know, Pio Perez, who says that some applied the name to a
-“lustre of 4 years,” while others thought that “13 years completed the
-katun.”[3] Again Pio Perez speaks of “the cycle of 52 years called by
-the Indians katun.” In none of these cases is any authority given for
-this use.[4]
-
-[3] Stephens, “Travels in Yucatan,” Appendix, p. 439.
-
-[4] Ibid., p. 440.
-
-It is probably safe to say that any use of the word “ahau” as meaning a
-katun, or any use of the word “katun” as meaning anything but 20 times
-360 days, or any use of the day symbol ahau as meaning a period of
-time, does not occur in any evidence which could be called contemporary
-or even approximately so. Don Pio Perez is, I fear, the only author
-who can be cited for the other side, and his opinion, though worthy of
-being listened to, is not to be relied upon without the support of, or
-against the evidence of, early authorities.
-
-The second question as to the name to be given to the period of 360
-days must be decided by the same authority.
-
-We have found that a katun is probably a score of periods of 360 days
-each, and it would be natural to suppose that the constituent parts of
-the katun, as mentioned in the Books of Chilan Balam, would be these
-periods of 360 days, but of this there is no absolute proof in the
-Books of Chilan Balam. The proof of this, however, is so strong in the
-Dresden Codex, where the series runs, 20 of the first order equals 1 of
-the second order, 18 of the second order equals 1 of the third order,
-and 20 of the third order equals 1 of the fourth, that no time need be
-wasted upon this part of the question. We do know, however, that each
-of these constituent parts is called a tun and that they are numbered
-as high as 13.
-
-The following list gives, I think, all the cases where the word “tun”
-is used in the Books of Chilan Balam:
-
-Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
-translates “the first year of the thirteenth ahau.” I think the proper
-translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
-Katun 13 Ahau.
-
-Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
-it was the tenth year of the eighth ahau,” while it should be “in Tun
-10 of Katun 8 Ahau.”
-
-In the Book of Tizimin we find that in
-
-Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
-year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
-Katun 13 Ahau.”
-
-Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
-on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”
-
-Also in the second Book of Chumayel, we find in
-
-Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
-third year in the first ahau,” when it should be “in Tun 3 of Katun 1
-Ahau.”
-
-Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
-seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
-Katun 8 Ahau.”
-
-Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
-“in the first year of the eleventh ahau, it was also in this katun,”
-when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
-“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
-of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
-Ahau.”
-
-These two katuns are evidently the same--one date being in Tun 1 and
-the other in Tun 7 of the same katun--and yet Brinton translated the
-first as being in the 11th katun and the other as being in the 11th
-ahau katun.
-
-Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
-“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
-Katun 9 Ahau.”
-
-Although Brinton has almost always translated “tun” by “year,” it is
-very evident from the above that the Mayas called the native division
-of the katun “tun.”
-
-It may further be noted that the word “kin” is used for day in the way
-of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
-on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
-paragraph 7 of the first Book of Chumayel, the same statement is made.
-
-May it not then be fairly assumed that the Mayas called the day or the
-unit of their calendrical numeration “kin,” their 360-day period “tun,”
-and the period of 20 tuns “katun,” as Dr. Seler has suggested?
-
-The third question is as to the so-called period of “ahau katun.” I
-give below all the cases in which Brinton has used the word, and in all
-but one of them the Maya has “ahau u katunil”; and in one case Brinton
-has translated a sentence as “it was the eleventh ahau katun,” while
-exactly similar phrases (with the exception of the number) have been
-translated by him as “4 Ahau was the name of the katun.” In the phrase
-in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
-katun” appears, the whole context makes it evident that a katun and not
-an ahau katun, if there was such a period, is meant. The paragraph says
-“9 Ahau; no stone was taken at this time; in this katun came the Bishop
-Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
-Brinton makes it read in the first clause that while Bishop Toral came
-in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
-katun.”
-
-Dr. Tozzer, whose knowledge of the Maya languages, gained in long
-residence among the Maya Indians of Yucatan and Chiapas, enables him
-to speak with authority, writes me as follows: “The form u katunil
-of ahau ukatunil, for example,” in paragraph 3 of the second Book
-of Chumayel, p. 167, “is probably possessive, and it would then be
-literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
-strengthen the point against joining the two together as Ahaukatun.”
-
-In the second Book of Chumayel, p. 167, paragraph 3, “uucpiztun uaxac
-ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
-year of the 8th Ahau katun, in this katun, etc.” There is no authority
-for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
-Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
-Tun 7 of Ahau eight’s Katun.”
-
-Again, in paragraph 5, the translation of “Hun ahau--tu hunpiztun ychil
-hun ahau u katunile” is given, “The first ahau--in the first year of
-the first ahau katun.” It should be “1 Ahau--in Tun 1 of the Katun 1
-Ahau, &c.”
-
-Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
-“in the seventh year of the eleventh ahau katun,” when it should be “in
-Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
-followed by “in this katun.”
-
-Again in paragraph 9 we read “Bolon Ahau--lay katun yax ulci obispo
-Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
-which Brinton translates “The ninth ahau--in this katun first came
-the bishop Brother Francisco Toral; he arrived in the sixth year of
-the ninth ahau katun.” It should be “9 Ahau--in this katun--in Tun 6
-of Katun 9 Ahau.” This is the only place in the Maya where the words
-“ahau katun” appear together. But the context makes it clear that “ahau
-katun” is not a period of time. The paragraph begins with “9 Ahau,” and
-speaks of it as a katun during which Bishop Toral arrived, and then
-proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
-which can mean nothing else than the “Katun 9 Ahau.”
-
-In the third Book of Chumayel, paragraphs 5 and 6, Brinton translates
-“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
-Ahau.”
-
-In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
-katun” instead of “Katun 8 Ahau” (note here that this is the same “8
-Ahau,” when Chichen Itza was deserted for Champoton).
-
-Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
-katun” instead of “Katun 13 Ahau.”
-
-Also “Buluc ahau u kaba u katunil” is here translated “it was the
-eleventh ahau katun,” while in paragraph 3 a similar sentence is
-translated “4 Ahau was the name of the katun.”
-
-Thus an ahau katun is not mentioned in the Books of Chilan Balam in
-spite of Brinton’s translation, and neither is it mentioned by Landa,
-in spite of Brasseur de Bourbourg’s insertions. In fact the only
-evidence of it is the assertion of Don Pio Perez. I do not mean to say
-that the period of 6 × 52 years = 312 years may not have had a name,
-nor that “ahau katun” may not be the name of some period, but so far we
-have no trustworthy contemporary evidence of either of these statements.
-
-*** END OF THE PROJECT GUTENBERG EBOOK MAYAN NOMENCLATURE ***
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+*** START OF THE PROJECT GUTENBERG EBOOK 67879 ***
+
+  MAYAN NOMENCLATURE
+
+
+  BY
+  CHARLES P. BOWDITCH
+
+
+  _Privately Printed_
+
+
+  CAMBRIDGE
+  THE UNIVERSITY PRESS
+  1906
+
+
+It has long been well known that the Mexican numeration is vigesimal,
+and, as far as I know, there is no proof that it was ever used in the
+calculation of long reaches of time. The Cakchiquel numeration is also
+vigesimal, and Brinton states (Maya Chronicles, p. 44) that the Maya
+numeration is also vigesimal, giving
+
+  20 units = one kal   = 20
+  20 kal   = one bak   = 400
+  20 bak   = one pic   = 8000
+  20 pic   = one calab = 160000, etc.
+
+But this Maya system is never used in connection with days. Wherever a
+long number of days is referred to, we find invariably the following
+system in use:
+
+  20 units              = one of the second term
+  18 of the second term = one of the third term
+  20 of the third term  = one of the fourth term
+  20 of the fourth term = one of the fifth term.
+
+And this system is, as far as we know, used for nothing else but for
+reckoning days. The only difference between the first system and the
+second is that in the first system twenty of the second term equal one
+of the third, while in the second system eighteen of the second equal
+one of the third. This difference is, of course, essential, and it
+seems most probable that the change was introduced in order to bring
+the third term as near the length of the year as possible, and to
+conform the day numeration to the number of days and months in the year.
+
+Professor Cyrus Thomas is unwilling to see in this anything more than
+the counters by which to count the days, and denies to it the name of
+a calendar; but as the system of day numeration is different from
+the usual system, and is used only for counting days, and as this
+system counts forward in almost every case in the inscriptions, and in
+a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
+8 Cumhu, it seems impossible to see any difference between it and a
+calendar system.
+
+It was certainly to be hoped that the designations which Dr. Seler
+gave to these Maya periods of time in his “Die Monumente von Copan,
+etc.,”[1] would have been accepted by Americanists, especially since
+very good reasons were given by Seler for their adoption. But this
+view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
+latter in his “Maya Calendar, Part II.,” published in the “Report of
+the Bureau of American Ethnology,” still calls the period of 20 days
+a chuen and that of 360 days an ahau, while the former in his article
+on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
+1904 issue of the “Zeitschrift für Ethnologie,” makes the following
+statement: “The katun has also been supposed to be 24 × 365 = 8760 days
+long (and I held this view for a long time), indeed the long period
+of 52 × 365 = 18,980 days is also occasionally designated with the
+word, while the sixth multiple of this member or 113,800 is called
+an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
+periods of 1, 20, and 7200 days respectively.
+
+[1] See Seler, “Gesammelte Abhandlungen zur Amerikanischen Sprach- und
+Alterthumskunde,” Vol. I. p. 722.
+
+Such statements from such learned scholars must attract attention,
+especially as it is not the first time that they have made similar
+statements. If they give a correct statement of facts, it shows that
+the system of the Maya numeration or calendar was in a woful condition,
+as far as its nomenclature was concerned. It will be well, therefore,
+to take up this question of nomenclature anew. In all matters of this
+kind it is wise, while giving due value to the views of later writers,
+to place the most dependence for the solution of such questions upon
+contemporary or nearly contemporary evidence.
+
+And where is such evidence to be found? Though there are several
+Spanish writers who lived in the sixteenth century who have written
+on the Nahuas, Bishop Landa is the earliest Spanish authority who has
+dealt with Maya customs and history. And the only Maya authorities of
+an early date that the student has access to are the papers contained
+in Brinton’s Maya Chronicles, the principal of which are the Books
+of Chilan Balam, which Dr. Brinton declares “to constitute about all
+that remains to us ... of the ancient history of the peninsula” as
+far as he knows. Yet, in making objection to certain views of Dr.
+Seler, Dr. Förstemann says, “It is based on certain statements in the
+Books of Chilan Balam, a very dubious source according to Seler’s own
+assertion.” I am at a loss to know why such sweeping condemnation
+should be made of these books, for though the copies from which Dr.
+Brinton quotes may not be very old, these copies hand down to us
+records which must be of very great age. Dr. Förstemann himself quotes
+from them with approval, and it is certain that whatever may be their
+historical value, the evidence which they give incidentally cannot fail
+to be of great value. This evidence will, I think, prove--
+
+First, that the period of 20 times 360 days was called a katun and not
+an ahau.
+
+Second, that each of the constituent parts of a katun was called a tun.
+
+Third, that no such period of time as an ahaukatun is mentioned in the
+Books of Chilan Balam.
+
+The first assertion may seem difficult to prove when in far the larger
+number of cases where a separate katun is mentioned in the Books of
+Chilan Balam the word “ahau” seems to be substituted for “katun.”
+This is true in all five of the Books of Chilan Balam published by
+Brinton. But the reason of this is very evident, for it will be seen by
+a careful perusal that the word “ahaus” is never used when katuns in
+general are spoken of, and that whenever the word “ahau” is apparently
+given as a synonym of “katun,” it is merely the name of a particular
+katun and it always has a number attached to it and this number is the
+number of the day ahau with which a given katun ended. Further, this
+number is never an ordinal number, as translated by Brinton, but a
+cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
+in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
+the quotations from Brinton this substitution is made.
+
+It may be here stated that the inscriptions all show that where an
+even uinal is given (and therefore where an even tun, katun, or cycle
+is given) the day is Ahau. If then it was desirable to distinguish the
+katuns from each other, two methods could be used: either count them
+numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
+which the preceding katun had ended. The former method is found in the
+inscriptions and the Dresden Codex, the latter in the Books of Chilan
+Balam. The second method would not be possible if each katun ended
+with the same numbered ahau. But 7200 is not divisible by 13 without a
+remainder, but equals 13 × 553 + 11. If then a particular katun ended
+with 13 Ahau, the next would end with Ahau, but the number attached
+to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
+would end with 9, the next with 7, and so on. The katuns then would be
+known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
+Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.
+
+Taking up, therefore, No. I. of the Books of Chilan Balam, published by
+Brinton--that of Mani--we find in the paragraph numbered 1 by Brinton
+“This is the arrangement of the katuns” not “of the ahaus,” and in
+paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
+This is followed by the statement “When they set out for this country,
+it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
+2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
+etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
+and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
+are called fourscore years is equally clear. In paragraph 4 we have “4
+Ahau, 2 Ahau, 13 Ahau--threescore years they ruled Ziyan caan, etc.”
+Here three katuns are called threescore years.
+
+This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
+were each equal to a score of years of 365 days each. When, however,
+we try to account for the numbering of the katuns on this basis, we
+find that the numbers of the ahaus ending each katun would come in the
+following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
+while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
+10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”[2]
+which occurs in paragraph 3, is taken literally, there would seem to be
+no explanation of this difficulty; but if we consider that these books
+used these words as we often use them now as meaning approximately
+“years,” and if we substitute the third term of the numeral series
+as found in the codices for the word “years”--in other words, if we
+substitute 360 for 365--we find then that the katuns or scores of 360
+days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
+10, etc., as has been said and as given in the Books of Chilan Balam.
+This has been shown by Seler, Goodman, and others.
+
+[2] It is very probable that “años” is merely a gloss--and an erroneous
+one at that.
+
+It will then be a good working theory that the score of 360 days is
+called a katun, and that each katun is distinguished by the name of
+an ahau with its proper number, with which a katun ended. That the
+ahau and its number are merely the name of the katun and not the katun
+itself is shown in No. 5 of Brinton’s Books of Chilan Balam,--the
+Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
+the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
+paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
+was a synonym for “katun” would be as foolish as to say of a family
+containing John Smith, Mary Smith, and James Smith, that John and Mary
+and James were all synonyms of Smith, when they were merely names to
+distinguish one Smith from another.
+
+This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
+“Maya Chronicles”), where
+
+  Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”
+   ”   9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”
+   ”  10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”
+   ”  12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”
+   ”  15 says “u katunil ho ahau,” “In the katun 5 Ahau.”
+
+Also in the Book of Tizimin (pp. 139 et seq. of Brinton):
+
+  Par. 6, “Uaxac ahau--lay u katunil,” “8 Ahau--in this katun.”
+   ”   14, “Bolon ahau--lai--u katunil,” “9 Ahau--in this katun.”
+   ”   15, “Vuc ahau--u katunil,” “7 Ahau--in this katun.”
+
+Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):
+
+  Par. 2, “Uaxac ahau--layli u katunil,” “8 Ahau--in this katun.”
+   ”   8, “Bolon ahau--u katunil,” “9 Ahau--in this katun.”
+
+Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):
+
+  Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”
+            “laix u katunil,” “in this katun.”
+   ”   5, “Hun ahau--lay u katunil,” “1 Ahau--in this katun.”
+   ”   8, “Buluc ahau--laix u katunil,” “11 Ahau--in this katun.”
+          “Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”
+   ”   9, “Bolon ahau--lay katun,” “9 Ahau--in this katun.”
+          “Uac Ahau--lay u katunil,” “6 Ahau--in this katun.”
+
+I can find no excuse for considering “ahau” as a synonym for “katun” in
+these Books of Chilan Balam. And _a priori_ it is difficult to conceive
+of a numeral system being made up by a nation as cultivated as the
+Mayas, by which the name of a day should be taken to mean a period of
+time, with all the chances of error which might arise from such use.
+Moreover, if this were the case, it would be natural to suppose that in
+the inscriptions and codices the day sign ahau might be found meaning
+7200 days, and yet I am unaware that a single instance of this exists
+on the monuments or in the codices. There are one or two cases in the
+inscriptions where this has been suggested as being possible, but it is
+very far from being proved or from even having strong evidence in favor
+of such an explanation.
+
+Dr. Förstemann says that at times the name “katun” was given to the
+period of 18,980 days; but the only authority for this use is, as
+far as I know, Pio Perez, who says that some applied the name to a
+“lustre of 4 years,” while others thought that “13 years completed the
+katun.”[3] Again Pio Perez speaks of “the cycle of 52 years called by
+the Indians katun.” In none of these cases is any authority given for
+this use.[4]
+
+[3] Stephens, “Travels in Yucatan,” Appendix, p. 439.
+
+[4] Ibid., p. 440.
+
+It is probably safe to say that any use of the word “ahau” as meaning a
+katun, or any use of the word “katun” as meaning anything but 20 times
+360 days, or any use of the day symbol ahau as meaning a period of
+time, does not occur in any evidence which could be called contemporary
+or even approximately so. Don Pio Perez is, I fear, the only author
+who can be cited for the other side, and his opinion, though worthy of
+being listened to, is not to be relied upon without the support of, or
+against the evidence of, early authorities.
+
+The second question as to the name to be given to the period of 360
+days must be decided by the same authority.
+
+We have found that a katun is probably a score of periods of 360 days
+each, and it would be natural to suppose that the constituent parts of
+the katun, as mentioned in the Books of Chilan Balam, would be these
+periods of 360 days, but of this there is no absolute proof in the
+Books of Chilan Balam. The proof of this, however, is so strong in the
+Dresden Codex, where the series runs, 20 of the first order equals 1 of
+the second order, 18 of the second order equals 1 of the third order,
+and 20 of the third order equals 1 of the fourth, that no time need be
+wasted upon this part of the question. We do know, however, that each
+of these constituent parts is called a tun and that they are numbered
+as high as 13.
+
+The following list gives, I think, all the cases where the word “tun”
+is used in the Books of Chilan Balam:
+
+Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
+translates “the first year of the thirteenth ahau.” I think the proper
+translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
+Katun 13 Ahau.
+
+Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
+it was the tenth year of the eighth ahau,” while it should be “in Tun
+10 of Katun 8 Ahau.”
+
+In the Book of Tizimin we find that in
+
+Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
+year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
+Katun 13 Ahau.”
+
+Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
+on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”
+
+Also in the second Book of Chumayel, we find in
+
+Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
+third year in the first ahau,” when it should be “in Tun 3 of Katun 1
+Ahau.”
+
+Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
+seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
+Katun 8 Ahau.”
+
+Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
+“in the first year of the eleventh ahau, it was also in this katun,”
+when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
+“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
+of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
+Ahau.”
+
+These two katuns are evidently the same--one date being in Tun 1 and
+the other in Tun 7 of the same katun--and yet Brinton translated the
+first as being in the 11th katun and the other as being in the 11th
+ahau katun.
+
+Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
+“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
+Katun 9 Ahau.”
+
+Although Brinton has almost always translated “tun” by “year,” it is
+very evident from the above that the Mayas called the native division
+of the katun “tun.”
+
+It may further be noted that the word “kin” is used for day in the way
+of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
+on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
+paragraph 7 of the first Book of Chumayel, the same statement is made.
+
+May it not then be fairly assumed that the Mayas called the day or the
+unit of their calendrical numeration “kin,” their 360-day period “tun,”
+and the period of 20 tuns “katun,” as Dr. Seler has suggested?
+
+The third question is as to the so-called period of “ahau katun.” I
+give below all the cases in which Brinton has used the word, and in all
+but one of them the Maya has “ahau u katunil”; and in one case Brinton
+has translated a sentence as “it was the eleventh ahau katun,” while
+exactly similar phrases (with the exception of the number) have been
+translated by him as “4 Ahau was the name of the katun.” In the phrase
+in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
+katun” appears, the whole context makes it evident that a katun and not
+an ahau katun, if there was such a period, is meant. The paragraph says
+“9 Ahau; no stone was taken at this time; in this katun came the Bishop
+Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
+Brinton makes it read in the first clause that while Bishop Toral came
+in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
+katun.”
+
+Dr. Tozzer, whose knowledge of the Maya languages, gained in long
+residence among the Maya Indians of Yucatan and Chiapas, enables him
+to speak with authority, writes me as follows: “The form u katunil
+of ahau ukatunil, for example,” in paragraph 3 of the second Book
+of Chumayel, p. 167, “is probably possessive, and it would then be
+literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
+strengthen the point against joining the two together as Ahaukatun.”
+
+In the second Book of Chumayel, p. 167, paragraph 3, “uucpiztun uaxac
+ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
+year of the 8th Ahau katun, in this katun, etc.” There is no authority
+for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
+Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
+Tun 7 of Ahau eight’s Katun.”
+
+Again, in paragraph 5, the translation of “Hun ahau--tu hunpiztun ychil
+hun ahau u katunile” is given, “The first ahau--in the first year of
+the first ahau katun.” It should be “1 Ahau--in Tun 1 of the Katun 1
+Ahau, &c.”
+
+Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
+“in the seventh year of the eleventh ahau katun,” when it should be “in
+Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
+followed by “in this katun.”
+
+Again in paragraph 9 we read “Bolon Ahau--lay katun yax ulci obispo
+Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
+which Brinton translates “The ninth ahau--in this katun first came
+the bishop Brother Francisco Toral; he arrived in the sixth year of
+the ninth ahau katun.” It should be “9 Ahau--in this katun--in Tun 6
+of Katun 9 Ahau.” This is the only place in the Maya where the words
+“ahau katun” appear together. But the context makes it clear that “ahau
+katun” is not a period of time. The paragraph begins with “9 Ahau,” and
+speaks of it as a katun during which Bishop Toral arrived, and then
+proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
+which can mean nothing else than the “Katun 9 Ahau.”
+
+In the third Book of Chumayel, paragraphs 5 and 6, Brinton translates
+“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
+Ahau.”
+
+In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
+katun” instead of “Katun 8 Ahau” (note here that this is the same “8
+Ahau,” when Chichen Itza was deserted for Champoton).
+
+Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
+katun” instead of “Katun 13 Ahau.”
+
+Also “Buluc ahau u kaba u katunil” is here translated “it was the
+eleventh ahau katun,” while in paragraph 3 a similar sentence is
+translated “4 Ahau was the name of the katun.”
+
+Thus an ahau katun is not mentioned in the Books of Chilan Balam in
+spite of Brinton’s translation, and neither is it mentioned by Landa,
+in spite of Brasseur de Bourbourg’s insertions. In fact the only
+evidence of it is the assertion of Don Pio Perez. I do not mean to say
+that the period of 6 × 52 years = 312 years may not have had a name,
+nor that “ahau katun” may not be the name of some period, but so far we
+have no trustworthy contemporary evidence of either of these statements.
+
+*** END OF THE PROJECT GUTENBERG EBOOK 67879 ***
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-<body>
-<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Mayan Nomenclature, by Charles P. Bowditch</p>
-<div style='display:block; margin:1em 0'>
-This eBook is for the use of anyone anywhere in the United States and
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-</div>
-
-<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Mayan Nomenclature</p>
-<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Charles P. Bowditch</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Release Date: April 19, 2022 [eBook #67879]</p>
-<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p>
-  <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: The Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)</p>
-<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK MAYAN NOMENCLATURE ***</div>
-
-
-
-
-<h1>  MAYAN NOMENCLATURE</h1>
-
-
-<p class="center p2"><span class="small">BY</span><br />
-  CHARLES P. BOWDITCH</p>
-
-
-<p class="center small p2">  <i>Privately Printed</i></p>
-
-
-<p class="center p4">  CAMBRIDGE<br />
-  THE UNIVERSITY PRESS<br />
-  1906
-</p>
-<hr class="chap x-ebookmaker-drop" />
-<div class="chapter">
-
-<p>It has long been well known that the Mexican numeration is vigesimal,
-and, as far as I know, there is no proof that it was ever used in the
-calculation of long reaches of time. The Cakchiquel numeration is also
-vigesimal, and Brinton states (Maya Chronicles, <abbr title="page">p.</abbr> 44) that the Maya
-numeration is also vigesimal, giving</p>
-
-<table class="autotable">
-<tr><td>20 units</td><td>=</td><td>one kal</td><td>=</td><td>20</td></tr>
-<tr><td>20 kal</td><td>=</td><td>one bak</td><td>=</td><td>400</td></tr>
-<tr><td>20 bak</td><td>=</td><td>one pic</td><td>=</td><td>8000</td></tr>
-<tr><td>20 pic</td><td>=</td><td>one calab</td><td>=</td><td>160000, etc.</td></tr>
-</table>
-
-<p>But this Maya system is never used in connection with days. Wherever a
-long number of days is referred to, we find invariably the following
-system in use:</p>
-
-<table class="autotable">
-<tr><td>20 units</td><td>=</td><td>one of the second term</td></tr>
-<tr><td>18 of the second term</td><td>=</td><td>one of the third term</td></tr>
-<tr><td>20 of the third term</td><td>=</td><td>one of the fourth term</td></tr>
-<tr><td>20 of the fourth term</td><td>=</td><td>one of the fifth term.</td></tr>
-</table>
-
-<p>And this system is, as far as we know, used for nothing else but for
-reckoning days. The only difference between the first system and the
-second is that in the first system twenty of the second term equal one
-of the third, while in the second system eighteen of the second equal
-one of the third. This difference is, of course, essential, and it
-seems most probable that the change was introduced in order to bring
-the third term as near the length of the year as possible, and to
-conform the day numeration to the number of days and months in the year.</p>
-
-<p>Professor Cyrus Thomas is unwilling to see in this anything more than
-the counters by which to count the days, and denies to it the name of
-a calendar; but as the system of day numeration is<span class="pagenum" id="Page_2">[Pg 2]</span> different from
-the usual system, and is used only for counting days, and as this
-system counts forward in almost every case in the inscriptions, and in
-a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
-8 Cumhu, it seems impossible to see any difference between it and a
-calendar system.</p>
-
-<p>It was certainly to be hoped that the designations which Dr. Seler
-gave to these Maya periods of time in his “Die Monumente von Copan,
-etc.,”<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a> would have been accepted by Americanists, especially since
-very good reasons were given by Seler for their adoption. But this
-view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
-latter in his “Maya Calendar, Part II.,” published in the “Report of
-the Bureau of American Ethnology,” still calls the period of 20 days
-a chuen and that of 360 days an ahau, while the former in his article
-on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
-1904 issue of the “Zeitschrift für Ethnologie,” makes the following
-statement: “The katun has also been supposed to be 24 × 365 = 8760 days
-long (and I held this view for a long time), indeed the long period
-of 52 × 365 = 18,980 days is also occasionally designated with the
-word, while the sixth multiple of this member or 113,800 is called
-an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
-periods of 1, 20, and 7200 days respectively.</p>
-
-<div class="footnote">
-
-<p><a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a> See Seler, “<span lang="de" xml:lang="de">Gesammelte Abhandlungen zur Amerikanischen
-Sprach- und Alterthumskunde,</span>” <abbr title="volume">Vol.</abbr> I. <abbr title="page">p.</abbr> 722.</p>
-
-</div>
-
-<p>Such statements from such learned scholars must attract attention,
-especially as it is not the first time that they have made similar
-statements. If they give a correct statement of facts, it shows that
-the system of the Maya numeration or calendar was in a woful condition,
-as far as its nomenclature was concerned. It will be well, therefore,
-to take up this question of nomenclature anew. In all matters of this
-kind it is wise, while giving due value to the views of later writers,
-to place the most dependence for the solution of such questions upon
-contemporary or nearly contemporary evidence.</p>
-
-<p><span class="pagenum" id="Page_3">[Pg 3]</span></p>
-
-<p>And where is such evidence to be found? Though there are several
-Spanish writers who lived in the sixteenth century who have written
-on the Nahuas, Bishop Landa is the earliest Spanish authority who has
-dealt with Maya customs and history. And the only Maya authorities of
-an early date that the student has access to are the papers contained
-in Brinton’s Maya Chronicles, the principal of which are the Books
-of Chilan Balam, which Dr. Brinton declares “to constitute about all
-that remains to us ... of the ancient history of the peninsula” as
-far as he knows. Yet, in making objection to certain views of Dr.
-Seler, Dr. Förstemann says, “It is based on certain statements in the
-Books of Chilan Balam, a very dubious source according to Seler’s own
-assertion.” I am at a loss to know why such sweeping condemnation
-should be made of these books, for though the copies from which Dr.
-Brinton quotes may not be very old, these copies hand down to us
-records which must be of very great age. Dr. Förstemann himself quotes
-from them with approval, and it is certain that whatever may be their
-historical value, the evidence which they give incidentally cannot fail
-to be of great value. This evidence will, I think, prove—</p>
-
-<p>First, that the period of 20 times 360 days was called a katun and not
-an ahau.</p>
-
-<p>Second, that each of the constituent parts of a katun was called a tun.</p>
-
-<p>Third, that no such period of time as an ahaukatun is mentioned in the
-Books of Chilan Balam.</p>
-
-<p>The first assertion may seem difficult to prove when in far the larger
-number of cases where a separate katun is mentioned in the Books of
-Chilan Balam the word “ahau” seems to be substituted for “katun.”
-This is true in all five of the Books of Chilan Balam published by
-Brinton. But the reason of this is very evident, for it will be seen by
-a careful perusal that the word “ahaus” is never used when katuns in
-general are spoken of, and that whenever the word “ahau” is apparently
-given as a synonym of “katun,” it is<span class="pagenum" id="Page_4">[Pg 4]</span> merely the name of a particular
-katun and it always has a number attached to it and this number is the
-number of the day ahau with which a given katun ended. Further, this
-number is never an ordinal number, as translated by Brinton, but a
-cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
-in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
-the quotations from Brinton this substitution is made.</p>
-
-<p>It may be here stated that the inscriptions all show that where an
-even uinal is given (and therefore where an even tun, katun, or cycle
-is given) the day is Ahau. If then it was desirable to distinguish the
-katuns from each other, two methods could be used: either count them
-numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
-which the preceding katun had ended. The former method is found in the
-inscriptions and the Dresden Codex, the latter in the Books of Chilan
-Balam. The second method would not be possible if each katun ended
-with the same numbered ahau. But 7200 is not divisible by 13 without a
-remainder, but equals 13 × 553 + 11. If then a particular katun ended
-with 13 Ahau, the next would end with Ahau, but the number attached
-to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
-would end with 9, the next with 7, and so on. The katuns then would be
-known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
-Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.</p>
-
-<p>Taking up, therefore, <abbr title="number">No.</abbr> I. of the Books of Chilan Balam, published by
-Brinton—that of Mani—we find in the paragraph numbered 1 by Brinton
-“This is the arrangement of the katuns” not “of the ahaus,” and in
-paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
-This is followed by the statement “When they set out for this country,
-it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
-2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
-etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
-and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
-are<span class="pagenum" id="Page_5">[Pg 5]</span> called fourscore years is equally clear. In paragraph 4 we have “4
-Ahau, 2 Ahau, 13 Ahau—threescore years they ruled Ziyan caan, etc.”
-Here three katuns are called threescore years.</p>
-
-<p>This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
-were each equal to a score of years of 365 days each. When, however,
-we try to account for the numbering of the katuns on this basis, we
-find that the numbers of the ahaus ending each katun would come in the
-following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
-while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
-10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a>
-which occurs in paragraph 3, is taken literally, there would seem to be
-no explanation of this difficulty; but if we consider that these books
-used these words as we often use them now as meaning approximately
-“years,” and if we substitute the third term of the numeral series
-as found in the codices for the word “years”—in other words, if we
-substitute 360 for 365—we find then that the katuns or scores of 360
-days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
-10, etc., as has been said and as given in the Books of Chilan Balam.
-This has been shown by Seler, Goodman, and others.</p>
-
-<div class="footnote">
-
-<p><a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a> It is very probable that “años” is merely a gloss—and an
-erroneous one at that.</p>
-
-</div>
-
-<p>It will then be a good working theory that the score of 360 days is
-called a katun, and that each katun is distinguished by the name of
-an ahau with its proper number, with which a katun ended. That the
-ahau and its number are merely the name of the katun and not the katun
-itself is shown in <abbr title="number">No.</abbr> 5 of Brinton’s Books of Chilan Balam,—the
-Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
-the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
-paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
-was a synonym for “katun” would be as foolish as to say of a family
-containing John Smith, Mary Smith, and James Smith, that John and Mary
-and James were all synonyms of Smith, when they were merely names to
-distinguish one Smith from another.</p>
-
-<p><span class="pagenum" id="Page_6">[Pg 6]</span></p>
-
-<p>This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
-“Maya Chronicles”), where</p>
-
-<p class="poetry">
-<span style="margin-left: 1em;">Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”</span><br />
-<span style="margin-left: 2em;">”&#160;  9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”</span><br />
-<span style="margin-left: 2em;">”&#160; 10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”</span><br />
-<span style="margin-left: 2em;">”&#160; 12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”</span><br />
-<span style="margin-left: 2em;">”&#160; 15 says “u katunil ho ahau,” “In the katun 5 Ahau.”</span><br />
-</p>
-
-<p>Also in the Book of Tizimin (pp. 139 et seq. of Brinton):</p>
-
-<p class="poetry">
-<span style="margin-left: 1em;">Par. 6, “Uaxac ahau—lay u katunil,” “8 Ahau—in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  14, “Bolon ahau—lai—u katunil,” “9 Ahau—in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  15, “Vuc ahau—u katunil,” “7 Ahau—in this katun.”</span><br />
-</p>
-
-<p>Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):</p>
-
-<p class="poetry">
-<span style="margin-left: 1em;">Par. 2, “Uaxac ahau—layli u katunil,” “8 Ahau—in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  8, “Bolon ahau—u katunil,” “9 Ahau—in this katun.”</span><br />
-</p>
-
-<p>Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):</p>
-
-<p class="poetry">
-<span style="margin-left: 1em;">Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”</span><br />
-<span style="margin-left: 6em;">“laix u katunil,” “in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  5, “Hun ahau—lay u katunil,” “1 Ahau—in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  8, “Buluc ahau—laix u katunil,” “11 Ahau—in this katun.”</span><br />
-<span style="margin-left: 5em;">“Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”</span><br />
-<span style="margin-left: 2em;">”&#160;  9, “Bolon ahau—lay katun,” “9 Ahau—in this katun.”</span><br />
-<span style="margin-left: 5em;">“Uac Ahau—lay u katunil,” “6 Ahau—in this katun.”</span><br />
-</p>
-
-<p>I can find no excuse for considering “ahau” as a synonym for “katun”
-in these Books of Chilan Balam. And <i lang="la" xml:lang="la">a priori</i> it is difficult to
-conceive of a numeral system being made up by a nation as cultivated as
-the Mayas, by which the name of a day should be taken to mean a period
-of time, with all the chances of error which might arise from such use.
-Moreover, if this were the case, it would be natural to suppose that in
-the inscriptions and codices the day sign ahau might be found meaning
-7200 days, and yet I am<span class="pagenum" id="Page_7">[Pg 7]</span> unaware that a single instance of this exists
-on the monuments or in the codices. There are one or two cases in the
-inscriptions where this has been suggested as being possible, but it is
-very far from being proved or from even having strong evidence in favor
-of such an explanation.</p>
-
-<p>Dr. Förstemann says that at times the name “katun” was given to the
-period of 18,980 days; but the only authority for this use is, as
-far as I know, Pio Perez, who says that some applied the name to a
-“lustre of 4 years,” while others thought that “13 years completed the
-katun.”<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a> Again Pio Perez speaks of “the cycle of 52 years called by
-the Indians katun.” In none of these cases is any authority given for
-this use.<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a></p>
-
-<div class="footnote">
-
-<p><a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a> Stephens, “Travels in Yucatan,” Appendix, <abbr title="page">p.</abbr> 439.</p>
-
-</div>
-
-<div class="footnote">
-
-<p><a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a> Ibid., <abbr title="page">p.</abbr> 440.</p>
-
-</div>
-
-<p>It is probably safe to say that any use of the word “ahau” as meaning a
-katun, or any use of the word “katun” as meaning anything but 20 times
-360 days, or any use of the day symbol ahau as meaning a period of
-time, does not occur in any evidence which could be called contemporary
-or even approximately so. Don Pio Perez is, I fear, the only author
-who can be cited for the other side, and his opinion, though worthy of
-being listened to, is not to be relied upon without the support of, or
-against the evidence of, early authorities.</p>
-
-<p>The second question as to the name to be given to the period of 360
-days must be decided by the same authority.</p>
-
-<p>We have found that a katun is probably a score of periods of 360 days
-each, and it would be natural to suppose that the constituent parts of
-the katun, as mentioned in the Books of Chilan Balam, would be these
-periods of 360 days, but of this there is no absolute proof in the
-Books of Chilan Balam. The proof of this, however, is so strong in the
-Dresden Codex, where the series runs, 20 of the first order equals 1 of
-the second order, 18 of the second order equals 1 of the third order,
-and 20 of the third order equals 1 of the fourth, that no time need be
-wasted upon this part<span class="pagenum" id="Page_8">[Pg 8]</span> of the question. We do know, however, that each
-of these constituent parts is called a tun and that they are numbered
-as high as 13.</p>
-
-<p>The following list gives, I think, all the cases where the word “tun”
-is used in the Books of Chilan Balam:</p>
-
-<p>Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
-translates “the first year of the thirteenth ahau.” I think the proper
-translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
-Katun 13 Ahau.</p>
-
-<p>Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
-it was the tenth year of the eighth ahau,” while it should be “in Tun
-10 of Katun 8 Ahau.”</p>
-
-<p>In the Book of Tizimin we find that in</p>
-
-<p>Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
-year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
-Katun 13 Ahau.”</p>
-
-<p>Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
-on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”</p>
-
-<p>Also in the second Book of Chumayel, we find in</p>
-
-<p>Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
-third year in the first ahau,” when it should be “in Tun 3 of Katun 1
-Ahau.”</p>
-
-<p>Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
-seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
-Katun 8 Ahau.”</p>
-
-<p>Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
-“in the first year of the eleventh ahau, it was also in this katun,”
-when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
-“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
-of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
-Ahau.”</p>
-
-<p>These two katuns are evidently the same—one date being in Tun 1 and
-the other in Tun 7 of the same katun—and yet Brinton<span class="pagenum" id="Page_9">[Pg 9]</span> translated the
-first as being in the 11th katun and the other as being in the 11th
-ahau katun.</p>
-
-<p>Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
-“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
-Katun 9 Ahau.”</p>
-
-<p>Although Brinton has almost always translated “tun” by “year,” it is
-very evident from the above that the Mayas called the native division
-of the katun “tun.”</p>
-
-<p>It may further be noted that the word “kin” is used for day in the way
-of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
-on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
-paragraph 7 of the first Book of Chumayel, the same statement is made.</p>
-
-<p>May it not then be fairly assumed that the Mayas called the day or the
-unit of their calendrical numeration “kin,” their 360-day period “tun,”
-and the period of 20 tuns “katun,” as Dr. Seler has suggested?</p>
-
-<p>The third question is as to the so-called period of “ahau katun.” I
-give below all the cases in which Brinton has used the word, and in all
-but one of them the Maya has “ahau u katunil”; and in one case Brinton
-has translated a sentence as “it was the eleventh ahau katun,” while
-exactly similar phrases (with the exception of the number) have been
-translated by him as “4 Ahau was the name of the katun.” In the phrase
-in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
-katun” appears, the whole context makes it evident that a katun and not
-an ahau katun, if there was such a period, is meant. The paragraph says
-“9 Ahau; no stone was taken at this time; in this katun came the Bishop
-Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
-Brinton makes it read in the first clause that while Bishop Toral came
-in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
-katun.”</p>
-
-<p>Dr. Tozzer, whose knowledge of the Maya languages, gained in long
-residence among the Maya Indians of Yucatan and Chiapas,<span class="pagenum" id="Page_10">[Pg 10]</span> enables him
-to speak with authority, writes me as follows: “The form u katunil
-of ahau ukatunil, for example,” in paragraph 3 of the second Book
-of Chumayel, <abbr title="page">p.</abbr> 167, “is probably possessive, and it would then be
-literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
-strengthen the point against joining the two together as Ahaukatun.”</p>
-
-<p>In the second Book of Chumayel, <abbr title="page">p.</abbr> 167, paragraph 3, “uucpiztun uaxac
-ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
-year of the 8th Ahau katun, in this katun, etc.” There is no authority
-for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
-Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
-Tun 7 of Ahau eight’s Katun.”</p>
-
-<p>Again, in paragraph 5, the translation of “Hun ahau—tu hunpiztun ychil
-hun ahau u katunile” is given, “The first ahau—in the first year of
-the first ahau katun.” It should be “1 Ahau—in Tun 1 of the Katun 1
-Ahau, &amp;c.”</p>
-
-<p>Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
-“in the seventh year of the eleventh ahau katun,” when it should be “in
-Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
-followed by “in this katun.”</p>
-
-<p>Again in paragraph 9 we read “Bolon Ahau—lay katun yax ulci obispo
-Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
-which Brinton translates “The ninth ahau—in this katun first came
-the bishop Brother Francisco Toral; he arrived in the sixth year of
-the ninth ahau katun.” It should be “9 Ahau—in this katun—in Tun 6
-of Katun 9 Ahau.” This is the only place in the Maya where the words
-“ahau katun” appear together. But the context makes it clear that “ahau
-katun” is not a period of time. The paragraph begins with “9 Ahau,” and
-speaks of it as a katun during which Bishop Toral arrived, and then
-proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
-which can mean nothing else than the “Katun 9 Ahau.”</p>
-
-<p>In the third Book of Chumayel, paragraphs 5 and 6, Brinton<span class="pagenum" id="Page_11">[Pg 11]</span> translates
-“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
-Ahau.”</p>
-
-<p>In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
-katun” instead of “Katun 8 Ahau” (note here that this is the same “8
-Ahau,” when Chichen Itza was deserted for Champoton).</p>
-
-<p>Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
-katun” instead of “Katun 13 Ahau.”</p>
-
-<p>Also “Buluc ahau u kaba u katunil” is here translated “it was the
-eleventh ahau katun,” while in paragraph 3 a similar sentence is
-translated “4 Ahau was the name of the katun.”</p>
-
-<p>Thus an ahau katun is not mentioned in the Books of Chilan Balam in
-spite of Brinton’s translation, and neither is it mentioned by Landa,
-in spite of Brasseur de Bourbourg’s insertions. In fact the only
-evidence of it is the assertion of Don Pio Perez. I do not mean to say
-that the period of 6 × 52 years = 312 years may not have had a name,
-nor that “ahau katun” may not be the name of some period, but so far we
-have no trustworthy contemporary evidence of either of these statements.</p>
-
-<hr class="chap x-ebookmaker-drop" />
-<div class="chapter transnote">
-
-<h2>Transcriber's Note</h2>
-
-<p>The cover image was created by the transcriber and is placed in the public domain.</p>
-</div>
-</div>
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+      Mayan Nomenclature, by Charles P. Bowditch—A Project Gutenberg eBook
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+</head>
+<body>
+<div>*** START OF THE PROJECT GUTENBERG EBOOK 67879 ***</div>
+
+
+
+
+<h1>  MAYAN NOMENCLATURE</h1>
+
+
+<p class="center p2"><span class="small">BY</span><br />
+  CHARLES P. BOWDITCH</p>
+
+
+<p class="center small p2">  <i>Privately Printed</i></p>
+
+
+<p class="center p4">  CAMBRIDGE<br />
+  THE UNIVERSITY PRESS<br />
+  1906
+</p>
+<hr class="chap x-ebookmaker-drop" />
+<div class="chapter">
+
+<p>It has long been well known that the Mexican numeration is vigesimal,
+and, as far as I know, there is no proof that it was ever used in the
+calculation of long reaches of time. The Cakchiquel numeration is also
+vigesimal, and Brinton states (Maya Chronicles, <abbr title="page">p.</abbr> 44) that the Maya
+numeration is also vigesimal, giving</p>
+
+<table class="autotable">
+<tr><td>20 units</td><td>=</td><td>one kal</td><td>=</td><td>20</td></tr>
+<tr><td>20 kal</td><td>=</td><td>one bak</td><td>=</td><td>400</td></tr>
+<tr><td>20 bak</td><td>=</td><td>one pic</td><td>=</td><td>8000</td></tr>
+<tr><td>20 pic</td><td>=</td><td>one calab</td><td>=</td><td>160000, etc.</td></tr>
+</table>
+
+<p>But this Maya system is never used in connection with days. Wherever a
+long number of days is referred to, we find invariably the following
+system in use:</p>
+
+<table class="autotable">
+<tr><td>20 units</td><td>=</td><td>one of the second term</td></tr>
+<tr><td>18 of the second term</td><td>=</td><td>one of the third term</td></tr>
+<tr><td>20 of the third term</td><td>=</td><td>one of the fourth term</td></tr>
+<tr><td>20 of the fourth term</td><td>=</td><td>one of the fifth term.</td></tr>
+</table>
+
+<p>And this system is, as far as we know, used for nothing else but for
+reckoning days. The only difference between the first system and the
+second is that in the first system twenty of the second term equal one
+of the third, while in the second system eighteen of the second equal
+one of the third. This difference is, of course, essential, and it
+seems most probable that the change was introduced in order to bring
+the third term as near the length of the year as possible, and to
+conform the day numeration to the number of days and months in the year.</p>
+
+<p>Professor Cyrus Thomas is unwilling to see in this anything more than
+the counters by which to count the days, and denies to it the name of
+a calendar; but as the system of day numeration is<span class="pagenum" id="Page_2">[Pg 2]</span> different from
+the usual system, and is used only for counting days, and as this
+system counts forward in almost every case in the inscriptions, and in
+a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
+8 Cumhu, it seems impossible to see any difference between it and a
+calendar system.</p>
+
+<p>It was certainly to be hoped that the designations which Dr. Seler
+gave to these Maya periods of time in his “Die Monumente von Copan,
+etc.,”<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a> would have been accepted by Americanists, especially since
+very good reasons were given by Seler for their adoption. But this
+view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
+latter in his “Maya Calendar, Part II.,” published in the “Report of
+the Bureau of American Ethnology,” still calls the period of 20 days
+a chuen and that of 360 days an ahau, while the former in his article
+on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
+1904 issue of the “Zeitschrift für Ethnologie,” makes the following
+statement: “The katun has also been supposed to be 24 × 365 = 8760 days
+long (and I held this view for a long time), indeed the long period
+of 52 × 365 = 18,980 days is also occasionally designated with the
+word, while the sixth multiple of this member or 113,800 is called
+an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
+periods of 1, 20, and 7200 days respectively.</p>
+
+<div class="footnote">
+
+<p><a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a> See Seler, “<span lang="de" xml:lang="de">Gesammelte Abhandlungen zur Amerikanischen
+Sprach- und Alterthumskunde,</span>” <abbr title="volume">Vol.</abbr> I. <abbr title="page">p.</abbr> 722.</p>
+
+</div>
+
+<p>Such statements from such learned scholars must attract attention,
+especially as it is not the first time that they have made similar
+statements. If they give a correct statement of facts, it shows that
+the system of the Maya numeration or calendar was in a woful condition,
+as far as its nomenclature was concerned. It will be well, therefore,
+to take up this question of nomenclature anew. In all matters of this
+kind it is wise, while giving due value to the views of later writers,
+to place the most dependence for the solution of such questions upon
+contemporary or nearly contemporary evidence.</p>
+
+<p><span class="pagenum" id="Page_3">[Pg 3]</span></p>
+
+<p>And where is such evidence to be found? Though there are several
+Spanish writers who lived in the sixteenth century who have written
+on the Nahuas, Bishop Landa is the earliest Spanish authority who has
+dealt with Maya customs and history. And the only Maya authorities of
+an early date that the student has access to are the papers contained
+in Brinton’s Maya Chronicles, the principal of which are the Books
+of Chilan Balam, which Dr. Brinton declares “to constitute about all
+that remains to us ... of the ancient history of the peninsula” as
+far as he knows. Yet, in making objection to certain views of Dr.
+Seler, Dr. Förstemann says, “It is based on certain statements in the
+Books of Chilan Balam, a very dubious source according to Seler’s own
+assertion.” I am at a loss to know why such sweeping condemnation
+should be made of these books, for though the copies from which Dr.
+Brinton quotes may not be very old, these copies hand down to us
+records which must be of very great age. Dr. Förstemann himself quotes
+from them with approval, and it is certain that whatever may be their
+historical value, the evidence which they give incidentally cannot fail
+to be of great value. This evidence will, I think, prove—</p>
+
+<p>First, that the period of 20 times 360 days was called a katun and not
+an ahau.</p>
+
+<p>Second, that each of the constituent parts of a katun was called a tun.</p>
+
+<p>Third, that no such period of time as an ahaukatun is mentioned in the
+Books of Chilan Balam.</p>
+
+<p>The first assertion may seem difficult to prove when in far the larger
+number of cases where a separate katun is mentioned in the Books of
+Chilan Balam the word “ahau” seems to be substituted for “katun.”
+This is true in all five of the Books of Chilan Balam published by
+Brinton. But the reason of this is very evident, for it will be seen by
+a careful perusal that the word “ahaus” is never used when katuns in
+general are spoken of, and that whenever the word “ahau” is apparently
+given as a synonym of “katun,” it is<span class="pagenum" id="Page_4">[Pg 4]</span> merely the name of a particular
+katun and it always has a number attached to it and this number is the
+number of the day ahau with which a given katun ended. Further, this
+number is never an ordinal number, as translated by Brinton, but a
+cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
+in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
+the quotations from Brinton this substitution is made.</p>
+
+<p>It may be here stated that the inscriptions all show that where an
+even uinal is given (and therefore where an even tun, katun, or cycle
+is given) the day is Ahau. If then it was desirable to distinguish the
+katuns from each other, two methods could be used: either count them
+numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
+which the preceding katun had ended. The former method is found in the
+inscriptions and the Dresden Codex, the latter in the Books of Chilan
+Balam. The second method would not be possible if each katun ended
+with the same numbered ahau. But 7200 is not divisible by 13 without a
+remainder, but equals 13 × 553 + 11. If then a particular katun ended
+with 13 Ahau, the next would end with Ahau, but the number attached
+to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
+would end with 9, the next with 7, and so on. The katuns then would be
+known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
+Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.</p>
+
+<p>Taking up, therefore, <abbr title="number">No.</abbr> I. of the Books of Chilan Balam, published by
+Brinton—that of Mani—we find in the paragraph numbered 1 by Brinton
+“This is the arrangement of the katuns” not “of the ahaus,” and in
+paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
+This is followed by the statement “When they set out for this country,
+it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
+2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
+etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
+and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
+are<span class="pagenum" id="Page_5">[Pg 5]</span> called fourscore years is equally clear. In paragraph 4 we have “4
+Ahau, 2 Ahau, 13 Ahau—threescore years they ruled Ziyan caan, etc.”
+Here three katuns are called threescore years.</p>
+
+<p>This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
+were each equal to a score of years of 365 days each. When, however,
+we try to account for the numbering of the katuns on this basis, we
+find that the numbers of the ahaus ending each katun would come in the
+following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
+while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
+10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a>
+which occurs in paragraph 3, is taken literally, there would seem to be
+no explanation of this difficulty; but if we consider that these books
+used these words as we often use them now as meaning approximately
+“years,” and if we substitute the third term of the numeral series
+as found in the codices for the word “years”—in other words, if we
+substitute 360 for 365—we find then that the katuns or scores of 360
+days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
+10, etc., as has been said and as given in the Books of Chilan Balam.
+This has been shown by Seler, Goodman, and others.</p>
+
+<div class="footnote">
+
+<p><a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a> It is very probable that “años” is merely a gloss—and an
+erroneous one at that.</p>
+
+</div>
+
+<p>It will then be a good working theory that the score of 360 days is
+called a katun, and that each katun is distinguished by the name of
+an ahau with its proper number, with which a katun ended. That the
+ahau and its number are merely the name of the katun and not the katun
+itself is shown in <abbr title="number">No.</abbr> 5 of Brinton’s Books of Chilan Balam,—the
+Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
+the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
+paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
+was a synonym for “katun” would be as foolish as to say of a family
+containing John Smith, Mary Smith, and James Smith, that John and Mary
+and James were all synonyms of Smith, when they were merely names to
+distinguish one Smith from another.</p>
+
+<p><span class="pagenum" id="Page_6">[Pg 6]</span></p>
+
+<p>This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
+“Maya Chronicles”), where</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160;  9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 15 says “u katunil ho ahau,” “In the katun 5 Ahau.”</span><br />
+</p>
+
+<p>Also in the Book of Tizimin (pp. 139 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 6, “Uaxac ahau—lay u katunil,” “8 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  14, “Bolon ahau—lai—u katunil,” “9 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  15, “Vuc ahau—u katunil,” “7 Ahau—in this katun.”</span><br />
+</p>
+
+<p>Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 2, “Uaxac ahau—layli u katunil,” “8 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  8, “Bolon ahau—u katunil,” “9 Ahau—in this katun.”</span><br />
+</p>
+
+<p>Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”</span><br />
+<span style="margin-left: 6em;">“laix u katunil,” “in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  5, “Hun ahau—lay u katunil,” “1 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  8, “Buluc ahau—laix u katunil,” “11 Ahau—in this katun.”</span><br />
+<span style="margin-left: 5em;">“Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  9, “Bolon ahau—lay katun,” “9 Ahau—in this katun.”</span><br />
+<span style="margin-left: 5em;">“Uac Ahau—lay u katunil,” “6 Ahau—in this katun.”</span><br />
+</p>
+
+<p>I can find no excuse for considering “ahau” as a synonym for “katun”
+in these Books of Chilan Balam. And <i lang="la" xml:lang="la">a priori</i> it is difficult to
+conceive of a numeral system being made up by a nation as cultivated as
+the Mayas, by which the name of a day should be taken to mean a period
+of time, with all the chances of error which might arise from such use.
+Moreover, if this were the case, it would be natural to suppose that in
+the inscriptions and codices the day sign ahau might be found meaning
+7200 days, and yet I am<span class="pagenum" id="Page_7">[Pg 7]</span> unaware that a single instance of this exists
+on the monuments or in the codices. There are one or two cases in the
+inscriptions where this has been suggested as being possible, but it is
+very far from being proved or from even having strong evidence in favor
+of such an explanation.</p>
+
+<p>Dr. Förstemann says that at times the name “katun” was given to the
+period of 18,980 days; but the only authority for this use is, as
+far as I know, Pio Perez, who says that some applied the name to a
+“lustre of 4 years,” while others thought that “13 years completed the
+katun.”<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a> Again Pio Perez speaks of “the cycle of 52 years called by
+the Indians katun.” In none of these cases is any authority given for
+this use.<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a></p>
+
+<div class="footnote">
+
+<p><a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a> Stephens, “Travels in Yucatan,” Appendix, <abbr title="page">p.</abbr> 439.</p>
+
+</div>
+
+<div class="footnote">
+
+<p><a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a> Ibid., <abbr title="page">p.</abbr> 440.</p>
+
+</div>
+
+<p>It is probably safe to say that any use of the word “ahau” as meaning a
+katun, or any use of the word “katun” as meaning anything but 20 times
+360 days, or any use of the day symbol ahau as meaning a period of
+time, does not occur in any evidence which could be called contemporary
+or even approximately so. Don Pio Perez is, I fear, the only author
+who can be cited for the other side, and his opinion, though worthy of
+being listened to, is not to be relied upon without the support of, or
+against the evidence of, early authorities.</p>
+
+<p>The second question as to the name to be given to the period of 360
+days must be decided by the same authority.</p>
+
+<p>We have found that a katun is probably a score of periods of 360 days
+each, and it would be natural to suppose that the constituent parts of
+the katun, as mentioned in the Books of Chilan Balam, would be these
+periods of 360 days, but of this there is no absolute proof in the
+Books of Chilan Balam. The proof of this, however, is so strong in the
+Dresden Codex, where the series runs, 20 of the first order equals 1 of
+the second order, 18 of the second order equals 1 of the third order,
+and 20 of the third order equals 1 of the fourth, that no time need be
+wasted upon this part<span class="pagenum" id="Page_8">[Pg 8]</span> of the question. We do know, however, that each
+of these constituent parts is called a tun and that they are numbered
+as high as 13.</p>
+
+<p>The following list gives, I think, all the cases where the word “tun”
+is used in the Books of Chilan Balam:</p>
+
+<p>Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
+translates “the first year of the thirteenth ahau.” I think the proper
+translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
+Katun 13 Ahau.</p>
+
+<p>Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
+it was the tenth year of the eighth ahau,” while it should be “in Tun
+10 of Katun 8 Ahau.”</p>
+
+<p>In the Book of Tizimin we find that in</p>
+
+<p>Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
+year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
+Katun 13 Ahau.”</p>
+
+<p>Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
+on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”</p>
+
+<p>Also in the second Book of Chumayel, we find in</p>
+
+<p>Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
+third year in the first ahau,” when it should be “in Tun 3 of Katun 1
+Ahau.”</p>
+
+<p>Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
+seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
+Katun 8 Ahau.”</p>
+
+<p>Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
+“in the first year of the eleventh ahau, it was also in this katun,”
+when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
+“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
+of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
+Ahau.”</p>
+
+<p>These two katuns are evidently the same—one date being in Tun 1 and
+the other in Tun 7 of the same katun—and yet Brinton<span class="pagenum" id="Page_9">[Pg 9]</span> translated the
+first as being in the 11th katun and the other as being in the 11th
+ahau katun.</p>
+
+<p>Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
+“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
+Katun 9 Ahau.”</p>
+
+<p>Although Brinton has almost always translated “tun” by “year,” it is
+very evident from the above that the Mayas called the native division
+of the katun “tun.”</p>
+
+<p>It may further be noted that the word “kin” is used for day in the way
+of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
+on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
+paragraph 7 of the first Book of Chumayel, the same statement is made.</p>
+
+<p>May it not then be fairly assumed that the Mayas called the day or the
+unit of their calendrical numeration “kin,” their 360-day period “tun,”
+and the period of 20 tuns “katun,” as Dr. Seler has suggested?</p>
+
+<p>The third question is as to the so-called period of “ahau katun.” I
+give below all the cases in which Brinton has used the word, and in all
+but one of them the Maya has “ahau u katunil”; and in one case Brinton
+has translated a sentence as “it was the eleventh ahau katun,” while
+exactly similar phrases (with the exception of the number) have been
+translated by him as “4 Ahau was the name of the katun.” In the phrase
+in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
+katun” appears, the whole context makes it evident that a katun and not
+an ahau katun, if there was such a period, is meant. The paragraph says
+“9 Ahau; no stone was taken at this time; in this katun came the Bishop
+Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
+Brinton makes it read in the first clause that while Bishop Toral came
+in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
+katun.”</p>
+
+<p>Dr. Tozzer, whose knowledge of the Maya languages, gained in long
+residence among the Maya Indians of Yucatan and Chiapas,<span class="pagenum" id="Page_10">[Pg 10]</span> enables him
+to speak with authority, writes me as follows: “The form u katunil
+of ahau ukatunil, for example,” in paragraph 3 of the second Book
+of Chumayel, <abbr title="page">p.</abbr> 167, “is probably possessive, and it would then be
+literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
+strengthen the point against joining the two together as Ahaukatun.”</p>
+
+<p>In the second Book of Chumayel, <abbr title="page">p.</abbr> 167, paragraph 3, “uucpiztun uaxac
+ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
+year of the 8th Ahau katun, in this katun, etc.” There is no authority
+for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
+Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
+Tun 7 of Ahau eight’s Katun.”</p>
+
+<p>Again, in paragraph 5, the translation of “Hun ahau—tu hunpiztun ychil
+hun ahau u katunile” is given, “The first ahau—in the first year of
+the first ahau katun.” It should be “1 Ahau—in Tun 1 of the Katun 1
+Ahau, &amp;c.”</p>
+
+<p>Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
+“in the seventh year of the eleventh ahau katun,” when it should be “in
+Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
+followed by “in this katun.”</p>
+
+<p>Again in paragraph 9 we read “Bolon Ahau—lay katun yax ulci obispo
+Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
+which Brinton translates “The ninth ahau—in this katun first came
+the bishop Brother Francisco Toral; he arrived in the sixth year of
+the ninth ahau katun.” It should be “9 Ahau—in this katun—in Tun 6
+of Katun 9 Ahau.” This is the only place in the Maya where the words
+“ahau katun” appear together. But the context makes it clear that “ahau
+katun” is not a period of time. The paragraph begins with “9 Ahau,” and
+speaks of it as a katun during which Bishop Toral arrived, and then
+proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
+which can mean nothing else than the “Katun 9 Ahau.”</p>
+
+<p>In the third Book of Chumayel, paragraphs 5 and 6, Brinton<span class="pagenum" id="Page_11">[Pg 11]</span> translates
+“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
+Ahau.”</p>
+
+<p>In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
+katun” instead of “Katun 8 Ahau” (note here that this is the same “8
+Ahau,” when Chichen Itza was deserted for Champoton).</p>
+
+<p>Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
+katun” instead of “Katun 13 Ahau.”</p>
+
+<p>Also “Buluc ahau u kaba u katunil” is here translated “it was the
+eleventh ahau katun,” while in paragraph 3 a similar sentence is
+translated “4 Ahau was the name of the katun.”</p>
+
+<p>Thus an ahau katun is not mentioned in the Books of Chilan Balam in
+spite of Brinton’s translation, and neither is it mentioned by Landa,
+in spite of Brasseur de Bourbourg’s insertions. In fact the only
+evidence of it is the assertion of Don Pio Perez. I do not mean to say
+that the period of 6 × 52 years = 312 years may not have had a name,
+nor that “ahau katun” may not be the name of some period, but so far we
+have no trustworthy contemporary evidence of either of these statements.</p>
+
+<hr class="chap x-ebookmaker-drop" />
+<div class="chapter transnote">
+
+<h2>Transcriber's Note</h2>
+
+<p>The cover image was created by the transcriber and is placed in the public domain.</p>
+</div>
+</div>
+<div>*** END OF THE PROJECT GUTENBERG EBOOK 67879 ***</div>
+</body>
+</html>
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+The Project Gutenberg eBook of Mayan Nomenclature, by Charles P.
+Bowditch
+
+This eBook is for the use of anyone anywhere in the United States and
+most other parts of the world 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. If you are not located in the United States, you
+will have to check the laws of the country where you are located before
+using this eBook.
+
+Title: Mayan Nomenclature
+
+Author: Charles P. Bowditch
+
+Release Date: April 19, 2022 [eBook #67879]
+
+Language: English
+
+Produced by: The Online Distributed Proofreading Team at
+             https://www.pgdp.net (This file was produced from images
+             generously made available by The Internet Archive)
+
+*** START OF THE PROJECT GUTENBERG EBOOK MAYAN NOMENCLATURE ***
+
+
+
+
+
+  MAYAN NOMENCLATURE
+
+
+  BY
+  CHARLES P. BOWDITCH
+
+
+  _Privately Printed_
+
+
+  CAMBRIDGE
+  THE UNIVERSITY PRESS
+  1906
+
+
+It has long been well known that the Mexican numeration is vigesimal,
+and, as far as I know, there is no proof that it was ever used in the
+calculation of long reaches of time. The Cakchiquel numeration is also
+vigesimal, and Brinton states (Maya Chronicles, p. 44) that the Maya
+numeration is also vigesimal, giving
+
+  20 units = one kal   = 20
+  20 kal   = one bak   = 400
+  20 bak   = one pic   = 8000
+  20 pic   = one calab = 160000, etc.
+
+But this Maya system is never used in connection with days. Wherever a
+long number of days is referred to, we find invariably the following
+system in use:
+
+  20 units              = one of the second term
+  18 of the second term = one of the third term
+  20 of the third term  = one of the fourth term
+  20 of the fourth term = one of the fifth term.
+
+And this system is, as far as we know, used for nothing else but for
+reckoning days. The only difference between the first system and the
+second is that in the first system twenty of the second term equal one
+of the third, while in the second system eighteen of the second equal
+one of the third. This difference is, of course, essential, and it
+seems most probable that the change was introduced in order to bring
+the third term as near the length of the year as possible, and to
+conform the day numeration to the number of days and months in the year.
+
+Professor Cyrus Thomas is unwilling to see in this anything more than
+the counters by which to count the days, and denies to it the name of
+a calendar; but as the system of day numeration is different from
+the usual system, and is used only for counting days, and as this
+system counts forward in almost every case in the inscriptions, and in
+a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
+8 Cumhu, it seems impossible to see any difference between it and a
+calendar system.
+
+It was certainly to be hoped that the designations which Dr. Seler
+gave to these Maya periods of time in his “Die Monumente von Copan,
+etc.,”[1] would have been accepted by Americanists, especially since
+very good reasons were given by Seler for their adoption. But this
+view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
+latter in his “Maya Calendar, Part II.,” published in the “Report of
+the Bureau of American Ethnology,” still calls the period of 20 days
+a chuen and that of 360 days an ahau, while the former in his article
+on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
+1904 issue of the “Zeitschrift für Ethnologie,” makes the following
+statement: “The katun has also been supposed to be 24 × 365 = 8760 days
+long (and I held this view for a long time), indeed the long period
+of 52 × 365 = 18,980 days is also occasionally designated with the
+word, while the sixth multiple of this member or 113,800 is called
+an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
+periods of 1, 20, and 7200 days respectively.
+
+[1] See Seler, “Gesammelte Abhandlungen zur Amerikanischen Sprach- und
+Alterthumskunde,” Vol. I. p. 722.
+
+Such statements from such learned scholars must attract attention,
+especially as it is not the first time that they have made similar
+statements. If they give a correct statement of facts, it shows that
+the system of the Maya numeration or calendar was in a woful condition,
+as far as its nomenclature was concerned. It will be well, therefore,
+to take up this question of nomenclature anew. In all matters of this
+kind it is wise, while giving due value to the views of later writers,
+to place the most dependence for the solution of such questions upon
+contemporary or nearly contemporary evidence.
+
+And where is such evidence to be found? Though there are several
+Spanish writers who lived in the sixteenth century who have written
+on the Nahuas, Bishop Landa is the earliest Spanish authority who has
+dealt with Maya customs and history. And the only Maya authorities of
+an early date that the student has access to are the papers contained
+in Brinton’s Maya Chronicles, the principal of which are the Books
+of Chilan Balam, which Dr. Brinton declares “to constitute about all
+that remains to us ... of the ancient history of the peninsula” as
+far as he knows. Yet, in making objection to certain views of Dr.
+Seler, Dr. Förstemann says, “It is based on certain statements in the
+Books of Chilan Balam, a very dubious source according to Seler’s own
+assertion.” I am at a loss to know why such sweeping condemnation
+should be made of these books, for though the copies from which Dr.
+Brinton quotes may not be very old, these copies hand down to us
+records which must be of very great age. Dr. Förstemann himself quotes
+from them with approval, and it is certain that whatever may be their
+historical value, the evidence which they give incidentally cannot fail
+to be of great value. This evidence will, I think, prove--
+
+First, that the period of 20 times 360 days was called a katun and not
+an ahau.
+
+Second, that each of the constituent parts of a katun was called a tun.
+
+Third, that no such period of time as an ahaukatun is mentioned in the
+Books of Chilan Balam.
+
+The first assertion may seem difficult to prove when in far the larger
+number of cases where a separate katun is mentioned in the Books of
+Chilan Balam the word “ahau” seems to be substituted for “katun.”
+This is true in all five of the Books of Chilan Balam published by
+Brinton. But the reason of this is very evident, for it will be seen by
+a careful perusal that the word “ahaus” is never used when katuns in
+general are spoken of, and that whenever the word “ahau” is apparently
+given as a synonym of “katun,” it is merely the name of a particular
+katun and it always has a number attached to it and this number is the
+number of the day ahau with which a given katun ended. Further, this
+number is never an ordinal number, as translated by Brinton, but a
+cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
+in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
+the quotations from Brinton this substitution is made.
+
+It may be here stated that the inscriptions all show that where an
+even uinal is given (and therefore where an even tun, katun, or cycle
+is given) the day is Ahau. If then it was desirable to distinguish the
+katuns from each other, two methods could be used: either count them
+numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
+which the preceding katun had ended. The former method is found in the
+inscriptions and the Dresden Codex, the latter in the Books of Chilan
+Balam. The second method would not be possible if each katun ended
+with the same numbered ahau. But 7200 is not divisible by 13 without a
+remainder, but equals 13 × 553 + 11. If then a particular katun ended
+with 13 Ahau, the next would end with Ahau, but the number attached
+to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
+would end with 9, the next with 7, and so on. The katuns then would be
+known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
+Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.
+
+Taking up, therefore, No. I. of the Books of Chilan Balam, published by
+Brinton--that of Mani--we find in the paragraph numbered 1 by Brinton
+“This is the arrangement of the katuns” not “of the ahaus,” and in
+paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
+This is followed by the statement “When they set out for this country,
+it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
+2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
+etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
+and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
+are called fourscore years is equally clear. In paragraph 4 we have “4
+Ahau, 2 Ahau, 13 Ahau--threescore years they ruled Ziyan caan, etc.”
+Here three katuns are called threescore years.
+
+This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
+were each equal to a score of years of 365 days each. When, however,
+we try to account for the numbering of the katuns on this basis, we
+find that the numbers of the ahaus ending each katun would come in the
+following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
+while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
+10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”[2]
+which occurs in paragraph 3, is taken literally, there would seem to be
+no explanation of this difficulty; but if we consider that these books
+used these words as we often use them now as meaning approximately
+“years,” and if we substitute the third term of the numeral series
+as found in the codices for the word “years”--in other words, if we
+substitute 360 for 365--we find then that the katuns or scores of 360
+days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
+10, etc., as has been said and as given in the Books of Chilan Balam.
+This has been shown by Seler, Goodman, and others.
+
+[2] It is very probable that “años” is merely a gloss--and an erroneous
+one at that.
+
+It will then be a good working theory that the score of 360 days is
+called a katun, and that each katun is distinguished by the name of
+an ahau with its proper number, with which a katun ended. That the
+ahau and its number are merely the name of the katun and not the katun
+itself is shown in No. 5 of Brinton’s Books of Chilan Balam,--the
+Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
+the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
+paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
+was a synonym for “katun” would be as foolish as to say of a family
+containing John Smith, Mary Smith, and James Smith, that John and Mary
+and James were all synonyms of Smith, when they were merely names to
+distinguish one Smith from another.
+
+This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
+“Maya Chronicles”), where
+
+  Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”
+   ”   9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”
+   ”  10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”
+   ”  12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”
+   ”  15 says “u katunil ho ahau,” “In the katun 5 Ahau.”
+
+Also in the Book of Tizimin (pp. 139 et seq. of Brinton):
+
+  Par. 6, “Uaxac ahau--lay u katunil,” “8 Ahau--in this katun.”
+   ”   14, “Bolon ahau--lai--u katunil,” “9 Ahau--in this katun.”
+   ”   15, “Vuc ahau--u katunil,” “7 Ahau--in this katun.”
+
+Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):
+
+  Par. 2, “Uaxac ahau--layli u katunil,” “8 Ahau--in this katun.”
+   ”   8, “Bolon ahau--u katunil,” “9 Ahau--in this katun.”
+
+Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):
+
+  Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”
+            “laix u katunil,” “in this katun.”
+   ”   5, “Hun ahau--lay u katunil,” “1 Ahau--in this katun.”
+   ”   8, “Buluc ahau--laix u katunil,” “11 Ahau--in this katun.”
+          “Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”
+   ”   9, “Bolon ahau--lay katun,” “9 Ahau--in this katun.”
+          “Uac Ahau--lay u katunil,” “6 Ahau--in this katun.”
+
+I can find no excuse for considering “ahau” as a synonym for “katun” in
+these Books of Chilan Balam. And _a priori_ it is difficult to conceive
+of a numeral system being made up by a nation as cultivated as the
+Mayas, by which the name of a day should be taken to mean a period of
+time, with all the chances of error which might arise from such use.
+Moreover, if this were the case, it would be natural to suppose that in
+the inscriptions and codices the day sign ahau might be found meaning
+7200 days, and yet I am unaware that a single instance of this exists
+on the monuments or in the codices. There are one or two cases in the
+inscriptions where this has been suggested as being possible, but it is
+very far from being proved or from even having strong evidence in favor
+of such an explanation.
+
+Dr. Förstemann says that at times the name “katun” was given to the
+period of 18,980 days; but the only authority for this use is, as
+far as I know, Pio Perez, who says that some applied the name to a
+“lustre of 4 years,” while others thought that “13 years completed the
+katun.”[3] Again Pio Perez speaks of “the cycle of 52 years called by
+the Indians katun.” In none of these cases is any authority given for
+this use.[4]
+
+[3] Stephens, “Travels in Yucatan,” Appendix, p. 439.
+
+[4] Ibid., p. 440.
+
+It is probably safe to say that any use of the word “ahau” as meaning a
+katun, or any use of the word “katun” as meaning anything but 20 times
+360 days, or any use of the day symbol ahau as meaning a period of
+time, does not occur in any evidence which could be called contemporary
+or even approximately so. Don Pio Perez is, I fear, the only author
+who can be cited for the other side, and his opinion, though worthy of
+being listened to, is not to be relied upon without the support of, or
+against the evidence of, early authorities.
+
+The second question as to the name to be given to the period of 360
+days must be decided by the same authority.
+
+We have found that a katun is probably a score of periods of 360 days
+each, and it would be natural to suppose that the constituent parts of
+the katun, as mentioned in the Books of Chilan Balam, would be these
+periods of 360 days, but of this there is no absolute proof in the
+Books of Chilan Balam. The proof of this, however, is so strong in the
+Dresden Codex, where the series runs, 20 of the first order equals 1 of
+the second order, 18 of the second order equals 1 of the third order,
+and 20 of the third order equals 1 of the fourth, that no time need be
+wasted upon this part of the question. We do know, however, that each
+of these constituent parts is called a tun and that they are numbered
+as high as 13.
+
+The following list gives, I think, all the cases where the word “tun”
+is used in the Books of Chilan Balam:
+
+Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
+translates “the first year of the thirteenth ahau.” I think the proper
+translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
+Katun 13 Ahau.
+
+Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
+it was the tenth year of the eighth ahau,” while it should be “in Tun
+10 of Katun 8 Ahau.”
+
+In the Book of Tizimin we find that in
+
+Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
+year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
+Katun 13 Ahau.”
+
+Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
+on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”
+
+Also in the second Book of Chumayel, we find in
+
+Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
+third year in the first ahau,” when it should be “in Tun 3 of Katun 1
+Ahau.”
+
+Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
+seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
+Katun 8 Ahau.”
+
+Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
+“in the first year of the eleventh ahau, it was also in this katun,”
+when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
+“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
+of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
+Ahau.”
+
+These two katuns are evidently the same--one date being in Tun 1 and
+the other in Tun 7 of the same katun--and yet Brinton translated the
+first as being in the 11th katun and the other as being in the 11th
+ahau katun.
+
+Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
+“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
+Katun 9 Ahau.”
+
+Although Brinton has almost always translated “tun” by “year,” it is
+very evident from the above that the Mayas called the native division
+of the katun “tun.”
+
+It may further be noted that the word “kin” is used for day in the way
+of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
+on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
+paragraph 7 of the first Book of Chumayel, the same statement is made.
+
+May it not then be fairly assumed that the Mayas called the day or the
+unit of their calendrical numeration “kin,” their 360-day period “tun,”
+and the period of 20 tuns “katun,” as Dr. Seler has suggested?
+
+The third question is as to the so-called period of “ahau katun.” I
+give below all the cases in which Brinton has used the word, and in all
+but one of them the Maya has “ahau u katunil”; and in one case Brinton
+has translated a sentence as “it was the eleventh ahau katun,” while
+exactly similar phrases (with the exception of the number) have been
+translated by him as “4 Ahau was the name of the katun.” In the phrase
+in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
+katun” appears, the whole context makes it evident that a katun and not
+an ahau katun, if there was such a period, is meant. The paragraph says
+“9 Ahau; no stone was taken at this time; in this katun came the Bishop
+Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
+Brinton makes it read in the first clause that while Bishop Toral came
+in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
+katun.”
+
+Dr. Tozzer, whose knowledge of the Maya languages, gained in long
+residence among the Maya Indians of Yucatan and Chiapas, enables him
+to speak with authority, writes me as follows: “The form u katunil
+of ahau ukatunil, for example,” in paragraph 3 of the second Book
+of Chumayel, p. 167, “is probably possessive, and it would then be
+literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
+strengthen the point against joining the two together as Ahaukatun.”
+
+In the second Book of Chumayel, p. 167, paragraph 3, “uucpiztun uaxac
+ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
+year of the 8th Ahau katun, in this katun, etc.” There is no authority
+for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
+Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
+Tun 7 of Ahau eight’s Katun.”
+
+Again, in paragraph 5, the translation of “Hun ahau--tu hunpiztun ychil
+hun ahau u katunile” is given, “The first ahau--in the first year of
+the first ahau katun.” It should be “1 Ahau--in Tun 1 of the Katun 1
+Ahau, &c.”
+
+Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
+“in the seventh year of the eleventh ahau katun,” when it should be “in
+Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
+followed by “in this katun.”
+
+Again in paragraph 9 we read “Bolon Ahau--lay katun yax ulci obispo
+Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
+which Brinton translates “The ninth ahau--in this katun first came
+the bishop Brother Francisco Toral; he arrived in the sixth year of
+the ninth ahau katun.” It should be “9 Ahau--in this katun--in Tun 6
+of Katun 9 Ahau.” This is the only place in the Maya where the words
+“ahau katun” appear together. But the context makes it clear that “ahau
+katun” is not a period of time. The paragraph begins with “9 Ahau,” and
+speaks of it as a katun during which Bishop Toral arrived, and then
+proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
+which can mean nothing else than the “Katun 9 Ahau.”
+
+In the third Book of Chumayel, paragraphs 5 and 6, Brinton translates
+“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
+Ahau.”
+
+In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
+katun” instead of “Katun 8 Ahau” (note here that this is the same “8
+Ahau,” when Chichen Itza was deserted for Champoton).
+
+Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
+katun” instead of “Katun 13 Ahau.”
+
+Also “Buluc ahau u kaba u katunil” is here translated “it was the
+eleventh ahau katun,” while in paragraph 3 a similar sentence is
+translated “4 Ahau was the name of the katun.”
+
+Thus an ahau katun is not mentioned in the Books of Chilan Balam in
+spite of Brinton’s translation, and neither is it mentioned by Landa,
+in spite of Brasseur de Bourbourg’s insertions. In fact the only
+evidence of it is the assertion of Don Pio Perez. I do not mean to say
+that the period of 6 × 52 years = 312 years may not have had a name,
+nor that “ahau katun” may not be the name of some period, but so far we
+have no trustworthy contemporary evidence of either of these statements.
+
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+      Mayan Nomenclature, by Charles P. Bowditch—A Project Gutenberg eBook
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+<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Mayan Nomenclature, by Charles P. Bowditch</p>
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+
+<p style='display:block; margin-top:1em; margin-bottom:1em; margin-left:2em; text-indent:-2em'>Title: Mayan Nomenclature</p>
+<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Charles P. Bowditch</p>
+<p style='display:block; text-indent:0; margin:1em 0'>Release Date: April 19, 2022 [eBook #67879]</p>
+<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p>
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+<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK MAYAN NOMENCLATURE ***</div>
+
+
+
+
+<h1>  MAYAN NOMENCLATURE</h1>
+
+
+<p class="center p2"><span class="small">BY</span><br />
+  CHARLES P. BOWDITCH</p>
+
+
+<p class="center small p2">  <i>Privately Printed</i></p>
+
+
+<p class="center p4">  CAMBRIDGE<br />
+  THE UNIVERSITY PRESS<br />
+  1906
+</p>
+<hr class="chap x-ebookmaker-drop" />
+<div class="chapter">
+
+<p>It has long been well known that the Mexican numeration is vigesimal,
+and, as far as I know, there is no proof that it was ever used in the
+calculation of long reaches of time. The Cakchiquel numeration is also
+vigesimal, and Brinton states (Maya Chronicles, <abbr title="page">p.</abbr> 44) that the Maya
+numeration is also vigesimal, giving</p>
+
+<table class="autotable">
+<tr><td>20 units</td><td>=</td><td>one kal</td><td>=</td><td>20</td></tr>
+<tr><td>20 kal</td><td>=</td><td>one bak</td><td>=</td><td>400</td></tr>
+<tr><td>20 bak</td><td>=</td><td>one pic</td><td>=</td><td>8000</td></tr>
+<tr><td>20 pic</td><td>=</td><td>one calab</td><td>=</td><td>160000, etc.</td></tr>
+</table>
+
+<p>But this Maya system is never used in connection with days. Wherever a
+long number of days is referred to, we find invariably the following
+system in use:</p>
+
+<table class="autotable">
+<tr><td>20 units</td><td>=</td><td>one of the second term</td></tr>
+<tr><td>18 of the second term</td><td>=</td><td>one of the third term</td></tr>
+<tr><td>20 of the third term</td><td>=</td><td>one of the fourth term</td></tr>
+<tr><td>20 of the fourth term</td><td>=</td><td>one of the fifth term.</td></tr>
+</table>
+
+<p>And this system is, as far as we know, used for nothing else but for
+reckoning days. The only difference between the first system and the
+second is that in the first system twenty of the second term equal one
+of the third, while in the second system eighteen of the second equal
+one of the third. This difference is, of course, essential, and it
+seems most probable that the change was introduced in order to bring
+the third term as near the length of the year as possible, and to
+conform the day numeration to the number of days and months in the year.</p>
+
+<p>Professor Cyrus Thomas is unwilling to see in this anything more than
+the counters by which to count the days, and denies to it the name of
+a calendar; but as the system of day numeration is<span class="pagenum" id="Page_2">[Pg 2]</span> different from
+the usual system, and is used only for counting days, and as this
+system counts forward in almost every case in the inscriptions, and in
+a majority of cases in the Dresden Codex, from a fixed date, 4 Ahau
+8 Cumhu, it seems impossible to see any difference between it and a
+calendar system.</p>
+
+<p>It was certainly to be hoped that the designations which Dr. Seler
+gave to these Maya periods of time in his “Die Monumente von Copan,
+etc.,”<a id="FNanchor_1" href="#Footnote_1" class="fnanchor">[1]</a> would have been accepted by Americanists, especially since
+very good reasons were given by Seler for their adoption. But this
+view does not meet the approval of Dr. Förstemann or Dr. Thomas. The
+latter in his “Maya Calendar, Part II.,” published in the “Report of
+the Bureau of American Ethnology,” still calls the period of 20 days
+a chuen and that of 360 days an ahau, while the former in his article
+on “Die Lage der Ahaus bei den Mayas,” published in Part I. of the
+1904 issue of the “Zeitschrift für Ethnologie,” makes the following
+statement: “The katun has also been supposed to be 24 × 365 = 8760 days
+long (and I held this view for a long time), indeed the long period
+of 52 × 365 = 18,980 days is also occasionally designated with the
+word, while the sixth multiple of this member or 113,800 is called
+an ahaukatun.” He uses the terms “day,” “uinal,” and “ahau” for the
+periods of 1, 20, and 7200 days respectively.</p>
+
+<div class="footnote">
+
+<p><a id="Footnote_1" href="#FNanchor_1" class="label">[1]</a> See Seler, “<span lang="de" xml:lang="de">Gesammelte Abhandlungen zur Amerikanischen
+Sprach- und Alterthumskunde,</span>” <abbr title="volume">Vol.</abbr> I. <abbr title="page">p.</abbr> 722.</p>
+
+</div>
+
+<p>Such statements from such learned scholars must attract attention,
+especially as it is not the first time that they have made similar
+statements. If they give a correct statement of facts, it shows that
+the system of the Maya numeration or calendar was in a woful condition,
+as far as its nomenclature was concerned. It will be well, therefore,
+to take up this question of nomenclature anew. In all matters of this
+kind it is wise, while giving due value to the views of later writers,
+to place the most dependence for the solution of such questions upon
+contemporary or nearly contemporary evidence.</p>
+
+<p><span class="pagenum" id="Page_3">[Pg 3]</span></p>
+
+<p>And where is such evidence to be found? Though there are several
+Spanish writers who lived in the sixteenth century who have written
+on the Nahuas, Bishop Landa is the earliest Spanish authority who has
+dealt with Maya customs and history. And the only Maya authorities of
+an early date that the student has access to are the papers contained
+in Brinton’s Maya Chronicles, the principal of which are the Books
+of Chilan Balam, which Dr. Brinton declares “to constitute about all
+that remains to us ... of the ancient history of the peninsula” as
+far as he knows. Yet, in making objection to certain views of Dr.
+Seler, Dr. Förstemann says, “It is based on certain statements in the
+Books of Chilan Balam, a very dubious source according to Seler’s own
+assertion.” I am at a loss to know why such sweeping condemnation
+should be made of these books, for though the copies from which Dr.
+Brinton quotes may not be very old, these copies hand down to us
+records which must be of very great age. Dr. Förstemann himself quotes
+from them with approval, and it is certain that whatever may be their
+historical value, the evidence which they give incidentally cannot fail
+to be of great value. This evidence will, I think, prove—</p>
+
+<p>First, that the period of 20 times 360 days was called a katun and not
+an ahau.</p>
+
+<p>Second, that each of the constituent parts of a katun was called a tun.</p>
+
+<p>Third, that no such period of time as an ahaukatun is mentioned in the
+Books of Chilan Balam.</p>
+
+<p>The first assertion may seem difficult to prove when in far the larger
+number of cases where a separate katun is mentioned in the Books of
+Chilan Balam the word “ahau” seems to be substituted for “katun.”
+This is true in all five of the Books of Chilan Balam published by
+Brinton. But the reason of this is very evident, for it will be seen by
+a careful perusal that the word “ahaus” is never used when katuns in
+general are spoken of, and that whenever the word “ahau” is apparently
+given as a synonym of “katun,” it is<span class="pagenum" id="Page_4">[Pg 4]</span> merely the name of a particular
+katun and it always has a number attached to it and this number is the
+number of the day ahau with which a given katun ended. Further, this
+number is never an ordinal number, as translated by Brinton, but a
+cardinal number. Therefore 1, 2, 3, 4, 5, 6, etc. should be substituted
+in Brinton’s translation for 1st, 2d, 3d, 4th, 5th, 6th, etc., and in
+the quotations from Brinton this substitution is made.</p>
+
+<p>It may be here stated that the inscriptions all show that where an
+even uinal is given (and therefore where an even tun, katun, or cycle
+is given) the day is Ahau. If then it was desirable to distinguish the
+katuns from each other, two methods could be used: either count them
+numerically, 1, 2, 3, 4, etc., or name them from the day Ahau with
+which the preceding katun had ended. The former method is found in the
+inscriptions and the Dresden Codex, the latter in the Books of Chilan
+Balam. The second method would not be possible if each katun ended
+with the same numbered ahau. But 7200 is not divisible by 13 without a
+remainder, but equals 13 × 553 + 11. If then a particular katun ended
+with 13 Ahau, the next would end with Ahau, but the number attached
+to Ahau would be 13 + 11, or, deducting thirteens, 11. The next katun
+would end with 9, the next with 7, and so on. The katuns then would be
+known as katuns, 13 Ahau, 11 Ahau, 9 Ahau, 7 Ahau, 5 Ahau, 3 Ahau, 1
+Ahau, 12 Ahau, 10 Ahau, 8 Ahau, 6 Ahau, 4 Ahau, 2 Ahau, 13 Ahau, etc.</p>
+
+<p>Taking up, therefore, <abbr title="number">No.</abbr> I. of the Books of Chilan Balam, published by
+Brinton—that of Mani—we find in the paragraph numbered 1 by Brinton
+“This is the arrangement of the katuns” not “of the ahaus,” and in
+paragraph numbered 2 “Four katuns had passed, etc.” not “four ahaus.”
+This is followed by the statement “When they set out for this country,
+it was Ahau 8,” not “the 8th Ahau.” And then follows “6 Ahau, 4 Ahau,
+2 Ahau, fourscore years and one year, for it was Tun 1, 13 Ahau when,
+etc.” That 6 Ahau, 4 Ahau, 2 Ahau refer to the katuns is very clear,
+and that 4 katuns with the names 8 Ahau, 6 Ahau, 4 Ahau, and 2 Ahau
+are<span class="pagenum" id="Page_5">[Pg 5]</span> called fourscore years is equally clear. In paragraph 4 we have “4
+Ahau, 2 Ahau, 13 Ahau—threescore years they ruled Ziyan caan, etc.”
+Here three katuns are called threescore years.</p>
+
+<p>This would seem to show that the katuns called 4 Ahau, 2 Ahau, 13 Ahau,
+were each equal to a score of years of 365 days each. When, however,
+we try to account for the numbering of the katuns on this basis, we
+find that the numbers of the ahaus ending each katun would come in the
+following order: 11. 5. 12. 6. 13. 7. 1. 8. 2. 9. 3. 10. 4. 11, etc.,
+while the real order is given in the books as 11. 9. 7. 5. 3. 1. 12.
+10. 8. 6. 4. 2. 13, etc. If the word “haab” or the Spanish “años,”<a id="FNanchor_2" href="#Footnote_2" class="fnanchor">[2]</a>
+which occurs in paragraph 3, is taken literally, there would seem to be
+no explanation of this difficulty; but if we consider that these books
+used these words as we often use them now as meaning approximately
+“years,” and if we substitute the third term of the numeral series
+as found in the codices for the word “years”—in other words, if we
+substitute 360 for 365—we find then that the katuns or scores of 360
+days will end with a day Ahau with the numbers 11. 9. 7. 5. 3. 1. 12.
+10, etc., as has been said and as given in the Books of Chilan Balam.
+This has been shown by Seler, Goodman, and others.</p>
+
+<div class="footnote">
+
+<p><a id="Footnote_2" href="#FNanchor_2" class="label">[2]</a> It is very probable that “años” is merely a gloss—and an
+erroneous one at that.</p>
+
+</div>
+
+<p>It will then be a good working theory that the score of 360 days is
+called a katun, and that each katun is distinguished by the name of
+an ahau with its proper number, with which a katun ended. That the
+ahau and its number are merely the name of the katun and not the katun
+itself is shown in <abbr title="number">No.</abbr> 5 of Brinton’s Books of Chilan Balam,—the
+Book of Chumayel. Here in paragraph 1 we have “4 Ahau was the name of
+the katun,” in paragraph 3 “4 Ahau was the name of the katun,” and in
+paragraph 7 “11 Ahau was the name of the katun.” To say that “ahau”
+was a synonym for “katun” would be as foolish as to say of a family
+containing John Smith, Mary Smith, and James Smith, that John and Mary
+and James were all synonyms of Smith, when they were merely names to
+distinguish one Smith from another.</p>
+
+<p><span class="pagenum" id="Page_6">[Pg 6]</span></p>
+
+<p>This is also shown in the Book of Mani (pp. 96 et seq. of Brinton’s
+“Maya Chronicles”), where</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 8 says “Lai u katunil cabil ahau,” “In the katun 2 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160;  9 says “Lai u katunil buluc ahau,” “In the katun 11 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 10 says “Laili u katunil uaxac ahau,” “In the katun 8 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 12 says “lay u katunil uac ahau,” “In the katun 6 Ahau.”</span><br />
+<span style="margin-left: 2em;">”&#160; 15 says “u katunil ho ahau,” “In the katun 5 Ahau.”</span><br />
+</p>
+
+<p>Also in the Book of Tizimin (pp. 139 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 6, “Uaxac ahau—lay u katunil,” “8 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  14, “Bolon ahau—lai—u katunil,” “9 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  15, “Vuc ahau—u katunil,” “7 Ahau—in this katun.”</span><br />
+</p>
+
+<p>Also in the first Book of Chumayel (pp. 154 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 2, “Uaxac ahau—layli u katunil,” “8 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  8, “Bolon ahau—u katunil,” “9 Ahau—in this katun.”</span><br />
+</p>
+
+<p>Also in the second Book of Chumayel (pp. 166 et seq. of Brinton):</p>
+
+<p class="poetry">
+<span style="margin-left: 1em;">Par. 3, “Uaxac ahau u katunil,” “8 Ahau in this katun.”</span><br />
+<span style="margin-left: 6em;">“laix u katunil,” “in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  5, “Hun ahau—lay u katunil,” “1 Ahau—in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  8, “Buluc ahau—laix u katunil,” “11 Ahau—in this katun.”</span><br />
+<span style="margin-left: 5em;">“Buluc ahau. Laix u katunil,” “11 Ahau in this katun.”</span><br />
+<span style="margin-left: 2em;">”&#160;  9, “Bolon ahau—lay katun,” “9 Ahau—in this katun.”</span><br />
+<span style="margin-left: 5em;">“Uac Ahau—lay u katunil,” “6 Ahau—in this katun.”</span><br />
+</p>
+
+<p>I can find no excuse for considering “ahau” as a synonym for “katun”
+in these Books of Chilan Balam. And <i lang="la" xml:lang="la">a priori</i> it is difficult to
+conceive of a numeral system being made up by a nation as cultivated as
+the Mayas, by which the name of a day should be taken to mean a period
+of time, with all the chances of error which might arise from such use.
+Moreover, if this were the case, it would be natural to suppose that in
+the inscriptions and codices the day sign ahau might be found meaning
+7200 days, and yet I am<span class="pagenum" id="Page_7">[Pg 7]</span> unaware that a single instance of this exists
+on the monuments or in the codices. There are one or two cases in the
+inscriptions where this has been suggested as being possible, but it is
+very far from being proved or from even having strong evidence in favor
+of such an explanation.</p>
+
+<p>Dr. Förstemann says that at times the name “katun” was given to the
+period of 18,980 days; but the only authority for this use is, as
+far as I know, Pio Perez, who says that some applied the name to a
+“lustre of 4 years,” while others thought that “13 years completed the
+katun.”<a id="FNanchor_3" href="#Footnote_3" class="fnanchor">[3]</a> Again Pio Perez speaks of “the cycle of 52 years called by
+the Indians katun.” In none of these cases is any authority given for
+this use.<a id="FNanchor_4" href="#Footnote_4" class="fnanchor">[4]</a></p>
+
+<div class="footnote">
+
+<p><a id="Footnote_3" href="#FNanchor_3" class="label">[3]</a> Stephens, “Travels in Yucatan,” Appendix, <abbr title="page">p.</abbr> 439.</p>
+
+</div>
+
+<div class="footnote">
+
+<p><a id="Footnote_4" href="#FNanchor_4" class="label">[4]</a> Ibid., <abbr title="page">p.</abbr> 440.</p>
+
+</div>
+
+<p>It is probably safe to say that any use of the word “ahau” as meaning a
+katun, or any use of the word “katun” as meaning anything but 20 times
+360 days, or any use of the day symbol ahau as meaning a period of
+time, does not occur in any evidence which could be called contemporary
+or even approximately so. Don Pio Perez is, I fear, the only author
+who can be cited for the other side, and his opinion, though worthy of
+being listened to, is not to be relied upon without the support of, or
+against the evidence of, early authorities.</p>
+
+<p>The second question as to the name to be given to the period of 360
+days must be decided by the same authority.</p>
+
+<p>We have found that a katun is probably a score of periods of 360 days
+each, and it would be natural to suppose that the constituent parts of
+the katun, as mentioned in the Books of Chilan Balam, would be these
+periods of 360 days, but of this there is no absolute proof in the
+Books of Chilan Balam. The proof of this, however, is so strong in the
+Dresden Codex, where the series runs, 20 of the first order equals 1 of
+the second order, 18 of the second order equals 1 of the third order,
+and 20 of the third order equals 1 of the fourth, that no time need be
+wasted upon this part<span class="pagenum" id="Page_8">[Pg 8]</span> of the question. We do know, however, that each
+of these constituent parts is called a tun and that they are numbered
+as high as 13.</p>
+
+<p>The following list gives, I think, all the cases where the word “tun”
+is used in the Books of Chilan Balam:</p>
+
+<p>Book of Mani, paragraph 2, “Hun piztun oxlahun ahau,” which Brinton
+translates “the first year of the thirteenth ahau.” I think the proper
+translation to be “Tun 1 of Ahau 13,” meaning that 1 tun had passed of
+Katun 13 Ahau.</p>
+
+<p>Paragraph 9, “tu lahun tun uaxac ahau” is translated by Brinton, “and
+it was the tenth year of the eighth ahau,” while it should be “in Tun
+10 of Katun 8 Ahau.”</p>
+
+<p>In the Book of Tizimin we find that in</p>
+
+<p>Paragraph 1, “tu humpiztun ahoxlahunahau” is translated “to the first
+year of the thirteenth ahau,” while it should be “to (or in) Tun 1 of
+Katun 13 Ahau.”</p>
+
+<p>Paragraph 11, “Cabil ahau; oxlahun tun” is translated “The second ahau;
+on the thirteenth, etc.” It should be “on Katun 2 Ahau Tun 13, etc.”</p>
+
+<p>Also in the second Book of Chumayel, we find in</p>
+
+<p>Paragraph 2, “tu yoxpiztun ychil hun ahau,” which is translated “on the
+third year in the first ahau,” when it should be “in Tun 3 of Katun 1
+Ahau.”</p>
+
+<p>Paragraph 3, “Tu uucpiztun uaxac ahau u katunil” is translated “in the
+seventh year of the eight Ahau katun,” when it should be “in Tun 7 of
+Katun 8 Ahau.”</p>
+
+<p>Paragraph 8, “tu hunpiztun Buluc ahau. Laix u katunil” is translated
+“in the first year of the eleventh ahau, it was also in this katun,”
+when it should be “on Tun 1 of Katun 11 Ahau. In this Katun, etc.” Also
+“tu uucpiztun Buluc ahau u katunil” is translated “in the seventh year
+of the eleventh ahau katun,” when it should be “in Tun 7 of Katun 11
+Ahau.”</p>
+
+<p>These two katuns are evidently the same—one date being in Tun 1 and
+the other in Tun 7 of the same katun—and yet Brinton<span class="pagenum" id="Page_9">[Pg 9]</span> translated the
+first as being in the 11th katun and the other as being in the 11th
+ahau katun.</p>
+
+<p>Paragraph 9, “tu uacpiztun ychil ahBolon ahau katun lae.” is translated
+“in the sixth year of the ninth ahau katun.” It should be “in Tun 6 of
+Katun 9 Ahau.”</p>
+
+<p>Although Brinton has almost always translated “tun” by “year,” it is
+very evident from the above that the Mayas called the native division
+of the katun “tun.”</p>
+
+<p>It may further be noted that the word “kin” is used for day in the way
+of numeration in the Book of Mani, paragraph 13, “9 Imix was the day
+on which Ahpula died” and in paragraph 13 of the Book of Tizimin and
+paragraph 7 of the first Book of Chumayel, the same statement is made.</p>
+
+<p>May it not then be fairly assumed that the Mayas called the day or the
+unit of their calendrical numeration “kin,” their 360-day period “tun,”
+and the period of 20 tuns “katun,” as Dr. Seler has suggested?</p>
+
+<p>The third question is as to the so-called period of “ahau katun.” I
+give below all the cases in which Brinton has used the word, and in all
+but one of them the Maya has “ahau u katunil”; and in one case Brinton
+has translated a sentence as “it was the eleventh ahau katun,” while
+exactly similar phrases (with the exception of the number) have been
+translated by him as “4 Ahau was the name of the katun.” In the phrase
+in paragraph 9 of the second Book of Chumayel, where “ah Bolon ahau
+katun” appears, the whole context makes it evident that a katun and not
+an ahau katun, if there was such a period, is meant. The paragraph says
+“9 Ahau; no stone was taken at this time; in this katun came the Bishop
+Brother Francisco Toral; he arrived in Tun 6 of Katun 9 Ahau”; and yet
+Brinton makes it read in the first clause that while Bishop Toral came
+in a katun called 9 Ahau, he “arrived in Tun 6” of the “ninth Ahau
+katun.”</p>
+
+<p>Dr. Tozzer, whose knowledge of the Maya languages, gained in long
+residence among the Maya Indians of Yucatan and Chiapas,<span class="pagenum" id="Page_10">[Pg 10]</span> enables him
+to speak with authority, writes me as follows: “The form u katunil
+of ahau ukatunil, for example,” in paragraph 3 of the second Book
+of Chumayel, <abbr title="page">p.</abbr> 167, “is probably possessive, and it would then be
+literally ‘the Ahau 8, its Katun’ (the Ahau’s Katun) which might
+strengthen the point against joining the two together as Ahaukatun.”</p>
+
+<p>In the second Book of Chumayel, <abbr title="page">p.</abbr> 167, paragraph 3, “uucpiztun uaxac
+ahau u katunil; laix u katunil, etc.” Brinton translates “in the 7th
+year of the 8th Ahau katun, in this katun, etc.” There is no authority
+for translating ahau u katunil “ahau katun.” It should be “In Tun 7 of
+Katun 8 Ahau, in this katun, etc.,” or, as suggested by Dr. Tozzer, “In
+Tun 7 of Ahau eight’s Katun.”</p>
+
+<p>Again, in paragraph 5, the translation of “Hun ahau—tu hunpiztun ychil
+hun ahau u katunile” is given, “The first ahau—in the first year of
+the first ahau katun.” It should be “1 Ahau—in Tun 1 of the Katun 1
+Ahau, &amp;c.”</p>
+
+<p>Again, in paragraph 8 “tu uucpiztun Buluc Ahau u katunil” is translated
+“in the seventh year of the eleventh ahau katun,” when it should be “in
+Tun 7 of Katun 11 Ahau.” Just above “Tun 1 of 11 Ahau” is given and
+followed by “in this katun.”</p>
+
+<p>Again in paragraph 9 we read “Bolon Ahau—lay katun yax ulci obispo
+Fray Fran’co to Ral huli tu uacpiztun ychil ahBolon ahau katun lae,”
+which Brinton translates “The ninth ahau—in this katun first came
+the bishop Brother Francisco Toral; he arrived in the sixth year of
+the ninth ahau katun.” It should be “9 Ahau—in this katun—in Tun 6
+of Katun 9 Ahau.” This is the only place in the Maya where the words
+“ahau katun” appear together. But the context makes it clear that “ahau
+katun” is not a period of time. The paragraph begins with “9 Ahau,” and
+speaks of it as a katun during which Bishop Toral arrived, and then
+proceeds to say that he arrived in Tun 6 of this “ahBolon ahau katun,”
+which can mean nothing else than the “Katun 9 Ahau.”</p>
+
+<p>In the third Book of Chumayel, paragraphs 5 and 6, Brinton<span class="pagenum" id="Page_11">[Pg 11]</span> translates
+“Can ahau u katunil” as “The fourth ahau katun” instead of “Katun 4
+Ahau.”</p>
+
+<p>In paragraph 7 “Uaxac ahau u katunil” is translated “The eighth ahau
+katun” instead of “Katun 8 Ahau” (note here that this is the same “8
+Ahau,” when Chichen Itza was deserted for Champoton).</p>
+
+<p>Also “Oxlahun ahau u katunil” is translated “In the thirteenth ahau
+katun” instead of “Katun 13 Ahau.”</p>
+
+<p>Also “Buluc ahau u kaba u katunil” is here translated “it was the
+eleventh ahau katun,” while in paragraph 3 a similar sentence is
+translated “4 Ahau was the name of the katun.”</p>
+
+<p>Thus an ahau katun is not mentioned in the Books of Chilan Balam in
+spite of Brinton’s translation, and neither is it mentioned by Landa,
+in spite of Brasseur de Bourbourg’s insertions. In fact the only
+evidence of it is the assertion of Don Pio Perez. I do not mean to say
+that the period of 6 × 52 years = 312 years may not have had a name,
+nor that “ahau katun” may not be the name of some period, but so far we
+have no trustworthy contemporary evidence of either of these statements.</p>
+
+<hr class="chap x-ebookmaker-drop" />
+<div class="chapter transnote">
+
+<h2>Transcriber's Note</h2>
+
+<p>The cover image was created by the transcriber and is placed in the public domain.</p>
+</div>
+</div>
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author	nfenwick <nfenwick@pglaf.org>	2025-01-22 00:05:33 -0800
committer	nfenwick <nfenwick@pglaf.org>	2025-01-22 00:05:33 -0800
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