I have shown in the paper on the calendar system that at the time of reckoning .. 1This expression will be used everywhere to refer to the above-mentioned writing, published in this volume. As this note has been fully explained and discussed in the preceding paper, I pass at once to an examination of the general system of numbers of the Maya tribes.
THOMAS] MAYAN NUMERALS 863 Before commenting on the list, the names in some other dialects of
The names for the nuinljers6, T and S in this list appear, as mentioned above, to be compound words, with the terminal liorc indicating a suffix, or the radical with a preflx; no generally accepted explanation of the terms has yet been given. 1(» is also composed of inniil. hand, and tloAitli, bust or torso of the man; in other words, the two hands.
THOMAS] NAHUATLAN NUMERALS 867
NAHUATLAN NUMERALS
NUMERALS OF CALIFORNIA TRIBES 871 The five followinof lists from Califoniiu dialects olitaiiied and fur-
THOMAS] OTHOMIAN AND ZOQUEAN NUMERALS 873 OTHOMIAX FAMILY
CHIAPANECAX FAMILY
THOMAS] ORIGIN OF NUMBER NAMES 875
Akkuma Perez nu beeksisu bifa durii jechichaa hoi ture. ni danda'ama. Maqaan ."> in .tokko tokko(>loqoda garee Shosiionean "hundaa" kan agarsiisu fakkaata, shakkii tokko malee quba harkaa hunda kan agarsiisudha, fakkeenyaaf Cheniehuevi, Capote Uta keessatti.
Sirrummaa yaada armaan olii maqaa 8f jedhu keessaa xiqqaa ta'a. Tarkaanfii itti aanu irratti—75—tartiiba akka 55tti jijjiiri, for, instead of say-. 76 ce-caayo-taa-bi-tobi=5froni SO-f1,orce-tai)a-qui2ahachaa-taa=4irraa. 96 co-caayo-qiiioa-l)i-tobi=5 kan lOO-fl, yookaan ce-tapa-quizahachaa-cayoa.
THOMAS] ZAPOTEC NUMERALS 887
Ti panagpapada ti still para iti '20
To make the formation of the names clearer, the list from 1 to 10 given so far is repeated here.
THOMAS] MAZATEC NUMERALS 889
The intermediate numbers in this system are always added (> before l)ase and not. as you saw. many others, on what follows, nor are they su))ti'acted from a higher base or nuiiiber. Some of ihfnuinlxTluuiitswliiciiap])ear to follow somewhat closely that the quinary-vigesimal system has been presented, the next method of counting to which attention is called is that used by the Maya. As . this system is that in which most interest centers because of it.'< .. in relation to the numbers found in the codices and inscriptions, we shall dwell more fully on it than we have on the others. l)beginning with the numbers used by the Maya proper (Yucatecs).. as our basis, the series given by Beltranin his ArtedelIdiomaMaya. . l) to place the interpretations or equivalents of the terms on the right.
Before alluding to the change which takes place in the next step, attention is paid to lahun^ nametor10. Dr. Brinton says it is apparently compounded of hih and hun, and gives as a possible sign, 'one (man) ends.' Calling 20 a result, for the sake of simplicity, the counting from 21 to 39 may be thus illustrated: hun-tu-Jcal, 1 in the result, or first result; .. ca-tu-kal,2 in result, etc.
THOMAS] HUASTECA AND QUICHE NUMERALS 895
Therefore, from this observation, it appears that this change in numbers only started with the last 20 sharks to complete the SOO. Although the term may indicate a number that is the same as 1200-399, it certainly does not indicate any complete process of that number.
THOMAS] CAKCHIQUEL NUMEKALS 899
dr. Brinton, in his Grammar of the Cakchiquel Language of Guatemala (page t)S), translated from a manuscript in the library of the American Philosophical Society, gives the following additional figures.
THOMAS] POKONCHI NUMERALS 901 The following list of Pokonchi numerals is from Stoll's Maya-
80, the corresponding term for which is kiincul.. or whether tiie term for 40, or literally 2X20, there must be either a difference in pronunciation not marked in the vocabulary, or an error in y)rintin, fr- The data at hand afford no means of determining LT designations of inserted ;v as in hunxkakal; it is evident that it plays the same role as/• liefore «, as in ro.rhd.
THOMAS] IXIL NUMEKALS 905
THOMAS] MIXE AND ZOQUE NUMERALS 907
THOMAS] OTHOMI NUMERALS 909 The Yaquis say for 5 scsarclicn; and counting from 5 to 5 [more] say nosarclirre 10,
Since this is unlikely to be the intended number, the error must be in the name. If we do this, we will get the required number, with positive evidence that this is the case.
THOMAS] OPATA AND TOTONACA NUMERALS 911
One or two of the dialects belong to that part of South America near the Isthmus of Panama, but are given because it appears that the tribes speaking them used the "native calendar." That.
MISCELLANEOUS LISTS 1)15
MISCELLANEOUS LISTS 917
DISCUSSION AND COMPARISONS
This, however, is merely in accordance with the recognized athnit}' of the first three idioms with flicNahuatl. It is somewhat singulai' that two otluM- idioms of the same family, this vocabulary of wdiichare given by MrPowers, follow the decimal instead of this vigi'simal system. It appears to be in use among the Chibchasor Muyscas, a group extending both north and south of the Isthmus.
It was used in some of the three countries on the Orinoco, in eastern Brazil and in Pai-aguay. These facts are sufficient to show that ethnic lines do not always determine the scope of the system. They are brought together in the order of the groups, the Nahuatlan, which is the most extensive and the first to arise.
COMPARISONS 929
COMPARISONS 931
Numbers 44 to 48, belonging to the extreme southern dialects, have been added merely for purposes of comparison. In the tribes from the border of Mexico northward, with the exception of those belonging to the Nahuatlán group, most of whom have been noticed, we find nothing in numbers, so far as the records show, and show any connection other than that in accordance with the linguistic classification proposed by Major. Powell. An obvious approach to names in some of the Shoshonean dialects can be observed in the Konkau, Nishinam, and Nakum dialects given earlier.
Before I close this chapter, attention must be directed to one point which, so far as I know, has not been discussed, but in connection with which. Take the following count of time actually found in one of the CcMitrals. days, until the day of 1Eb, the 5th day of the monthZac. Since 1 cycle equals 20 katuns, 1 katun equals 20 aliaus. As a certain day had to be arrived at, and the numbers were in every order of units, and the total had to be transferred to years of 365 days each, and the excess months and days to be found, there is no (>necessary to reduce^ this) (>even the primary means , that on days—and then find out by division or otherwise,.
THOMAS) METHOD OF COMPUTATION 933 That they had tinio tables In- which they could compute intervals of
THOMAS) CALCULATION METHOD 933Who had tinio tables In which they could calculate the intervals of. T may, however, have more to say on this subject in a subsequent paper, in which 1 propose to discuss the Quirigua inscriptions.
NUMBERS IN THE MEXICAN CODICES
The J-ears could be obtained in the same way by repeated subti'actions from overplus with ordinaiy.
NUMBEKS IN THE MEXICAN CODICES 935 The da.vs as represented in the codices when placed in regular succes-
THOMAS] NUMBERS IN THE MEXICAN CODICES 937 The symbols of the days are sliown
Like the series on the pages mentioned (the order is from left to right), two hundred and sixty days, or twenty and thirteen days, the Mexican passes through. Because this division into .5 and S, while 6 and 7 is the usual method, is not clear unless it was best adapted to the size of the original page, or by introducing the 5. The color undoubtedly had a sign. This nification is understood at least by the priests, but as far as we know there is no way to determine this to this day.
THOMAS] NUMBERS IN MEXICAN CODEXES 989 we see l)y the indicated symbols of the yeai for Tochtli, Acatl, Tec])atl,.
THOMAS] NUMBERS IN THE MEXICAN CODICES 989 we see the yeai's indicated l)y the symbols for Tochtli, Acatl, Tec])atl,
THOMAS] NUMBERS IN MEXICAN CODECS 989 we see yeai indicated l)y symbols for Tochtli, Acatl, Tec])atl, . replace dots or circles and day names for S3 symbols. The pages are given in order of numbering, the l)utares to be read in the opposite direction, beginning with the 22nd.
THOMAS] NUMBEKS IN THE MEXICAN CODICES 941 Plate 22
THOMAS] NUMBEKS IN THE MEXICAN CODICES 941Plate 22 . section of the lower line are five day symbols: for convenience I have placed the names in columns, the upper one corresponding to the symbol on the left of the plate. The arrangement of Plates 5 to 10 (inclusive) is the same, except that the tlays in the upper line follow each other in regular order without interval, and that the counters belong to the lower line A'ary. The counter in the lower half of plate 0.5 is 9, and the lowest day in the column to the right is Cipactli.
The upper series of plates 4 and 3 have five days for each section arranged in the same way as the column in the lower half. The counters in between express the intervals between the left day of the bottom line of one tile and the left day of the bottom line of the next tile, etc. With two exceptions (upper divisions of plates 20 and 21). there are six counters in each column; in exceptions there are 4 in a column.
NUMBERS IN THK MEXICAN CODICES 945
THOMAS] NUMBERS IN THE MEXICAN CODICES 947
TIIK MYSTIC AND CKKEMOMIAL TSK OF NUMBERS
The number 4 was therefore a number that would naturally become prominent, and would necessarily be connected with the recognition of the essential points. The "cult of the quarters" in the mystical and ceremonial I'ites was therefore a natural outgrowth of the recognition of these points. The cult of the United States and the recognition of the number of calls to it has been carried almost to an extreme among the Mexican and Central American tribes.
The cross also appears to be associated with the cult of the (juarters, especially as the four-pointed) spear St Andrew's cross on plate 7(> of the Borgian codex). of the Tutidxiu, that they were four. For example, there is scarcely a page of the Troano, Dresden, or Cortesian codices without one of four groups (usually columns) of five days, arranged in some regular order, related to the accompanying symbolic figures and numbers.
MY.STIU USE OF NUMBERS 951 One thing worthy of notice in this diag-rani (figure 41) is that one
Tradition draws the ancestors of the Mexicans from seven caves; they come as seven ti-ibes, the offspring of seven brothers. It is stated in the Kx explanation of the Codex Telleriano-Kemensisthiit born on the day !• Ehecatl would prosper as a merchant, while he who was born on the day Itzcuintli. would l)e a great magician. Why twenty days were adopted as a period and a division of the year has not yet received any entirely satisfactory explanation, though it is generally accepted that it was chosen because the arithmetical system of these tribes was vigesimal.
It seems likely, as suggested by Dr. Brinton that the twenty-day period is derived from tine \'igesimal. of the number system, but this does not explain the origin of the peculiarity of the strange time system, which does not seem to relate to any natural phenomenon except the earth's annual revolution. How-. This evidence had to]) be replaced by the fact that all inscriptions and codices are based on the counting of time in a month of twenty daj', and the numbering of days on 13, the latter also being a factor in other counts of inscriptions and codices. This Avill j^robabiy represent the introduction of a twenty-day period, but not the introduction of the 13th.
