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Ma EN a kw ‘ie elite y eset ee Petia ay ye) Stns s42 A Nite oe mut neat * Me nt 4 ee sty Petsisie sees os Rae ef ¥ ea * 2 eae ri = = es +s, ee > ae ae a NINETEENTH ANNUAL REPORT OF THE BUREAU OF AMERICAN ETHNOLOGY TO THE SECRETARY OF THE SMITHSONIAN INSPIPUTION ESO 28 BY eRe eke ONY 6 seu eae DIRECTOR GING) ARs ©) GE ACE S EAC E laa WASHING TON GOVERNMENT PRINTING OFFICE 1900 ACCOMPANYING PAPERS o (CONTINUED) mya ‘TUSAYAN MIGRATION TRADITIONS BY JESSE WALTER FEWKES 573 - — = , CONTENTS TUG OG CC iO eee esa ee SSeushSsceue sSecose cose sbecso ges Eeueae MhesHopiu puehlosia.sa- aasceece-eeee ee ees eee tessa senses sas asics Sitesvon Old! Wrallpifsae- .cscee sea se se ie eem oman seen nace ee ae Se Siecle IPE GLsTOL OpanishiCONtaCke = = aes esas see ee ee ein ee = ya Clans living or extinct in Walpi and Sichumovi -.--.-....--.--.------------ Gianairornieno KONA Desa meena se ee ae oe See eee aa ace sec ee ack Clans from Palatkwabi and the Little Colorado -.-.....-..------------- ie Clans from Muiobi and New Mexican pueblos .-......-.---------------- 584 Chronologic sequence of the advent of clans. -_...--.----------------------- 585 Glanstromekokonabieecesteees cee sac - eee ee oeee sees aa occa ei== 587 REV ayGlANS ee eee eee ee ee oan a: = cia eee ae ee Be ole ais naisineci eins 587 INP Gavelgen bite oad 5 aoa san oes cGeee sesso se eens asosueSueC eS acEroE 590 Clans from Palatkwabi and the Little Colorado pueblos. ...----..----------- 594 Teper rata Aus ces 6 ee neta Ben se aes Foe See aaa ass 595 Teal Dae), Saes Sas US eCE Op Ber Beene nics dace aa ao atenees cade aces 596 Clans from Muiobi and New Mexican pueblos _-.-...-..--..------------ --- 604 FTIONAUNC LAMB eNee ees anak ioe ied nes aac eee ee eer pees Seer ences SEER MEE 604 IG) Moja (A ing a- Oka nba RARE Meee Cues BeSoasdane coe auegeneaaedane 604 PTOTIATIIEG ATSB ee eer cers, oo siorc aie ere ai eee Gat Stecss asie 606 iReienbats, Greystoke Glenn ee Aaa seperaroceceasoceeecusenaansepspooodses 607 IPakabrelansiee see et see eras las on ee eee eee ai /-sii hse 608 IN savory Leak wan aiGlanis sects nese < ase t= Caco ee eae nee = =e ok Sa eee 610 Total membership of Walpi and Sichumovi clans......--.---.-------------- 614 PET am OF NTIS ear ee See oe oo nea i Se ee eee one a weee cies 614 (CORO 18 hic (ENE Ss jasper eosasancasea= ces. ce= cede eeceroe ase oeee 617 IPS etoerisetames) Glo WWM pee one eee eee se fe sec sedees See ec eco cececeneee= 622 iReheroussocietiesizrom) Tok Ona Di == a= see es et 624 Saake-Ambelope sOcletless-= sae stem eee ase ae ae = 624 Religious societies from Palatkwabi --..-..--.----.---.---------------- 626 IAAP Ibeniy ANSOCLELICS =. mis rate a eee me el ee r= 626 IPAtuh lbs atk SOCLEILES = oo ome aeeete ess aie =e Blea oe ie ee aia 627 TS [IEP RON) BCS Cini aeeeaens so aenscncSecsbcubde ee ae seodse pee oCOnce 630 Katcina cults from New Mexican pueblos.------...----.------------------- 630 Aulee haba ON PE ap bass nccedscccass cCosSaed apes saeeak egUepeBocene seas 63 Geen OUI, So Ue ERE ARES Soe he cos 5 ace ase ade sade eee epee ones 631 WHaecemncen ciel) gescaeesnoassscomeccoess es5= se asbocesaseecouseeeceas 63 Conclusion See e ee te eee a ee ee eee eee aeiee a meriseinesiermeiay= oa 633 TUSAYAN MIGRATION TRADITIONS By Jesse WALTER FEWKES INTRODUCTION The observant traveler in Arizona will often have his attention attracted by mounds of rock and earth, indicative of former habita- tions, which are widely distributed over this territory. These mounds, which are almost numberless, are the remains of villages formerly inhabited by sedentary populations, and are particularly abundant near springs or streams. Similar remains, varying in size from simple hillocks to clusters arranged in regular form, also occur in inaccessible canyons or on the tops of high mesas. The architectural characteristics of ancient Arizonian ruins are not all alike. The dwellings are sometimes found in the form of cayes hewn into a soft tufaceous rock, or as cliff houses built in caverns, or as pueblos constructed of adobe and situated in the plains. The great number of these ancient habitations now in ruins would indicate a large aboriginal population if they were simultaneously inhabited, but it is generally conceded that many of them were only temporarily occupied, and that at no one time in the history of Arizona were they all peopled by the ancients. Although there is evidence against the synchronous inhabitation of all these villages, there is reason to believe that the sedentary population was in the past evenly distributed over the whole pueblo region, but that in the six- teenth and seventeenth centuries causes were at work to concentrate it into certain limited areas. One of these areas of concentration was the present Moqui reservation, to which the people of the ancient vil- lages were forced for refuge from their foes. The Hopi villages were thus peopled by descendants of clans which once lived as far north as the territory of Utah, as far south as the Gila valley, and as far east as the upper Rio Grande. In these concentrated communities we may expect to find survivals of the culture of many of the ruined pueblos of Arizona, combined with that of colonies from the New Mexican villages of the Rio Grande and its tributaries. The problem oll 578 TUSAYAN MIGRATION TRADITIONS [ETH ANN. 19 before the student of the history of any one of the Hopi pueblos includes the origin and course of migration of the different groups of clans whose descendants now form the population of those villages. In preparing this paper the author has brought together such frag- ments of Hopi legendary history as could be gathered at Walpi. This account is not intended asa record of tribal genesis or creation myths, nor does it attempt a history from documentary sources of the deal- ings of the Spaniards or the Americans with the past or present inhab- itants of this pueblo. It lays no stress on the discovery of Walpi by Europeans or the several attempts at mission work, but considers Hopi stories of the advent of different clans, the direction whence they came and the sequence of their coming, where they formerly lived, and the customs which they brought to the pueblo where their descendants now live. In other words, it is an attempt to examine the composition of the present population of Walpi by clans, and to trace the trails of migration of those clans before they reached the village. It is published as an aid to the archeologist who may need traditions to guide him in the identification of the ruins of northern Arizona,’ and it is hoped that a discussion of the subject will bring into clear relief the composite origin of Hopi ritual, language, and secular customs. It is impossible to interpret the Hopi ritual without a clear idea of the present relationship between the existing clans and of their connec- tion with the religious societies. The growth of the Hopi ritual has gone on pari passu with the successive addition of new clans to the pueblo, and its evolution can not be comprehended without an under- standing of the sociologic development and the clan organization of the pueblo. This applies also to the Hopi language and to secular customs which, like the ritual, are composite, and have resulted from the union of families of somewhat different stages of culture, each speaking a characteristic language. What the idiom of each of these several component clans was before their consolidation we can best judge if we know the sites of their ancestral homes and the speech of the early kindred from whom they separated when they migrated to the Hopi mesas. So also with their other customs and their arts, all of which are composite and were introduced some from one direction, others from another. The legends which have served as the groundwork of this account of the history of Walpi were gathered mainly from the clans now living in the East mesa pueblos. Some of these legends have never been collected, although considerable work of great value which was done in this field by that enthusiastic student, the late A. M. Stephen, 1 The main types of pueblo ruins have been described, and what is now necessary is a study of the manners and customs of the people who once inhabited them. This work implies an intimate knowledge of the ethnology of the suryivors, and a determination of the survivors’ identity may be had from migration legends of clans now living in the pueblos. FEWKES] ACCURACY OF TRADITIONS 579 was published in Mindeleff’s account of the architecture of Tusayan.' This material has been critically examined, and certain significant variations have been found which are embodied in the present article. There remains much material on the migrations of Hopi clans yet to be gathered, and the identification by archeologic methods of many sites of ancient habitations is yet to be made. This work, however, can best be done under guidance of the Indians by an ethno-drcheolo- gist, who can bring as a preparation for his work an intimate knowl- edge of the present life of the Hopi villagers. While engaged in collecting the migration legends of different Hopi clans the author has consulted, when possible, the clan chiefs. Wiki, Wikyatiwa, and Kopeli have furnished the migration legends of the Snake clans, Anawita those of the Rain-cloud, and Hani the Tobacco legends. Piitce has given the author the story of the Horn and Flute and Pautiwa that of the Eagle clans. The legends of the neighboring pueblo of Hano, the history of which is intimately connected with that of Walpi, were obtained from Kalakwai and others. As was to be expected, since human memory is fallible, different men of equal honesty vary considerably in their accounts, and hence the collector of the unrecorded history of Walpi soon recognizes that it is best not to give too much weight to stories of clans to which the inform- ant does not belong. An honest traditionist immediately declares his ignorance of the history of a clan not his own, and in the presence of a man of that clan wiil refer to him when questioned. Some of the older men take a pride in the history of their respective clans, and claim to know more than others; but many know or care little of the history of their clans, and when interrogated refer to their clan chief. Yo this class belong most of the young men, especially those who have attended school, where little encouragement is given to pupils to gain knowledge of the history of their ancestors. THE HOPI PUEBLOS The present Hopi pueblos are seven in number, and are situated on three table-lands, called East mesa, Middle mesa, and Oraibi. The inhabitants of six of these villages speak the Hopi language and of one the Tanoan. The East mesa has two Hopi pueblos—Walpi and Sichu- movi—and a Tewa village called Hano. About 7 miles in an air line from the Kast mesa is the Middle mesa, upon which are situated three towns, called Mishongnovi, Shipaulovi, and Shunopovi. The largest Hopi pueblo, called Oraibi, is situated about 20 miles westward from Walpi. Walpi is regarded as the most ancient Tusayan pueblo, its settle- ment dating from before the middle of the sixteenth century. The 1Eighth Annual Report of the Bureau of Ethnology. 580 TUSAYAN MIGRATION TRADITIONS (ETH, ANN. 1y neighboring pueblo, Sichumovi, was settled by foreign colonists about the middle of the eighteenth century, while Hano was founded by Tewa clans at the beginning of the same century. Two of the Middle mesa pueblos are mentioned by name in docu- ments of the seventeenth century, and one, Shipauloyi, was probably founded not far from 1750. Oraibi is known to be an old pueblo, being also mentioned by name in early Spanish records; but it is more modern than Shunopovi, hay- ing been founded by a chief named Matcito from the latter town.* The Hopi language as spoken in Oraibi is somewhat different in pro- nunciation from that of the other Hopi pueblos, but this difference is not more than dialectic, so that the six Hopi pueblos may be said to speak the same tongue. The people of Hano, however, speak a Tanoan dialect which the Hopi do not understand. Sires oF Otp WaALpPr The first site of Walpi on the East mesa which has been positively identified was on the northern side of the terrace which surrounds this rocky height, below the present town. ‘The ground plan of this settle- ment is still clearly indicated by the remains of old walls, the size and arrangement of the rooms being still traceable without difficulty. This was probably the position of the pueblo in the sixteenth century, when its population was limited to the Snake, Horn, and Flute clans, and when the Spaniards first came into the country. It was also the site of the pueblo during the troubles with the inhabitants of the neighbor- ing pueblo Sikyatki, which culminated in the destruction of the latter town. The Walpians found this situation exposed to the attacks of their enemies, and consequently moved their pueblo one stage higher, to the top of the projecting spur at the western end of the mesa. On this site the Walpians lived through the mission epoch (1628-1680), and a chapel, the outlines of which may still be traced, was erected there. This second site of the pueblo is called Kisakobi, and the Spanish mission house Niicaki. As the walls of the first and second settle- ments almost adjoin, it may have been that portions of the two were inhabited synchronously. The amount of débris around these former settlements indicates that both were inhabited for a considerable period, and evidently the size of the combined villages was not less than that of the present pueblo of Walpi. In this débris are found fragments of the finest old Tusayan ware, which bears pictography characteristic of the ancient epoch. The inroads of the Ute from the north and the Apache from the south hastened the abandonment of the early sites, but probably the main cause of the final move to the top of East mesa was a fear of 1Matcito is said to have lived for some time in a cave near Oraibi, at a rock still pointed out. FEWKES] RELIGIOUS INFLUENCE OF SPANIARDS 581 the return of the Spaniards after the murder of the padres in the Pueblo revolt of 1680. The Hopi abandoned Kisakobi about the close of the seventeenth century and moved their habitation to the top of East mesa, where a few houses may already have existed. At that time they transported much of the building material from Kisakobi, using the beams of the mission for the roofs and floors of new kivas and houses, in which they may still be seen. The name Walpi was apparently not applied to the settlement before this last change of location, which may account for its absence from Espejo’s list of Hopi towns in 1583. The earliest documentary men- tion of Walpi was ‘**Gualpi,” in 1680, or about the time the pueblo was moyed to its present site. Parts of Kisakobi and modern Walpi may have been simultaneously inhabited for several years, but between 1680 and 1700 the rooms at Kisakobi’ were completely abandoned. EFFECTS OF SPANISH CONTACT The advent of the Spaniards, in the middle of the sixteenth century, does not seem to have made a lasting impression on the Hopi, for no account of the first coming of Europeans is preserved in their stories. Undoubtedly the Hopi regarded these earliest visits in much the same manner as they did the frequent forays of the hostile Ute, Navaho, and Apache, They were no doubt profoundly impressed by firearms, and e¢reatly astonished at the horses, but special stories of the incidents of that time have long ago been lost. There survive many accounts of the life of the Spanish priests of a later epoch, with references to the building of the missions, but none of the Hopi have a good word , to say of this period in their history. The influence of the zealous fathers in their attempts to convert the Hopi to Christianity seems to have been ephemeral. While the padres may have introduced some slight modifications into the native ritual, with more exalted ideas of God, as a whole the products of these changes, if there were any, can not now be disentangled from purely aboriginal beliefs and customs. | The new cult brought by the priests was at first welcomed by the Indians, and no objection was made to it, for toleration in religious things is characteristic of most primitive men. The Hopi objected to the propagandist spirit, and strongly resented the efforts of the padres to make them abandon their time-honored religious practices (as the making of dolls or idols and the performance of ceremonial dances), and to accept the administration of Christian baptism. The Hopi further declare that the early padres practically tried to enslave them or to compel them to work without compensation. They obliged the natives to bring water from distant springs, and to haul logs from the distant mountains for the construction of the mission buildings. Per- 1 Ki, pueblo, saka, ladder, obi, locative: ‘‘ Place of the Ladder-town.”’ 582 TUSAYAN MIGRATION TRADITIONS [ETH. ANN, 19 haps sheep, horses, iron implements, and cloth were given in return for this service, or possibly they were not adequately paid. The Hopi maintain that they were not; but whether justly or not, time has not eradicated the feeling of deep hatred with which the Spanish mission epoch is now regarded by these Indians. A few relics of the Spanish dominion still remain in Walpi. Some of the beams and flooring of the old mission are still to be seen in kivas and private houses,’ and one or two old doors and windows date back to pre-American occupancy. There are also a few iron hoes— survivals of this early time—and metallic bells, the antiquity of which is doubtful. No Spanish written records are preserved in Tusayan, and nothing of Spanish manufacture has thus far been detected on any of the altars at Walpi. The lasting benefit of the Spanish régime was the gift of sheep, horses, goats, burros, and various fruits and seeds.” CLANS LIVING OR EXTINCT IN WALPI AND SICHUMOVI Tn the following lists the component clans of Walpi and Sichumoyi are referred to their former homes: 1. Clans from Tokonabi (southern Utah): Teiia (Snake), Ala (Horn). 2. Clans from Palatkwabi (southern Arizona) and the Little Colo- rado: Patun (Squash)*, Lenya? (Flute), Patki (Cloud), Kiikiite (Lizard), Piba (Tobacco), Titwa (Sand), Tabo (Rabbit). 3. Clans from the Muiohi (Rio Grande valley), and New Mexican pueblos, (Zuni, Acoma, Jemez, etc.): Honau (Bear), Kokop (Firewood), Pakab (Reed), Asa (Tansy-mustard), Buli (Butterfly), Honani (Badger). Although the original clans which settled Sichumoyi belonged to group 38, and this is practically a New Mexican pueblo in the Hopi country, the descendants of the original settlers haye so intermarried with the Hopi that their linguistic characteristics are lost. 1. CLans FROM TOKONABI Teiia group Mia WID Wiles a2 scoeese Snake clan. Tohott witiwW =-=---..- Puma clan. ER Wwiwitiwa os... see Dove clan. NG CUR ih Wnens ote, see Cactus clan. Muni Av Wilsons oo Opuntia (cactus) clan. 1 Decorated beams from the mission may be seen in Pautiwa’s house. “The Hopi names of these, which are corrupted Spanish (kanela, sheep; kavayo, horse; melone, melon, ete.), show the sources of these inestimable gifts which haye profoundly modified the modern life of the Hopi. 8 Extinct in Walpi and Sichumoyi. on (oa) (Sw) FEWKES] CLANS OF WALPI AND SICHUMOVI 1. Cuans rrom Toxonani—Continued alla clans of the Ala-Lefiya group * --Horn clan. Deer clan. Antelope clan. Ala withwit ..-- Sowint winwt- - Teubio winwt - Teaizra witwii. --._- 2, CLANS FROM PALATKWABI AND THE LirrLE CoLorapo Paiuri growp Patun wiftwil ....._._- Squash clan. Atoko wittwit --....._. Crane clan. ele swihtwitteeree ees Pigeon-hawk clan. Mubic winiwtt 222-2... Sorrow-making clan. Lenya clans of the Ala-Lenya group? Cakwalenya wifwt-.--Blue- (Green-) flute clan. Macilefiya wifwit....-- Drab-flute clan. Panwti wiftwa......... Mountain-sheep clan. Lelenitu witwt -......- Flute clan. Patki group Batkinwitiwit 2-52.22: Rain-cloud clan. Kann waliwille= 2-220 5 _ = Maize clan. = Tanaka wittwtt ....-..- Rainbow clan. Talawipiki wifwt --_-- Lightning clan. Kwan winwtt- .......- Agave clan. Sivwapi witiwtt_....... Bigelovia graveolus clan. Pawikya winwtt...._../ Aquatic-animal clan Pakwa wifwtt_...-.._- Frog clan. -avatiya wiflwtl......- Tadpole clan. Tiiwa-Kikiite group Tiwa wifiwi..-......- Sand clan. Kuktite wiwit.......- Lizard clan. SHOUDL Sy bon 40 eee ee Flower or bush elan. Tabo-Piba group Tabo witwit .........- Rabbit clan. Sowi wifwt_.._.- -----Hare clan. Piba wiwt.-.........-Tobacco clan. 1The Ant clans (Anu, Tokoanu, Wukoanu, and Ciwanu) belong to this group, but the author isin doubt whether to assign them to the Ala or the Leitya division, the latter of which did: not come from Tokonabi. 584 TUSAYAN MIGRATION TRADITIONS [ETH. ANN, 19 3. CLANS FROM Mutropt anp New Mexican PUEBLOS Honau group Honau winwt. - Bear clan. Tokotei winwt .Wildeat clan. Teosro winwt- . Bluebird clan. Kokyan winwt -..--- -Spider clan. Asa or Teakwaina group (Abiquiu, via Zuni) Teakwaina wifiwt ----- Teakwaina (a katcina) clan. Hosboa wihwt -------- Road-runner or Pheasant clan. Pociwtl wittwil.---._-- Magpie clan. Rcisromwiliwitt= eee == Bunting clan. Katcina group (via Kicuba) Katcina witwit- ------- Kateina clan. Afiwuci wifwt.--...-- Crow clan. Gyazru witwt -----..- Parrot clan. Sikyatei winwt ------- Yellow-bird clan. Tawamana winwt ----- Bird clan. Salab winwt _...-.-- Stihub wiliwit--..----. Spruce clan. Jottonwood clan. Kokop group (Jemez, via Sikyatki) Kokop winwt-.------- Firewood clan. Teauiiewaniwill === .-2s2e— Coyote clan. Kwew wiwi-.------- Wolf clan. Sikyataiyo winwnt ----- Yellow-fox clan. Letaiyo winwt ....---- Gray-fox clan. Zrohono witwt ------- —.. Masiiwittwila-2=---e2-= Masautt (Death-god) clan. Kototo wifiwti..------- Eototo clan. Tuvou witwi -.------- Pifion clan. Hoko wifiwi..---.-.-- Juniper clan. Awata wifilwt..------- Bow clan. Sikyatci wifwu .....-- Bird (?) clan. Tuvatcl witwii-.---2.- Bird (?) clan. Pakab group Paka witiwtt-.------- Reed or arrow clan. Kwahu winwt..-..---- Eagle clan. Kwayo witiwi..-.-..- Hawk clan. Koyona winwnt. - Tawa wifwn --- .--Turkey clan. ..-Sun clan. _..War-god clan. ..-War-god clan. Piuikon winwt- - Palania winwnt- - - Cohu winwt Honani group (via Kicuba) Honani wifiwtl..-..-..- Badger clan. Muiyawu wifwt ---.-- Porcupine clan. Wicoko winwt..--..-- Turkey-buzzard clan. Bull withwill ee -e-=- == Butterfly clan. Katcina wiftwa-...--..- Kateina clan. FEWKES] NATIVE ACCOUNTS OF ARRIVAL OF CLANS 585 CHRONOLOGIC SEQUENCE OF THE ADVENT OF CLANS Traditions regarding the sequence of the arrival of clans conflict in details, although they coincide in general outline. Anawita, one of the best informed men of the Patki clans, has given the following order of the arrival of clans at Walpi: . Honau, Bear. Tetia, Snake. . Ala-~Lefiya, Horn-F lute. Kokop, Firewood. . Pakab, Reed. . Asa, Tansy-mustard. Patki, Cloud. 7., Kukute, Lizard; Tiiwa, Sand. Tabo, Rabbit; Piba, Tobacco. 8. Honani, Badger; Buli, Butterfly; Katcina. Dm 9 bo It will be noted that Anawita does not mention the Squash clan, probably because it is now extinct at Walpi: Wikyatiwa, of the Snake clan, gave the following sequence: 1. Teta, Snake. (ecutet Cloud. 2. Honau, Bear. 6.) Kukute-Tiwa, Lizard-Sand. 3. Kokop, Firewood. |Piba-Tabo, Tobaceo-Rabbit. 4. Pakab, Reed. 7. Honani, Badger. 5. Ala-Lefiya, Horn-Flute. 8. Katcina. 9. Asa, Tansy-mustard. Poyi, a very intelligent man of the Okuwun or Tewa Rain-cloud clan, gave the following sequence: 1. Tetia, Snake. 7. Isaut, Coyote. 2. Honau, Bear. Patki, Cloud. 3. Patun, Squash. 8 [Reukite-tiva Lizard-Sand. 4. Ala-Lefiya, Horn-Flute. Piba-Tabo, Tobacco-Rabbit. 5. Kokop, Firewood. g_|Katcina. 6. Asa, Tansy-mustard. *")Honani, Badger. The late A. M. Stephen obtained, in 1893, from five chiefs now dead,' the following sequence: 1. Honau, Bear. ie Firewood. 2. Tectia, Snake. “|Pakab, Reed. 3. Patun, Squash. 7 |Honani, Badger. 4. Ala-Lefiya, Horn-Flute. "|Kateina. Patki, Cloud. 8. Asa, Tansy-mustard. 5.) Tuwa-Kukiite, Sand-Lizard. 9. The clans of Hano pueblo. Tabo-Piba, Rabbit-Tobacco. Some of the inconsistencies in the foregoing lists may be explained by the fact that a misunderstanding existed between the natives and the author in regard to the information desired, the former believing in some instances that the sequence of arrival of clans at Walpi, and in others that the order of their advent into Tusayan, was desired. 1Cimo, Masaiumtiwa, Nasyufiweve, Hahawe, and Intiwa. 19 ETH, PT 2—O1L 2 586 TUSAYAN MIGRATION TRADITIONS [ETH. ANN, 19 Evidence has now been gathered that other villages than Walpi existed in the Hopi country at the time of the arrival of the Teciia clans. Studies of the ruin of Sikyatki show that this pueblo was older than Walpi, and consequently that the Kokop clans which founded it came into the Hopi country before the Tciia. The Lenya were also in this region when joined by the Ala (who left Tokonabi with the Teiia clans) and probably were living at Lenyanobi. Moreover, there is every reason to suspect that Awatobi also was inhabited in that early epoch. Bearing on these probabilities, the testimony of one of the Ala men, who did not confuse the Hopi country with the pueblo of Walpi, but called the author’s attention to the error of such confusion, is highly important. In his account of the sequence he declared that the Honau clan was the first to settle Walpi; but that about the same time the Kokop clan founded Sikyatki and the Lenya clan Lenyanobi. The Ala and Teiia peoples came into the country at about the same time, by different routes, the former joining the Lenya at Lenyanobi and the latter the Honau at Walpi. Sikyatki and Awatobi were in existence at that time. Although the Honau clan had not been at enmity with the Kokop, as both came from Muiobi (Rio Grande) and Jemez, the pueblo of combined Teiia and Honau clans was not on amicable terms with the people of Sikyatki. The outcome of the hostilities which followed was the overthrow of the Kokop clan of Sikyatki, ‘‘ while the Honau-Tciia people of Walpi conquered Masauu, the tutelary god of Sikyatki, who had given the Kokop a site for their pueblo.” The combined clans of the Ala-Lenya pueblo gained kinship with the Honau-Teciia through the Ala who had lived with the Teiia at Tokonabi. These two pueblos were peacefully united by the moving of the Ala-Lefya to Walpi. The tragic overthrow of Awatobi by its rival, Walpi, occurred later. Thus it seems that at an early period there had settled in the Hopi country three groups of clans, the Honau, the Kokop, and the Lenya and kindred Patun. ‘The Honau had a pueblo on the site of Walpi; the Kokop were settled at Sikyatki; the Patun on the Middle mesa; and the Lenya at Lenyanobi or Kwactapahu. The kindred Teiia and Ala clans, which had previously lived together at Tokonabi, entered the country by different routes. The Teiia joined the Honau at Walpi; the Ala the Lefya at Lefyanobi or Kwactapahu. The Honau-Teiia and the Ala-Lefya later consolidated at Walpi, and the town of the latter was abandoned. The combined people of Walpi destroyed the Kokop settlementat Sikyatki, as above stated, adding some of the survivors to its population. With the assistance of the Middle mesa clans Walpi overthrew and destroyed Awatobi. The settlement of Patki people at Pakatcomo was abandoned, some of the clans from that place remoy- ing to Walpi. The Honani, Asa, and other eastern clans sought Walpi asa home. The details of the above history are best brought out by an intimate discussion of each clan legend. FEWKES] THE TOUA CLANS 587 It may then be stated that while the main bodies of the three groups of clans from the north (Tokonabi), the south (Palatkwabi), and the east (Muiobi), settled at Walpi in the sequence given, individual clans of these groups were, so far as is known, of equal antiquity there; thus, while the majority of the clans from the Rio Grande were late arrivals, the Honau and Kokop were among the first to settle at the East mesa. The author has chosen the advent of the Snake clans as the epoch of the founding of modern Walpi, and for consecutive history he will consider the arrival of the clan groups in their order, namely, from Tokonabi, Palatkwabi, and Muiobi. CLANS FROM TOKONABI Tota Crans The clans known as the Teiia and the Ala‘ say that they formerly lived together at Tokonabi, which place, so far as can be learned, was near the junction of the Little Colorado with the Great Colorado, in southern Utah. The Teiia, or Snake, clans were dominant from the very first in Walpi, and their chief was, as late as the end of the seventeenth century, governor of the pueblo, for he it was who is said to have sent to the Tewa people of the Rio Grande for aid against hostile nomads. The following list contains the names of the men and women of the Snake clans now (January 1, 1900) living at Walpi: Census of Teiia clans at Walpi Men and boys | Women and girls Kopelia | Mamana Koyowaiamit Saliko Nuvawinu | Pobi Honyi | Kokyanmana Lomavoya Koteanapi Honauwt | Talasmuima | Wiki | Haso Wikyatiwa Kabuzru Uebema Cikwavensi Ahula Talakabu Sanna Sikyahoniwa | Moumi | Teoko aon zu a Since deceased. 1The Ala, by union with the Lefiya, later became the Ala-Lenya. There is no evidence that the latter clan ever lived at Tokonabi. 588 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 : * | | Mamana @ Nuvawinu? | a = _ > [ =e | | | | | Saliko? O* Wiki? Wikyatiwa? | ——— | | | | | eee a a Sa | Honyi? Lomavoya ? Talasmuima? | | | : Jer ~ | Kopeli¢ Koyowaiamn ? | | Haso? Kabuzrnu? | Talakabud Ahula Cikwavensi ? Pobi? Honauwnh + Kokyanmana@ | Uebema¢ Kotcanapi ? The different clans which, according to the legends, are associated with the Snake people are mentioned in an accompanying list (page 582). When the Snake settlement was first made at the northern base of the East mesa, the Snake, Puma, Dove, and Cactus peoples were possibly all represented, but the Snake clan was dominant and its chief was governor of the town. In their former life at Tokonabi the Huwi (Dove), Toho (Puma), Ala (Horn), and Teiia (Snake) were associated, and in some accounts the Tiiwa are also said to have been represented in this northern home. In most of the Patki traditions the Tiiwa are asserted to be a southern clan closely related to the Kiikiite (Lizard) people. The burden of the Snake legend’ is that in ancient times, when the Puma, Dove, and Horn clans lived at Tokonabi, a youth of the first named brought home as his wife a girl of the Snake clan. One of his ‘*brothers,” but of the Horn clan, also married a girl of the Snake clan, and it would seem that other members of the girl’s clan joined the Puma-Horn settlements. In passing, it may theoretically be sup- 1This legend is couched in the form of a mythic story of the adventures of the god Tiyo in the Underworld. FEWKES] HISTORY OF TCUA CLANS 589 posed that these women were of Shoshonean aftinity, possibly from a nomadic tribe, with which the Puma and Horn were thus united. As the offspring of the two Snake women did not get along well with the children of other clans at Tokonabi,’ the Puma, Snake, and Horn clans migrated southward. They started together, but the Horn soon separated from the other clans, which continued to a place 50 miles west of the East mesa, and built there a pueblo now called Wukoki. The ruins of this settlement are still to be seen. While the Puma and Snake clans were living at Wukoki one of their number, called Teamahia, left them to seek other clans which were said to be emerging from the Underworld in the far east. He went to the Upper Rio Grande to a place called Sotcaptukwi, near Santa Fe, where he met Pitiikonhoya, the war god, to whom he told the object of his quest. This person shot an arrow to a s/papu, or orifice, in the north, where people were emerging from the Underworld. The arrow returned to the sender, bringing the message” that the clans to which it was sent would travel toward the southwest, and that Teamahia should go westward if he wished to join them. He followed this direction and met the clans at Akokaiobi,* the Hopi name of Acoma, where, presumably, he joined them, and where their descendants still live. In answer to a question as to the identity of Teamahia, the narra- tor responded that the name signified the *‘ Ancients.” As the same term is used for certain ceremonial objects on the Antelope altar in the Snake dance, it may be possible, by a study of this ceremony, to give a more intelligent answer. Around the sand picture which constitutes an essential feature of this altar there is arranged a row of stone celts which are called teamahi During the altar songs one of the priests of the Sand clan, which is said to have lived with the Snake clan at Wukoki, rapped on the floor with one of these stone objects, for the purpose, it was said, of telegraphing to Acoma to the Tcamahia to join them in the Snake ceremony. On the eighth and ninth days of the dance Tcamahia came, and, while acting as asperger at the kisi or brush shelter, called out the invocation **‘ Awahia, teamahia,” ete., the Keres as invocation to warriors. The author is of the opinion that this asperger personates the old Teamahia of Wukoki, who parted from the Snake clans at that pueblo to seek his fortune in the east, finding it at Acoma. Among the clans associated with the Snake at Wukoki were the Puma and Sand. Per- haps Tcamahia, the warrior, belonged to one of these, possibly the former. The Puma fetish on the Antelope altar at Walpi may also be interpreted as indicative of a former association of the Puma and the 1 Tokonabi, possibly from toktci, wild-cat, and obi, the locative. 2 This reminds us of the use of the paho, or prayer stick, as a message bearer. 3 There is said to be a ruin on the Awatobi mesa called Akokaiobi. 590 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 Snake clans, and the sand picture of the mountain lion on the Snake altar of the same pueblo may admit of the same interpretation. The personation of the Puma-man in the exercises in the Snake kiva is regarded in the same way. These are all modern survivals indicative of the former association of Puma and Snake clans. Evidences of the contact of the Horn and Snake clans are also found in the ceremonial paraphernalia of the Snake dance, such as the two antelope heads on the Antelope altar at Oraibi and the many snake fetishes, to which it is hardly necessary to call special attention. But the strongest of all evidences that the Horn and Snake clans have been associated are the Hopi names of the two priesthoods which celebrate this great festival, namely, the Antelope and Snake fraternities. Thus in the Snake dance we find in the ceremonial paraphernalia totemic evidences of composition from at least three clans--the Puma, the Horn, and the Snake—which substantiates the legend that in ancient times these three lived together. When we study the Flute ceremony we shall see additional evidence that the Horn were once in contact with the Snake clans, notwithstanding that the Flute element, which predominates, had an origin different from that of the Horn. Awa-LENYA CiANs! The first addition to the settlement of Bear and Snake clans at Old Walpi was a group composed of Ala (Horn) and Lenya (Flute) clans. As this group was composite, their legends are likewise composed of at least two elements. They go back to two cultus heroes, the Deer youth and the Mountain-sheep youth, one of whom is the boy of the Horn clan who married one of the Snake girls, the other the male ancestor of the Flute clans. The numerous elements of the legends of the Horn-Flute clans which run parallel with those of the Snake are interpreted as due to the former life of the Horn with the Snake clans. The Flute legendists say that their ancestor descended to the Underworld, and that while there he drew a maid to him by playing on a flute. He married this girl in the Sun-house and she became the mother of the Flute clan. This legend is thought to bear traces of a different origin from any of the Horn legends, although it is mixed with Horn stories. After the Horn clans parted from the Snake people in their migra- tion southward from Tokonabi, they drifted into an eastern place called. Lokotaaka. How far eastward they went is not known, but from Lokotaaka they moved to Kisiwi, and then to Mofpa, where ruins are still to be seen. Continuing in their migration, which, after they left Lokotaaka, was toward the west, they came to a pueblo called Lenyanobi, ** Place of the Flute” (clans). There they evidently 1 As has been previously stated, the Leflya clans of the Ala-Leflya group came from Palatkwabi, but for convenience they are here considered with their associated clans from Tokonabi. FEWKES] THE ALA-LENYA CLANS 591 united with the Flute people, and from that time the group was com- posite. The combined clans did not remain at Lenyanobi, but moyed by way of Wikyaobi to a point called Ky ractapabi, where they were well within the present Hopi reservation. The route from Kwactapabi to Walpi, where they joined the Snake pueblo, was by Wipo, Kanelba, and Lefyaciipu, or Kokyanba (Spider spring). The spring known as Kwactapahu, situated a few miles from Walpi, is said to have been the site of a pueblo of the Horn-Flute clans for some time, and it was possibly while they were there that news of the Snake settlement at Walpi reached them. The chief of the pueblo sent Alosaka to spy out the country west and south of their settle- ment, and he returned with the report of the existence of the Snake town at Old Walpi. The Horn people, knowing that the Snake people must have made their way into the region after their separation, no doubt expected to find them as they journeyed westward. At all events, they recognized them as kindred. Kwactapahu was aban- doned, and the combined Horn-Flute clans were hospitably received by the Snake villagers. In the present Hopi ritual at Walpi there is a re smarkable confirma- tion of that part of the above legend which deals with the union of the clans from Kwactapahu and the people of Old Walpi. It is no less than a dramatization of the event with a cast of characters repre- senting the participants. About noon of the seventh day of the Flute ceremony, the Flute chief, accompanied by several members of the Flute priesthood, visited in sequence the springs mentioned above, where the Horn-Flute people had tarried during the latter part of their migration. They went first to Kanelba, about 5 miles from Walpi, thence to Wipo, still farther to the north, on the west side of the table-land of which the East mesa is a continuation. They then crossed the plain west of Wipo, and made their way onto the mesa which bounds the western edge of this plain. At a point called the Flute house they slept, and on the following morning went a mile beyond the Flute house to Kw: actapahu, where ceremonies were conducted and offerings made to the spring. The rites at Kwactapahu ended, the Flute priests retraced their steps, crossing the valley as their ancestors did in ancient times. At intervals they halted, set the tiponi or badge of office in position on the ground, and made symbols of rain clouds near by. One of the stopping places was near the mound called Tukinobi, on which there is a ruin of considerable size. They continued their course and approached the narrow neck of land ec: alled Hiitciovi, along which runs the trail by which Walpi is entered from the north. There they found a line of meal drawn across the trail which symbolized that no one could enter the pueblo. Entrance to Walpi was closed to the incoming personators of the ancient Horn-Flute clans. 592 TUSAYAN MIGRATION TRADITIONS (ETH. ANN.19 Back of this line, between it and the houses of the pueblo, stood the chiefs of the Bear and Snake clans. There was also a boy dressed like the Snake boy in the Antelope kiva rites, as well as two girls dressed and decorated similarly to the Snake maid in the same ceremony. As the Flute chief and his followers approached, the Bear chief challenged him, demanding, ‘‘ Who are you? Whence haye you come?” The Flute chief responded that they were kindred and knew the songs necessary to bring rain. Then the Bear chief took his tiponi from one of the girls, while the Antelope-Snake chief received his badge from the other. Holding them tenderly on their arms, they advanced and welcomed the Flute chief to their pueblo. As a symbol of acceptance the Flute chief gave prayer offerings to the girls, the line of meal barring entrance to the pueblo was brushed away, and a new line extending along the trail was made to symbolize that the entrance was again open. This symbolic reception of the Flute priests not only dramatizes a historic event in the growth of Walpi, but also displays a tendency to visit old sites of worship during ceremonies, and to regard water from ancient springs as efficacious in modern religious performances. — It is a common feature of great ceremonies to procure water from old springs for altar rites, and these springs are generally situated near ancestral habitations now in ruins. This tendency is illustrated in the Sio-calako or Zuni Calako cere- mony celebrated at Sichumovi in July, when the chiefs procure sacred water from a spring near St Johns, Arizona, called Wenima, the ancient home of the Hopi and Zuni Calako. The Kwakwantt chief obtains water for some of his ceremonies from a spring called Sipabi, where the Patki clans, who introduced the Kwakwantt, once lived. The Piba chief of the Tataukyamti procures water from Clear creek, near the ruin of Cakwabaiyaki, the former home of the Piba clans. Thus in instances where clans have migrated to new localities their chiefs often return to ancestral shrines, or make pilgrimages to old springs for the purpose of procuring water to use in their ritual. Ala-Leriya ( Walpi) | Men and boys | Women and girls | | | Ala phratry: Pontima Keli Pavatiya Nutice Piitei Turwa Tawakwahi Siohumi Nabi Humesi Palunhoya Komanaieci Makto | Talahoniwa (Tuba) FEWKES] THE ALA-LENYA CLANS Ala-Lenya 598 ( Walpi)—Continued Men and boys | Women and girls Suhimu Sokoni Niiunu Sikyabentima Tcono Pema Honyamtiwa Lefiya phratry: Ala phratry—Cont’d Tewaianima Tunoa | Sakbensi (Vensi) Tu'kwi | Tu'waninima Wapa Masainumko Hayi | Talawinka Wikpala Humita Nitioma | Tahomana Tatei | Kabi Sami Honka Pakabi Kwahonima Lomaventiwa Talakwabi Tuwasi Kuyaletsmina Sitka Sikyaiama Koyahoniwa He'wi Nayamtiwa Nawicoa Talawipiki Tubeoinima Sikyaiauma Nuyasi Tu'wi Sikwabi Taiyo | Sikyaletsi | Tu'vakuwi Ala ; ¥ * ge Piiteig > Se | | Pontima ¢ Pavatiyag Kelig aria fo are Turwa@ Siohumi ? THERE fo) Tewaianima 9 = a = | Tawakwabi¢ Nabi? Palufihoyay 594 TUSAYAN MIGRATION TRADITIONS (ETH. ANN, 19 Leiiya g | Sakbensi 2 Hayi¢ Q* } Tumnoa? Masainumko ? ~ | | Herwi? Wikpala? Tuwkwi¢ Tubeoinimn 2 = t Kabi9 Tahomana ? Nawicoa 9 Talawinka ? Sami? Pakabi¢ Nuvasi? Sikwabi®? HonkaY Sikyaiama 9 | | Sitkag? Tatci¢ Tuwasi? Sikyaletsi 2 Kwahonima ? Talakwabi? Kuyaletsmina ? | Naya mtiwag Talawipiki¢ Turwaninimt 9 Tuwigt Turvakuwi? Taiyo? Humita ? | Koyahoniwa CLANS FROM PALATKWABI AND THE LITTLE COLORADO PUEBLOS’ It is stated that the Little Colorado pueblos were settled by clans from the far south, or Palatkwabi, which accounts for their considera- tion under the above heading. There is good traditional and docu- 1 By the Little Colorado pueblos the author does not refer to ruins at the Cascades or between them and the river's mouth. The pueblos south and southeast of Hopi are included, FEWKE®] CLANS FROM PALATKWABI 595 mentary evidence that some of the pueblos now in ruins along the Little Colorado, due south of Walpi, were inhabited until near the close of the seventeenth century, but they were not all abandoned at the same time. Some of the clans went northward to the Hopi pueblos, others eastward to Zuni. Among the first groups to migrate north- ward was the Patun (Squash), which may have been accompanied by the Lenya or Flute. The former settled at the Middle mesa and Awatobi, the latter were later joined by the Ala at Lefiyanobi. As there were Patun clans in Awatobi, which was destroyed in 1700, this migration must have taken place before that year. The Patki group left Homolobi somewhat later, for it is said that they did not go to Awatobi, but as there were Piba clans in Awatobi, the Piba arrived in Tusayan before the destruction of the pueblo of the Bow people. It may have been that Pakatcomo, the Patki settle- ment in Tusayan, was founded before Awatobi fell, but the evidence seems to be contrary to such conclusion. Parun CLANS Among the first clans to migrate from the pueblos of the Little Colorado in quest of homes in northern Tusayan of which information has been gathered through legends were the Patun or Squash clans. They originally lived on the Little Colorado, southwest of the present Hopi pueblos, and were accompanied by the Atoko (Crane) and Kele (Pigeon-hawk) clans. They made a settlement at Teukubi, on the Middle mesa, which was afterward abandoned, the inhabitants removing to another pueblo of Squash clans, Old Mishongnovi. Some of the Squash clans went to Awatobi and others eventually to Walpi. The Squash clans which went to the East mesa are now extinct, so that it has not been possible to investigate their legends, but ample material for this study is still extant at the Middle mesa villages. In their life along the Little Colorado the Squash clans came in con- tact with many others, some of which followed them in their northward migration. There is reason to believe that among those they met were the Lenya clans, which may have preceded them in the journey. There are several reasons for associating the Lefiya with southern clans. In the Oraibi Flute altar the main image is a figurine with a single horn on the head resembling the pointed helmet worn only by the Kwakwantti, a society of the Patki clan, the southern origin of which is unquestionable. In most of the Flute altars there are two mounds of sand (talactcomo, ** pollen mound”) in which artificial flowers are inserted. The construction of similar flower mounds (athya sitcomov?) in the Underworld is mentioned in Piba and Patui legends of the origin of their Tataukyamai, Wiiwiitcimtn, and Mamzrautii societies. The Patun legends contain much about the cult of Alosaka (a germ god),’ LAlosaka is really another name for Muyinwa, the germ god, 596 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 which they say originated in the south. The personation of Alosaka is prominent in the Flute observance at Walpi. This Alosaka cult, which, as elsewhere shown, is in some way con- nected with the Mountain-sheep clan of the Flute group, is one of the most perplexing at Walpi. There is legendary evidence that Alosaka was introduced into Tusayan from the settlements along the Little Colorado, by Squash and kindred (Flute) clans, some of which joined the Horn, others went to Awatobi, and still others to the Middle mesa, where they founded Tecukubi and other pueblos. All the evi- dence would appear to indicate that the original home of this cult was in the south, and as the Squash and related clans (except the Flute) are extinct at Walpi, the perpetuation of the Alosaka ceremonies in that pueblo has fallen to other clans—the Asa and Honani—by which the nature of the cult has been somewhat modified. In the enumeration of the clans belonging to the Ala-Lefiya group, there is a Panwii or Mountain-sheep clan. This fact is significant, as the Aaltti or Alosaka wear artificial horns and personate Mountain- sheep in several ceremonies. In the New-fire ceremony, where Alosaka are personated, the per- sonations observe rites at the shrine of a being called Tuwapontumsi (*‘ Earth-altar woman”). The shrine has no statue of this being, but contains simply a block of petrified wood. Sikyahonauwi, an old man of the Tiiwa clan, made for me us his totem a figure with two horns, which he called Tuwapontumsi, a female complement of the double- horned Alosaka. In the Soyaluna, or Winter-solstice ceremony, we find a figure of Alosaka on the shield of the Ala-Leftya people, and at Oraibi a screen similarly decorated is found. It has not yet been determined, how- eyer, whether this Alosaka screen at Oraibi has any relation to the Ala-Lenya clans. The Alosaka cult was practiced at Awatobi, for the figurines of Alosaka used in that pueblo, as well as legends connected with them, are known. ‘This is explained on the theory that there were Patun and related Lenya clans in that ill-fated pueblo. PatK1 CLANS In the general designation ‘‘ Patki clans” are included the last group which sought refuge from their southern homes among the Hopi. This group includes the Kiikiite (Lizard), called also Tiitwa (Sand), the Tabo (Rabbit) and Piba (Tobacco), and the Rain-cloud. They say that they once lived on the Little Colorado, near Winslow, and when they entered the Walpi valley they built and occupied Pakatcomo, where they practiced a higher form of religion than that which existed in the pueblo founded by the Bear and Snake clans. An intimate study of the character of the surviving rites which these clans say they FEWKES] THE PATKI CLANS 597 introduced substantiates this claim of their legends, for all the cere- monies ascribed to southern clans are higher than the rite which came from Tokonabi. The original home of the Patki clans is called in their legends Palatkwabi, and is said to have been near San Carlos in the Gila valley, southern Arizona. The legends of this clan say that their ancestors were forced to leave their ancient home by reason of destruct- ive floods, due to Paliiliikof, the Great Snake, and they migrated northward along the trail indicated by the ruined pueblos mentioned in the following pages. From Kufchalpi, the most ancient pueblo of the Patki, probably, in the Palatkwabi region, they went on in turn to Utcevaca, Kwinapa, Jettipehika (the Navaho name of Teciibkwitcalobi, or Chaves pass), Homolobi (near Winslow), Sibabi (near Comar spring), and Pakatcomo (4 miles from Walpi). The last four ruins have been identified, and extensive archeological investigations have been con- ducted at the fourth and fifth. We thus have the names of three pueblos occupied by the Patki during their northern migration from Palatkwabi, before they arrived at Chaves pass, which have not yet been identified. These are Kwinapa, Utcevaca, and Kunchalpi. The determination of the sites of these villages, and a study of their archeology, would prove to be an impor- tant contribution to the knowledge of the origin of the Patki clans. Anawita, chief of the Patki, a very reliable man, can point them out to any archeologist who has the means to prosecute these studies in Arizona. When the Patki clans arrived in Tusayan they built the pueblo of Pakatcomo, from which some went to the Middle mesa and others to Walpi. The Patki traditionists say that when their ancestors lived at Pakatcomo the people of Walpi were in sore distress on account of the lack of rain and the consequent failure of crops, hence they invited the Patki to perform their rites to relieve them from calamity. This invitation was accepted, and the Patki societies erected their altars and sang their rain songs at Tawapa. Asa result there came over the land first a mist, then heavy rain with thunder and lightning. Although the latter alarmed the Walpi women, the men were grateful, and the Patki were admitted to the pueblo, which they later joined. There was probably also another reason for the abandonment of Pakat- como. The pueblo was in a very exposed position, and the Apache were raiding the surrounding country, even up to the very foothills of the East mesa. Pakatcomo was in the plain, and its inhabitants naturally sought the protection of Walpi on its inaccessible mesa site. Pakatcomo is a small ruin, with walls of stone, and closely resem- bles the ruins at Homolobi, but it was evidently not inhabited for a long time, as the quantity of débris about it is small, and there are only a few fragments of pottery in its mounds. 598 TUSAYAN MIGRATION TRADITIONS [ETH. ANN.19 Date of the removal of clans from Homotobi Historical documents of the sixteenth and seventeenth centuries point to the existence at that time of inhabited pueblos in the region west of Zuni and south of the present Hopi towns. We find constant references to the ‘‘Cipias” as living west of Zuni in the seventeenth century, but the name drops out of history in the century following.* Where did they go? Probably to Pakatcomo. In 1604 Juan de Onate, in search of the South sea (the Pacific), marched westward from Zuni to ** Mohoce” 12 or 14 leagues, where he crossed a river. This Mohoce is generally said to be modern Tusayan, which, unfortunately for the identification, is not west but northwest of Zuni, is three times the dis- tance mentioned, and is not on a river. Moreover, to visit the South sea, Onate had no reason to go to the northern or modern Hopi pueblos. He had been there in 1598, and had gone from them to the mines north of Prescott and returned to Zuni by a ‘‘shorter” route. Why should we suppose that he went out of his way from a direct route to the South sea on a subsequent journey? The line of march of Onate in 1604 was stated to be from Zuni west to Mohoce, which name is not restricted by the author to the present Hopi pueblos. The pueblos along the Little Colorado were in Mohoce, for, as we shall see, the Gilenos told Fray Francisco Garces in 1775 that ** la nacion Moquis” formerly extended to Rio Gila. In 1632 the Little Colorado settlements were still occupied, but by the middle of the seventeenth century the Apache had raided the ter- ritory between the settlements of sedentary Sobaipuri tribe of the San Pedro and those of the Hopi along the Little Colorado, preventing the trade between the tribes which had been common in the sixteenth century. In 1674 the hostiles had destroyed a Zuni pueblo, and there is every reason to believe had forced the clans in the Little Colorado valley northward to modern Tusayan. It is therefore highly probable that the pueblos in the neighborhood of Winslow were deserted in the latter half of the seventeenth century. The ** Kingdom of Totonteac,” which is mentioned in documentary accounts written in the sixteenth century, is now generally regarded as the same as Tusayan, but neither name was restricted to the pres- ent Moqui reservation in early times. There is every reason to sup- pose that when Coronado marched through New Mexico in quest of Cibola, the pueblos along the Little Colorado south of Walpi were inhabited, and that there were other inhabited pueblos, now in ruins, south of these. Totonteac may have been the name of one of these clusters” possibly as far south as Verde valley or Tonto basin; but 1In talking over traditions with Sufioitiwa, a member of the Asa clan, the author found that he placed the home of the Cipias or Zipias south of Laguna and east of Zuili. Whether these were related to the Cipias west of Zufli was not known to him. *Tusayan extended far south of Walpi in the sixteenth century. According to Castafeda it was 25 leagues from Cibola, which distance he later reduces in his account to 20 leagues. Espejo says that Zuni is another name for Cibola. Now, 20 leagues from Zufi,in the direction indicated, would not bring one to Walpi in northern Tusayan, but to some other Tusayan pueblos, possibly Homolobi. FEWKES] THE PATKI CLANS 599 Captain Melchior Diaz learned from the natives that ‘‘ Totonteac lies about seven days’ easy journey from Cibola. The country, the houses, and the people are of the same appearance as in Cibola. Cotton was said to grow there well, but I doubt this, for the climate is cold. Totonteac was stated to contain twelve towns, each of them greater than Cibola.” * The akove quotation is from Mendoza’s letter of April 17, 1540, but on August 3 of the same year Coronado wrote to Mendoza that the Cibolans informed him that the kingdom of Totonteac was “‘a hotte lake on the edge of which there are five or six houses.” In the same letter Coronado says: ** They tell me about seven cities which are at a considerable distance. . . . The first of these four places about which they know is called Tucano.” ” Certainly, if we judge from the contents of this letter, Coronado’s informants did not regard Totonteac and Tucano as the same cluster of towns or *‘kingdoms.” It seems more rational to believe that they were names applied to two different groups of villages, west and northwest of Cibola, respectively, neither of which may have been the present Hopi pueblos, but both may have been inhabited by clans which later found refuge in what is now the Moqui reservation. The old men of the Gila Indians told Gareés in 1775 that the **Moqui nation” formerly extended to the Gila, and that its people built the pueblos then in ruins in their country.* Patki ( Walpi and Sichumovi) Men and boys Women and girls = Bs =. = Supela Naciumsi Kwatcakwa Koitsyumsi Teazra Nemsi Sakwistiwa Nempka Suni Yuna | Citaimi Naciainima Kwazra Gnenapi | Makiwt Ku'yt Mowt Tcie 1 Letter of Don Antonio de Mendoza to Charles V, Ternaux-Compans, ser.1, tome Ix, p.292. Ibid., Nordenski6ld’s translation, p. 135. 2Winship, Coronado Expedition, p. 562. $“ Esta enemistad me la habian contado los Indios viejos de mi Mision los Gilenos, y Cocomarico- pas por cuya noticia he discurrido quela nacion Moquis se extendia antiquamente hasta el mismo Rio Gila: fundome para esto en las Ruinas que se hallaron desde Esta Rio hasta la tierra de los Apaches, y que lo las he visto entre las sierras de la Florida,’’ ete.—From a copy of the Diario in the Library of the Bureau of American Ethnology. Since this paper was written a translation of the Diario, with valuable notes, by that eminent scholar, the late Dr Elliott Coues, has been published (see On the Trail of a Spanish Pioneer, the Diary and Itinerary of Francisco Garcés, New York, 1900, vol. 11, p. 386). 600 TUSAYAN MIGRATION TRADITIONS Patki ( Walpi and Sichumovi)—Continued (ETH. ANN. 19 Men and boys Women and girls Unga Napwaisia Pocto Kumaletsima Kwaa Kumawensi Nacita Tuwabensi Namtti Penna Tu'ba Koinranumsi Nasanihoya Poliena Poule Tocia Talasnini Lenmana Poyona Naciumsi ? Teazragy Sakwistiway Nacitagy Tubeumsi ? * Supelag Kwatcakwag? Makiwi?¢ . | | Nemsi? Nempka@ i ae =e een | a Suii¢ Citaimuz Teie¢ Kwazragd Kuryu? | Napwaisia 9 Kumaletsima ? i Kotsyumsi ? Anawitagy Kwaadg Yura? Naciainima 9 Gnenapi 2 Talasnuni ? Povona?g 9* Penna Uiigag Mowt¢ Koinranumsi be} Poliena 9 =| | Pouled? Av(?) FEWKES] THE PATKI CLANS 601 Kumawensi 2 | Tuwabensi 2 Poctogy Lenmana 9 Tocia@? Twhbag Nasanihoya? Several members of the Patki clan live in Sichumovi. Their names follow: Men and boys Women and girls Anawita Sikyomana Teoshoniwt Kwamana Klea Loci Haiyuma Tazru Teoshoniwti 4 Sikyomana 9 | | iM Kwamana 9 Loci? | Sica Haiyum + Tazru? The Piba (Tobacco) and the intimately associated Tabo (Rabbit) and Sowi (Hare) clans are given a southern origin by their traditionalists. Some associate them with the Squash, others with the Water-house or Rain-cloud group, but all ascribe to them former habitations on the Little Colorado near Winslow. The ruin which now marks the site of their former home is probably that near the mouth of Cheylon fork, called Cakwabaiyaki. There is well-nigh strict uniformity in the statements that there were Piba clans in the village of Awatobi, and some say there were Piba people in the Patki settlement of Pakatcomo. The chief of the Piba clans at the former pueblo was Tapolo, who was the first Tataukyamu chief at Walpi; and Hani, who says he is a direct descendant of Tapolo,' is chief of the same religious society in that pueblo. 1Tapolo admitted the hostile Walpi into Awatobi on the night that the latter pueblo was destroyed. After the massacre he settled in Walpi. 19 ETH, pr 2—01——3 Piba-Tabo ( Walpi and Sichumovi) TUSAYAN MIGRATION TRADITIONS (ETH. ANN.19 Men and boys Hani Talashonima Nuatiwa Samimoki Teali Kwabehu Pimt Sikyaweamu Soma Siskyamu Masahoniwt Teaini Wisti Namoki Lapu Letaiyo Tinabi Talasi Tetthoya Lelentei Tiiktei Honauwtt Pitcika Kutcahonauwt Homovi Hani? | Women and girls Tciewuqti Tetwitigti Tubenumka Pofiyawika Owakoli Koitswi Siepnimana Sikyatci Tubi Koyoainimt Siumka Masainumsi Piba Teiewliqti 2 Teiiwt igti¢ Nuatiwa¢? | Samimoki? ] Kwabehu?y | Owakoli ? Koitswd 2 Kutcahonauwt 4 Sikyaweamu¢ | -onvawika Tubenumka 9 Soma? | Laput Sikyatei 2 Siepnimana ? Siumka ¢ | Piteikat Tubi FEWKES] Masainumsi ¢ | males THE PATKI CLANS 603 Tabo +0 2 er Letaiyo? Talasi? Tealig Namoki?¢ Titwa-Kikiite (Walpi and Sichumovi) Men and boys | Women and girls | Kakapti | Koiyabi Sikyabotima Gnapi Takala Kutco Sikyahonauwt Humiumka Teabi Sikoboli Teaka Wakoi Sutki Teozra Sania Nakwafnwuisi Taoma Kerwaunainimt Awata Payunmana Peryauma Sikyampu Lomatcoki Talaskubi Tubenhima Lalaito Pavatiya Tuwint Hahabi Cres ig | Sutkia Pavatiyal re Payunmana 2 Sikyampu ? Tuwinn?s (Henry) (Tom)! 2 * Teabig Teakaz Lomatcoki? Q* | ; Kuteo? Sikyahonauwh + | | | Kakapti? Sikyabotima? Takala¢# | Saniag SikoboliQ Wakoi9? Humiumka 9? Koiyabi? Teozra ie Talaskubi & Taoma? Hahabi¢ Peryaumag? 1Tom’s mother was of the Ala clan; whenshe died Tom was adopted into the Tiwa. 604 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 CLANS FROM MUIOBI AND NEW MEXICAN PUEBLOS Honau CLAN The author has been unable to gather much information regarding the early history of the Bear clan. Kotka, the chief, asserts that his people were the first to come to the Hopi country; that they formerly lived at Muiobi, the Rio Grande region, and that they ** overcame” Masauti, the ancient owner of Tusayan. The author is inclined to regard the Bear clan as one of the groups of Pueblo people from the vast which migrated to Tusayan at an early date, founding a pueblo on a site assigned to it by the Kokop, with whom it lived in friend- ship until the advent of the Snake people; his interpretation of the ‘overthrow of Masauti,” a tutelary god of Sikyatki, will be given later. There are at the present time only three members of the Honau clan in Walpi: Masaiumcei, the oldest woman, with her son, Kotka, the chief, and a daughter, Hofsi, wife of Tu"noa, the Flute chief. Hojisi has no children, and if none are born to her, the Honau clan, which was once most powerful in Walpi, will become extinct at the death of the chief and his sister. Honau ( Walpi) Masaiumcei 4 Kotka¢ 2 ale Koxor CLaNs The former home of the Kokop clans was Sikyatki, a pueblo now in ruins, about three miles north of Walpi. Archeologic evidence indi- cates that this pueblo was destroyed before the first contact of the Hopi with the Spaniards, and the Kokop legends declare that it was overthrown by Walpi. There was a clan in the Kokop group called the Masauti clan, and the Snake legends recount that Masauti formerly owned all the country, but that they, the Snake people, overcame him and received their title to the site of Walpi from him. This is believed to be a reference to the Sikyatki tragedy, and to indicate that Masaut, the God of Fire, was a tutelary god of the Kokop or Firewood people. Katci, the chief of the surviving Kokop clans, says that his people originally came from the pueblo of Jemez or the Jemez country, and that before they lived at Sikyatki they had a pueblo in Keams canyon. Others say that they also once lived at Eighteen-mile spring, between Cotton’s ranch (Pueblo Ganado) and Punci (Keams canyon); others that they drifted at one time into the eastern part of Antelope valley, where the ruin of their pueblo can still be seen. Archeologic investigation shows that Sikyatki was inhabited for many years, that its population was large, and that it had developed ceramic art in special lines characteristic of Tusayan ware. The technique 2Kotka really belongs to the Kokyan (Spider) clan of the Bear phratry. FEWKES] CLANS FROM MUIOBI 605 and pictography of Sikyatki pottery are distinctly Hopi, showing that the makers had developed a characteristic art which could have been attained only after a long interval. The peculiarities of this pottery are not found elsewhere in the Pueblo area and are not equaled by modern Hopi potters. These conditions indicate long residence in Tusayan. The being called Eototo has many resemblances to Masauti and may be the same being under another name. There was formerly an Eototo clan among the Kokop people, and the masks of the two per- sonifications are very similar. In Niman-kateina, in which Kototo is personated, the Kokop chief assumes that part. Kokop ( Walpi) Men and boys Women and girls Katci Sakabenka Maho | Kunowhuya Kunahia | Teveyaci Sami | Ani Teta Lekwati Koitswinu Hahaie Heya Nakwawainima Posiomana Kutenaiya Sakabenka 9 Kutenaiya 2 | | |: nl a ; Katei ¢ Kunahia 7 Maho ¢ Heya 7 During the last decades of the seventeenth century many clans fled from upper Rio Grande valley to the Hopi country. These were mainly Tewa people, for hardly had the Spaniards been driven out of New Mexico in 1680 than the eastern pueblos began to quarrel among themselves and, as a rule, the Tano and Tewa were worsted. A few of the former and many of the latter escaped to the province of Alaki (Horn house, Hopi country) between 1680 and 1700. About the middle of the eighteenth century many of the descend- ants of these fugitives were persuaded to return, being reestablished in new pueblos. It is highly probable that the people who were thus brought back belonged to Tanoan clans, and were not true Hopi, although called ‘t Moquis,” or *‘ Moquinos,” in the accounts of that time, from the fact that they had lived in the Hopi country. In other words, they were Tewa and Tano people who had fled to Tusayan, and not original Hopi. There has been a wave of migration from the Rio Grande to the Hopi country and then a return of the same people to their former homes. No considerable number of true Hopi have 606 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 migrated to the Rio Grande and remained there, but many Tewa people who fled to Tusayan have never returned to their former homes on the Rio Grande. This is an important fact, and partially explains the existence of so many Tanoan ceremonies in the Hopi pueblos, especially of the East mesa, where Tewan influence has been the strongest. The Hano villagers are of Tanoan stock, as were prob- ably the Asa, who were somewhat modified during their life at Zuni.’ No connected migration story of the Honani clans has yet been obtained, but it is said that they lived at Kicuba, and brought katcinas, which are now in their special keeping. The Katcina clan is also supposed to have come from eastern pueblos, but of that no cireum- stantial proof can yet be given. Hownant CLANs The Honani clans once lived at Tuwanacabi, north of the Hopi pueblos, where ruins are still to be seen. They say that the Honani katcinas came up from the Underworld at that point, and that they entrusted themselves to the special keeping of these clans. The Honani migrated to Oraibi from their home at Tuwanacabi, and later some of them went to the Middle mesa, and to Awatobi and Walpi. At the time of the Awatobi massacre, in 1700, some of the Honani women were carried to Mastcomo, near the Middle mesa, where they were divided among their captors, some being taken to Mishongnovyi, and others to Walpi. These women are not now represented by female descendantsin Walpi, as all the Honani women on the East mesa are domiciled in Sichumovi.* Evidences drawn from the pictography of modern pottery shows that the katcinas were late arrivals at Walpi, and their association with Honaniand Asa clans shows that these two groups were kindred. That the Honani claim to have the katcinas in their special keeping points the same way and supports the legends that this cult was a late addition to the preéxisting Hopi ritual. Honani (Sichumovi) Men and boys Women and girls Hozro Kelewugqti Monwt Kokaamu Apa | Teutcunamana Yakwa Kutcamana Totei (Zuni) Sikyanunuma Simotei Seziuta Yoyowaia 1 There is no doubt that the Asa people lived in Zufli, where they left some members of their elan. The descendants of these are now called Aiwahokwe. 2The ancestors of the Honani of Sichumovyi came to that pueblo from Oraibi. FE WKES] CLANS FROM MUIOBI 607 Monwid Yakwag Simotei¢ Kelewiiqti 9 Kokaamn ? | Sezutad ] | | Teuteunamana Kutcamana The Buli or Butterfly clan is regarded as the same as the Honani or Badger. It formerly lived at Awatobi, and, although not now repre- sented at Walpi, it is important in Sichumovi. Buli (Sichumovi) Men and boys Women and girls Ami | Siwikwabi Aksi Lakonemana Cikuli Neanufamana Sezuta Siomana Nanakoci Siwihonima Tabohia Koitshonsi Teoetki Yoyowaia Kotcama Avatcoya Siwikwabi? Lakonemana ? | | | | Amit Nanakocig¢ KoitshofsiQ Tabohia# Neanufiamana? Siomanad Aksi¢ Cikuli¢ Seziitay | Avatcoyagy Koteama Katerina on ANWucr CLANS The Katecina or Afiwuci clans were of late arrival at the East mesa, and are reported to have come from the east. The only ruins which have been identified as homes of these clans are Kieu and Winba, or Katcinaba, the small ruin of which is situated about 3 miles east of Sikyatki, in the foothills of the same mesa. There are at present very few people of this group at Walpi, and none at Sichumoyi. Hano contains a considerable number, which would indicate that the main body went to that settlement. The abandoned houses east of the main cluster of Hano, where the site of the Katcina-kiva was pointed out by Wehe, are said to have been once inhabited by people of this group. The modern houses of the Katcina clan of Hano are on the other side of the main house cluster. 608 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 Kateina or Atiwuei ( Walpi) Men and boys Women and girls Naka Komaletsi Kuki Nakwainumsi Lomayema Napwaiasi Talawint Lomaiumtiwa Tu'maia Sikyawisi Teoki Q* Naka?y Kiki? Komaletsi 2 | | Nakwainumsi ? Talawinid Teoki¢ Lomaiumtiwa? j | | Napwaiasi 2 Turmaia 7 Sikyawisi¢ PaKkaB CLANS The legends of the Pakab clans are somewhat conflicting, but Pau- tiwa, of the Eagle clan, has given the most intelligible account. His ancestors, he asserts, came from the eastern pueblos, and once inhab- ited a village, now in ruins, called Kwavonampi. This ruin has not been identified, but was probably not far fram Pueblo Ganado, and possibly may have been the same as Wukopakabi (*‘Great reed or arrow place”). It has been suggested that the Pakab (Arrow) was the same as the Awata (Bow) clan, which lived at Awatobi (** Place of the bow”), and additional evidence to support this suggestion is that the Bow priests came from the Bow clans. It is highly probable that the Pakab lived at Awatobi, where they were known as the Awata. According to Stephen, on authority of Pautiwa, the Eagle clan once lived at Citaimu, now a ruin at the foot of the Middle mesa, which they abandoned, part of the inhabitants going to Walpi, others to Mishongnoyi. The aftiliation of the Pakab ceremony has an important bearing on the question of clan origin. The Momtcita ceremony peculiar to the Pakab has strong resemblances to a Zuni rite. This ceremony occurs just after the winter solstice, and although it has never been thoroughly studied,’ the author has ample hearsay data concerning it. Pautiwa, 1The author witnessed the Ceremony in 1900, PEWKES| CLANS FROM MUIOBI 609 the Pakab chief, is also chief of a warrior society called Kalektaka, which the Hopi declare is the same as the Zuni ** Society of the Bow” (Api hlaushiwani). He has a figurine of Piiiikomhoya which corre- sponds with the Zuni Ahaiuta, and when he sets it in place his acts are identical with those of Naiuche, the Zuni Bow chief. On the walls of the room where it is kept there are figures of animals of the cardinal points identical with those at Zuni, and the public dance of the Momtcita resembles the War dance at the latter pueblo. The evidence is strong enough to show that the Momtcita is closely related to the warrior celebration of the Zuni Bow priests, and it is believed to have been derived from Zuni, from some pueblo colony of Zuni, or from the same source as the Zuni variant, which means that the Pakab clans are of Zuni origin. The probability that the Pakab (Reed, Arrow) clans were the same as the Awata (Bow) clans makes it possible that Awatobi was settled by the Pakab people. There is nothing in the Pakab legends to forbid this, but on the other hand there is nothing definite to support it except the important statement that there were Pakab people at Awatobi. The Pakab-Awata may then be regarded as the founders of Awatobi, and if this be true there must have been close kinship between Awatobi and Zuni, or some settlement or Pueblo whose inhabi- tants later went to Zuni. Pakab (Walpi and Sichumovi) Men and boys Women »nd girls Pautiwa | Nunsi! Kanu | Teoro | Piba | Kannae Kiitckwabi | Lenhonima Nae | Kokoma | Potea Payvunamana Winuta Ponyanumka Tuwasmi | Kumahabi Ciaum Sikwi 1Her arm was amputated years ago by Dr Jeremiah Sullivan (Urwici). Dr Sullivan lived for some years at Walpi, studying Hopi customs. 610 TUSAYAN MIGRATION TRADITIONS (ETH. ANN.19 Nunsi 9 | i} = == = =. | a Pautiwag Teoro? Kanu? Kannae 9 Pibag Winutag Tuwasmi?¢ | | | Ciaum# SikwiZ? Lefihonima ¢ TO 7 7 : Kokoma @ Pavuhhamana ¢ Kiitekwabi¢ Kumahabi ? Ponyanumka 9 Nae? Potecad Asa OR TCAKWAINA CLANS * The Asa clans are said to have formerly lived at Kaétibi, near Santa Fe (Alaviya),* and near Abiquiu. They are reputed to have originally been of Tewa ancestry, and to have left the Rio Grande at about the end of the sixteenth century. In their western migration they went to Tukwi (Santo Domingo) and from there to Kawaika (Laguna). From Kawaika they proceeded to Akokaiabi (Acoma), and thence to Sioki (Zuni), where some of this clan still live, being known to the Zuni as the Aiwakokwe clan. How long the Asa lived at the pueblo last named, and whether the Zuni ascribe to the clan an origin in the upper Rio Grande, are unknown. Some of the Asa continued their migration from Zuni, proceeding to the Awatobi mesa, where they built a pueblo called Teakwainaki (‘‘ village of the Teakwaina clans”), near the wagon road west of the extreme end of the mesa. It is said that katcinas were then with them. They did not remain at this village a long time, but continued to the East mesa. The site of their first village at this mesa is not clearly indicated by the legends; perhaps they joined the Tewa clans, their kindred, above the spring called Isba, and it is said by some that they aided the other Tewa in their fights with the Ute. The Asa legends recount that after they had been in Tusayan for some time they built houses on the end of the East mesa above the gap (Wala), east of Hano. Years of drought resulted in a famine, and the Asa moyed away to Canyon de Chelly, in the *t Navaho country,” where they lived in houses now in ruins. They intermarried with the Navaho, but ultimately returned to Walpi, and found that other Tewa clans occupied their former dwellings, whereupon the Walpi chief assigned them a site for a new village at the head of the ‘Stairway trail,” if they would defend it against enemies. Their houses for the greater part are now oO" 5S 1The cult of Teakwaina common to Zufii and the East mesa is ascribed to this clan. 2 Alta villa, Spanish ‘* High town,” FEWKES] ASA CLANS 611 in ruins, although one of them, east of the Wikwaliobi-kiva, is still inhabited by an old woman of the Asa clan. Toward the end of the eighteenth century the majority of the women of the Asa phratry moyed to another point on the East mesa and founded the pueblo of Sichumovi, where their descendants still live. The exodus of the Asa people to the Navaho country may have been about the year 1780, when Anza was governor of New Mexico. At that time we learn that the Hopi were in sore distress owing to the failure of their crops, as the legend also states, and many moved to the Navaho country, where men were killed and women *‘ reduced to slavery.” InSeptember of the year named, Anza found that two Hopi pueblos had been abandoned and that forty families had departed.' As the legends declare that the Asa left at about this time for the same region, it is probable that these were the people to whom Anza refers. It is not unlikely that the Asa and Tewa clans formed a part of the Tanoan people who were forced to leave the upper Rio Grande yalley directly after the great rebellion of 1680. Niel is said to have stated? that at about this time 4,000 Tanos went to Tusayan by way of Zuni, which is the trail the present Asa people say their ancestors took. We are told that they went to Alaki, and as the Ala (Horn) people were then strong at the settlements of Walpi, on the terrace of the East mesa, it is not improbable that their yillage was sometimes called Alaki, or ‘Horn pueblo.” From the Hopi side we find verification of this historical event, for it is said that many people came to them from the great river just after the rebellion of 1680. The number mentioned by Niel, the statement that they went to Oraibi, and indeed all that pertains to the ** kingdom founded by Trasquillo,” may have been from hearsay. At all events the Asa people do not seem to have gone to Oraibi, nor are their clans now represented at this pueblo. As hearing on the claim of Asa traditionists, the following quota- tion from that well-known scholar, Bandelier, has great importance: The modern town of Abiquiu stands almost on the site of an ancient village. The town was built in part by Genizaros or Indian captives, whom the Spaniards had rescued or purchased from their captors. The Tehuas of Santa Clara contend that most of these Genizaros came from the Moquis, and that therefore the old pueblo was called Josoge. * As the Asa legends claim the site or vicinity of Abiquiu as their Rio Grande home, it would have been a natural proceeding if any of 1See Bancroft, Works, vol. xv11 (New Mexico and Arizona), p. 186. 2See Bancroft, op. cit., and others. $ Final Report, part 2, p. 54. 612 TUSAYAN MIGRATION TRADITIONS LETH. ANN. 19 them resettled there when they went back. These ** Joso” (Hopi) were probably Tewa from the East mesa, and as some of the Asa returned to the Rio Grande in the middle of the eighteenth century, it would be quite natural for the Tewa to call the old pueblo on the site of Abi- quiu Josoge (** Hopi pueblo”). The Asa people, like the Honani, brought some katcinas to Walpi, among which may be mentioned Teakwaina. In the winter solstice meeting of the Asa, at which their peculiar fetishes are exhibited in the kiva, the Asa display as an heirloom an old mask called Teakwaina, which they claim to have brought with them when they came into the country. There is a striking likeness between this mask and those of Natacka, and it is suspected that the Asa brought the Natacka to the East mesa. It is instructive to note that the Asa are not represented in the Middle mesa pueblos and Oraibi, and important light could be shed on this question if we knew that the Natacka were also unrepre- sented in these villages. The author suspects, on good ground, that the Oraibi have no Natacka in the Powamti ceremony. The similarity in symbolism between the masks of Teakwaina, Natacka, and Calako taka is noteworthy, and it is not impossible that they are conceptions derived from Zuni or some Zuni settlement. The home of Calako was the present ruin of Winima, near St Johns, Arizona, from which place the Zuni Calako came, according to both Hopi and Zuni legends. The Hopi Calako is said to have come from the same place. It is likewise highly probable that the Asa introduced several other katcinas besides the Teakwainas. Sichumoyi, the present home of the Asa, is often called a Zuni pueblo, probably because it was settled by Asa (Aiwahokwe) clans from Zuni. This is probably the Hopi town which the Zuiis say is one of their pueblos in the Hopi country. Asa people at Walpi Men and boys Women ; Ametola Wukomana Nivati Sunoitiwt | Hauta Kiazru Hayo Tu'kia Afiwuci Talahoya (Soyoko) Mu'na 1 EWKES] ASA CLANS Asa people at Sichumovi Men and boys Women and girls 613 Hola Tuwanainimt Tuwakuku Polici Kukiutei Kiukwaiesi Mae Letaiomana Wacri Poboli Kipo Nuya Sikyatila Hanoko Lomanapoca Talawaisia Nivahonimt Suhtibmana Honainimi Sikavenka Sikyamuniwa Talamana Lomaiisba Hokona Turkwinamt Teoro Payashoya Masaiunima Kalektaka Hewi Taimu Palawica Suki Pucimana Pofici Poli Tu'wanumsi Omowt Pawaiasi Tabohoya Poboli 2 Tuwahainima? Tuwakiikii¢? Kiikiteif? Holag Turwanumsi 9 Polici 9 | ~ | SikavenkaQ? Talamana? HokonaQ Sikyamuniwag Kalektaka? Q* Q* Sikyatilag Lomanapoca? Suhtbmana 4 Mae? Wacri¢ Kiikwaiesi 9 | | Pucimana 9 Tabohoya? Kipog Letaiomana 9 Pawaiasig Poli? Mumad¢ Tiwkiag Talawaisia 4 | | Nuvahonimi? Honainimt 614 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 POPULATION OF WALPI AND SICHUMOVI BY CLANS Walpi Sichumovi PVs winlwilleeseeee eee 24 Asa TWIT Willits oo < soca 40 Honau winwt-...-.--- 3 Honani wifwt ..------ 13 Katcina wifiwi..-.-..--- 11 Buliswinwilees. oss ese 16 Patkiwiltwil= se see se oe 37 Patki winwi-.-.-....-- 8 Pakab winwnt --.------- 14 Tiawa-Kikite winwi.- 15 Kokop winwt.....---- 16 Pakab wifiwfl .-------- 4 sain ses eee ae 11 Piba-Tabo winwfi --- -- 21 Tiiwa-Kiikiite wihwi.. 14 Oraibi women........- Z Lenya wittww 2.2.2. -- 37 Ala will WUE ao! oe cree 22 Total ..-..-...---- 119 Piba-Tabo winwnt -.--- 16 Rota ar Pees 205 HANO CLANS The present people of Hano are, in the main, descendants of Tewa clans which are said to have come to the East mesa at the invitation of the Snake chief of Walpi about the end of the decade following the destruction of Awatobi. These clans still speak the Tewa language, but, owing to intermarriage, they are more closely related consanguin- rally to the Hopi than to those speaking the Tewa language along the upper Rio Grande. The traditions regarding the advent of the ancestors of the Hano people are more circumstantial than those of the other component peoples of Tusayan. The best traditionists state that the ancestors of these clans were invited by an old Snake chief, who was then the kimonwi or pueblo chief of Walpi, to leave their home in the upper Rio Grande valley and settle in Tusayan. The Ute were at that time harrying the Hopi, and four times an embassy bearing prayer sticks was sent by the Hopi to the Tewa chief. The fourth invitation was accepted, and the Tewa clans started westward. The original home of these clans is said to be Teewadi, and they claim that they speak the same language as the present people of the pueblos of (1) O'ke’; (2) Ka’po; (3) Po’kwoide; (4) Posonwt; (5) Nambe; and (6) Tetsogi. Their trail of migration is variously given. The following route is on the authority of Hatco: Leaving Tcewadi they went to Jemesi, or Jemez, where they rested, some say, a year. From Jemesi they continued to O'pinp o, called by the Hopi Pawikpa (*‘ Duck-water”). There they rested a short time, some say, another year, then continued to Kipo, or Honaupabi (Fort Wingate). From there they went on to the present site of Fort Detiance, and after halting there a year continued to Wukopakabi (Cot- ton’s ranch) aud to Puneci (Keams canyon). Passing through Puici, FEWK ES] HANO CLANS 615 they went on to the East mesa, where they built a pueblo on the high land near Isba, or Coyote spring. The site of their pueblo can still be seen here, and obscure house walls may be traced on the ridge of land to the left of the trail above the spring, near the rocky eminence valled Sikyaowatcomo (** Yellow-rock mound”’).! While living here they used a spring called Unba, near the peach trees west of the mound on which the old pueblo stands. This spring is now filled with sand, and its exact position is problematic, but a spring called Isba, on the east side of the old Hano pueblo, to which reference has previously been made, is still used by the Hano people.® The original Tewa clans were as follows: Tewa Hopi English Okuwan Patki Rain-cloud Sa Piba Tobacco Kolon Kae Corn Tenytik | Hekpai Pine Katcina Kateina Nan Tiiwa Sand *Kopeeli | ——— Pink-shell? *Kapo lo Atoko Crane *Koyanni Teosbiici Turquoise *Tan Tawa Sun *Pe Kokop? Firewood? Ke Honau Bear *Tayek *Tceta | Kiikiite Bivalve-shell *The clans whose names are preceded by an asterisk are now extinct. Legends current in Hano state that the first kimonwi, or chief, of the pueblo belonged to the Niifi towa. It will be noticed that several of these clans are named from the same objects from which certain Walpi clans derive their names. Thus at Hano we have Rain-cloud, Tobacco, Corn, Katcina, Sand, and Bear clans corresponding to the same at Walpi. The present village chief, Anote, belongs to the Sa (Tobacco) clan, and his predecessor, Kepo, was a member of the Kolon clan. It is reported that the first pueblo chief of the Tewa of Hano who migrated to Tusayan was 1The shrine of the Sun, used during the Taiitai rite, is situated to the east of this rock. In this shrine are placed, during the Soyalunia ceremony, the tawa saka paho (sun-ladder pahos), the omowt saka paho (raincloud-ladder-pahos), and several forms of hakwakwocis, or feathered strings. *This spring is owned by the Hano clans, and much of the water which they use is taken from it. The cleaning out of springs when, as often happens, they are filled with drift sand is one of the few instances of communal pueblo work performed by the Hopi. As this time arrives notice is given by the town crier, by direction of the chief (kimonwi), and all the men of the pueblo aid in the work. When Tawapa spring was cleaned out in the autumn of 1898 the male adults of Walpi worked there for three days, and the women cooked food near by, so that at the close of each day's work there wasa great feast. While the work was going on a circle of the old men smoked native eeremonial tobacco in ancient pipes. 616 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 Mapibi of the Nin (Sand) clan, and Potan of the Ke (Bear) clan is said to have succeeded Mapibi. There are no Tewa women belonging to the Hano clans living in Walpi, the pueblos of the Middle mesa, or Oraibi. The legends of their conflicts with the Ute, who were making hos- tile inroads upon the Hopi, have several variants, but all agree in stating that the Tewa fought with and defeated the Ute, and that the last stand of these nomads was made on the sand hill east of the mesa. Into that place the Ute had driven all the sheep which they had captured and made a rampart of their carcasses. This place now has the name Cikwitu’kwi (*‘ Meat mound”) from that occurrence. Here the Ute were defeated andall but a few (two or four) were killed. There is an enumeration of the number above the wagon trail to Hano a short distance below the gap (Wala). The men who were saved were released and sent back to join their kindred with the word that the Tewa bears had come to Tusayan to defend it. Since this event the inroads of the Ute have ceased. Asa reward for their aid in driving back the Ute, the Tewa were given for their farms all the land north of a line drawn through Wala, the gap, across the valleys on each side of the East mesa, at right angles to the mesa; there their farms and homes in the foothills near Isba are now situated. The land holdings of the Hopi clans are south of this line, and the new houses which they have built in the foothills are on the same side. Almost all the people of Hano speak Hopi as well as Tewa, but even the Hopi men married to Hano women do not understand the language of the pueblo in which they live. The people of Hano are among the most industrious of the inhabit- ants of the East mesa. Although they number only about 160, they have (in 1899) more children in the school at Keams canyon than all the other six pueblos, which number approximately 1,800 inhabitants. FEWKES] HANO CLANS Census oF Hano Cians Sa or Tobacco clan | Men and boys Women and girls Anote Okan Asena | Heli Ipwantiwa Kotu Howila Kwan Mota Nuci Yauma Tcebopi Tuwabema Palakae Kaptiwa or | Anote? Okan 2 Heli? Kotu? | | | Mota? | PalakaeQ Kaptiwa 7? Asena? Ipwantiwag Kwai 2 Tcepobi? Howila? Yaumay Nuci®? Tuwabema 4+ Kolon or Corn clan Men and boys Polaka Patunitupi Kano Toto Peke Kelo | Komaletiwa Kalaokun Tacena Oba Agaiyo Tcide Women and girls Koteaka Nampio Kwentcowt Akontcauwt Talikwia Awatcauwi Heele Afitce Kumpipi Pelé Kontce Teaiwt Kweckateaniwt 19 ETH, pr 2—U1——-4 618 TUSAYAN MIGRATION TRADITIONS (ETH. ANN. 19 Koteaka 9 Patuntupi¢ Polaka gy Kano? Nampio fe] | eee Kwentcowt 2 Kalaokui # Komaletiwagy Akonteauwnt 9 Talikwia ¢ Toto? Peke?# Kelo#? Heele? Awatcauwt | | i aaa Agaiyog | Teide? Obad Tacena? Afitce? | | | | | Teaiwh ? Kweckateatiwa 2 KontceQ Pelé? Kumpipi 2? Ke or Bear clan Men and boys Women and girls | Hatco Kaun Mepi Pobi Yoyebelli Ubi Palankwaamti Taletcan Yane Tcetcan Tegi Tcepella Cakwatotci Teakwaina {°) + Teakwainagy Kaui ? Hatco? Teetean 2 Pobi? | baa l Ubi9 Cakwatotci¢ Mepi¢ Yaleteah@ Tcepella? Yoyebelli¢ = Palafikwaama¢ FEWKEs] HANO CLANS Teniik or Pine clan ee ee ee Men and boys Women and girls Nato Kala Tae Katcinamana Lelo Naici Polialla Selapi Yodot Kele Pobitca Akantei Pobinella Tabomana Tope Koitswaiasi Altei Potei Yeba Urpobi Kuta Peta Paoba Ee Tolo Hokona Sapele eee 2 * | 7 Kele? Tabomana 2 Urpobi Peta? Pobinellag Akantci 2 | | | | Koitswaiasi 2 Paoba #7 Alteig Topey Ee? Yebas 2 * | Lelog Pobitcagy Kala? a | P Katcinamana 9 Naici? Poliallay Selapi? Natog Hokona ? Tolo? | Kurtag Sapele? Ea! g 620 TUSAYAN MIGRATION TRADITIONS [ETH. ANN. 19 Nai or Sand clan Men and boys Women and girls Poneauwi Pocilopobi Pocine | Talabensi Talaiumtiwa Kae Galakwai Avatca Kainali Aupobi Ku'wanhiptiwa Hermiumsi Tetokya Koatei Sia 2 * 1 | | Poncauwi? Pocilopobi 9 Pocineg? Sia? Talaiumtiwad Koatei? Talabensi 9 Avatea ? KaeQ | | Kurwanhiptiwad Tetokyad Hermiumsi ? | | Kainali¢ Aupobi? Galakwaidg Katcina clan Men and boys Women and girls Kwebehoya Taci Oyi Avaiyo Wehe Sibentima Tawihonima Tcuayauma Koloa Mali Okun Pintcena Kawaio Ku'yapi Su'tapki Kotcamu ) ! Nokontce Orkotce Kwenka Poteauwt Pen Pen Sawiyt Niiva Teao Awe Kalatean | Pobitcan Po'tza Yowailo Teanwi Keselo Paupobi FEWKES] HANO CLANS 621 Wehe? Sibentima? Tawihonima? Nokontee 2 | | Kwebehoyag Taci? Portza io) Pobitean 2 Kalatcan ¢ | | Kawaio? Kuryapi? Orkun? Pintcena gt Orkotee ¢ Oyi¢ Niiva 2 Avaiyo? Pen 2 Kwenka 2 Poteauwt 2 ed hd | a | | | | Koloag Mali¢ Teao? Surtapkig Awe? Tenayauma @ Peng Koteamug Sawiyt 2 Yowailog Teanwi? Keselo? Paupobi 2 7 Okuwan or Cloud clan Men and boys | Women and girls Kalakwai Kalai Tectia Wiwela! Yate Kelan Solo Pabe Koktcina Tceikwai Poyi Tukpa* Wati Moto? Peti Pemelle Sunitiwa Tazu* Polikwabi® Yowaan Sikyumka Saiya Kwentce Talitce Asou Yekwi Teéeé Suhub. Keko* Pobiteawtt Tawamana mana 1 Lives at Shufopovi. 2 Lives at Walpi. 3 Lives at Sichumoyi. 622 TUSAYAN MIGRATION TRADITIONS (ETH. ANN. 19 \ Kalakwai¢t Peti¢ Teeikwaig Talitce 2 Pobiteawt § Pemelleg Kalait Pabe? Kwentece 2 | | Tetiad Sikyumka ? Wiwelat 2 * i * Yowaan 9 ~ KekoQ Teé Asou ? TawamanaQ Suhubmana 9 | | ee sacl | Tazug Polikwabi¢ Suiitiwat | Solo? Yaneg Totals of Hano clans Sa towae sjcccoc.c6 oc soccc ceetecit cs seine cle ceeisee se see eee as emeeretmeceleceras 15 Krolon to wate oes Ree oe Se v nese en re ee Sr te te ee a eis Ce re Ae eee 25 Kis owas aoc cad a een win Sia lve cere Steet ane ate eho ee eee ara eet arene 14 U V=) Vol e700: eee een Oe vie) Se ee eo ae tee Get ee ae SBA AS Sea Sct 26 DS Foe Pan: Ee a ee en ee ate ea AS eee Sam SI 5G AO a COC aca 15 Katee stow air 2c ie oi occ eis Sea eS lee ee ee teen 32 Okuwafl ‘towaic oc aac te ronnie ee eee oneness © SOE eee ae eee eee a eeeeeee = 31 Doubtful. 2.2222 sce 2 eee oe Seale cits se eee eee Slee Se eee ieee ine 1 fo): ei een ee Ste es Se niente FAO Sa SO SSSR oS 159 RELIGIOUS SOCIETIES AT WALPI The personnel of the Walpi religious societies, so far as known, is given in the accompanying lists, which may be regarded as fairly com- plete for the male but only approximate for the female member- ship. Asa rule, the women members of a society may be said to be the members of the clan which introduced it, and some others. It FEWKES] RELIGIOUS SOCIETIES OF WALPI 623 is not necessary to mention the names of the participants in the katcina dances, as the organization may be said to include all the men and the older boys of the pueblo. So also the names of those who participate in the Soyalufia, or Winter-solstice gathering, are not given, for, from the nature of the festival, it includes all the families in the village. The following list includes the main religious societies in Walpi:! From Tokonabi NewibwimpkKide--- sees ee see Ala clans. eRG UNI Ki ey ae ee ee Tectia clans. From Palatkwabi and the Little Colorado pueblos (Kewalkeyran tiie er ose ee ee Patki clans. LAIR oN ew Sa oes Ss oseee eee Patki clans. ATLL GE oe apse ewe aim deed eS Patun clans. Watabisteniblet os. Soa. ase Patufi clans. eRe tau key 2 ee eee ee Piba clans. Mam Zrau tiles eer se Patun clans. @akwalleiiy astra. = aac ss Lefiya clans. Macilenvy aie ter aoe ee = see Lenya clans. From an Eastern pueblo, Kwavanompi (derived from Zuni?) Kalektakaera- eas scene scene ae Pakab clan. The Katcina society, which includes all males, practices the katcina cultus, and while each performance has its own derivation, all came from eastern pueblos. In order to show whence it came to Walpi each masked personage should be mentioned in order.” Katcina altarsof Powamti and Niman--.Kateina clans -.___-- Kicuba. HOtOtO See eee sasa-< cece aces ae Kokop clans -.------ Jemez. Sio Humis (Zuni) and Humis-_._____- Jemez clans?.......- Jemez. Calakon(Sioror7un) ese =) see eee Honani clans-.-___-- Zuni. Teakwaina (Natacka) .-...........-- PASE CLAN See mae =e se Zuni. RSIUG), See aeisies dA ae eh pe RRR ee 5 os Zuni. MACRO ME e oe eta Sata oe = ni TS eae ee Oe wi ocincecisn Navaho. WAG) fenbe at aah 5 anos eee ees BSCS Se Sao See wee Zuni. DERE je NS yl a i, Zuni. JAY eR Sb 0 3585 SSO Cee RI eEe nes Hos Soda ee aaa Zuni. SOM OMIM seer a8 lo eee eerie seaSe ees ce Several eastern pueblos. Sawyers ort cy Ee OR FR, ous he. St Keres pueblo?. IKON ONIN Owss eee see cra-t 3S ke ree Rar = SNV190 4O NOILNEIYLSIG SNIMOHS ONVH 4O NY¥1d OD WHOM Cit = {Omo ws ay — B | : Ed AXX “1d LYOd3Y¥ TVANNY HLNSSLANIN ADOTONHLS NYDIXYSWY JO NvY3YNSs MINDELEFF] INDIVIDUAL MIGRATIONS 647 clans are said to ** belong together.” In the olden days each phratry occupied its own quarters in the village, its own cluster or row, as the case might be, and while the custom is now much broken down, just how far it has ceased to exercise its influence is yet to be determined. In the pueblo social system descent and inheritance are in the female line. This custom is widely distributed among the tribes of mankind all over the world and has an obvious basis. Among the Pueblos it works in a peculiar manner. Under the old rule, when a man marries, not having any house of his own, he goes to his wife’s home and is adopted into her clan. The children also belong to the mother and are members of her clan. -In many of the villages at the present day a man may marry any woman who will marry him, but in former times marriage within the clan, and sometimes within the phratry, was rig- idly prohibited. Thus it happened that a clan in which there were many girls would grow and increase in importance, while one in which the children were all boys would become extinct. There was thus a constant ebb and flow of population within each clan and consequently in the home or houses of each clan. The clans themselves were not fixed units; new ones were born and old ones died, as children of one sex or the other predominated. The creation of clans was a continuous process. Thus, in the Corn clan of Tusayan, under favorable conditions there grew up subclans claiming connection with the root, stem, leaves, blossom, pollen, ete. In time the relations of clans and subclans became extremely complex; hence the aggrega- tion into larger units or phratries. The clan isa great artificial family, and when it comprises many girls it must necessarily grow. Such is also the case with the individual family, for as the men who are adopted into it by marriage take up their quarters in the family home and children are born to them more space is required. But additional rooms, which are still the family property, must be built in the family quarter, and by a long-established rule they must be built adjoining and connected with those already occupied. Therefore in each village there are constant changes in the plan; new rooms are added here, old rooms abandoned there. It is in miniature a duplication of the pro- cess previously sketched as due to the use of outlying shelters. It is not unusual to find in an inhabited village a number of rooms under construction, while within a few steps or perhaps in the same row there are rooms vacant and going to decay. Many visitors to Tusayan, noticing such vacant and abandoned rooms, have stated that the popu- lation was diminishing, but the inference was not sound. On the other hand, the addition of rooms does not necessarily mean growth in population. New rooms might be added year after year when the population was actually diminishing; such has been the case in a number of the villages. But the way in which rooms are added may suggest something of the conditions of life at the time of building. 648 LOCALIZATION OF TUSAYAN CLANS ELH. ANN.19 The addition of rooms on the ground floor, and the consequent exten- sion of the ground plan of a house cluster, indicates different condi- tions from those which must have prevailed when the village, without extending its bounds, grew more and more compact by the addition of small rooms in the upper stories. The traditions collected from the Hopi by the late A. M. Stephen, part of which have been published,' present a vivid picture of the conditions under which the people lived. The ancestors of the present inhabitants of the villages reached Tusayan in little bands at various times and from various directions. Their migrations occupied yery many years, although there were a few movements in which the people came all together from some distant point. Related clans commonly built together, the newcomers seeking and usually obtaining permission to build with their kindred; thus clusters of rooms were formed, each inhabited by a clan or a phratry. As occupancy continued over long periods, these clusters became more or less joined together, and the lines of division on the ground became more or less obliterated in cases, but the actual division of the people remained the same and the quar- ters were just as much separated and divided to those who knew where the lines fell. But as a rule the separation of the clusters is apparent to everyone; it can nearly always be traced in the ground plans of ruins, and even in the great valley pueblos, which were probably inhabited continuously for several centuries, the principal divisions may still be made out. In the simpler plans the clusters are usually well separated, and the irregularities of the plan indicate with a fair degree of clearness the approximate length of time during which the site was occupied. A plan of this character is reproduced in figure 3, showing a ruin near Moenkapi, a farming settlement of the people of Oraibi situated about 45 miles from that village. There were altogether 21 rooms, disposed in three rows so as to partially inclose three sides of an open space or court. The rows are divided into four distinct clusters, with a single room outside, forming a total of five locations in a village which housed at most twenty-five or thirty persons. The continuity of the wall lines and comparative regularity of the rooms within each cluster, the uniformity in height of the rooms, which, if the débris upon the ground may be accepted as a criterion, was one story, and the general uniformity in the character of the masonry, all suggest that the site was occupied a short time only. This suggestion is aided by the almost complete absence of pottery fragments. It is a safe inference that persons of at least five different clans occupied this site. A plan of interest in connection with the last is that shown in plate xx1, which illustrates the modern village of Moenkapi, occupied only during the summer. Here we have two main clusters and two 1A Study of Pueblo Architecture, in the Kaghth Annual Report of the Bureuwu of Ethnology. SNV1O 4O NOILNSINLSIC DSNIMOHS IAONDNOHSIW 4O Nv7d SMO FELETV 02 = acKON v IAXX “Td LYOd34 TVANNY HLNSSLININ ADOTONHLS NYDIYSWY JO Nv3ayuNnE MINDELEFF] CLAN LOCALIZATION AS SHOWN BY PLANS 649 detached houses, but the clusters are not nearly so regular as in the plan aboye, nor are the wall lines continuous to the same extent. This place is spoken of by the people of Oraibi as of recent establish- ment, but it has certainly been occupied for a much longer period than was the ruin near it. It is apparent from an inspection of the plan that the clusters were formed by the addition of room after room as year by year more people used the place in summer. It will be noticed that the rooms constituting the upper right-hand corner of the larger cluster on the map, while distinct from the other rooms, are still attached to them, while two other rooms in the immediate vicinity Fic. 3—Plan of ruin showing brief occupancy. are wholly detached. This indicates that the cluster was occupied by one clan or by related families, while the detached houses were the homes of other families not related to them. Thus we have in this village, comprising about the same number of rooms as the ruin first described, at least four distinct clans. Detached rooms, such as those shown on these plans, always indi- cate a family or person not connected directly with the rest of the inhabitants, perhaps the representative of some other clan or people. A stranger coming into a village and wishing to build would be required to erect his house on such a separate site. In the village of Sichumoyi (shown in plan in plate xxrv) there are two such detached 650 LOCALIZATION OF TUSAYAN CLANS [BPH. ANN. 19 houses directly in front of the main row. One had been built and was inhabited at the time when the map was made by a white man who made his home there, while the other, which had been abandoned and was falling into ruin, was built some years before by a Navaho who wished to live in the village. The former was subsequently sur- rendered by the white man and occupied by some of the natives. The localization of clans worked both ways. Not only was a member of a clan required to build with his own people, but outsiders were required to build outside of the cluster. The same requirement is illustrated in plate xxi, which shows the plan of Hawikf, one of the ancient ‘*Seven Cities of Cibola,” near the present Zuni. The standing walls which occupy the southeastern corner of the ruin are the remains of an adobe church, while the build- ings which stood near and to the north of it, now marked only by lines of débris, were the mission buildings and offices connected with the church. They are pointed out as such by the natives of Zuni to-day. All these buildings were set apart und were distinct from the village proper, which occupied the crest of the hill, while the buildings mentioned were on the flat below. This was the first discovered city of Cibola,! the first pueblo village seen by the friar Niza in 1539, and the first village stormed by Coro- nado and his men in 1540. It was abandoned about 1670 (7) on account of the depredations of the Apache. The plan shows that the site was inhabited for a long time, and that the village grew up by the addition of room after room as space was needed by the people. Notwithstand- ing the fact that no standing walls remain, and that the place was aban- doned over two centuries ago, six or seven house-clusters can still be made out in addition to the buildings erected by or for the monks in the flat below. Dense clustering, such as this, indicates prolonged occu- pancy by a considerable number of people, and probably two centuries at least would be required to produce sucha plan. The long and com- paratively narrow row to the left of the main cluster suggests an addition of much later date than the main portion of the village. The maps of the villages Walpi, Sichumovi, Hano, Mishongnoyi, Shipaulovi, and Oraibi, which are presented herewith, show the dis- tribution of the clans at the time the surveys were made (about 1883). At first glance the clans appear to be located with the utmost irregularity and apparently without system, but a closer study shows that notwith- standing the centuries which have elapsed since the period covered by the old traditions of the arrival of clans* the latter are in a measure corroborated by the maps. It is also apparent that notwithstanding the breakdown of the old system, whereby related peoples were required to build together, traces of it can still be seen. It is a matter of regret 1See Hodge, First Discovered City of Cibola, in American Anthropologist, yii1, April, 1895 2 These traditions are given in detail in the preceding paper.—Eb. BUREAU OF AMERICAN ETHNOLOGY NINETEENTH ANNUAL REPORT PL. XXVII A. KOEN i CO. BALTIMORE . PLAN OF SHIPAULOV] SHOWING DISTRIBUTION OF CLANS MINDELEFF] that the data are incomplete. The accompanying table shows the dis- tribution of the families within the villages at the time of the surveys, but some of the clans represented, which do not appear in the tradi- tions collected, are necessarily given as standing alone or belonging to unknown phratries, as their phratral relations were not deter- The clustering of houses was a requirement of the phratry mined. rather than of the clan. CLAN DISTRIBUTION IN TUSA YAN Beane CS clomm nicl wins nisi , Rope families -.......-.--.- |spiaer fares ee se =~ = jSnake families -........-.-- \Cactus families...........-. Horn families ...-- +Plute families ...-...-.-..-- | Firewood femiliesse.— =... Hawk families.........-.... ee LheeMbl eee Ss eeneceearoc Katcina families ........... , Paroquet families {Cottonwood families PAIR AT AINTH Se tetra Sens co aac Badger families ..-. Water (Corn) families. ..__. Water (Cloud) families. -... Reedifamilies).....--..---.: Lizard families ) Rabbit families............. Sand families Tobaeco famili Sivwap (Shrub) families. -.. Coyote families. -.-....:.---- Oywilkfamiliess ences. cece... - Red Ant families...........- | BOWMAMIUIES) 2. see === 5 Squash familie Snovwitamiltesi 2 oo. 1-22 --- Batkimitamiiess osc -2- sss. j) Mothitamilies<.......------- Grane'families-.- <<... .2-.5:- Meseal-cake families Distribution of families : el & Z B. = SI S| 3 = A 3 se z = S S = a | & 3 Ei 6 = | | =a Mates cd| Gas eect 6 9 | 6 5 6 peeeeerel Hanan rl aama tan yl eee eal Beso 5 SH emcee | teniseceel eetceer] boceaaaA 2 3 i ee |e ye eee | ee 6 De |) tee olteee sce eee |) eee ee Bae eee 1 5 Rae sanea looseness enactod nocso<5rl bosoanee 5 PAT pe eseccd paos= ene meesesed Goce lsooncosd| 2 ES otace hesoeece! beisSesed | BP eoopdarse sconcnor 3 1 | Soe 8 heal Bete ieee 6 23 al 1 2 1 15 9 29 gears |e cel oceeoee Dic rersces 1 3 Py Nieecessul-sossans A Ne ctincasce 1 5 11 3 3 3 9 0 Beeeaital aeeernee Gcececee 13 Che ereeen | 80 |e 13 24 fey Sees { 5h te seeees 9 19 s 3 6 | 4 tad | Soeci oa 22 (Wi Beeossq Onaccoda beqeacte meadeboce 31 1 4 De eserets Weeeeee 20 3 1 Bee PScpetodl .acerers| sae eectss 11 15 it? | eaeee 8 9 | 1 it] DA aera ak (ee ee Lene 4 D6 len eS || Pern eee eneaa |e eee estan S 2 2 | Sse 2 ile ||eers 17 22 Oe Be res Gesell sane ha eee 9 abl 9 jl eceeee se tetcoe| |aoeere| cease Meee v eis |e coceeks oe (acest se Recent | Pao 4 4 4 1 Wea ae Ue A ecicesce) Menenasel eseeae 1 2 ores |seenec. |Sseerce|E BA tae Gees es: 1 1 Rerere ee [ote Scike ot [ Soc epen: S| Oe el 1 1 Yaullen me 35 58 22 149 340 The determination of the clans shown on the maps was made by the late A. M. Stephen, whose qualifications for the work were exceptional. Doubtless there are some errors in it, for it is a difficult matter to 652 LOCALIZATION OF TUSAYAN CLANS (ETH. ANN. 19 determine the relationships of nearly 400 families, and the work was brought to an end before it was entirely finished. But the maps illustrate a phase of life of the village builders which has not hereto- fore attracted attention, and which has had a very important effect on the architecture of the people. Through the operation of the old custom of localizing clans, although it is now not rigidly adhered to as formerly, the plans of all the villages have been modified. The maps here presented show them as they were in 1883, but ina few cases known to the writer the changes up to 1888 are shown by dotted lines. If now or in the future new surveys of the villages be made and the clans be relocated, a mass of data will be obtained which will throw much light on some of the conditions of pueblo life, and especially on the social conditions which have exercised an important influence on pueblo architecture. The table showing the distribution of families in the villages presents also the number of families. The most numerous were the Water people, comprising in various clans no fewer than 121 families, or over a third of the total number. These were among the last people to arrive in Tusayan and they are well distributed throughout the yil- lages. It will be noticed, also, that while a scattering of clans through- out the villages was the rule, some of them, generally the older ones, were confined to one village or were concentrated in one village with perhaps one or two families in others. The Snow people were found only in Walpi, but these may be properly Water people and of recent origin. The Snake people were represented by 5 families in Walpi and 1 in Oraibi, although they were among the first to arrive in Tusayan, and for a long time exercised proprietary rights over the entire region and dictated to each incoming clan where it should locate. The largest clan of all, the Reed clan, was represented by 6 families in Walpi and 25 in Oraibi, a total of 31 families, or, by applying the general average of persons to a family, by 155 persons. In Oraibi, the largest vil- lage, there were 21 distinct clans, although 7 of them were represented by only 1 family each. In Shipaulovi, the smallest village, there were 20 families of 2 clans, and three-fourths of the inhabitants belonged to one of them. In addition there is one family of the Water people, and in fact in each of the villages one or more clans is represented by one family only. It will be noticed that in Shipaulovi the two clans were still well separated and occupied distinct quarters, although the houses of the village were continuous. The scattered appearance of the clans on the maps is more apparent than real. It is unfortunate that the phratral relations of the clans could not be completely determined, and it is probable that were this done the clans would be found to be well grouped even now. Even the insufficient data that we have appear to show a tendency on the part of the clans to form into groups at the present day, notwithstand- ADOTONHLS NVOINYSWY JO NVaHNns WAYY "Id |HOday IWOANNV HLNSSLSNIN SNV10 SO NOILNEIYLSIG DSNIMOHS Islv¥O 40 NV1d SNV19D 4O NOILNSINLSIG DSNIMOHS Islv¥uO 4O NVJd WAXX “Id LYOdSY IWANNVY HIN33L3NIN ADOIONHLA NwOldaWv JO nvayng MINDELEFF] DESIRABILITY OF NEW SURVEY 653 ing the partial disintegration of the old system. At the present time the house of the priestess of the clan is considered the home of that clan, and she has much to say about proposed marriages and other social functions. There is no doubt that in ancient times the localiza- tion of clans was rigidly enforced, as much by circumstances as by rule, and the ground plans of all the ruins were formed by it. As has been before suggested, a resurvey of the villages of Tusayan and a relocation of the clans, after an interval of some years, would probably develop data of the greatest value to the student of pueblo architecture, when compared with the plans here presented. MOUNDS IN NORTHERN HONDURAS BY THOMAS GANN CONTENTS Tmtroductton ee wse cee scien ates asc acne ocee (sce ee mse seinecisiectiinjascoes Dist ULODPO Mune Nn OUNGS) series soem = oe oe rare ae eee eee see ee nacre Charactenisticsrotmmoundileme = 22a... scescc meee cee cece peewee ee neer eons Paimtingsioniunenvallsiwithimem ound)! ose see eee eas aes cess = Historical data gained by study of mound 1-.--.-.---.--------------------- The builders of the mound-buried temple -.....------.....-----.------- the destroyers ofthe mound-buried temple=-- <= - 2-5. 20ss354 > naa (WK ey LiL PTlellolel Te rel [EJE= = ai Soe > 0-09 = ~ TH BYANOENES CO, BALTIMORE MO. ' RITA PAINTED STUCCO ON WEST WALL, MOUND 1, SANTA we GANN] GLYPHS IN THE PAINTINGS 671 codices. The lower part of the glyph placed immediately above the head of figure 6, plate Xxrx, is a typical representation of Imix, the first day of the Maya month; and possibly the upper part of the glyph placed in front of the face of figure 9, plate Xxrx, is meant to repre- sent the same day. In the first case there can be no doubt as to the identity of the symbol, for all its characteristic features are present, namely, the black spot at the top, the semicircle of dots below, and below this again the row of perpendicular lines. The second symbol is not by any means so typical. A small circle takes the place of the black spot, the dots are wanting, and the perpendicular lines are hooked at their summits; nor does it seem possible that in the same painting such wide variation should occur. The outer and upper of the three component parts of the glyph opposite figure 6, plate xxrx, may possibly be meant to represent Akbal, the third day of the Maya month, though it bears a strong resemblance to the Ahau sign. The lower right-hand part of the glyph opposite the left foot of figure 8, plate xx1x, evidently corresponds to the lower part of the glyph opposite the face of figure 9, plate xx1x; there can be little doubt that both these symbols represent Manik, the seventh day of the Maya month. In dealing with this symbol in his Day Symbols of the Maya Year,’ Professor Cyrus Thomas says: As Brasseur de Bourbourg has suggested, this [i. e., the Manik symbol] appears to have been taken from the partially closed hand, where the points of the fingers are brought round close to the tip of the thumb. Whether intended to show the palm or back outward is uncertain, though apparently the latter. ... As this inter- pretation of the symbol is quite different from that given by other writers, some evi- dence to justify it is presented here. It will be observed that immediately below the Manik symbol, in front of the face of figure 9, plate xx1x, there is represented a right hand with the fingers flexed toward the tip of the thumb, the back of the hand being outward; the outline of this hand is almost pre- cisely similar to that of the Manik symbol placed immediately aboye it, thus confirming, I think, beyond question, Professor Thomas’s inter- pretation of the signification of the symbol, both as to the fact of its representing the human hand and as to the position in which the hand was held. The lower right-hand part of the glyph placed above figure 4, plate xxrx, bears a strong resemblance to the symbol used in the Troano codex to represent Cauac, the 19th day of the Maya month. The upper right-hand division of the glyph placed in front of the head of figure 8, plate xxx, is remarkably like the symbol used in the codices for Ben, the 13th day of the Maya month; the chief difference between the two is that in the codices the line which divides the glyph in two parts is horizontal, whereas in the painting it 1Cyrus Thomas, Day Symbols of the Maya Year; Washington, 1897, p. 232. 672 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 is vertical. Immediately behind the head of the individual portrayed in figure 5, plate xxrx, will be observed a gylph made up of five com- ponent parts, two above and three below. The upper left-hand division and the lower central division unquestionably form together the Maya symbol for the cardinal point east, named ‘‘likin’”—the lower division standing for ‘‘kin,” day, and the upper or Ahau symbol for **li,” the consonant element of which is ‘*].” This is the generally accepted interpretation of the symbol, but in the present case it can hardly hold good, for above the Ahau symbol are two bars and three dots, which stand for 13 (each bar representing 5, and each dot 1), showing that the Ahau symbol, though combined with the kin symbol, is not, at least here, used phonetically, but is employed simply to represent the last day of the Maya month. Turning again to the figures themselves we can not help being struck with their remarkable resemblance to those of Yucatan and south- eastern Mexico on the one hand, and to those found in the ruined cities of Guatemala‘and Honduras on the other. The most striking points of general resemblance are the similarity in shape and fashion of the headdresses, sandals, wrist and leg ornaments, the conventional treatment to be observed in all the human figures, and the fact that all are shown in profile. In the receding forehead, hooked nose, and somewhat prominent chin, which are characteristic of nearly all the figures, they resemble perhaps more closely the bas-reliefs of Palenque and Lorillard City than those of Yucatan and Honduras. The vast headdress, composed of jewels and plumes of feathers, decorated in most cases with the head of an animal immediately above the face— employed as a distinctive sign or badge by the upper class—the enormous square or round ear ornaments, with a pendant from the center, the sandals, elaborately decorated from heel to instep, and fastened in front with a gaily-colored bow, the wristlets of beads, also in many cases decorated with bows, the circlets, worn round the legs either just above the knee or just above the ankle, together with the nose and lip ornaments, are all common to Mexico, Yucatan, Guatemala, and Honduras. But besides showing these points of general resemblance, certain of the figures appear, when allowance is made for the differences which would necessarily exist between a bas-relief cut in stone and a paint- ing, to be almost identical with those found elsewhere. These are figures 3, 4, 5, and 8, plate xxx. The resemblance between figure 3, plate xxx, and the left-hand figure in the Temple of the Cross at Palenque has already been adverted to, and this figure bears an equally strong resemblance to a bas-relief in stone from the ruined city of Labphak, in Yucatan.’ In each case the figure is holding elevated in one hand a small object, on which is squatting a dwarf or baby, which is 1 John L, Stephens, Incidents of Travel in Yucatan, vol. 1, p. 164. GANN] BUILDERS OF THE TEMPLE 673 apparently being presented as an offering or sacrifice. The dress of the two figures is very similar. A huge headdress projecting forward for a considerable distance above the face is ornamented with feathers and jewels; a bead-decorated cape and the usual large earrings are worn by both. In the glyph placed above the Labphak figure is seen a cross, and the same symbol is also to be observed in the head- dress. In the glyph placed between figures 3 and 4, plate xxx, the same symbol also appears. The cross is in both cases of the same shape. In figures + and 5, plate xxx, the lower part is unfortunately very much damaged; but if the upper part of the figures be compared with the bas-relief sculpture in the Temple of the Cross at Palenque, it will be seen that the subject is the same. In the center of the pic- ture is a symbolic bird with a long tail and eagle’s talons, standing in the one case on top of a cross, in the other on top of an Ahau symbol, and on each side is a human figure apparently making offer- ines to this bird. Above figure 4 the cross forms a prominent part of the hieroglyph. The resemblance between figure 8, plate xxx, and the bas-relief in stone from Casa 4 at Palenque’ has already been noticed. The huge prominent noses, the toothless jaws and prominent chins, the similar headdresses with the eagles’ heads in front, and especially the feather- decorated serpents twined around the bodies, show, without doubt, that both of these figures are meant to represent the god Quetzalcoatl. On the strength of this evidence, then, I think we may fairly infer: (a) That this building was the work of people of the same nation which built the ruined cities of Yucatan, Gautemala, and Honduras; but that, as their style and method of execution were more like those of the builders of the cities of southeastern Mexico, they were probably more closely allied to, and more nearly contemporaneous with, them than with the builders of the other cities. (>) That in the absence of all other evidence the hieroglyphics would alone prove that the building was the work of a branch of the Maya Toltec nation. THe DrsTROYERS OF THE MouND-COVERED TEMPLE We can pass now to the second question, namely, by whom, and why, was the building destroyed and the mound erected over it? In certain other mounds at Santa Rita, immediately to be described, there were found, buried superficially in each mound, the fragments of two pottery images, and more deeply a number of small painted pottery animals, the latter either inside of or immediately adjacent to large pottery urns. The similarity between these clay figures and 1 John L. Stephens, Incidents of Travel in Central America, vol. 11, p. 353. 674 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 those painted upon the temple wall is very marked. The same con- ventional treatment is to be observed in both. The huge head, the small body and limbs, the elaborate headdress, the large round ear- rings, and highly ornate sandals are the same; and in two of the clay images, figures 1 and 3, plate xxxi1, monstrous heads similar to those worn by the figures on the stucco are worn as ornaments in front of the headdresses. Figure 2, plate xxxiv, represents the lower part of the face of one of these clay idols. If it be compared with the head of fig- ure 1, plate xxx1, and with the head held in the left hand of figure 3, plate xxx1, both from the wall, it will be seen that the beard and mus- tache are treated in the same conventional manner in each, In figure 1, plate xxx1u1, the curious ornament below the left eye of the face in the idol’s headdress is the same as that below the eye of figure 8, plate xxx. Again, the ornament held in the hand of figure 1, plate xxx, is precisely similar to one dug up with figure 2, plate xxxu. These instances of correspondence in detail are very numerous, but enough has been cited to show that it is impossible to look upon the resemblance between the clay figures and the painted stucco as fortuitous. We must, on the contrary, regard them as the work of the same people. It is of interest to note here that the monster’s face which decorates the headdress of figure 3, plate xxxu, is the counterpart of a face found at Quirigua, and described at some length by Mr Diesseldorf.* There is also a close resemblance in coloring, ornamentation, and gen- eral style between the painted stucco and the painted pottery animals. The same colors are used and the same fine black lines are employed for outlining in each case. If figures 3, 4, and 7, of plate xxxty, be compared with the snakes’ heads seen to the right of figure 8, plate xxx, and with the snake’s head below figure 9, plate xxrx, it will be seen that exactly the same ornament is placed both above and below the eye in each case. The central part of mound 2, from which some of these animals came, was constructed almost entirely of large blocks of lime- stone, and on some of these, which were squared, traces of painted stucco were still visible, similar to that found on some of the stones which formed the mound around the painted wall and no doubt hay- ing the same origin, i. e., the broken down south wall of the building. Mound 2 had also been erected over a building, and it was on its floor that the umm and animals had been placed when the top was added to the mound. Furthermore, if the painted walls of the temple had been wantonly destroyed by an enemy, or by some barbarous tribe coming down from the north, the destruction would have been complete; nor would they have taken such care, as we have seen was taken, to preserve the greater part of the painting by erecting a mound around it. 1See Aus den Verhandlungen der Berliner Anthropologischen Gesellschaft. Ordentliche Sitzung vom 2lten Dec., 1895. GANN] DESTROYERS OF THE TEMPLE 675 We may therefore, [ think, safely conclude that the builders of the temple or their descendants were also its destroyers, though their method of destruction—paradoxical as it sounds—preserved it for pos- terity probably better than any contrivance which they could have employed for its permanent preservation. As to the reason for this partial destruction and burial of the tem- ple, we know that the Maya regarded the five intercalary days at the end of each year as unlucky and ill-omened, and that during them they were in the habit of destroying their household pottery utensils, together with some of their small household gods, which were renewed again for the new year. Furthermore, they intercalated twelve and one-half days at the end of every cycle, or period of fifty-two years, which were regarded as especially ill-omened.* It is not improbable that this painted stucco partially underwent the fate of other images of the gods during one of these especially unlucky periods at the end of the cycle;* for, as I have pointed out, the stucco had evidently been renewed twice, as two layers were found beneath the most superficial one. These obliterations and renewals may have taken place periodically as the unlucky periods came round and passed, till finally the period came when the temple was itself destroyed in the manner already described. While searching for mounds in the bush about 15 miles north of Santa Rita I came across a large inclosure, the walls of which were 4 feet thick, and, though much broken down, had been about 6 feet in height. The inclosure was in the form of a parallelogram, three- quarters of a mile long by half a mile broad. Within it were the ruins of a church, in very fair preservation, the chancel, with the exception of its roof, being quite perfect. This had evidently been a fortified inclosure built by the Spaniards, and, from the fact that it was so near to Bacalar, which was one of their earliest settlements in Yucatan, and that all record of it has been lost, it was probably erected not very long after the conquest. It may be that the wor- shipers at the Santa Rita temple, finding themselves in such close proximity to a fortified Spanish settlement, and knowing that the conquerors took every means in their power to propagate the new and eradicate the old religion, as a last resort employed this method of preserving at least a portion of the sanctuary of their god from the sacrilegious hands of the invaders. Either of the foregoing explana- tions would account for the manner in which the temple had been at the same time destroyed and preserved. 1See Antonio Gama, Descripcion, parte 1, p.52 et seq. Dr Cyrus Thomas denies any intercalation beyond the annual one, and his proof certainly appears convincing. See Cyrus Thomas, The Maya Year, p. 48. 2**As soon as they were assured by the new fire that a new century, according to their belief, was granted to them by the gods, they employed the thirteen following days . . . in repairing their tem- ples and houses and in making every preparation for the grand festivals of the new century.’’- Francisco Clayigero, History of Mexico, book 6, sec. XXVI. 676 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 . PrRoBABLE DATE OF THE BUILDING OF THE TEMPLE Let us turn to the probable age of the temple. We know on the authority of Veytia and Ixtlilxochitl, probably the most reliable of the historians who chronicle the dim and uncertain early history of the Toltec, that the remnant of that nation after pestilence and dis- astrous wars had decimated them, migrating from: Tula, found their way, some to southern Mexico, where they founded Palenque and Lorillard, others farther south still to Guatemala and Honduras, while others turned eastward into Yucatan.’ This migration took place somewhere about the end of the eleventh century.” A long period must haye been necessary for the scattered remnant of the Toltee to have made this long journey of nearly 1,000 miles, before reaching the shores of the Caribbean sea, on foot, crossing rivers, swamps, and mountains, and encountering everywhere a barrier of dense and impenetrable bush. Probably a century would be rather under than over the mark in estimating the time necessary for this emigration and for the people to have become sufliciently settled in their new home to erect an elaborately decorated temple. This would place the date of the erection of the temple somewhere between the end of the twelfth and the end of the fifteenth century; but if, as I before suggested, the painted stucco was renewed only at the end of every cycle of fifty-two years, and the burial of the temple was caused by the fear of Spanish invasion, then, as there were two layers beneath the outermost layer of stucco, the temple must have been atdeast 104 years old at the time of its destruction; and judging from the bright- ness of coloring and excellent preservation of those parts of the paint- ing spared by the dampness, the outer layer could not have been applied for any great length of time when the mound was erected which preserved it to the present day—which would place the date of the erection of the temple toward the end of the fourteenth or begin- ning of the fifteenth century. The general design painted on the stucco appears to be continu- ous around the building, and to represent, first, a battle; next, the prisoners being led captive, some undergoing torture; finally, the worship of Quetzalcoatl and the offering of sacrifices to the god of death. On the east wall was depicted a spirited contest between two warriors, though the tracing in this case gives but a poor idea of the original. The first eight figures of the east half of the north wall evidently represent prisoners. The west half of the north wall shows the worship of Quetzalcoatl, the god himself being depicted at the western extremity of the wall elaborately dressed and ornamented. 1 Francisco Clavigero, History of Mexico, vol. 1, book 2, p. 89. 2Ixtlilxochitl, Historia Chichemeca, cap.3. Veytia, Hist. Antiqua, vol. I, cap. 33. GANS] MOUNDS 3 AND 4 6770 On the west wall two heads and other objects are being offered to the Mexican god of death. Figure 3, on the west wall, offering the heads—one in each hand— is obviously one of the victors; but there appears to be little or no difference between his appearance, dress, and ornamentation and that of the prisoners shown in figures 1 to 8, plate xxrx, which would apparently indicate that the combatants were, if not of the same, at least of kindred nations. OTHER MOUND-BURIED STRUCTURES Two other mounds at Santa Rita were erected over the ruins of buildings, namely, those marked 3 and 4 in the plan, figure 4. Mound 8 was situated 115 yards southeast of the painted wall, was almost circular at the base, pyramidal in shape, 62 yards in cireumfer- ence, and 10 feet high at its highest point. By digging into this mound a wall running north and south was found about 2 feet below the surface. This wall, when exposed in its whole extent, was found to be 18 feet long, 16 inches thick, and built of roughly squared blocks of limestone held together by mortar, which was rotten and crumbling. The summit of the wall was irregular and varied in height from 4 to 7 feet; it extended to the ground level and stood upon a floor of hard cement. At its south end this wall was broken off short; at its north end it joined a wall running east and west, but this latter extended only 2 or 3 feet, and was then broken down. Neither inside nor out- side were any traces of painted stucco to be found on either of these walls, nor, in the excavation of the mound, which was built of earth, limestone dust, and rough blocks of stone, were any stones found with traces of stucco adherent to them. There was no cornice on the wall. Numerous pieces of pottery were found in the mound, some rough and ill made, others painted red, black, yellow, and brown, and a few glazed. Mound 4 was 86 yards in circumference, oval at the base, conical in shape, and 6 feet high at its highest point. Immediately beneath the surface a wall was found running east and west. It was very similar to the wall last described, being built of blocks of roughly squared lime- stone. it varied in height from 4 to 6 feet, rested on a floor of hard cement similar to that found in the last mound, was not covered with stucco either inside or out, and had been broken off short at both ends. The mound itself was composed of earth, limestone dust, and rough blocks of limestone. Numerous potsherds were found within it, both plain and painted. It was situated 195 yards almost due north of mound 3. The two last-described ruins differed from the one covered with stucco in that they rested on the ground level, whereas the latter stood on a platform raised 2 feet above it. 19 ETH, Pr 2 8 678 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 MOUNDS CONTAINING POTTERY, IDOLS, AND ANIMAL EFFIGIES Mounds of the second class, namely, those containing, superficially, the fragments of two pottery idols, and more deeply or on the ground level a number of small painted pottery animals, either within or immediately around a pottery urn, next claim our attention. Three mounds of this kind were excavated at Santa Rita—2, 5, and 6 on the plan. Mound 2 was situated nearly 500 yards east of the large central mound; it was 30 yards long, 25 yards wide, 96 yards in circumference, and 18 feet high at its highest part. The north- ern face of the mound sloped gently down from the summit to Fic. 6—Plan of mound 2, Santa Rita. A, B, Pillars. G, K, Walls. E, Place where birds’ bones were found. N, Circular chamber. D Place where idols were found. F, Place where cabbage-palm was found. C, Place where painteé animals were found. the base; the southern face was almost perpendicular. When the upper layer of the mound was removed it was found to consist of dark-brown loam with a few pieces of limestone embedded in it. At the bottom of this layer and resting on the one immediately beneath it were found fragments of two idols and a quantity of birds’ bones, together with the inferior maxilla of a small rodent. The head of one of these idols (supposed by Mr Diesseldorf to be the conventional portrait of Cuculean) is shown in figure 3, plate xxxm. The remarkable VLlIld VINVS 9 ONV § ‘@ SGNNOW WOYS S10d! 40 Sdav3H GANN] MOUND 2 679 resemblance of the head which adorns its headdress to one found at Quirigua has already been noted. The rest of this idol and the whole of the one which was found with it are so badly broken as not to be worth figuring. The bones were those of the curassow, and, judging by the number of long leg bones which were found in good preserva- tion, probably represented the remains of five or six birds. The bones were found at a point marked E on the plan of the mound (figure 6), close to the idols. With the idols were found a number of rough unpainted potsherds. Immediately beneath the loam the mound was covered with a flat, evenly applied layer of mortar, from 6 to 8 inches in thickness; it was soft and friable and contained in its substance numer- ous large pieces of limestone. The next layer was composed of lime- stone blocks, the interstices between which were filled with limestone dust. A large number of the stones were squared, and some retained pieces of painted stucco still adherent to them, haying evidently at one time formed part of the south wall of the temple already described. Embedded in the top of this layer, at the point marked F in the plan, was found a piece of cabbage-palm stem 5 feet long, but so wormeaten and decayed that it was impossible to tell what its original use had been. Within this layer the broken tops of two square pillars, A and B in the plan, and of two walls, G and K, on either side of them, first appeared. These two pillars oecupied a nearly central position in the mound; they were 3 feet square and were built of large blocks of nicely cut stone. The summits were uneven and had evidently been broken off; the distance between the pillars was 6 feet. The walls were in line with the pillars, placed on either side of them, at a distance of 6 feet from each; they were 3 feet thick, built of nicely squared blocks of limestone, and were broken off at the top and outer ends. The sum- mits of these walls and pillars were at a depth of 24 feet below the surface of the mound; they passed down through the next two layers— one of cement, one of blocks of limestone—and rested on the tough, thick cement layer which lay immediately over the foundation of the mound. They were + feet high and at one time evidently had formed part of the portico of a building with three wide entrances. Judging from the very large proportion of squared stones which were used in the construction of the upper layers of this mound, it would seem that the greater part of the stones of this building had been used in construct- ing the mound which covered its ruins. The next layer was of cement, 6 to 8 inches thick, and spread evenly over the mound, forming a table- like surface; the cement was rotten and friable. The layer immediately beneath this was composed of blocks of limestone, the majority of which were squared, and so tightly were they packed together with limestone dust that the mass was almost as difficult to dig into as if it had been masonry. In the lower part of this layer, 6 feet below the sur- face of the mound, at a point marked C in the plan, the pottery urn, 680 MOUNDS IN NORTHERN HONDURAS [ETH. ANN.19 figure 7), was discovered. This urn was 12 inches in height and 46 inches in circumference at its widest part; it was made of smooth, hard pottery, having a uniform thickness of three-sixteenths of an inch; it was unpainted and unglazed, was without a cover, and con- sequently was full of limestone dust. It rested on the layer of hard cement immediately underlying the layer in which it was buried. This urn, unlike the others, was not inclosed ina stone cyst, and was unfor- tunately much damaged by a blow of the pickax. Placed all around and above the urn, within 2 inches of it, were found 10 small painted pottery animals and two flint spear heads. The animals consisted of Fic. 7—Pottery urns from mounds 2, 5, and 6, Santa Rita. four tigers, five turtles, and one double-headed animal, probably intended to represent an alligator. Two of the animals were placed at each of the four cardinal points around the urn and two above it. The tigers, of which one is represented in figure 6, plate xXxx1v, are 44 inches in height, and are painted red all over. They are represented as sitting up on their hind legs, with their mouths open and tongues protruding. Each animal is hollow and has a small round hole in the center of the back communicating with the interior. One tiger was placed on either side of the urn. All were precisely alike in size and coloring. Of the turtles (see figure 6, plate xxxim, and figure 1, plate XXXV) five were found. One was placed on either side of the urn BUREAU OF AMERICAN ETHNOLOGY NINETEENTH ANNUAL REPORT PL. XXXiIll HUMAN AND ANIMAL EFFIGIES FROM MOUNDS 2, 5, AND 6, SANTA RITA a oad : [ am 1%, Pal, * PNA ree as 4 (Ass ay BUREAU OF AMERICAN ETHNOLOGY NINETEENTH ANNUAL REPORT PL. XXXIV ANIMAL EFFIGIES AND IDOL’S HEAD FROM MOUNDS 2 AND 6, SANTA RITA GANS] CONTENTS OF MOUND 2 681 and one immediately above it. They vary in length from 5$ to 64 inches. The bodies of two of them are colored red throughout, the other three are unpainted. The eyes of all are colored black, the eye- brows light blue outlined in black, and the nose red. At the fore- part of the body on either side are two human hands and arms, the former tightly closed. The mouth is widely open, and from it protrudes a human head, which the animal is apparently in the act of swallowing. The face belonging to this head is colored light blue, the mouth and lips red, and the eyes and eyebrows black (see pists xxxy, 1). In the ears are large round earrings, which, having c: wught in the angle to the turtle’s mouth on either side, are ¢ appar’ enue giving him some difficulty in swallowing the head. The turtles are all hol- low and are perforated in the center of the back by a round hole, 1 inch in diameter, which communicates with the interior. When the animals were found, this hole was covered with a small, pyramidal, earthenware stopper, which in plate XXXII, 6, is seen in situ. The last animal (see plate xxx, 5) is 74 inches in length, and has two heads, one at either end. The specimen shown in the plate was dug up in mound 6, presently to he described, but it is so like the one from mound 2, both in shape and in coloring, that one illustration serves for both. One head is certainly that of an alligator, as is apparent from the huge mouth, formidable teeth, and double row of projections running down the back. Within the widely opened jaws of the animal is seen a human face, the mouth, chin, and forehead of whic h, as well as the inside of the alligator’s mouth, are irregularly smear aa with red paint, evidently meant to represent blood. The body of this dou- ble-headed animal is unpainted, but is covered with small red spots sharply outlined in black. The other head possesses two eves and a snout, together an a single row of large curved teeth running from the snout to the neck. There is no sign of a lower-jaw. Placed on either side of each head is a human hand and arm having the wrists ornamented with a circle of small, round disks of pottery, colored red. The body is hollow, and midway between the two heads, on its dorsal surface, is a small round hole, communic ating with the interior, and covered with a pyramidal stopper, seen in situ in the figure. Within the cavity of the body were found three small oval beads, two of jade and one of some orange-red stone, all nicely polished; a very small obsidian core, 14 ine ches in length and about the thickness of a pencil; and a small flat chip of grayish chert. This animal, together with one of the turtles, was placed above the urn. The two spear- heads are leaf-shape and are 4 and 3 inches in length, respectively. Both are nicely chipped from yellowish flint, the smaller of the two being grooved on either side at the base, probably for greater security in hafting. 682 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 The layer immediately below that which contained these animals was composed of very tough cement and covered the whole mound evenly. It was so hard that even with a pickax it was difficult to make any impression on it. It was 12 inches thick and of a light yellowish color. Upon it rested the two pillars and fragments of walls already referred to, together with the pottery urn. Below this cement layer and reaching to the ground level the mound was built of large blocks of limestone, rough and unhewn, but neatly fitted together without any mortar or earth between them. Not one of these blocks was worked or showed traces of stucco. Extending downward from the cement layer to the ground leyel through this last layer was a small circular cyst at the point marked N on the plan. Its upper opening was covered with a slab, over which the cement was continuous. Its floor was the ground, and its sides, though neatly built, were not plastered. It was 3 feet in diameter and contained nothing but a quantity of charcoal. It seems evident that before this mound was erected there stood on its site a building, of which part of the north wall is now all that remains. This building was erected on a solid stone platform, raised 10 feet above the ground level, and covered with a thick layer of very hard cement. The mound was constructed partly from the stones taken from this building and partly from those of the temple before described. The urn, the painted animals, the idols, and the bones were placed within the mound atthe time the building was destroyed and the upper part of the mound erected over its ruins: the urn and the animals on what had been the floor of the building, the idols and the bones more superficially in the mound. The original stone platform on which the building had stood formed the base of the mound. The second of these animal mounds, 5 on the plan, was situated 345 yards almost due north of the great central mound. It was 52 yards in circumference, oval at the base, conical in shape, and 5 feet high at its highest point. It was built of earth and limestone dust, together with rough blocks of limestone, none of which were squared or showed any traces of stucco adherent to them. Almost in the center of the mound, a little less than 1 foot below the surface, frag- ments of two clay idols were discovered, consisting of arms, legs, and portions of two bodies. The face shown in figure 1, plate xxx, is that of one of the idols. ‘The other head and the remaining pieces are so much damaged that they are not worth figuring. On reaching the ground level, directly in the center of the mound, a small stone cyst or chamber was discovered. It was 18 inches in length, 12 inches in breadth, and 12 inches in height. The floor was the ground; the roof and walls were made of single, roughly hewn, flat slabs of stone. Within this cyst appeared the small pottery urm shown in figure 7c, BUREAU OF AMERICAN ETHNOLOGY NINETEENTH ANNUAL REPORT PL. XXXV ANIMAL EFFIGIES FROM MOUNDS 2 AND 6, SANTA RITA NATURAL SIZE AMOEN CO. BALTIMORE GANN] CONTENTS OF MOUNDS 5 AND 6 683 This urn is 5 inches in height and 274 inches in circumference at its widest part, and is made of unpainted, unglazed pottery, one-eighth inch in thickness throughout. It is covered by a mushroom-shape lid with a small semicircular handle. Unfortunately, in lifting the flat stone which formed the roof of the cyst the point of the pickax was driven through the lid. Within this small urn lay the double- headed alligator shown in figure 1, plate xxxmr. This animal is 8$ inches long from the tip of one snout to the tip of the other. Pro- truding from the widely opened jaws of each of the heads appears a human face. The mouth of each of these faces is decorated with two small circular lip ornaments, one attached to each of its angles, all exactly similar to those seen on the mouth of the idol shown in plate xxx, 2. The faces where they are in contact with the animal’s jaws, and the jaws themselves, are daubed with red paint to represent blood; other parts of the faces and the whole of the body and: the heads of the animal are painted dark green. The third and last mound of this kind, 6 in the plan, was situated 933 yards southwest of the large central mound. It was the smallest of the three, and was circular at the base, conical in shape, 30 feet in diameter, 32 yards in circumference, and 5 feet high at its summit. Nearly 2 feet below the surface, toward the center of the mound, a large quantity of very rude, ill-made pottery was discovered, together with the fragments of two pottery idols. One of these is by far the finest and most perfect found in any of the mounds. It is 164 inches in height from the top of the headdress to the sole of the sandal, and is shown in figure 2, plate xxxm. ‘The left arm was also found, but has not been joined on in the figure. The pieces were not all together, but were spread about over an area of two square yards. The other idol was so fragmentary that it was not worth figuring; but the lower half of the face, as it differed from all the rest in possess- ing a beard and mustache, is shown in figure 2, plate xxxrv. Two small, oval, clay beads were found with the idols. This mound was composed throughout of earth and large, rough blocks of limestone. Within 50 yards of it is an excavation of some size, from which the material to construct it was probably obtained. When the ground level was reached a small stone cyst built of roughly hewn slabs appeared. It was 2 feet long, 2 feet broad, and 18 inches high. When the stone slab which formed the roof was removed the urn shown in figure 7¢@ was found. This urn was circular in shape, 114 inches high, and 37 inches in circumference at its widest part, and stood on three long, round, hollow legs. It was of unpainted pottery three-sixteenths inch thick throughout, and was coyered by a mush- room-shape lid with a semicircular handle. When the lid was removed 19 small objects were found within the urn, completely filling it. Of these, 13 represent animals, 1 a fish, and + human figures, while 1 is 654 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 a small circular jar, decorated outside with a human figure support- ing itself on its forearms, the legs being held up in the air. Of the animals, + are tigers, 1 of which is shown in plate xxxmr, 4, and in plate xxxvi. Each is 44 inches in height. The body is colored white and covered with red spots encircled with black. The head is red, the ears white, and the eyes black. Each has a collar of small, oblong pieces of pottery colored alternately green, white, and red. The male genital organs are prominently represented, as the animals are sitting up on their hind legs. Each figure is hollow, and is perforated at the back by a small round opening. There are 9 alligator-like animals, 1 of which has already been described, as it is the exact counterpart of the one found in mound 2.‘ Others are shown in figures 3, 4, 5, and 7 of plate xxxrv, and in plate xxxv, 2. Four of the 9 resemble figure 5, and are evidently intended to repre- sent alligators, judging by the shape of the body and legs, the spines on the tail, and the double row of excrescences extending along the center of the head and back. They vary from 54 to 7 inches in length. The bodies of two of them are colored red, and of two, white; the eyes and spines of all are colored black. A black streak passes around the jaws, and the forefeet are divided into three toes by thin black lines. The bodies are all hollow, with a circular opening in the center of the back covered by a pyramidal stopper, seen in situ in the figure. Figures 3 and 4, plate xxxrv, are not unlike the preceding, but they have the curious curyed ornaments before noticed both above and below the eyes. The tails are bifid, and the figures possess a horn-like excrescence attached to the tip of the nose. The double row of tuber- cles extending along the head and back is wanting. Figure 7 and plate xxxVv, 2, differ from figures 3 and 4 in possessing a pair of lateral, fin-like limbs instead of four legs, and figure 7 has a single, triangular dorsal fin placed in the center of the back. The hole communicating with the interior is at the side, to allow for the dorsal fin, and there is no stopper covering it. The bodies of two of the last four animals are red, and of two, white. The ornaments above the eyes are painted light green, out- lined in red. Figure 1, plate xxx1v, is probably intended to represent a shark. The body, which is 7 inches long, was first painted white and afterward red, but most of the paint has worn off. Figure 3, plate XXX, Shows a small round pot, 3 inches in height, to the outside of which is attached a human figure supporting itself on its forearms while its legs are held up in the air above the head. On the head is worn the usual enormous feather-decorated headdress, and around the forehead, wrists, and ankles are bands of small round pottery disks. The face There can be little doubt that this animal, together with its @uplicate, also the double-headed alligator, and the turtles, are all intended to represent the Aztee Cipactli, a mythie animal at times taking the form of a swordfish, a shark, an alligator, and an iguana; it symbolizes the earth, and, as in the above eases, is often represented with a human head between the jaws to signify that all flesh returns to its original earth, and to death, 3ZIS IWYNLVN WLIW VLNVS ‘9 GNNOW WO¥S ADISd3a YadIL IAXXX “Id LYOd3Y¥ IVANNY HLNASLANIN 3ZIS IWYNLYN VLIY VLNVYS ‘9 GNNOW WOYS ADIS43 NVWOH WAXXX “Td LYOd3yY TIWANNY HLN3S3SLININ ADOTONHL3S NYOIYSWY JO Nyauns GANN] SYMBOLISM OF EFFIGIES 685 is colored blue, the mouth red, the eyes white, and the eyebrows black. This ornament of a human figure supporting itself on the forearms while the legs are held above the head is not an uncommon one, as I have two vases similarly ornamented, one found in a mound on the Chetumal bay, the other in a mound near Rio Hondo. It is also seen as a bas-relief on stone over a doorway at Tulum, on the coast of Yucatan, and is scratched on the stucco among a number of other figures at Mount Molony, on the borders of Guatemala and British Honduras. The last of the contents of the urn is shown in figure 2, plate xxxmr. There were four of these figures, all precisely alike. Each is 4 inches in height, and represents a mar in a squatting posi- tion, holding in front of him, with both hands, a veil, which conceals him from forehead to feet. The body is colored white and the arms red. Across the forehead is a red stripe, and the veil is colored with alternate red and white vertical bands. The headdress differs from that usually associated with the ancient inhabitants of Central Amer- ica and reminds one somewhat of representations of the ancient Egyp- tian headdress. No human bones were found associated with any of these animals, and it seems probable, judging from the excellent state of preservation in which the birds’ bones taken from mound 6 were found, that had there been a human interment, some trace of it would have been dis- covered. Mounds 5 and 6 were evidently built for the special purpose of containing the idols, urns, and animals which were found within them. In mound 2, on the other hand, the objects were placed on a preexisting platform which had supported a building, and were covered by a capping of earth and stones, the latter taken mostly from the build- ing. All the animals appear to symbolize death and destructiveness. The tiger, the alligator, and the shark must have been, in the bush, the river, and the sea, respectively, the most destructive animals known to the aboriginal inhabitants; and inthe one exceptional case of the turtle, which might be looked upon as a comparatively harmless animal, it is represented in the act of devouring a human being. A LOOKOUT MOUND Turning to the third class of mounds, we will take first the large cen- tral mound, 7, around which the others appear to be grouped. It is circular at the base, conical in shape, 57 feet in height, 471 feet in circumference, and is built of blocks of limestone held together with mortar. Indeed, so hard is it all over that the idea of excavating it had to be given up. On the south side of this mound, and, continous with it, is a circular earthwork 100 yards in diameter. The walls inclosing the circular space vary from 10 to 25 feet in height. They are higher toward the north, where they are continuous with the large mound, and lower toward the south, where an opening 30 feet wide 686 MOUNDS IN NORTHERN HONDURAS (ETH. ANN. 19 gives access to the inclosure. About 20 yards south of this opening is a small mound 4 or 5 feet in height. In the center of the space, inclosed by the earth walls, stands a small mound 3 feet in height and 40 feet in circumference. Excavations were made in the earth wall, in the space inclosed by it, and in the small mound in the center of the space. Nothing, however, was found except a few pot- sherds such as may be found by digging almost anywhere on the estate. The walls were found to be built of earth and limestone blocks. Immediately to the north of the mound is a huge excavation, from which limestone has been quarried. There can be little doubt that this was the source whence material to build both walls and mound was drawn. This large mound and the inclosed space adjoining probably formed together a lookout station and a fort. The mound itself is one of a series, all of which possess certain characteristics, marking them as lookout or signal mounds. They are all more than 50 feet in height, and have a flat, table-like surface at the top, a compara- tively small base, and consequently very steep sides. They are always surrounded by a number of smaller mounds of various sizes and uses, which probably indicate the site of ancient populous centers; and they are usually, though not invariably, associated with an earthwork fortification, either actually joined to them, as at Santa Rita, or at some little distance away, as at Adventura, the next mound of the kind in the series, which will be described at another time. Such of these mounds as have been opened haye not contained pottery or stone objects, or anything to show that they had been used as sepulchers. As has been proved by experiment, a large fire lighted on the flat sur- face at the top of any one of these mounds can be seen plainly over the intervening bush—the country being perfectly flat—either by the smoke during the day, or by the flame during the night, from the top of the mound on either side of it in the chain. Beginning at the top of Chetumal bay, these mounds extend in a chain for nearly 150 niles, first following the coast line, then trending inland in a south- westerly direction. The intervals between them are in no case greater than 12 miles or less than 6 miles. Each of the mounds forming part of such an extended chain, along which it was easy to convey intelli- gence either by day or by night, standing also in the center of the town or village and adjacent to a fortified position into which the inhabitants could retire, would form a most useful signal station from which to observe and communicate the approach of an enemy, either by sea or land; and there can, I think, be little doubt that this was the use for which they were designed. A SEPULCHER MOUND. At a distance of 691 yards almost due east of the large central mound was situated the mound marked 9 in the plan. This was the only mound exeayated on the whole estate which had unquestionably MYOMHLYVWS HLIM ‘WLIY VLNVS LV (2) GNNOW LNOWOOT WWYLN3O Lvay9d | _—_—_$ $$$ — $$ —————— INAXXX “Id LHOd3Y TIVWANNVY HLN33SLSNIN ASOIONHLS NVOINSWY 40 NV3SYNS GANS] CONTENTS OF MOUND 8 687 been used solely for sepulchral purposes. It was one of the smallest mounds explored, being only 15 yards in circumference and 33 feet in height at its highest point. It was nearly circular at the base and flat on top, and was built of earth and rough blocks of limestone. Nearly in the center of the mound, at the ground level, a human skeleton was discovered, the head pointing toward the north. The bones were so brittle that in the attempt to remove them they were very much damaged. The skull was full of earth, and, while being lifted out, it collapsed into numberless pieces from its own weight and that of the earth which it contained. The fragments of the bones were removed, and, after exposure to the air for a few days, they hardened consider- ably and could be handled without injury to them. The bones were apparently those of a male of from 5 feet 4 inches to 5 feet 6 inches in height. Lying by the side of the skeleton were a conch shell with the apex broken smoothly off, as if it had been used as a trumpet, numerous broken pieces of conch shells, a roughly chipped flint spear- head 43 inches in length, and an oval flint hammer stone. Associated with these two latter implements were four sharp-pointed conical pieces of shell, the ends of which had evidently been ground to a point as if for use as boring implements. They were manufactured from the whorls in the interior of conch shells. The contents of this mound appear so unlike to the contents of the other mounds at Santa Rita that one can not help thinking that it belongs either to a different people or a different period. This supposition is rendered more probable by the fact that along the shores of the Chetumal bay, a few miles from Santa Rita, the sea is rapidly encroaching and expos- ing interments very similar to the one described, except that in most cases no mound marks the position of the grave. The sharp shell implements are invariably to be found in these graves, together with pottery and flint implements, all exceedingly rude and archaic. UNCLASSIFIED MOUNDS Three hundred and ninety yards to the northwest of the large central mound was situated the mound marked 8 in the plan. This mound was roughly circular, flat on the top, 90 yards in circumference, and 5 feet high at its highest part. I was informed by some of the old laborers on the estate that some years previously, while stones were being dug from this mound for the purpose of erecting a tank, a num- ber of what they described as large stone idols had been discovered. Of these [ was, unfortunately, unable to discover the subsequent history; but there can be little doubt that, together with the other stones, they were squared for building purposes. This is rendered more probable by the fact that in examining a well close at hand, which had been built at that time, I discovered a large stone tiger’s head projecting inward from the masonry, into which it had been built. As, however, the whole mound had not been dug down I set to work excavating that 688 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 portion of it which was left. It was composed of earth and blocks of limestone. Ata depth of about 2 feet below the surface were found (1) a large tiger’s head cut in stone; (2) a turtle cut in stone and colored; (8) the lower part of a human mask; (4) a small, smooth, globular piece of jade. Potsherds, both painted and plain, were found in large quantities at all depths throughout the mound. The tiger’s head, which measured 18 inches from the forehead to the tip of the protruded tongue, evidently at one time formed a gargoyle- like ornament on some building, as behind the head the stone from which it was cut had been squared for a distance of 14 inches, obyi- ously for the purpose of being built into masonry. The head is, as is well shown in plate xxxrx, much weathered, the soft limestone being eaten away to such an extent that at first sight it is dificult to determine what it is meant to represent. If this head be compared with the tiger, figure 4+, plate xxxm1, it will be seen that, in the shape of the head, contour of the face, protrud- ing, pendant tongue, prominent round eyes, and square upper incisor teeth, the resemblance is sufficiently strong to warrant the assumption that both are products of the same race, if not of the same artist. The turtle is 18 inches in length by 12 inches in breadth, and is nicely cut from a single block of limestone. It is an exact copy of the turtle shown in figure 6, plate xxx, excepting that the mouth, instead of containing a human head, is closed. The whole animal is painted red, and in the center of the back is a round hole. leading to a considerable cavity which has been hollowed out in the interior. The hole is covered by a circular disk of limestone 3 inches in diameter. The human mask is made of rough pottery. The upper part of the face is missing; it is 34 inches from ear to ear; the mouth is puckered up into a small, round hole as if in the act of whistling. The mound marked 10 on the plan was 98 yards in circumference, and very flat, nowhere exceeding 34 feet in height. It was constructed throughout of small pieces of limestone mixed with clay, and con- tained an enormous quantity of potsherds. These were for the most part rough and ill-made, but a few were painted and glazed. Nothing further was found in the mound till the ground level was reached, when an equilateral triangle, built of stone, was disclosed. Each side of the triangle was 18 feet in length, and was composed of roughly cut slabs of stone stuck upright in the ground and in contact on either side with similar slabs. The sides of the triangle varied in height from 8 to 18S inches. The upper edges were irregular, the lower sunk to a depth of 5 or 6 inches in the ground. The stones were remoyed and the earth dug up, both in the center and along the sides of the triangle, but nothing whatever was discovered. The mound marked 11 on the plan was situated 1,130 yards southwest of the large central mound. As, in all the former mounds which had been excavated, whatever of interest they had contained SANE] CONTENTS OF MOUND 17 689 had been found at or near the center, an excavation 14 feet by 7 feet was first made in the center of this mound down to the ground level. For the first 3 feet the mound was composed of yery small stones and earth. Beneath these was a layer of rough blocks of limestone and limestone dust reaching to the ground level. At a depth of about 4 feet a smooth, oval, flattened stone 5 inches in length was found, the marks on which showed that it had been used as a whetstone. With the exception of potsherds, nothing else was found in this excavation, which was afterward enlarged on all sides, but with a similar result, nothing whatever but stones and earth being found. The mounds 12, 13, 14, 15, and 16 in the plan lay ina group to the northeast of the large central mound, and within 200 yards of it. They were all circular at the base and roughly conical, and were all nearly of the same size, varying from 30 to 35 yards in circum- ference and from 4 to 6 feet in height. In contents and construction they all proved so much alike that a description of one will suffice for all. The two upper feet consisted of earth, with a few blocks of lime- stone; beneath this, to the ground level, the mound was built of lime- stone blocks, the interstices between which were filled in with limestone dust. A few potsherds were found, for the most part rough and unpainted. At a depth varying from 2 to 3 feet, or about midway between the summit of the mound and the ground level in each case, a small stone cyst was found, 18 inches square, the walls, roof, and floor each composed of a single slab of roughly cut stone. These cysts were in all cases perfectly empty, and were placed as nearly as possible in the center of the mound. Nothing further was found in any of the mounds. The mound marked 17 on the plan stood 500 yards almost due sast of the large central mound. It was oyal in shape, flattened on the top, 85 yards in circumference, and 6 feet high at its highest point. The northern face was almost perpendicular; the southern sloped gradually to the ground level. The upper two feet consisted of earth and blocks of limestone. Near the center of the mound, at a depth of 1 foot, were found the fragments of two idols very similar to those found in mounds 2, 5, and 6. Close to these were found: (1) The flat, triangular head of a serpent, with protruding, forked tongue; this was made of pottery, and had been broken off from the body; (2) a small, pyramidal pottery stopper, like those placed over the openings in the pottery animals; (3) a dragon’s head in pottery, with an elaborately decorated headdress; (+) a small pottery mold, 4 inches in height, for making masks. After first oiling the inside of it, J filled this mold with plaster of paris, and it turned out a face very like figure 3, plate xxx, but without the headdress. Beneath the layer of earth and limestone came a layer of limestone blocks, many of which were squared. This was the last mound opened, and as in mounds of similar construction in which two broken idols had been 690 MOUNDS IN NORTHERN HONDURAS (ETH. ANN, 19 found superficially, an urn with pottery animals had inyariably been found on digging deeper, I felt almost certain that here, also, they would be discovered toward the center of the mound. But though an excavation 15 by 8 feet was made through the center down to the ground level, nothing further was brought to light. UNEXCAVATED MOUNDS Turning next to those mounds at Santa Rita which have not as yet been excavated, we find that the first of these, 18 on the plan, is by far the largest mound on the estate, and is indeed the largest mound that I have seen in the colony. It is situated 100 yards almost due south of the large central mound, is 412 yards in circumference, oval in shape, flat on the top, and 10 feet high. This mound has never been dug into. Mound 19 is very similar to. the last and is in line with it and the large central mound. It is 10 feet high at its highest part, roughly circular at the base, and 270 yards in circumference. Mound 20 on the plan is situated 400 yards southwest of the large central mound. It resembles in shape the two preceding mounds, but ismuch the smallest and lowest of the three, being 83 yards in cir- cumference, flat at the top, circular at the base, and 35 feet high at its highest point. These three mounds have been described as being typical of a class of mound which is numerous in the bush all round the estate and throughout the whole of the northern district of the colony. Mounds 18 and 20 exhibit the greatest variation in size and height found among this class, all the members of which are intermediate in size between these two. I have opened only one of these mounds as yet, but as nothing was discovered inside except potsherds, I was not much encouraged to proceed with the excavation of the others. Mound 21 is situated about 1,000 yards southwest of the large central mound. It is almost semicircular in shape, and is 30 yards in length, measured along the curve. The east end is much broader and higher than the west; the mound, in fact, resembles the half of a pear, in which the stem has been bent round through a semicircle toward the head. The mound is 5 feet high and 24 feet broad at its head, and gradually lessens till it is only 8 feet high and 8 feet broad at its tail. The convexity faces north, the concavity south. At the point marked 22 on the plan there are several of these mounds yery like the one just described, both in shape and size. A number of similarly shaped mounds are found in the bush surrounding the estate, and in other parts of the district they are common. At Sateneja, a village on the coast about 20 miles from Santa Rita, a large number of these mounds of various sizes are so arranged as nearly to inclose a roughly BUREAU OF AMERICAN ETHNOLOGY NINETEENTH ANNUAL REPORT PL. XXXIX STONE TIGER HEAD FROM MOUND 8, SANTA RITA GANN] MOUND 23—UNDERGROUND RESERVOIRS 691 circular space very near the seashore. Their concavities all face toward the space which they inclose; their conyexities face outward, and they were obviously constructedfor defensive purposes. Occasionally these mounds are almost circular, the narrow pointed end being produced onward till it passes the broad end, leaving a space 2 or 3 yards across between them as an exit or entrance. These mounds vary in length along the curve from 30 to 100 yards, and in height from 2 to15 feet. Ihave opened several of them in various places, but never found anything in them, which fact strengthens the presumption in favor of their being used solely for defensive pur- poses. Some of those at Sateneja contained a large number of conch shells; but these shellfish are very plentiful along the coast, and when the fish had been extracted the accumulated shells were probably used, merely in place of stones, to build up the mound. Mound 23 on the plan, situated 217 yards southwest of the large central mound, resembles the latter very closely. It consists of two portions—a large mound, and to the south of this a circular space inclosed by earthen walls, through which is an opening to the south. This mound is 25 feet in height, conical in shape, circular at the base, and slightly over 400 feet in circumference. The walls of the earth- work are continued into it on its south side. Unlike the large central mound, it is loosely built of earth and stone. The walls of the circular earthwork where they join the mound are 12 feet high, but as they approach the opening they become gradually lower. The circular space included within the walls is 80 yards in diameter. UNDERGROUND ROCK-HEWN RESERVOIRS Scattered about irregularly among these mounds and in the adja- cent bush are a number of circular openings in the ground, leading to small oval chambers hollowed out in the limestone rock. Into some of these chambers it is quite easy to descend, but others have become blocked up, either from the roof caving in or from débris falling through the opening and obstructing it. Those that I have examined are precisely alike in construction and shape, differing only in size, and a description of one, which is situated within a few yards of the mound marked 3 in the plan, will serve for all. The upper opening is 3 feet in diameter; that part of it which passes through the surface earth is built round with blocks of limestone. Three feet below the surface the opening terminates in the first step of a half-spiral staircase cut in the limestone, which leads to the floor of the chamber. The chamber itself is 18 feet long by 10 feet broad; the roof is arched, the highest part being just below the entrance; the opposite end is so low that it can not be reached without crawling on the hands and knees. The floor is slightly concave, giving the whole 692 MOUNDS IN NORTHERN HONDURAS [ETH. ANN. 19 somewhat an ege-shape appearance. It has been covered through- out with a layer of hard plaster, but a good deal of this has peeled off and is lying about on the floor. Nothing whatever was found in any of these chambers except the earth and rubbish which had fallen in through the opening. I have found eight of these chambers within an area of about 1 square mile around the mounds, and doubtless many more exist, concealed by the bush. I first discovered chambers of this kind in the western district of British Honduras, but I did not then think that they had been used as reservoirs for water, as several existed close to the Mopan river, where excellent drinking water could be obtained even in the driest season, and in one case a chamber of this kind had been used as a sepulcher. Stephens, in his book on Yucatan,’ mentions these chambers, of which he came across several near Uxmal. He was of the opinion that they had been used as reservoirs for water in the dry season, and I am now also of this opinion, as it would have been impossible for the builders of the mounds and buildings at Santa Rita to have brought their fresh water from the nearest natural supply, which is the Rio Nuevo, situated at a distance of 5 miles from the estate, from which it is separated by an almost impassable swamp. Nor could wells have supplied the aboriginal inhabitants with water, for not only have no traces of any been discovered, but wells which have been sunk on the estate in recent years have reached water so brackish that it is quite unfit for human consumption. 1John L. Stephens, Incidents of Travel in Yucatan, vol. I, p. 232. MAYAN CALENDAR SYSTEMS BY CYARUU Sea ELONEAS, 19 nTH, Pr 2—9 693 CONTENTS Prefatonymnotes ioe. 2s: 2 oa2 aclaeciee cece lose Time series in the codices and inscriptions - - hes Wresdeni codex —-esereen eee eee Inscriptions at Palenque -...----------- Maibletior the) Cross se= ass === ae Rabletioithel suns asssee =~ esse Tablet of the Foliated Cross-----.-- Temple of Inscriptions. ---...-.----- Tikal inscriptions Gopankinseriptionse=s==== sees sees StelapAteese ac aaast en eemes esac SUG) 13} oo poco acodpicesdascosanac Stela C StelayD esas teen eae ee Stele E and F StelecvhHand len. <2c-esscosteceeces Stela J StelauMice: G2s-22 ee ease re aera Stelaini-w- = coke .cee cece cee eee Stela P All (ars @) Sap ae os ae eee eee Al tariSyes = seccc cs eee eae eaaeraee Inscription at Piedras Negras......-.--- SUMMARy <2s=s5 55-22-55) see aslecose ees Mr Goodman’s system of Mayan chronology Imitialiseniese=sesscasocsece te eee ee eee Identity of systems and characters of the different tribes. -......--.----.---- Numeral symbols in the codices -.-.--.----- In the Dresden codex mother codices: - o<.-<2/- sea Seco Working tables Page 699 715 715 SIs ss ss OowWMOO DS D an v2) io’) CS ie Mics (IS TS FS I TS TS i Tn Oh ts (as (ns (it Gta | ie) Pirate XL. Xo LIT: XLIT1a. XLII. XLIV. Figure 8. oF 10. 11. 12. 13. iO SRS AS nOeNES A portion of the Tablet of the Cross, Palenque -----....--.------- Temple of the Sun; inscribed panel on the back of the sanctuary. Temple of the Foliated Cross; inscribed panel on the back wall of (HOG) ROMO NURIA a5 ere co obeaosse denechnso sees easaes GOBASE EOSS Thaksrahoyntorn Oye elk Clo eehte oo. seas o ope hoses odeanosossasoe Gilyphstiromystelard. | Copan sae sass eee ane eee ee = aren ene Upper division of plates 51 and 52, Dresden codex. ......-------- Moe Cavern Sram) voll so sacsesnssosmsencerasesosvesssaccoseCoSTeD Devs Dowie Gham Vell oan ease moreeseoemecencssescosuSScuSsSEeSESe “Navan ighngia tsypurloell 2 em eeeeasoaronsoss Has Obens Jao Dee nacaeeaeTe Mae CYB AVON ello econo ease sess - seco sass SeceuSassanensaacuc GMa CAillerarslerescoysbavel Eh Aan| Kelle on sao aeooe ce cooemsope see cueadeseEs Mherday:symbolssean. eee seems sees es alee eee te seme = sebhemonthysym pols yeseese serene ase eee eee eee ace ae ~weartotplateyz4 sUresdenicodex= == seem eee era ee ee = "Partrofiplatel69! Dresdenicod exes ase= eee a = een alae aS . Inseription on the middle space of the Tablet of the Cross, Palenque . Inscription on the right slab of the Tablet of the Cross, Palenque. . Part of the inscription on the wall of the Temple of Inscriptions, IPallenquese sees ee ae ee eee eae eee tase SPartiobtheimscriptioorat, Wulcalipssen es eee a sae eee cel = . Inscription at Piedras Negras, Yucatan .....-.-.....------------ HG lyphyironiplateyio..Dresd cnaCOde xara ae see sac ese seen nce ee ee 2. Figures from plate 72, Dresden codex.......-------------------- — MAYAN CALENDAR SYSTEMS. By Cyrus THomas PREFATORY NOTES The recent explorations in Central America and southern Mexico by Maudslay, Holmes, the Peabody Museum, and others have brought to light so much new material that a modification in some respects of conclusions based on the data previously obtained is required. It is expedient, therefore, to bring conclusions and deductions into harmony with the new data. At present, however, attention will be limited to an examination and discussion of the inscriptions and the Dresden codex in the light of this additional material and of the recent discoy- eries In regard thereto. That progress toward the ultimate and correct interpretation of these inscriptions and of the codices and symbolic figures will be slow is well understood, and that more or less modification of previous views will follow as the result of new discoveries is to be expected. ‘This fact is well illustrated in the Old World in the efforts of archeologists and linguists to reach a positive and satisfactory conclusion in regard to the so-called Hittite remains. The most important material for the object of this paper, relating to the inscriptions, is found in the data obtained by Mr Maudslay dur- ing his explorations of the ruins of Copan, Quirigua, Tikal, and Palen- que. Although the ruins of the last-named place have been described and figured again and again, it was not until Mr Maudslay’s clear and large photographs of the inscriptions were published that the data relating thereto—save that on the slab in U. S. National Museum— were in a condition to be satisfactorily studied by those interested in the subject. New light has also been thrown on the inscriptions by certain discoveries made by Mr J. T. Goodman and Dr E. Férstemann in regard to the signification of some of the glyphs. The positive results so far obtained by attempts to explain the inscriptions and codices, including those obtained by Mr Goodman and Dr Férstemann, relate almost wholly to the time and numeral symbols. In his elaborate and important memoir, Mr Goodman 699 700 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 announces certain discoveries in regard to the signification and use of characters in the inscriptions, which, if verified, will materially modify previous opinions in regard thereto and will bear on future attempts at interpretation of the inscriptions; he also announces other discoveries tending to show that the opinions hitherto held in regard to the Maya time system are erroneous in many respects; and since these announce- ments form part of Mr Maudslay’s great work, Biologia Centrali- Americana, a review of the entire subject would seem timely. The present paper will be limited to an examination of the time and numeral symbols, time counts and time systems of the Mayan tribes, as indicated by the codices and inscriptions, and will avoid, so far as is possible, rediscussion of points considered as satisfactorily settled previous to the appearance of Mr Goodman’s memoir entitled The Archaic Maya Inscriptions (1897). The discussion will be based on a personal examination of the Dresden codex and the inscriptions, the former in Dr Férstemann’s photographic reproduction and the latter chiefly in the magnificent photographic (autotype) reproductions by A. P. Maudslay in the archologic portion of his Biologia Centrali- Americana; but the actual examinations have extended to all the more important Mayan inscriptions in the U.S. National Museum, the Pea- body Museum in Cambridge, the collection of the American Anti- quarian Society in Worcester, the American Museum of Natural History in New York, and the Museum of Archeology connected with the University of Pennsylvania in Philadelphia.* The discussion will be conducted in the light of the recent discoveries, some of which will, as we proceed, appear to be valid and of great importance in the study of Central American paleography. As one object in view will be to test Mr Goodman’s interpretations, his work will be used in analyzing the symbols of the inscriptions and the time systems of the Mayan tribes as a basis of comparison in regard to the several points of which it treats. I shall therefore have very frequent occasions to refer to it, not in the spirit of criticism, but simply in behalf of scientific accuracy, as well as of other workers, differing from him where I believe he is wrong and agreeing with him where I believe he is right. The mode of examination will be, so far as possible, by inspection of the glyphs and mathematical demonstration by means of the numeral symbols. In addition to the objects mentioned as in view in preparing this paper, it is expected that the comparisons and examinations to be made will show to some degree how far the glyphs found at Copan, Tikal, and Palenque, used as time and numeral symbols, agree as to form and signification, and how far they agree in these respects with the characters of the Dresden codex; and will also show whether or 1Grateful acknowledgments are made to the officers of these institutions for courteous assistance. THOMAS] PREFATORY NOTES TO1 not the same time or calendar system was used in all, and in what respect the system presented by Mr Goodman differs from that gener- ally understood and set forth by other writers—for if he is right in apprehending that previous investigators haye been at fault in regard to the Mayan time system, it is important, in view of future investigations, that this be clearly shown and the error be pointed out. A comparison of the time systems of the Maya, Nahuatl, and Zapotec tribes has been made to some extent from the historic standpoint. This comparison indicates that the time systems used by these tribes were substantially the same. As attention will be given almost exclusively to the examination of the time series and time systems of the codices and inscriptions, it is necessary, in order that the reader may follow closely and apply the tests himself, that the apparatus to be used be placed before him. This will involve some repetition of what has been given in my pre- vious papers; but in order to use Mr Goodman’s discoveries in com- parisons it is necessary to adopt some scheme of applying them which can be introduced here, as his tables cover more than 100 large quarto pages. This, I have found, can be done, after a little study and prac- tice, by means of two or three short tables, each occupying less than a page. They are therefore inserted with such explanations as are neces- sary to show how they are to be used. One of these tables which will be used in making comparisons is that numbered 3, on page 21 of my Maya Year,and entitled there ‘* Days and Months of the four Series of Years.” It is inserted here as table 1. (ETH. ANN. 19 SYSTEMS MAYAN CALENDAR 702 qyjuour jo skuq te MG 4 uRqeyp (Ps JR tale 8) qo Wo tele ey = Alt 88 ud] cell (2) AN RL XT Gs oO) ees ued OL i? (OW ts lat WIE te ty Gey uent;) GS ge AR aki! 20 pe We 2 tal ai ono] 4) ate qeure’y DCS i 0] yluRyy (UE iP (WIR TR ta) iinen@) OE tS th rs uRYyoorgy9, Cen Gane Gee I ff uBy, Green Lineecee tcieen reqyy JE tele) IES AL ye BY vale ER ep XTUIT CAN AG We iy (OYE te ney TTF © Linens owned (ME Gea EE (BURZI nod GRUBZIT IGE wanyy) 20 onqnyy, JEU] LABIAL TUTTO) UBTpOIY) uBy [eqQAly AI XIU] ney y own) qeurzsy urge Ure) Udy x] uog rvod Uog [as ror), uRyporyy) uvy PQA V AI XIU] ney oeney QeUuRZsy ueqey qt ud] x] uag kG uony) 90 ono qeure’y ivod YRULR'T AL XI] neyy oeneg9 qeuezy uRqey) qi) ud] =I uegq qa uenyO 20 ono] qRue’y LOB taqip) uBqovigy) uBy PQA aBod [BQH V supah fo sarsas wof ay) fo syjwou pun sing—{ A1avy, THOMAS] THE MAYA YEAR 703 Each month consisted of 20 days, each day having its particular name, as follows: Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Mulue, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Ezanab, Cauac, Ahau, Imix, Ik. The order or sequence here given was always maintained, though the month did not always begin with the same day, since, according to the peculiar arrangement of the calendar, as used in the Dresden codex and the inscriptions,’ it might begin with (and only with) Alhal, Lamat, Ben, and Ezanab, as is shown in table 1. If it began with Akbal the second day would be Kan, the others following in the order given; if with Lamat, then Mulue would be the second, and so on; if with Ben, Ix would be the second, Men the third, and so on to Eb, the last; if with Ezanab, Cauac, Ahau, etc., would follow, always in the order given. The first day of the year would therefore necessarily be the first day of the months during that year. As the year was divided into eighteen months of twenty days each (always named and arranged in the following order: 1 Pop 7 Yaxkin 13 Mae 2 Uo 8 Mol . 14 Kankin 3 Zip 9 Chen 15 Muan 4 Tzoz (or Zotz) 10 Yax 16 Pax 5 Tzec 11 Zae 17 Kayab 6 Xul 12 Ceh 18 Cumhu), making 360 days, and five days to make the 365 were added at th end of the 18th month (Cumhu), the names following in proper orde1 it follows as a necessary result that the count in the day series would be thrown forward five days each year. If the year (or month) began with Akbal, the last day of the 18th month would be Ik; counting five days—Akbal, Kan, Chicchan, Cimi, and Manik—would bring us to Lamat, the first day of the next year. The numbering of the days was peculiar; it did not correspond with the days of the month as we count them, but was limited to 13, fol- lowed by 1, 2, etc, up to 13, this order proceeding without variation, thus: 1 Akbal 6 Lamat 11 Ben 3 Ezanab 2 Kan 7 Mulue ex: 4+ Cauac 3 Chiechan 8 Oc 13 Men 5 Ahau 4 Cimi 9 Chuen 1 Cib 6 Imix 5 Manik 10 Eb 2 Caban 7 Ik If the list continued 8 Akbal, 9 Kan, 10 Chicchan, ete., would follow. Hence, it is readily seen that by continuing the series each day name would in the course of time have all the thirteen numerals 1It is possible that the inscriptions of the Yucatan peninsula will be found to follow the system of the Troano and Cortesian codices and the codex used by Landa, should any inscribed dates be found. TO04 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 attached to it. The round is completed in 13 months, as will be seen by table 2. TasLe 2—The months, days, and numerals for the year 1 Akbal | | & | & = Months 7 S\non Pe a pe alee i ae | ; a | | r 2 ° S| NS | SN 5 cs © ot a a S os zi 3 = = PINJSlalah lala lola No | A\l4S 1A 1S) = Days }2] 243] 4] 5/6] 7 | 8 | 9 | 20) a1) 12) 18) 14| 15 | 16] 17] 18 | b ea | ee S| — Akbal ......- 1 s 2| 9| 3] 10 4/11} 5/12| 6/33] 7] 1| 8] 2] 9] 8) 10 Kerns ee 2) 9 | Sito 4) aah) 5) 12) ers | 7) |) si 24) oN silo a yaa Chicchan....| 310] 4/31] 5/12) 6/13] 7) 1] 8] 2) 9/ 8|)10) 4/11) 5] 22 | Ginine ee 4/1] 5/12) 6 (aks | Gaels) Oo!) Giles yam) 2 11 | 5/12] 6] 18 Manik....... 5} 12) 6|318! 7] 1) 8) 2) 9) 8/10) 4) a1) 5) 12) 6) as) 7) 1 | Lamat....... 6) 1013 | iva | femelle 2191). ler On| elt oa| | cpl t | ck al ten ies | eee Muluc....... 7/1] 8] 2| 9| 3} 10 | 4|11] 5 }2| 6) 38] 7] 1| 8] 2) 9]-..... Oce cee (ON || aptly] NP ste)| a] Be N GPoeI | yp) aE EN), 91) eh etd {Poe Chuen ....... 1] 3 N s10) Pas etal) 75} 20 || MG |V-1S | eerie e e Sees SN wea en eae) tc | eee 1D Besecaeeeee HY feeutar |] Gy) bh | aes | el aI] I) a) e)]) BY ey) P| eT) | | Bens poses u| 5}12| 6113| 7| 1] 8| 2| 9| 8]20| 4/1] 5] 12| 6} a8)... 1b ee eae | 12) 6/13) 7| 1] 8] 2| 9] 8/30) 4/11) 5/12) 6) 18) 7) 1)...... Men ..-..--0- 133; 7] 1] 8] 2| 9} 8]10| 4/11| 5] 22] 638] 7] 4 tN cee Gibs sees: 1 be 2 i} 3 | 10 4/11 5; 12) 6) 138 7 1 5 Pa SiN esac Cabapeeer 2| 9| 3}10| 4/1| 5/22| 6|13| 7| 1| 8| 2] 9| 3] 20| 4|...... Ezanab ...... 3] 00)! 4) a0} 5) 02)) W184) 7) mW] 8) 21 (9) eo)! ait ad |) 5 ee eee Cauac ....--. s|a4| 5|22] 6ias| 7| 2) 8} 2) 9 | s\20| 4/1] 5 | si2)|| ne) eee INTE okececr PM BEE ee aap eT ED] ENR I) SeE || ay) ed | S/H |lac-50: imix G)|/18)) 7} at) 8,2] 9) Sh} tol) Aalto) 25) 28 VenaSAli ez!) anes Dg ees e Soe 7| 1) 8) 2) 9! 3/10) 4) u jz 6 UE PA | Ed PSP 2) eee In giving a date, therefore, instead of giving the day name alone, the day and number both are necessary, thus: 4 Ahau, 3 Kan, 11 Ik, ete. But to complete the date so that it can be located in the 52-year cycle of the Mayas, the ‘‘ calendar round,” as Mr Goodman calls it, or in its proper relative position, it is necessary to haye the month and day of the month, thus: 4 Ahau 18 Ceh; that is to say, + Ahau, the eighteenth day of the (twelfth) month Ceh. The numbering of the months never changes; that is, Ceh is always the twelfth, Pop always the first, Uo the second, and so on. As may be seen from what has been stated, the years must begin (under the system here followed) with the days Akbal, Lamat, Ben, and Ezanab, following each other in regular order, and before the possible changes have been completed each must receive the entire 13 numerals; hence it is apparent that the period necessary to cover these changes is 52 years (4X13). If the year begin with 1 Akbal (hence valled the year 1 Akbal), it will end (counting 365 days) with 1 Manik. As the next day is 2 Lamat, this will be the first day of the next year (2 Lamat). This year will end with 2 Eb and the next will begin with 3 Ben. This will end with 3 Caban and the next begin with + Ezanab. THOMAS] ORDER OF tHE YEARS 705 This will end with + Ik and the next will begin with 5 Akbal, and so on until the number 13 is reached, when the count begins again with 1. The order in which the years follow one another through a complete cycle of years, or calendar round, is shown in the annexed table (8). TABLE 3 Akbal Lamat Ben Ezanab 1 yh 8 4 5 | 6 aed ee 9 10 11 12 13 1 2 3 4 45 6 | 7 8 9 10 11 12 13 1 2 3 + 5 6 7 8 9 10 11 12 13 1 2 3 4 5 6 7 8 9 | 10 11 12 13 This is to be followed in the order of the numbers, 1, 2, 3, 4, 5, ete. As all the possible changes are completed in a cycle of years, or cal- endar round (we use the term ‘‘cycle of years” to distinguish it from the period to which Goodman has unfortunately applied the name “cycle,” which is not the same as the 52-year period, which he calls ‘calendar round”), it always begins or is supposed to begin with 1 Akbal, 1 Lamat, 1 Ben, or 1 Ezanab, according to the order or system adopted, and ends with the year 13. According to the system adopted here it always begins with 1 Akbal. It is stated above that these tables apply to the ‘‘system adopted here.” For the benefit of those not thoroughly familiar with this subject an explanation is necessary. As the Maya calendar is an orderly rotation of days, months, and years subject to the rules above stated, resulting from the numbering by 13, the 20 days to the month, 18 months to the year, and the 5 added days, any + days of the 20 days, selected at intervals of 5 in the series, could be adopted as dominical days. For example, it appears from the Troano codex that the people where it was made (supposed to have been those of the peninsula of Yucatan) selected Kan, Muluc, Ix, and Cauac as the dominical days, while the Tzental, with whose system the Dresden codex corresponds, selected (if the count of the days of the month began with 1) Akbal, 706 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 Lamat, Ben, and Ezanab. Mr Goodman, howeyer, contends that the dominical days used in the inscriptions were Ik, Manik, Eb, and Caban, but instead of commencing the numbering of the days of the month with 1 and continuing with 2, 3, ete., to 20, he begins the count with 20, following it with 1, 2, 3, ete., to 19. In other words, instead of call- ing the first day of the month 1, he calls it 20 (these, it must be remembered, are not the day numbers, which never exceed 13, but the numbers of the days of the month). This system is in fact, as will be seen by reference to table + (page 745), the same—with one dif- erence, which will be explained hereafter—as using Akbal, Lamat, Ben, and Ezanab as the dominical days; for, as will be seen by this table, Akbal, in Ik years, though by position the second day of the month, is numbered the first precisely as it is in Akbal years in our table 1. Another point necessary to settle absolutely the system is to know which of the dominical days was placed first in commencing the fifty-two year period—in other words, what was the initial day. In table 3 it has been assumed first, that the years of this period began with 1, which has also been assumed by Mr Goodman, and second, that this first year was an Akbal year; but Mr Goodman holds that according to his system it was an Ik year, which, as has been explained, accords with our Akbal year. He expresses also an opinion that Caban was possibly the initial day. Although this question does not affect the lower time periods, it is apparent that it does affect the numbering of the years of the fifty-two year period. This subject will, however, be referred to again, Turning now to our table 1, we will try to make as clear as possi- ble the method of using it so as to avoid the introduction of a multi- plicity of tables. The year 1 Akbal written out in full would be as shown in table 2. It will be seen that the five figure columns after the thirteenth—to wit, the fourteenth, fifteenth, sixteenth, seventeenth, and eighteenth, numbering from left to right—are precisely the same as the first, second, third, fourth, and fifth, and that the five added or intercalary days are the same as the first five of the sixth column. As the series continued endlessly in this order, I have eliminated in my table 1 the last five columns and five added days, using the first, second, third, fourth, and fifth, and the first five days of the sixth instead. In counting forward (by which is meant to the right), if the number of months to be counted is not completed on reaching the last or right-hand column, we go back to the first. If, as is frequently the case, our count is to be backward over past or preceding months, it must then be toward the left, and after reaching the first or left-hand column we go to the right-hand column. In other words, it is a continuous round in whichever direction we are moying, to the right being for- ward in time and to the left backward. THOMAS] USE OF TABLE 1 707 Suppose we wish to know in what year the date 6 Ahau 3 Zotz— that is, 6 Ahau, the 3d day of the fourth month (Zotz)—falls. Looking to the year columns (table 1), we see that Ahau can be the 3d day of the month only in Ezanab years. Looking along the line opposite running through the figure (or month) columns, we find 6 in the seventh column. As this is in the fourth month, to find the first we must count back (to the left) three columns, which brings us to the column headed by 9 (that is, the column whose top figure is 9); hence our year is 9 Ezanab. Now let us trace this year through by the table and find the first day of the next year. Beginning with the column headed 9, we count to the right nine columns, which brings us to the last; then we go back to the first (left-hand) and count eight. This reckoning brings us to the column headed 11. Counting 5 days down the next column (headed 5), we find that the next—the 6th day of the month—is 10 Akbal, which,as will be seen by our table of years (table 3), is correct. To follow out this year, we must begin with the month column headed 10, as this is the first month (Pop) of the year 10 Akbal. As any one day can fall on only four different days of the month, as Ahau on the 18th in Akbal years, on the 13th in Lamat years, on the 8th in Ben years, and on the 3d in Ezanab years, a mere inspec- tion of the table will at once detect a date erroneous in this respect. For example, there can be no day Manik on the 3d, 9th, or 16th of the month, ete. Suppose we wish to find on what date the 600th day counting forward from 7 Cib 4 Mae will fall. Looking at the table (1), we see that Cib can be the 4th day of the month only in Ben years. Running along the line opposite (horizontal line) through the figure columns, we find 7 in the column headed 4. As Mac is the thirteenth month of the year, we must count back thirteen months or columns to reach the first month of the year. Counting back the seven columns to the first (left), we then go to the last (right) and count six columns. This brings us to that headed 11; hence the year is 11 Ben, and the next year must be 12 Ezanab. As 7 Cib 4 Mac is the 4th day of the thirteenth month, there will remain of this month 16 days, 5 whole months (100 days), and the added 5 days to complete the year, or, in other words, 121 days. Sub- tracting this from 600, there remain 479 days to be counted, and deducting from this 365 days, or one year, 114 days remain to be counted on the next year, which must be 13 Akbal. As 114 days equal 5 months and 14 days, we begin with the figure column of our table headed 13, and count forward 5 months (including this one), and counting down the next month (column headed 9) 14 days, we reach the figure 9, and opposite it in the Akbal column find the day Cib. The date reached is therefore 9 Cib, 14th day of the (sixth) month. 708 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 Xul, in the year 13 Akbal. Turning to our table of years (3), we see that 11 Ben is the third year in the Ben column, or the eleventh year of the cycle of years, and that 12 Ezanab and 13 Akbal follow. We are thus enabled to correctly locate these dates in the cycle of years. These statements and examples, with the illustrations which follow, will enable the reader to use the tables and to follow the present investigations. The order in which the characters in the codices and inscriptions are to be read has been fully explained in my previous publications, and so generally accepted that it is unnecessary to explain it here, especially as it is indicated in the quotation from Maudslay’s work given immediately below. This author, speaking of the order in which the inscriptions are to be read, says (Biologia Centrali-Americana, Archeology, part 2, Text, November, 1890, p. 39): With regard to the order in which the hieroglyphics should be read, Professor Cyrus Thomas has shown, from an examination of the Palenque tablets, that when a single column only of glyphs is met with, it should be read from the top to bottom, and that when there is an even number of columns, the glyphs are to be read in double columns from top to bottom, and from left to right. I myself came to the same conclusion from an entirely independent examination of inscriptions from Quirigua and Copan, and this order is adopted in numbering the glyphs on the fol- lowing plates. As I have also shown that this is usually, though not always, the order in which the glyphs of the codices, when in columns, are to be read, a conclusion which is now accepted by all investigators of Maya symbolic writing, we have in this fact one point of agreement between the codices and inscriptions at Palenque, Copan, Tikal, and Quirigua. The use of dots and short straight lines to indicate numerals up to 19 (each dot counting 1 and each short line 5), as in the codices, is also universal in the inscriptions, as is admitted by Mr Maudslay. He has also confirmed my suggestion (Study of the Manuscript Troano, pp. 202-203) that the little loops connected, in certain cases, with these number symbols have no signification. He says (op. cit., p. 39): ** There is no reason to suppose that any different system of notation is employed on the sculptured monuments; it was not, however, usual to leave blank spaces when carving the numerals 1, 2, 6, 7, 11, 12, 16,17 in stone, but to fill up the space thus: MOA, 1; OPM O, 2; MOG, 6; OlGDIOs Gctcr: —— As the ordinary numeral symbols, the dots and lines (which are neyer used to signify a higher single number than 19), have been so frequently explained and are incidentally referred to in what precedes, I pass to those discovered by Dr Férstemann and Mr Goodman, as I shall have frequent occasion to use them, but will not discuss at this point the general theory presented by the latter, nor his other THOMAS] NUMERAL SYMBOLS 709 supposed discoveries. He follows, as stated above, the order in read- ing the inscriptions first explained by me, and accepts the interpreta- tion of the ordinary time symbols which has been universally adopted, with the single exception of that found in the Dresden codex, which has generally been explained as the symbol for ‘‘ naught,” or nothing. This will be again referred to hereafter. Previous to the appearance of Mr Goodman’s work, the following discoveries in regard to the numeral and time systems as given in the codices, in addition to what has been already presented herein, had been made and explained: That this symbol ED) was used, in count- ing time, to represent the number 20; that this character @qp>, some- what variable in form, and usually colored red, was used to indicate “naught” or nothing; and that a certain prefix to month symbols, usually in the form of a double circle, thus é. was used to denote 20, signifying, when thus used, the 20th day of the month. It was fur- ther ascertained, as may be seen by reference to papers by Dr Foérste- mann and myself explanatory of time series in the Dresden codex, that the orders of units in counting long periods, the day being the primary or lowest unit, was as follows: 20, 18, 20, 20, 20; that is to say, 20 units of the first order make one of the second order, 18 units of the second order make one of the third order, 20 units of the third order make one of the fourth order, 20 units of the fourth order make one of the fifth order, and 20 units of the fifth order make one of the sixth order. These different units, save those of the first order, were not expressed by specific symbols, but by position, that is, by being placed one above another, as is here shown, the lowest indicating the first, the next above the second order, and so on. 9 units of the fifth order, s¢ss, 9 cycles. 9 units of the fourth order, 388, 9 katuns. 9 units of the third order, £88, 9 ahaus. se 16 units of the second order, =, 16 chuens. 0 units of the first order, @D, 0 days. For the purpose of explanation and comparison I have placed to the left of the symbols their equivalents in Arabie numerals, and in the column to the right the equivalents according to Mr Goodman’s nomenclature, which will be explained a little further on. This example is not an arbitrary one, but is taken from plate xxrv of the Dresden Codex, and has been selected because it was explained by Dr Forstemann, so far as the numbers and count are concerned, in 1887 (Zur Entzifferung der Mayahandschriften, 4, 1887). According 19 rH, PT 2 10 710 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 to Dr Férstemann the number of days indicated by these numeral symbols as thus placed is 1,364,360, the length of the periods being as follows: Days. INGY ClO PS Deca) feb tyes Soe ee ercresee state eee Sats nec eee 144, 000 kaput cao eo cee tole oe ale eaters ores eters 7, 200 Dah sue. cos, Sct wai aeoe mee sise Sooke sees aoe 360 Be) aT ea I a eee eM ne tee ae ane Eee 20 Now let us test it by Mr Goodman’s system, using his own tables (last page of his paper) for this purpose: Days. One Clegaee tre ta feeiner tae pte ee te a eae 1, 296, 000 Oikatune tees ace era stole ee see sem See eer 64, 800 9 ANA = se ee Res oe se clssoee water ciecjeertate 3, 240 16 CHUCNE eee 2c ee ee ee eee 320 DEW Eidoscccasonc cack oc cocr cn sotahaespuadsesuseeso 0 1, 364, 360 It is evident from this result that this, so far as the system is con- cerned, is, up to the fifth order of units, precisely that discovered and applied by Dr Foérstemann, except as to the *‘naught” symbol. Even the very order and method of expressing a series which Mr Goodman uses, so far as applicable to the codices, was, as will be seen a little further on, used by Dr Foérstemann. In order that I may not do injustice to Dr Foérstemann when I speak of the discoveries by Mr Goodman, it is proper to add that not only had he discovered and applied to the time series of the Dresden codex the orders of units accepted and used by Mr Goodman, but had determined as early as 1891 the value of the symbols designated ‘‘ahau” and *‘katun,” as appears from his article Zur Maya-Chronologie in the Zeitschrift fiir Ethnologie for that year. Mr Goodman’s paper was not published until 1897, though it is apparent from his preface that it was com- pleted in 1895. If Dr Férstemann had not seen Mr Goodman’s paper when his article entitled Die Kreuzinschrift von Palenque, was published in the Globus in 1897—which makes no mention of the former, though referring to works on the subject—it is evident he had discovered independently the value of the symbols which Good- man designates chuen and cycle. To the 360-day period he applied the name *‘ old year” under the supposition that in an earlier stage of their culture the Mayas counted only 360 days to the year; and to the 7,200-day period the name ‘‘old ahau.” However, it appears from his Entzifferung der Mayahandschrift, number tv, 1894, that as early as June of this year he had calculated correctly the value of some six or eight numeral series on the stelae and altars of Copan from Maudslay’s work. This implies necessarily a knowledge of the value of the so-called time periods, and indicates that he had made THOMAS] NUMERAL SYMBOLS (alit this discovery independently, unless he had received some informa- tion on the subject from Maudslay of which I have no knowledge. It is apparent from a statement by the latter author in part 2 of his work, published in 1890, that the values of these symbols, save that of the chuen, were yet unknown to him. However, as Dr Férstemann seems to have fallen short of the discovery of their uses and the appli- vation of them, the chief credit of the discovery must be awarded to Mr Goodman. This discovery, which must cancel a number of previous specula- tions and affect to a large extent all attempts at interpretation of the inscriptions and codices, consists, first, in finding out the fact that in the inscriptions the orders of units above the first, to wit, his so-called chuens, ahaus, katuns, and cycles, were not indicated by position as in the codices, but each had its distinct character or glyph; second, in determining these characters and their values; and, third, in showing from the inscriptions the order in which they are generally arranged and the manner in which the truth of this discovery may be demon- strated. He has also discovered that a certain character, which he terms a ‘‘ calendar round symbo!,” was used to indicate the period of 52 years, which has heretofore usually been designated a ‘‘ cycle” or ‘‘eycle of years,” and also that certain face characters are used as numeral symbols. As we shall have occasion to use these in our investigation of the inscriptions, the usual forms of the principal ones (using Mr Goodman’s names) will be shown here and his other claimed discoveries will be considered hereafter. TuHEr CHUEN This character usually has a numeral symbol on top and at the left side, the former indicating the number of chuens and the latter the added or overplus days. Fic. 8—The chuen symbol. ale? MAYAN CALENDAR SYSTEMS [ETH. ANN.19 THe AAU The numeral indicating the number of ahaus is usually placed at the left. Fic. 9—The ahau symbol. Tor Karun The numeral indicating the number of katuns is usually placed at the left side, though occasionally at the top. EZ (ALT) ow Fic. 10—The katun symbol. THE CYCLE The numeral in this case is also usually at the left side. eo Raasricns (OMIT a b c d Fic. 11—The eyele symbol. THe CALENDAR RounpD The numeral is usually at the left side. Fie, 12—The calendar round symbol. THOMAS] DAY SYMBOLS (Ale? The forms of the day symbols usually found in the inscriptions are as shown in figure 13. The month symbols usual in the inseriptions, including what Mr Goodman claims is the symbol for the five added days or Uayeb, are shown in figure 14. The typical and usual form of the chuen is shown in the first two glyphs of figure 8 (a, 46). If the number at the top were 3 (three S55) Kan Cimi @ Manik Lamat Mulue Oc Chuen Eb Men @ (oy) Caban Ahau [E, Thy S Ih Ahau Ahau Ahau Ahau Fic. 13—The day symbols. dots or balls), it would signify three chuens or 60 days (320); the number at the side if 12 would denote 12 days. It would then read 12 days, 3 chuens, or 3 chuens, 12 days, which together would equal 72 days. This is the only counter or time period symbol which has two numbers attached. It may as well be stated here, to prevent confusion or misunderstanding in regard to our use of terms, that for convenience in our comparisons Mr Goodman’s names of these several symbols and the time periods he supposes them to represent will be used, although 714 MAYAN CALENDAR SYSTEMS ETH, ANN. 19 I am firmly convinced, for reasons which will be shown hereafter, that they are nothing more than orders of units or multipliers. Therefore, when they are spoken of as ‘* time periods,” or by the names given, this must be borne in mind. The typical and usual form of the ahau is shown in the first three glyphs of figure 9 (a, 4, c). This symbol denotes 360 days, which must be multiplied by the numeral—usually at the side—to obtain the full number of days indicated. The name ahau as here used must not be confounded with the day-name Ahau.'| The use of the same name for two different purposes is unfortunate and confusing. The usual form of the katun is shown in the first two glyphs of fig- Zotz Tzec Chen ) Kankin Pax Kayab Cumhu Uayeb Fic. 14d—The month symbols. ure 10 (a, 4). The attached numeral, if 1 or 2, is frequently at the top, though usually at the side. As this symbol represents 7,200 days, the number of days indicated is 7,200 multiplied by the attached numeral. The usual eyele symbol is shown by the first glyph of figure 11 (q). As the cycle is 144,000 days, 144,000 must be multiplied by the attached numeral to obtain the total number of days. The great cycle will be referred to hereafter, and the other forms of the chuen, ahau, katun, and cycle will be discussed as the series by which their values are determined are examined, 1The day name is always written with a capital, the ahau denoting a period with a small letter, THOMAS] NUMERAL SYSTEMS 715 TIME SERIES IN THE CODICES AND INSCRIPTIONS THE DrespEN CopEXx As the Dresden codex is now so generally known, it will be made the point of departure and the first examples showing the method of counting time will be taken from it. In this examination further com- parison will be made between the system used by Mr Goodman in count- ing time series and that first made known by Dr Foérstemann and used by him and myself in the papers relating to this subject which have been published. As I have somewhat fully illustrated and explained in my Aids to the Study of the Maya Codices (in Sixth Ann. Rep. Bur. Ethnology), a considerable number of the time series of the Dresden codex, in which the figures do not rise above the fourth order of units, the examples referred to here will be those involving high numbers, in order to strengthen the proof of Dr Férstemann’s theory and to establish clearly the respective values of the units in the higher orders. These will also necessarily indicate the calendar system in vogue, to which it is desirable to call special attention. The names of the several orders of units is a matter which failed to receive attention until the subject was taken up by Mr Goodman; those that he has applied are unfortunate and can result only in con- fusion so long as they remain in vogue. Dr Brinton remarks that ‘No doubt each of these periods of time had its appropriate name in the technical language of the Maya astronomers, and also its cor- responding character in their writing. None of them has been recorded by the Spanish writers, but from the analogy of the Nahuatl script and language, and from cer.ainin dications in the Maay writings, we may surmise that some of these technical terms were from one of the radicals meaning ‘to tie, or fasten together,’ and that the corresponding signs would either directly (that is, pictorially) or ikonomatically (that is, by similarity of sound) express this idea” (Primer, pp. 30, 31). He suggests ba/ for the 360-day period, and pic for the 7,200-day period, and fal for the 20-day period. The name chuen, which Mr Goodman has applied to the month equiva- lent, the 20-day period, was adopted by him because of the resem- blance of the glyph to the symbol of the day Chuen. This duplicates the name in the time series. The same objection applies to the names ahau, katun, and cycle; each of these is now applied in three different senses in the calendar system, ahau being used as a day name, as a name of the 24 or 20 year period, and now for the unit of the third order, or 360-day period; katun for the 24 or 20 year period, with ahau prefixed for the 312-year period, and for the unit of the fourth order, or 7,200-day period; and cycle for the 52-year period, also sometimes for the 260-day period, and now for the unit of the 716 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 fifth order or the 144,000-day period. Férstemann, as has been already stated, applies the name *‘old year” to the 360-day period, apparently under the idea that it at some previous time constituted the full year; “old ahau” to the 7,200-day period (a fourth application of this term); and *‘old katun” to a period of 18,720 days or 52 ‘* old years” (52 X 360 = 72 260). To express 9 cycles, 12 katuns, 18 ahaus, 5 chuens, 16 days, Mr Goodman uses this abbreviation: 9-12-18-5 x 16, the < indicating that the two numbers between which it stands are usually attached to one symbol. Dr Férstemann, as an abbreviation to express the same orders of units, uses the same method, omitting only the x, thus: 10, 19, 6, 0, 8 (Zur Entzitferung der Mayahand- schriften, 1887, p. 6). It will perhaps be as well to insert here what I have to say in refer- ence to Mr Goodman’s expressions in regard to, and use of, the term ahau as applied to atime period. The names applied to time periods as a means by which to refer to them are comparatively unimportant, unless such application involves other questions. We quote first the following passage from his work (p. 21): I now come to what has been a stumbling-block to every one who has hitherto attempted to deal with the Mayarecords. It has been known that the Mayas reckoned time by ahaus, katuns, cycles, and great cycles, but what was the precise length of any of these periods has been a debatable question. Some have contended, with the best of proof apparently, that the katun is a period of twenty years, while others have maintained, with proof equally as good, that it is a period of twenty-four years. The truth is, it is neither. The contention arose from a misapprehension, or total ignorance rather, of the Maya chronological scheme. It was taken for granted that a year of 365 days must necessarily enter into the reckoning; whereas the moment the Mayas departed from specitic dates and embarked upon an extended time reckoning, they left their annual calendar behind and made use of a separate chronological one. The use of the term ahau-katun is avoided everywhere in these pages. Such a period never existed, except as a delusion of Don Pio Perez and his misguided fol- lowers. The error originated from a misconception of the Yucatec method of dis- tinguishing the katuns. The ahau was numbered according to its position in the katun, as the eighth, tenth, or the sixth from the close; but the katun was desig- nated by the particular number of the day Ahau with which it ended. Thus, for instance, it might sometimes be spoken of as the katun 10 Ahau; and at other times by a mere reversal of the phrase, as the 10 Ahau katun. More frequently, however, the term katun was not used at all, its existence and number being implied by simple mention of the ahau date. But there was no ahau-katun. On page 23, in speaking of the ahau, he adds: This period is the real basis of the Maya chronological system. Everything proceeds by ahaus, till in succession the katuns, cycles, great cycles, and grand era are formed from them. The ahau is a period of 360 days—the sum of the days in the eighteen regular months—and derives its name undoubtedly from the fact that it always begins with the day Ahau. It is the period, not between two Ahaus with the same numeral, but between the second two with a differentiation of four in their day numbering. Movy- ing forward with this progression of four it results that the ahaus follow each other THOMAS] THE AHAU alu in the order of 9, 5. 1, 10, 6, 2, 11, 7, 3, 12, 8, 4, 13, 9, 5, 1, and so on—an order of suc- cession that Perez quotes from an unnamed manuscript, but whose significance he failed to grasp. Twenty ahaus constitute a katun. They are numerated: 20, 1, 2, 3, ete, up to 19. Finally, in speaking of the katun (p. 24), he says: Itis over this period that the battle royal has been fought. The question of twenty or twenty-four years has raged undeterminedly for more than half a century. As the facts themselves will show the folly of the whole contention, I pass it by without awarding to any individual combatant the discredit of his partisanship. Twenty years of 365 days make 7,300 days. The katun does not reach that far, falling a hundred days short, as a multiplication of its constituent parts will show: 360 * 20=7,200. In consequence of the day Ahau beginning the ahaus, it must also begin the katuns; and the ahaus succeeding each other by differences of four, as 9, 5, 1, 10, 6, 2,11, 7, 3, 12, 8, 4, 13, 9, 5, 1, 10, 6, 2, 11, 7, ete, it results that the order of the katuns, composed as they are of twenty ahaus, must be one in which each succeeding katun begins with a day number two less than its forerunner—thus: 11, 9, 7,5, 3, 1, 12, 10, 8, 6, 4, 2, 13, 11, ete. The katuns are numerated in the same manner as the ahaus: 20, 1, 2, 3, etc, up to 19. Let us examine these expressions so far as they relate to the ahau and bear upon the Maya system as developed in the record. He says the ahau is a period of 360 days, ‘‘and derives its name undoubtedly from the fact that it always begins with the day Ahau.” This is undoubtedly the use he makes of it; but was it used by the Mayas in this sense? That he has derived this name as applied to the period of 360 days from the inscriptions appears nowhere in his work. He nowhere asserts or pretends to claim that the symbol denoting this period is in any sense phonetic, giving this name. The only early native authorities to which we can appeal are the Chronicles. To these, therefore, we refer, following Dr Brinton’s translation. In the Chronicle from the Book of Chilan Balam of Mani, the ahaus are numbered over and over again as containing each twenty years. In the thirteenth paragraph (p. 103) it is said ‘‘in the thirteenth ahau Ahpula died; for six years the count of the thirteenth ahau will not be ended.” It is evident from this, be the count confused and even erroneous, that the author considered the ahau as composed of more than six years. The Chronicle of Chumayel also speaks of the sixth year of the thirteenth ahau, the seventh year of the eighth ahau katun (uaxac ahau u katunil), and the first year of the first ahau katun (ahau u katunile). Another Chronicle of Chumayel expressly makes ahau the equivalent of katun—‘‘the fourth ahau was the name of the katun”—and uses ahau, katun, and ahau katun as synonyms (ahau u katunil). It is evident from these extracts, be the originals trustworthy or not, that Mr Goodman could not have found therein evidence for his application of the term ahau. Nor can it be obtained from Landa, 718 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 who expressly mentions “‘primero ano de la era de buluc-ahau,” and of the natives doing homage to the various ahaus for ten years each. Mr Goodman’s radical error, as we shall see, is taking numerical nota- tion for a time system. The first example to which attention is called is taken from plate 24 of the Dresden codex, and includes that portion of a long series running up the plate which is shown in our figure 15. If the order in which the series ascends be that in which it is to be followed, it is evident this must be from right to left, taking the lower division first, thus: D2, C2, B2, AY (in the lower division), then D1, C1, Bl, and Al (in the upper division). But the plan of the series may be the reverse of this, as it is pos- sible that it runs back in time, and is to be read from left to right the dif- ferences between the columns being subtracted instead of added; the result is, however, the same. As there are no month symbols by means of which to determine the years, and our only object in referring to the series is to show the value of the symbols according to the relative positions e200 cee 6002 egy they occupy in relation to one another, the order in which they are to be read, /@e- ; sae = — - © = —. and the value of the counters, it is not 2 om , material in which direction the series be taken. We will therefore follow i. e., from right the ascending order STAVian DEL UAMainGS EA RCE UATIEY to left, beginning with D2 (right-hand Fic. 15—Part of plate 24, Dresden codex. ¢olumn in lower division). Using Goodman’s names, and subtracting D2 from C2 (the ovals which are red in the original being counted as naught) thus: C2 D2 Diff. Katuns.... 4 3 Albausts.ss)0 13 s Chuens ... 2 0 2 Dayseseeee 0 0 0 we find the difference to be 8 ahaus, 2 chuens, 0 days. As the day at the foot of the column (D2) is 8 Ahau, without an accompanying month symbol, we may select in our table 1 any 8 Ahau and assign it to any month, as the count will hold good. For convenience we select 8, the third number in the figure column headed 6, and find Ahau opposite in the Ezanab column. Assuming the month to be Pop, the first month of the year, the year will be 6 Ezanab. As eight ahaus contain 2,880 days, and two chuens 40 days— THOMAS] PLATE 24, DRESDEN CODEX 719 together 2,920 days—we subtract therefrom 362, the remaining days of the year 6 Ezanab, thus: Days 8 ahaus...--- 2,880 2 chuens. -.-- 40 2; 920 362 Dividing this remainder (2,558) by 365, we find the number of years to be seven, with an overplus of three cays. Looking now to our table of years (3) and counting forward seven years from 6 Ezanab, we reach 13 Ben. As the next year is 1 Ezanab, we look in table 1 to the column headed 1 and count down this to the third day. This brings us to 3, and we find Ahau opposite in the Ezanab column. The day reached is therefore 3 Ahau, which is the day at the bottom of col- umn C2 in our figure 8, showing the count to be correct. This example, however, involves another question raised by Mr Goodman. It will be noticed that in column D2 of our figure the day place and the chuen place is each filled by an oval figure (red in the original) instead of the ordinary numeral symbols, and that in column C2 the day place is filled by a similar oval figure. In my cal- culation given above I have counted these as equivalent to ciphers (0), or nothing. Mr Goodman observes (page 64) that a number of persons have declared this to be a sign for naught, adding: ‘‘They were led into this mistake, undoubtedly, by its peculiar use and position. It is employed in the codices solely to designate initial periods, and in that position it is the equivalent of 20 in all cases except that of the chuen, where, like the other 20-signs, it denotes but 18.” As the example now under consideration affords an opportunity of testing this inter- pretation, we will do so. It is apparent from what has been shown that the correct result is obtained by counting these symbols as naught. If the same result be obtained by counting them as signs of full count—that is, 20—or as 18 where filling the chuen place, the test fails to disclose the correct use of them. Counting the total days in each column and subtracting the sum of D2 from that of C2, the result is as follows: C2 D2 ASkatuns eee cs acces 28, 800 SIkatunspassesaacce ss 21, 600 Wala eee set Ales: 360 USP Soncksenescoas 4, 680 Dehnivenserrre ee sce ee 40 Stchuens so shoe cee 360 Dany Giese rates cto aac 20 iD aiy steer 2 sere erate are ee 20 Total days ----- 29, 220 Total days ...... 26, 660 720 MAYAN CALENDAR SYSTEMS (ETH. ANN. 19 Assuming, as before, 8 Ahau, at the bottom of column D2, to be the 3d day of the month Pop in the year 6 Ezanab, we subtract from 2.560 days 362, the remaining days of the year 6 Ezanab. This leaves 2,198, which, divided by 365, gives 6 years and an overplus of 8 days. Count- ing from the year 6 Ezanab (table 3) 6 years, we reach the year 12 Lamat. The next year will be 13 Ben. Turning to table 1 and count- ing 8 days down the column headed 13 (as the eighth day from the beginning of the year must fall in Pop, the first month of the year), we reach the numeral 7, and find opposite in the Ben column the day Ahau; hence the day reached is 7 Ahau, and not 3 Ahau, as it should be. The addition of days to the total difference by even twenties will, of course, bring the count back to Ahau, hence the test lies in the number attached to it. It appears, therefore, so far as this example is concerned, that these oval symbols stand for naught, and not for 20 and 18, as inferred by Mr Goodman. It will be observed that the same symbol appears in the other columns of figure 8 copied from plate xxiv, Dresden codex. Positive proof that this oval is used for naught is found on plate 50 of the Dresden codex, which may be seen in plate 1 of my Maya Year. The oval in the bottom line filling the month or chuen place can reach the required day only when counted as naught, as may be verified by reference to the series of days given in the same work. In the quotation above from Mr Goodman’s work in relation to the red oval symbol which I have counted as naught, he says: ‘* It is employed in the codices solely to designate initial periods.” Precisely what he means by this remark I fail to comprehend. When the symbols are found in the same time series in the month place and in the imme- diately following day place, and then at odd years and months apart in a continuous series, how they can be used to designate initial periods is difficult to understand, unless very short periods are alluded to. That the symbol for no day, or naught, in the day place will indicate the beginning of a month in the count which is to follow is undoubt- edly true, and when it is in the month place a new year will follow, and so on. This is also true when 20 days, 18 months, 20 ahaus, ete, are counted. If this be what Mr Goodman means, he is correct; but it is hardly the idea conveyed by his language, which apparently refers to ‘initial periods,” as though of a katun, cycle, or calendar round. The next column to the left (B2) has 4 katuns, 9 ahaus, +4 chuens, 0 days, and at the bottom 11 ahau. Subtracting from this column the column C2, already given, we have the following result: B2 C2 Diff. Katuns....-- 1 4 AUD SUSE yee 9 ] 8 Chuens. ..... 4 2 2 Daysitesseoce 0 0 0 THOMAS] PLATE 24, DRESDEN CODEX (om The remainder, 8 ahaus and 2 chuens, equals 2,920 days, and is pre- cisely the same as the difference between the preceding columns. As the date reached by column C2 was 3 Ahau, the 3d day of Pop, the first month in the year 1 Ezanab, we subtract as before 362, the remaining days of the year 1 Ezanab, from 2,920. This leaves 2,558 days, or 7 years and 3 days. Counting from the year 1 Ezanab (table 3), 7 years, we reach 8 Ben, the next year being 9 Ezanab. Counting down the figure column headed 9 (table 1), 3 days, we reach the numeral 11 and find Ahau opposite in the Ezanab column. ‘The day reached is therefore 11 Ahau, 3 Pop, the first month of the year 9 Ezanab, and corresponds with the day at the foot of column B2 in the plate. As the difference between column A2 and Bz2 is precisely the same as that between the other columns (8 ahaus 2 chuens), we have only to count 7 years and 3 days from the close of the year 9 Ezanab. This brings us to the 3d day of the month Pop in the year 4 Ezanab, which we find, by referring to Table I, to be 6 Ahau, corresponding with the day at the bottom of column AY. It must be remembered, however, that the years mentioned have been those following the arbitrary selection for convenience in calculating, as nothing has been discoy- ered in the series to determine these. This could be ascertained if the top series were uninjured, so as to carry on the count to the lower left-hand series, which have definite dates. Passing now to the upper division of our figure, we notice that the day at the bottom of each column is 1 Ahau and that the day place in each is filled by the oval symbol, denoting, according to our interpre- tation, naught. As the series ascends toward the left, the columns will be taken in the same order as those of the lower division. We therefore subtract D1 from C1: Cl D1 Diff. Katunsteesse 4 1 3 AUS See ee 12 5 7 Chuens22-25 = 8 5 3 Dayeaaeeeae 0 0 0 The difference is 3 katuns (=21,600 days), 7 ahaus (=2,520 days), 3 chuens (=60 days), and no odd days. The total is 24,180 days. As the number is large, exceeding a 52-year period or calendar round, we can subtract the greatest possible number of these periods (in this case only one) without in any way affecting the result so far as reach- ing the proper date is concerned, but the number of years thus embraced are to be counted in making up the true interval between the dates. As 1 Ahau may be the 3d day of the first month (Pop) of the year 12 Ezanab, we select this as our starting point. One calendar round equals 18,980 days, which subtracted from 24,180 leave 5,200 days. Taking from this number 362—the remaining 722 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 days of the year 12 Ezanab—and dividing the remainder (4,838) by 365, we obtain 13 years and an overplus of 93 days, or 4 months and 13 days. Counting on our table 3,13 years from 12 Ezanab, we reach 12 Akbal. As the next year is 13 Lamat, we count forward on table 1, 4 months and 13 days. This brings us to 1, the 13th day in the column headed 2, and opposite, in the Lamat column, we find the day Ahau, agreeing with the date at the foot of the column C1 of our figure. The date here is therefore 1 Ahau, the 13th day of Tzeec, the 5th month of the year 13 Lamat, according to the assumed initial date. As the differences between the columns of the upper division of our figure are not the same, a calculation must be made in each case to make the proof positive. Subtracting column Cl from Bl, we find the remainder to be 4 katuns, 18 ahaus, 17 chuens, 0 days, together equal to 35,620 days. Subtracting one calendar round—18,980—there remain 16,640 days. As our last date was 1 Ahau, the 13th day of Tzec, the 5th month of the year 13 Lamat, our count now must be from this date. Subtract- ing 272—the remaining days of this year—from 16,640 and dividing the remainder by 365, we obtain 44 years and an oyerplus of 308 days. Referring to table 3 and counting 44 years from 13 Lamat, we reach 5 Lamat. As the next year is 6 Ben, we count 308 days, or 15 months and 8 days, in this year. This brings us to the 8th day of the 16th month (the column headed 7), which we find is 1, and opposite, in the Ben column, the day Ahau, which agrees with the plate. The date therefore is 1 Ahau, the 8th day of Pax, the 16th month of the year 6 Ben. Subtracting column Bl from Al, we find the difference to be 16 katuns, 2 ahaus, 15 chuens, 0 days, equal to 116,220 days. Subtracting 6 calendar rounds, or 113,880 days, we get the remainder 2,340. As our last date was 1 Ahau, 8th day of Pax, 16th month of the year 6 Ben, we subtract from 2,340 days 57, the remaining days of the year 6 Ben. This leaves 2,283 days, which divided by 365 gives 6 years and an overplus of 93 days. Counting on table 3, 6 years from 6 Ben, we reach 12 Albal, the next year being 13 Lamat. Counting on table 1, 93 days, or 4 months and 13 days, beginning with the column headed 13, and 13 days down the column headed 2, we reach 1, and find opposite, in the Lamat column, the day Ahau, which agrees with the plate. The dates obtained are, it must be remembered, based on the assumed starting point 1 Ahau, 13 Tzec, year 13 Lamat; this, however, does not affect the correctness of the result. As has been stated, to obtain the true interval where calendar rounds (or cycles of 52 years) have been subtracted, these must be added. The true interval, therefore, between column B1 and A1 of our figure 8 is 6X 52+4+6=318 years and 57+-93 days, or 318 years 7 months and 10 days. THOMAS] PLATE 69, DRESDEN CODEX 723 These examples are suflicient to prove beyond any reasonable doubt the correctness of Dr Férstemann’s method of counting the time symbols of the Dresden codex, and that his orders of units, or time periods, used in counting, up to and including the cycle, were pre- cisely the same as those subsequently presented and used by Mr Good- man in his work. It also shows that my calendar tables 1 and 3 have the days, months, and years arranged consistently with the Dresden codex, and that they can be successfully used in examining and tracing the long or high time counts, at least so far as tried. We might dis- miss the Dresden codex with these examples but for the fact that there are some series reaching still higher figures to which Dr Férstemann has called attention. Therefore, before passing to the inscriptions, a few of these will be noticed and the attempt to connect the dates which seem to be related will be made—something which has not been done by Dr Férstemann, and in which the proof of his theory lies. We take as the first example the two series, black and red, running up the folds of the serpent figure, plate 69, following Dr Férstemann’s method and assuming that the two series are connected. ‘They are as follows, Goodman’s names being attached: Red | Black Difference Ll — ——— Days Great cycles - - 4 4 Oequalsieessa=s= 0 | (Gycleseeeeeee 6 5 OWequalseeeee-- = 0 Katuns=-22-—- 1 19 lvequalseee-seee- 7, 200 INEM coconec 0 1g) 7 @epellesaspsacs 2,520 Chuens2=-=-—- 13 12 i requalse= a2-=e5- 20 DaySts sees 10 8 Demequallestac mean 2 Days below... 9 Ix 4 Eb Difference in days. 9, 742 The total days of the two columns as given by Dr Férstemann are as follows: DRY syo le oS See aR ecole Se ee ea a 12, 391, 470 No) Yoltcs 2 8 ee erate oe = os Ok ore ECS oe ee ga 12, 381, 728 IDITfeTeNnCeys epee ee ee nae ee eee ee 9, 742 Same as above. As the month symbols are obliterated, we will assume 4+ Eb under the black column to be the 5th day of the month Pop in the year 13 Lamat. Subtracting 360, the remaining days of the year 13 Lamat, from 9742, and dividing the remainder by 365, we obtain 25 years and 257 days, or 25 years 12 months and 17 days. Examining table 3, and counting forward from 13 Lamat 25 years, we reach 12 Ben. As the next year is 13 Ezanab, counting on table 1, 12 months and 17 724 MAYAN CALENDAR SYSTEMS (ETH. ANN. 19 days on this year, we reach 9 Ix, the 17th day of Mac, the 13th month of the year 13 Ezanab, which corresponds with the day under the red column. As the columns and totals are precisely as given by Dr Férstemann (Zur Entzifferung der Mayahandschriften, 1891, p. 17), we have proof here of the correctness of his system and of the value assigned the several orders of units or time periods which, in one of the series, involves very high numbers, and also proof that they are precisely the same as the time periods used by Mr Goodman in his work, which appeared six years later, with the one exception noted below. In calculating these series, Dr Férstemann has assumed that 20 units of the fifth order make one of the sixth order; or, to use Mr Goodman’s nomenclature, that 20 cycles make one great cycle. Although the latter author counts but 13 cycles to the great cycle, according to the chronological system he believes was used by the authors of the inscriptions, he admits that in the Dresden codex the count was 20, which is evident from plate 31, where the place of the fifth order of units (cycles) has the number 19. As the opportunity is afforded here of testing on a higher unit Mr Goodman’s theory that the red oval indicates full count (20 where this is the proper number, or 18 where that is the number), I shall use it. As will be seen by reference to page 723 where the series are given, the ahaus of the red: series are counted as 0 (naught), when according to Mr Goodman’s theory they should be 20, Let us try the calculation with this number. Subtracting the black from the red as before, the result is as follows: Great Cycles Cycles Katuns Ahaus Chuens Days 4 6 | 20 13 10 4 5 19 13 12 8 Difference... --- 2 7 ] 2 This difference reduced to days gives 16,942 instead of 9,742, as by the former method. Assuming 4 Eb under the black column, as before, to be the 5th day of the month Pop in the year 13 Lamat, we subtract 360, the remaining days of the year 13 Lamat, from 16,942, and, dividing the remainder by 365, obtain 45 years and an overplus of 157 days—7 months 17 days. By table 3 we find that counting 45 years from 13 Lamat brings us to 6 Ben, the next year being 7 Ezanab. By table 1 we ascertain that the 17th day of the Sth month of this year is 7 Ix. This is wrong, as it should be 9 Ix, the day number being the test in this case, as the addition of even months will nee- essarily bring us back to the same day. ‘This shows Mr Goodman’s theory on this point to be incorrect so far as the Dresden codex is concerned, where this particular symbol is chiefly, if not exclusively, used. Our next example is from plate 62, is, like the preceding, in the THOMAS] PLATE 62, DRESDEN CODEX 25 folds of a serpent (the one to the right), and consists of two series, one black, the other red. These have also been calculated by Dr For- stemann and arranged according to the order of units as given here. Mr Goodman’s names are given opposite and differences to the right. Black Red | Difference Days | Great cycles .__..- | 4 4 0 equals ---- 0 Oy clesa. sme. 1525 6 6 0 equals _--. 0 | Sains eee eee 9 1 8 equal.-_--- 57, 600 Wee ausseeee kee ce 15 9 5 equal-_-_--- 1, 800 @huensses. -sa5=5: 12 15 15 equal .=-- 300 DaySeaeienee ae a5 19 0 | .19 equal ---- 19 = =) & Days below-..---- 3 Kan | 13 Akbal | Dotaleee==- 59, 719 NOMI easssésccs 16 Uo 1 Kankin Dr Foérstemann’s totals are as follows: SILVA (se oe ee an Soe eMeciasE GE aa Sate 12, 454, 459 TREC ee te area rh eee te A= eee che eel ne eee ee 12, 394, 740 MUiienence yee anes see ee eee eee 59, 719 showing his result to be precisely the same as that obtained by using the Goodman periods, or rather showing the Goodman periods to be precisely the same as those used by Dr Férstemann with one excep- tion. Before proceeding, it is necessary to notice that the day Kan is never the 16th day of the month, but may be the 17th, therefore the date 3 Kan 16 Uo, under the black column, must be changed to 3 Kan 17 Uo. In this example the counting must be backward in the order of time if we proceed from the lower to the higher series. Subtracting 3 calendar rounds (56,940 days) from 59,719, the differ- ence given above, the remainder is 2,779 days. As 13 Akbal 1 Kankin, is the first day of the fourteenth month of the year 13 Akbal, we count backward from this date. In counting backward, if we start with—that is, include—the day named, the day sought will be the next beyond the last day counted. As 1 Kankin is the two hundred and sixty-first day of the year 13 Akbal, we subtract this number from 2,779, and, dividing the remainder by 365, obtain 6 years and a surplus of 328 days, taking from this the 5 added or inter- calary days there remain 323, or 16 months and 3 days to be counted back on the year reached. Counting back on our table 3 6 years from the year 13 Akbal, we reach 7 Ben, the next year being 6 Lamat. Subtracting 16 months and 3 days from 18 months, the remainder is 1 month and 17 days; hence the day reached will be the seventeenth day of the month Uo in the year 6 Lamat. This, by reference to table 1, 19 ETH, PT 2 11 726 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 is found to be 8 Kan, the same day as that below the column of black numerals, when the correction from 16 to 17 has been made. As this paper is designed in part as a help to those commencing the study of the codices and inscriptions, we will, like the surveyor who sights back and forth to insure accuracy, trace this series forward, a process which should, as a matter of course, result correctly if our count was right in tracing it backward. Starting with 3 Kan, the 17th day of the second month Uo, in the year 6 Lamat, we count forward to the end of this year 328 days, which, subtracted from 2,779, the remainder given above, leave 2,451 days to be counted. Dividing by 365, we obtain 6 years and an overplus of 261 days, or 13 months and 1 day. Counting forward on table 3 6 years from the year 6 Lamat, we reach 12 Ezanab, the next year being 13 Akbal. Counting on table 1 the term of 13 months and 1 day, beginning with the column headed 13, we reach the same 13, and opposite in the Akbal column find the day Akbal. The date is there- fore 13 Akbal, the Ist day of the fourteenth month—Kankin—of the year 13 Akbal, which proves the process to be correct. Our next example consists of the two series, same plate of the Dres- den codex, placed in the folds of the left serpent, as follows (pretixing Goodman’s names as before): Red Black | Difference Days Great cycles ------ 4 } 0 equals ---- 0 Gycles-e2. fe tec: = | 6 6 0 equals. --- 0 Keating sae a= | 11 7 3 equal_-_-: 21, 600 Amauss Aees soso 10 12 ee equales=se 6, 480 @huens2e eee ese if 4 | 2 equal.--.- 40 Dayss-- cose oee 2 10) |/1:2) vequalss=== 12 Days below .-.-.---- 3) bc 3 Cimi Total... 28, 132 Monthseesee me = 7 Pax 14 Kayab | Subtracting from 28,132 one calendar round—18,980 days—leaves 9,152 days. As it is somewhat easier to count forward than back- ward, though the other order appears really to be the one adopted here, we will begin with the date under the red column—3% Ix the 7th day of the sixteenth month (Pax) of the year 9 Lamat. As there remain 58 days in this year after the date given, we subtract this number from 9,152 and divide the remainder by 365, and obtain 24 years and an overplus of 334 days, or 16 months and 14 days. Referring to table 3, we find that by counting forward 24 years from 9 Lamat, we reach 7 Lamat, the next year being 8 Ben. By table 1 we tind THOMAS] PLATE 62, DRESDEN CODEX 727 that the 14th day of the seventeenth month (Kayab) of this year is 3 Cimi, which proves the calculation to be correct. To those familiar with the Dresden codex it will be apparent that the month symbol used under the red column looks as much if not more like that for Tzec than that for Pax, yet, as it has elements of both and as the calculation works out only with Pax, it has been assumed that this is the month intended. That the month Tzee can not in any way be made consistent with the numbers of the series is easily made manifest thus: 3 Ix, the 7th day of the fifth month Tzec, will fall only in the year 8 Lamat, and 3 Cimi, the 14th day of the seventeenth month Kayab, only in the year 8 Ben. Looking on table 3, we see that in counting forward from 8 Lamat to 8 Ben we pass over an interval of only 12 years, and in counting backward over an interval of 38 years. As the interval shown by the numerals is (after one calendar round, which does not affect the count, has been sub- tracted) 9,152 days, it is apparent that 7 Tzec can not be the date intended. Férstemann’s totals of these series are as follow: CC enter ear ae sm a Suis sh a ee ee 12, 466, 942 Ta kage eet teiaioie reo ice ee Ee oe 12, 438, 810 Difference eee seas aoe Sete ee ee eee 28, 132 showing precisely the difference given above. The absolute difference between the two dates is 2 months 18 days+52 years+24 years+16 months+14 days, which, together, equal 77 years and 27 days. The immense stretch of these periods is a point not to be overlooked. One of those referred to amounts to 12,466,942 days, or 34,156 years and 2 days, counting 20 cycles to the great cycle, according to Férste- mann’s method. This brings up again the question as to the number of units of the fifth order to form one of the sixth, or, using Good- man’s terms, the number of cycles which make a great cycle. Although the discussion of this question would perhaps be more appropriate after we have considered the inscriptions, it may as well be introduced here. Mr Goodman, while holding 13 as the number in the inscriptions, admits that in the Dresden codex 20 was the number used; but this admission only renders the subject more complicated, as there is no reason to believe that a different rule prevailed in the inscriptions from that in the codex. That the vigesimal system of notation was the rule among the Maya tribes is well known, the use of 18 units of the second order to make one of the third, in time counting, having apparently been adopted for convenience in bringing the month into the calcula- tion. This fact, though not positive proof of regular vigesimal suc- cession elsewhere in the time system, is sufficient to justify the assumption of regularity, unless satisfactory evidence of variation can be adduced. Although the last example reaches to the great cycle, and inyolyes 728 MAYAN CALENDAR SYSTEMS (ETH. ANN. 19 the count of cycles, it does not afford the proof necessary to decide this question, as is apparent by trial, as the difference between the two series will be the same whether we count 20 cycles to the great cycle or 13. There is, however, one series in the codex (plate 31) heretofore referred to which will decide this point. This, which is in the right half of the upper division, is as follows: 19 cycles 9 katuns 9 ahaus 3 chuens 0 days There is also one series in the inscriptions found on Maudslay’s Stela N of the Copan ruins which seems to settle the question. This is as follows: 14 great cycles 17 cycles 19 katuns 10 ahaus 0 chuens 0 days This reckoning, however, Mr Goodman assures us ‘‘is not only wrong, but absurd as well. The cycles run only to 13, and no such reckoning backward or forward from the initial date would reach a 1 Ahau 8 Chen,” the next date, the first being 1 Ahau 8 Zip. He changes it to 14 great cycles, 8 cycles, 15 katuns, 10 ahaus, 18 chuens, 20 days. It is true that, with the interpretation given of the date characters and the chuens and days, the reckoning backward or forward would not reach 1 Ahau 8 Chen. But this interpretation is by no means certain throughout. In the first place, it is not certain, judging by Maudslay’s photograph, that the chuen symbol does not have a numeral 1 at the left, as it is like one on Stela C, where, according to Maudslay’s drawing, there is 1, and the count may possibly, as will hereafter appear, reach back to some more distant date, as is found to be the case in several inscriptions. However, Mr Goodman inter- prets it differently. In the second place, the month symbol of this last date can not with absolute certainty be interpreted Chen; for as shown by the photo- graph it may be Yax, Zac, or Ceh, apparently Zac. The numerals attached to the higher periods are clear and distinct, but the month symbol of the first date, which is upside down, is as much like Uo as like Zip, if we judge by Mr Goodman’s month figures. If we suppose the sign to the left of the chuen symbol to be 1 and the number of ahaus to be 9 instead of 10, the reckoning from 1 Ahau 8 Zip will bring us to | Ahau 8 Mol, the eighth month, instead of the ninth. This change, however, would not be justified, nor is the change made THOMAS] PLATE 51, DRESDEN CODEX (29 by Mr Goodman until he has clearly proved not only that 13 cycles form a great cycle, but also that his arrangement of the chronologic system, which will be referred to further on, is correct. While the series of the codex which have been given as examples work out correctly, it must be admitted that there are others which can not be successfully traced without arbitrary corrections. Neyer- theless, those given, and others rising to the fifth order of units that might be noted, which give correct results, are sufficient to prove the rule. Before we leave the codex, reference will be made to some series with double numbers—that is, one series interpolated with another, one of which Dr Foérstemann is inclined to believe is a cor- rection of the other. In these cases the interpolated series, or sup- posed correction, is in red, the other in black. As an example, we take the following series from plate 51, using Goodman’s names: Black Red | Black Red a - Le = Wer@yclessee- oes 1 Be | 1 2 IKatunpe see | 8 4 6 11 ADAMS. Sates etc 4 15 11 10 Wn@ boenseeese sees | 14 12 10 | 11 Dayste cee tec S28 | 0 0 0 0 Day below .--.---- | 12 Lamat 12 Lamat Subtracting the black of the right pair from the black of the left, we get the remainders 1, 13,4, 0; that is, 1 katun, 13 ahaus, + chuens, 0 days, making 11,960 days. As no month number is given, we assume 12 Lamat to be the first day (1 Pop) of the year 12 Lamat. Subtract- ing 364, the remaining days of this year, from 11,960, and dividing the remainder by 365, we obtain 31 years and an overplus of 281 days or 14 months and 1 day. By table 3 we ascertain that 31 years from 12 Lamat bring us to + Akbal, the next year being 5 Lamat. By table 1 we ascertain that the first day of the fifteenth month is 12 Lamat, the proper date. The difference between the red series of the two pairs is 13 katuns, 5 ahaus, 1 chuen, 0 days, equal to 95,420 days. Subtracting from this 5 calendar rounds (94,900 days) 520 days remain. Assuming 12 Lamat to be the first day of the year 12 Lamat, and subtracting 364, the remaining days of this year, from 520, we get 156 days or 7 months and 16 days, to be counted on the next year, which is 13 Ben. This reckoning reaches 12 Lamat, the sixteenth day of the month Mol. The result in both cases is correct, so far as the dates reached are con- cerned, but the interval between the black series is only 364 days+31 730 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 years+281 days, while that between the red series.is more than 261 years. It is possible, therefore, that the red, which run through the several columns of this and the following plate, represent an independent series. There are, however, some interpolations which clearly appear to be corrections; for example, these two series on plate 59: Black Red Sy By (0) 6 9 0 | 6 9:10 YR (0) | ea 460 | The day below each is 13 Muluc. Using the difference between the 2 ahaus, + chuens, 0 days, equal to 810 days—and taking 13 Mulue, the 2d day of the month Pop in the year 12 Lamatasour starting point (always count- black series ing forward when it is not otherwise stated), we reach the day 4 Cauac, 2 Tzec, year 1 Ezanab, not the correct date, as it should be 13 Mulue. Using the difference between the red series—4 ahaus, 6 chuens, 0 days = 1,560 days—assuming the same starting point as before (13 Mulue 2 Pop, year 12 Lamat), and counting forward 1,560 days, we reach 13 Muluc, 2 Tzec, year 3 Lamat. This is a correct result, and indicates that the red numerals were inserted as a correction. On plate 69 we find a series (figure 16) repre- sented by symbols of the same form as those in the inscriptions. The glyphs Al, B1 represent the first date—+ Ahau 8 Cumbhu (eighteenth month)—which must fall in the year 8 Ben. At A7, B7 is the next date—9 Kan 12 Kayab. The intermediate counters, comparing with those dis- covered by Goodman in the inscriptions, are as follows: A5, 15 katuns; B5, 9 ahaus; A6, 4 chuens; B6,4 days. There are other characters with numerals between the two dates, some of which may be hereafter explained, but none of Fic. 16—Part of plate 6, these, as will be shown hereafter, are customar- Dresden codex, 4 : . ily counted as part of the time interval. As I may have occasion to refer again to this series and the exactly similar one on plate 61, I shall only show at present the way in which it is to be used, and call attention to the exact similarity of THOMAS] PLATE 69, DRESDEN CODEX 731 the time symbols to those of the inscriptions already figured and those presented farther on. By referring to @ and 4 of figure 10, showing the katun symbols, the strong resemblance to glyph A5 of the series now under consid- eration is at once seen. The resemblance of B5 to a and 4, figure 9, showing the ahau signs, is also apparent, as is A6 to the chuen symbol, figure 8. B6 is the kin or day symbol. Here it seems the numbers denoting days are not attached to the chuen symbol, as is usual in the inscriptions, the day, in the abstract sense, having its appropriate symbol, to which the numerals denoting the number of days are attached. As the usual order in which the glyphs are to be read is from the top downward, by twos and twos where there are two columns, we will take the first pair, Al and B1, as the date from which to count. This, as already stated, is 4 Ahau, the 8th day of the 18th month—Cumhu— of the year 8 Ben, which, as will be seen by referring to our table 3, is the forty-seventh year of the cycle of years, or calendar round. Changing these time periods to days— Days Sess te Ee Oe or ren at epee) 108, 000 OPO pbc gases: Sea een OEE ree te 3, 240 CUES See eee eel: sinc ces bicie as Cee eee 80 DERE Se sl EE ee ey Re Es 4 The aggregate is --. 111, 324 Subtract 5 calendar rounds 94, 900 here: TeEMsin = = - as Oe ee ee eee ee eee 16, 424 Subtracting from this remainder 17, the number of remaining days in the year 8 Ben, from 4 Ahau 8 Cumhu, and dividing the remainder by 365, we obtain 44 years and 347 days, equal to 17 months and 7 days. Counting forward on table 3, 44 years, we reach 13 Ben, the next year being 1 Ezanab. Turning to table 1 we find that 17 months and 7 days bring us to 9 Kan, 7 Cumhu, instead of 9 Kan 12 Kayab, which is given on the plate. Counting backward from 4 Ahau 8 Cumhu, as the symbols apparently indicate should be done (if the order be as in the inscriptions), results in a still wider variation from the correct date, assuming that the symbols on the plate—which are very distinct and unmistakable—are correct. If the dates on the plate are correct, the first falls in the year 8 Ben, and the latter in 3 Ben. Counting forward there would be an interval (omitting the calendar rounds) of only 7 years and the fractions of the 2 years in which the two dates fall, manifestly too small for the numeral symbols. Counting backward there would be an interval (omitting the calendar rounds) of 43 years and the fractions of the 2 date- years, making, in all, 16,076 days, or 348 days short of that required by the time symbols after deducting the calendar rounds. As there (32 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 are other symbols between the dates with numerals attached, it is pos- sible the explanation needed is found in them. In the parallel pas- sage on plate 61, which appears to have the same beginning and end- ing date, there is but one dot to the chuen symbol (indicating 1 chuen) and the symbol for 3 days. This gives a total (omitting the calendar rounds) of 16,363 days. But this gives no satisfactory result. I have dwelt somewhat at length on these series as they are the only ones with two legible dates in the codex which show the higher time periods in symbols. They will serve, however, to show the close relation which this codex bears to the inscriptions, to which we will now turn, beginning with those at Palenque. INSCRIPTIONS AT PALENQUE Before proceeding with these, in order to show exactly Mr Good- man’s method of calculating a series from the inscriptions, I present as an example one which he has fully worked out. This series is found in the inscription of the Temple of the Sun, at Palenque. It will be more critically examined hereafter by comparison with Mauds- lay’s photograph. At present I use Goodman’s determination merely for the purpose of illustrating the method of reckoning. The dates and intervening time periods as he gives them are as follows: 4 Ahau, 8 — (month not identifiable), 16 days, 5 chuens, 15 ahaus, 12 katuns, and 9 cycles, followed by the date 2 Cib, 14 Mol. Reducing these time periods to days, the result is as follows: Days 9 cy clestea..2 26 shane = secs eee ee ean 1, 296, 000 1A 211000 41 ee ee a aE ae ei PE = este Se 86, 400 AS ghia soe 3 ts ea ee ee ees 6, 480 Si chuenias sae oe oe ete a ee er ee ee 100 HC (0 Ei: peepee ne aoe pe an ne a eeent ey Oe eS eS 16 AGE y exe ees ee ye ee nee Ee 1,388,996 ° Deduct 7sicalendan rounds! =-)-4-44- oe ee eae 1, 385, 540 THISHOAVERE: = salle cierto aoe eC ee eee 3, 456 As the first date can not be fully determined, it will be necessary to count back from the second date—2 Cib 14 Mol, which falls in the year 5 Akbal. Subtracting 154, the preceding days of this year, from 3,456 and dividing the remainder by 365, we obtain 9 years and 17 days. Deducting 5 for the added days, there remain 12 to be counted back on the last month of the year 8 Ben, which we find by counting back on table 3 is the year in which the first date falls. This gives + Ahau 8 Cumhu, which is, no doubt, correct, as this date is a very common one on the Palenque inscriptions. rae RT NINETEENTH ANNUAL REP L i I} Se CHEN 5% =< at o es] = - 7 een ee Ne ” - ; Mote Sor R A i >: ” je Y os Pat Ss - fe ae ’ tae . A ats ~ 7 » r q - 7 rs L 4 ye ° ; ; @ : ; A w) 7 7 7 s ? A) Se ° va . Fe + ay « ¥ aT; ot f ' Y : - / 4 tof ‘ : : yale ye f. , ¥ J a, 4 , sad ' Cp SS OT Sears é } - - t x? / Se 2

RS ae PS — q — Ww x 2 “ 7 . mney "a RA, 3 | noe * 4 ~~. . 4 NR Sys, SSN ~ . - iy Se | ity 5 oss ‘ Ne | . . Sas aa Y amped ~~ As tak niger Ne A PORTION OF THE TABLET OF THE CROSS, PALENQUE. PHOTOGRAPHED FROM A PLASTER CAST. THOMAS] TABLET OF THE CROSS 7338 Mr Goodman, after ascertaining the number of days in the time periods precisely as they are given above, proceeds as follows: From these [1,388,996 days] we deduct as many calendar rounds as possible, being 73, or 1,383,540 days, leaying 3,456. From these we take 155, the number of days from the beginning of the year to 14 Mol, that being the only date we are cer- tain of. This leayes 3,301 days. From these deduct all the years possible, being 9, or 3,285 days. There are now but 16 days left. Reckoning back from the end of the year, we find these reach to 8 Cumhu [according to his method of numbering the days of the month], a circumstance that enables us easily to recognize the strange sign as a variant of the symbol for that month. Turning now to the Annual Calendar, we find that 4 Ahau-8 Cumhu occurs on page 7, and, passing oyer 9 years till we come to page 17, we find that 2 Cib falls on the 14th of Mol in that year. Thus we are satisfied that the strange month sign is a symbol for Cumhu, and that the cycles, katuns, ahaus, chuens, and days represent the period between the two dates, the full reading being: 9-12-18-5 x16, from 4 Ahau-8 Cumhnu, the beginning of the great cycle, to 2 Cib-14 Mol. As our process is intended to be independent of Mr Goodman’s tables, it is necessary for us to divide by 365 in order to find the inter- vening years, and to determine the full date including the year, which Mr Goodman fails to do. TABLET OF THE CROSS Proceeding now with the Palenque inscriptions. Attention is directed first to that on the so-called Tablet of the Cross, the right slab of which is fortunately safely housed in the United States National Museum. The inscription on this slab is well known through the excellent autotype in Dr Rau’s paper entitled Palenque Tablet, but, in order to place the record before the reader in as complete a form as is possible, I have given a copy in figure 177, and a copy of Maudslay’s photograph of the left slab im figure plate xn; a drawing of the few characters above the arms of the right priest in the middle space is shown in figure 17%. As this is the most important of all the known Mayan inscrip- tions, for the purpose of testing Mr Goodman’s discoveries, I shall examine it somewhat fully, and to this end give below a list of the dates and series in the order they stand, beginning with the large initial on the left slab. It is necessary, however, first to notice some- what particularly the initial series of the left slab. The first character of this series is the large glyph covering spaces Al, Bl, and A2, B2. This Mr Goodman interprets as the great cycle, which is equivalent to the sixth order of units. I am inclined to believe this interpretation is correct. The reasons for this belief are the form of the body or chief element of the glyph, which is similar to that of the ahau and katun; and the fact that it always follows in the ascending scale (counting backward or upward) the cycle, there being, so far as known, no exception to this rule in the (34 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 initial series. This is shown not only in initial series like the one here represented, where numeral prefixes are face characters, but in a number of others where the ordinary units, balls and lines, Fic, 17a—Inseription on the right slab of the Tablet of the Cross, Palenque. are prefixed to the glyphs representing the lower orders (cycles, katuns, ete.). Another reason for this belief is that positive evidence is found in the Dresden codex and in the inscriptions that there is an THOMAS] TABLET OF THE CROSS 735 order of units above the fifth, or cycle; that is to say, a sixth, or great eyele, as Mr Goodman calls it. This being true, there is every rea- Ge>: SS a oy x é = o= B=} ey mh f u (— he Fie. 17>—Inscription on the middle space of fhe Tablet of the Cross, Palenque. son to believe that it would be represented in the inscriptions by a special character. Examining the seven succeeding double glyphs in the order in which they stand, they are found to be as follows: A3, B3,a face character and 736 MAYAN CALENDAR SYSTEMS LETH. ANN. 19 the cycle symbol (see figure 11a); A+, B4, a face character and the katun symbol (see figure 107); A5, B5, a face character and the ahau symbol (see figure 94); A6, B6, a face character and the chuen symbol (see figure 87); AT, BT, an unknown character (dise with hand across it) and the symbol for day (kin) in the abstract sense, same as the lower portion of the symbol for the month Yaxkin. At AS, BS, a face char- acter and the symbol for the day Ahau; A9, B9, a face character and the symbol for the month Tzec. These are interpreted by Mr Good- man as follows: ‘*53-12-19-13-4+x 20—8 Ahau 18 Tzec”; that is to say, the fifty-third great cycle, 12 cycles, 19 katuns, 13 ahaus, +4 chuens, 20 days, to 8 Ahau 18 Tzec. From this it is seen that be interprets the prefixed face characters as numerals, assigning to each a particular number determined by the minor details or otherwise. Omitting, for the present, consideration of the number given to the great cycle, let us see if there is any reason for believing that he is cor- rect in assigning numeral values to the face characters attached to the time-period symbols, or, as we term them, symbols of the orders of units. Taking the known time-period symbols in this series, observing the recular descending order in which they stand, and being aware of the fact that in several other similar initial series the face characters are replaced by the ordinary numeral symbols (balls or dots and short lines), the evidence seems to justify Mr Goodman’s belief. Another strong point in favor of this belief is that at AS, BS, and AY, BY, which contain the symbols for the day Ahau and the month Tzec, we most certainly find a date which could not be complete without attached numerals. As the places of the numerals are filled by face characters, the most reasonable conclusion is that they represent these numerals. The evidence therefore in favor of Mr Goodman’s theory seems to justify its acceptance. But here the question arises, what evidence have we that the numbers assigned to these face glyphs are correct Admitting that they are numeral symbols, it is certain that they do not indicate numbers higher than 20, almost certainly not exceeding 19, as there are other symbols for full count or 20. It is also certain that the one attached to the symbol for the day Ahau does not exceed 13. and that the one attached to the chuen symbol does not exceed 18. We are thus enabled to limit very materially the field of inquiry, but to be entirely satisfactory there must be actual demonstration. If 8 Ahau 18 Tzee could be connected by intervening numbers with a following date this would be demonstration that the numbers given to the date symbols are correct. As will be seen farther on, Mr Goodman connects it by means of series 4 (left slab), given below, with 9 Ik (glyph E9); but the month date reached is 20 Chen instead of 20 Zac, as given in the inscription. While we may accept this as possibly or eyen probably a correct result, yet it is not demonstration; moreover, (what appears to be an equally probable and more acceptable explana- THOMAS] TABLET OF THE CROSS Cx tion, as will be shown farther on) by simply adding two days to the first numeral series connection will be made with the date of the third series. There is, however, as will be seen, at least one initial series with face characters in place of numerals where connection is properly made according to Mr Goodman’s number with a following date. As there will be occasion to refer frequently to the series on the different divisions of the tablet we give here a list of these series in the order in which they occur, beginning with the closing date of the initial series on the left slab, the years being added in parentheses. The numeral series are given in cycles, katuns, ahaus, chuens, and days, followed by their equivalent in days placed to the right; and where the sum is greater than a calendar round, the remainder, after subtracting the calendar rounds, is also shown. The term ** left slab” (though not strictly correct) is used only te include the six columns at the left; ‘‘right slab,” the six columns at the right; and ‘‘middle space,” to include the entire space between the six columns at the left and the six columns at the right. The series as here given are based on inspection: Left slab See Days 8 Ahau 18 Tzec (2 Akbal) | 1 Ahau 18 Zotz (2 Akbal) 1 | at? Oe ee mee 5 i em ne et eR 2,980 | 4 Ahau 8 Cumhu (8 Ben) | vy) 1 Ol RES aS eM as Hp soe eo ae Bae CSOD ACen paEEee 542 | 13 Ik 20 Mol (10 Akbal) ON let er Smel zen ON(274°920idays) pee neritic sie eas = 9, 200 9 Ik 15 Ceh (9 Lamat) || iF St OD (COOP) cons ccsccoegasaumanseenace | 13, 242 9 Ik 20 Zac (11 Akbal) 5 SPO) LO 12) 22) (47904 2idays) paee sess = osteo os 4,542 9 Ik (no month) 6 | UR eaieY es Ge reste ose socio ore ae ete al Ie ere eerie 9,513 (The next date comes in the middle space) Middle space 13 Ahau 18 Kankin? or Kayab? 3? 4? or 8? ? 3 ? (not determinable) 738 MAYAN CALENDAR SYSTEMS (ETH. ANN, 19 Right slab | il: St 2? 20 Pop 5 Cimi? 14 Kayab? | GR ety en Sap e oo ee prs acosansnasdeseanoooucccce 8,034 | 1 Kan 2 Kayab? (5 Akbal?) 11 Lamat 6 Xul (10 Akbal) 2 [Sie Sigs Ries pene area: as See ere Sea ee 4,749 2 Caban 10 Xul (10 Lamat) 3 Bet Sh ah oe see eee oes ea eee ee a ee 123 | | 8 Ahau 13 Ceh (10 Lamat) 4 tee) IP We ee aaa sobs coe cosadesrsdttesccnetooessa5¢ ) 10,118 | 3 Ezanab 11 Xul (10 Lamat) 5 11.6 Ste St ic etee oo rreretc ae ee ee ee or eee ere 13, 138 Ya tay 2 (Alhau?) women ss= ? (Tzec?) beeesac ? 20 Zotz 6 eG) (Gas Ome as eel ieee ais aha ron Seo eee ee 14, 176 5 Kan 12 Kayab (12 Ben) 7 Py Pp CNN ee ok SAS Sobre egc Sane ee SR oSSa RE St 15, 217 imix 4 S22 ? (Zip or Ceh) 8 ] ly WS joe sec cndest ss ckistsen cea eccsese ween ee 381 7 Kan 17 Mol (7 Lamat) 9 Ca Tater? i pane gc eee Bee, RR oe etareeP a a at 4k 17, 367 11 Cib? 14 Kayab? (3 Akbal?) | 1O:| VOCOe T7P gee De tit G Os ee ee ee 7,002? | (No date follows to the close) The first day of the left slab—8 Ahau 18 Tzec—has the numbers given in face characters, as has been stated; those given are according to Mr Goodman’s interpretation. The date following number 4, left slab, is corrected by Mr Goodman from 9 Ik 20 Zae to 9 Ik 20 Chen. Mr Goodman corrects the number of days in the sixth series, left slab, from 9,513 to 9,512. The month of the date (13 Ahau 18 Xul? or Kayab?) in the middle space, Mr Maudslay, in his drawing (part 5), probably inspired by Mr Goodman, is inclined to give as Kankin, in which he is probably cor- rect. The nearly obliterate glyph which follows he gives as 8—‘ 3 Kayab. This interpretation is, however, exceedingly doubtful. Maudslay, in his drawing of the middle space (part 10), gives 13 as the number of chuens in the second series. He is also evidently inclined to give the first date on the right slab (11—? 20 Pop) as 11 Caban 20 Pop; and the second, 5 Cimi 14 Kayab, as is indicated in the preceding list. Though there is some doubt as to the number of THOMAS] TABLET OF THE CROSS 739 chuens, first series, right slab, this author follows Rau’s restoration and gives it as 5, yet it may possibly be + or but 3, as the glyph is exactly in the line of a break repaired by Dr Rau. The number of chuens as well as days in the fifth series of the right slab is uncertain. Maudslay indicates 8 for the former and 18 for the latter, which is apparently correct. The two dates following this series, except the month (20 Zotz) of the second, are almost entirely obliterated. I believe the day of the first to be Ahau. Maudslay does not attempt a restoration, but agrees with my suggestion as to the month. He suggests Caban as the day of the second date. He gives Zip as the month in the date following the seventh series of this slab. The date following the ninth series he gives as 11 Chicchan 13 Yax or Chen, his figure being uncertain. The number of ahaus in the tenth series is left uncertain by him; he apparently prefers 16, though his figure may be construed as 18. The three lines (15) are distinct in the inscription, but the number of balls forming the fourth line is uncertain; the number seems to me to be 16 or 17, In referring to the inscription, Rau’s scheme, given on page 61 of his Palenque Tablet—to wit, letters above for each column and numbers at the sides for the lines—will be followed here (not Maudslay’s), it being remembered that the columns, where there are more than one, are to be read two and two from the top downward, single columns from the top downward, and single lines from left to right. Referring now to the left slab, we will first point out the location in the inscription of the glyphs denoting the several dates and numeral series, the latter being reversed to agree with the order in which they come in the inscription, the first date—8 Ahau 18 Tzec—heing that with which the initial series terminated. 8 Ahau (A8 B8) 18 Tzec (A9 BY) Series 1 Ahau (A16) 18 Zotz (B16) JME oe Ses 0 days 5 chuens (D1) 8 ahaus (C2) + Ahau (D3) 8 Cumhu (C4) Second .-.-.- 2 days 9 chuens (D5) 1 ahau (C6) 13 Ik (C9) 20 Mol (D9) Aovigal ease 0 days 12 chuens (D13) 3 ahaus (C14) 18 katuns (D14) 1 cyele (C15) 9 Ik (E1) 15 Ceh (F1) iNowbansy SA se 2 days 11 chuens (E5) 7 ahaus (F5) 1 katun (E6) 2 cycles (F6) 9 Ik (E9) 20 Zac (F9) Ritth) 225205 2 days 12 chuens (E10) 10 ahaus (F10) 6 katuns (E11) 3 eycles (#11) 9 Ik (F12) no month given Sixes 13 days 7 chuens (F15) 6 ahaus (E16) 1 katun (F16) We begin, therefore, in our attempt to trace the series and con- nect the dates with 8 Ahau 18 Tzec (as Mr Goodman interprets the numeral face characters), which falls in the year 2 Akbal. As it is followed by another date (1 Ahau 18 Zotz) without any recognized 740 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 intervening numeral intended to be used as a connecting series, we must assume that if it is connected with any of the following dates it must be by means of one of the series coming after the second date. Mr Goodman does not begin his attempts at tracing the connections in the inscription on this slab with the first date, but, after noticing the initial series, and taking 1 Ahau 18 Zotz as his starting point, says (page 135): After three glyphs, which are probably directives stating that the computation is from that date, there is a reckoning of 8-520 [that is, 8 ahaus 5 chuens 20 days], with the directive signs repeated, to 4 Ahau 8 Cumhu [the third date given above]. * * * This reckoning is a mistake. It should be either 6-14 20, the distance from 8 Ahau 18 Tzee to 4 Ahau 8 Cumhu, or 6-15 20, the distance from 1 Ahau 18 Zotz—imore likely the latter, as it will presently be seen that other reckonings go back to that date. Before veferring to Mr Goodman’s suggestions, we find by trial that this first date (S Ahau 18 Tzec, year 2 Akbal) will not connect with any of the dates on the left slab, nor middle space, by either of the numeral series as given. If, however, we add two days to the first numeral series, making it 2,982 days, and count forward from 8 Ahau 18 Tzec, we reach 13 Ik 20 Mol in the year 10 Akbal, the date following the second series. This, it is true, skips over the immediately following date (4 Ahau 8 Cumhu, year $ Ben), but if we subtract the second numeral series (542) from the first (2,982. as cor- rected) the remainder, 2,440, counting forward from the same date, will bring us exactly to 4 Ahau 8 Cumhu 8 Ben. Are these two coincident correct results to be considered accidental? They might be but for the additional fact that if 542 be subtracted from the sum of the first three series (first, second, third) with added two days to the first, the remainder, counting forward from 8 Ahau 18 Tzee 2 Akbal, will reach 9 Ik 15 Ceh 9 Lamat, the date following the third numeral series. Turning now to Mr Goodman’s explanation of the first series and the accompanying dates, I notice first the fact that here as elsewhere he interprets what I consider the symbol for naught (0) as equivalent to 20; thus the number of days of the first series instead of 2,980 would be, following his explanation, 3,000—that is to say, the numeral series, as he gives it, is 8 ahaus 5 chuens 20 days, my interpretation being 8S ahaus 5 chuens 0 days. The chuen symbol here is of the usual form, that shown in figure 1 a; the ahau is a face form sivnilar to that shown at figure 24. That there is a mistake here, as Mr Goodman asserts, is evident, if the two dates given, 1 Ahau 18 Zotz and 4 Ahau 8 Cumhu, are to be connected by the intermediate time periods. As 1 Ahau 18 Zotz falls in the year 2 Akbal, and 4 Ahau 8 Cumhu in the year 8 Ben, the interval is six years and the fractional days of the two years THOMAS] TABLET OF THE CROSS 741 2 Akbal and 8 Ben), the total, in days, being 2,825, whereas the inter- mediate time periods, as interpreted by Mr Goodman, give 3,000, or, omitting the 20 days, according to Maudslay’s interpretation of the symbol, which appears to be correct, 2,980 days. It is apparent there- fore that there is some mistake here—that is, supposing the theory that the two dates are intended to be connected by the intermediate time symbols be true. Mr Goodman suggests two ways of making the correction—first, by assuming 8 Ahau 18 Tzec to be the date from which to count, and changing the intermediate numeral series from 8 ahaus 5 chuens to 6 ahaus 14 chuens, thus making two radical alterations; in other words, a new numeral series to fit the case. This he obtains by subtracting the initial series as he has given it, from the 13 cycles composing his fifty-third great cycle, thus— 13— 0— 0— 0—0 Ise 40) 6—14—0 His other method is to change the intermediate time periods or numeral series to 6 ahaus 15 chuens—which is also making a new series—and to count from 1 Ahau 18 Zotz. In making these proposed changes Mr Goodman seems to drop out of view his 20 days, as in fact he does throughout in his calculations. He gives the full count—20 for days, ahaus, and katuns, and 18 for chuens—in noting the numeral series, but appears to treat them as naughts in his calculations. This is evident from the numbers he gives in the present instance. As conclusive evidence on this point it is only necessary to refer to the preface to his ‘* perpetual chrono- logical calendar” (op. cit., not paged), where he says of the series 9—15—20—18 x 20, ‘there are no days, chuens, or ahaus in this date.” Mr Maudslay, in his illustration of Goodman’s method of interpreta- tion before the Royal Society of England, June 17, 1897, in which he uses a newly discovered inscription (see figure 20), counts the char- acter at the side of a chuen symbol (C1), precisely like that attached to our chuen, as equivalent to naught. In the case he refers to there are two lines above the symbol, counted as 10 chuens. Speaking of it he says: Cl is the chuen sign with the numeral 10 (two bars=10) above it and a “full count”’ sign at the side. Whether the 10 applies to the chuens or days can only be determined by experiment, and such experiment in this case shows that the reckon- ing intended to be expressed is 10 chuens and a ‘‘full count’’ of days—that is, for practical purposes 10 chuens only, for as in the last reckoning, when the full count of chuens was expressed in the ahaus, so here the full count of days is expressed in the chuens. In other words, that the character at the side simply means that no 19 ETH, Pr 2 12 742 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 days are to be counted, and so his figures giving the number of days show. But this,as has been shown, will not suftice to correct the mis- take in our example. However, a very slight change, as 1 have shown, which Mr Goodman failed to find, which is simply adding 2 days to the time periods, will suffice to bring the series into harmony with the theory, and at the same time to verify his determination of the face numerals attached to the terminal date of the initial series—8 Ahau 18 Tzee (year 2 Akbal). Although the initial series will be discussed farther on, it will per- haps be best to indicate here the probable processes by which Mr Goodman reached his conclusions in regard to the series now under consideration. According to the system which he has adopted and which he claims was the chronologic system of the inscriptions, 13 cycles, or units of the fifth order, make 1 great cycle, or 1 unit of the sixth order, and 73 great cycles complete what he terms the ‘‘grand era.” As this system will be more fully explained farther on, it is only neces- sary to state here that he concludes from his investigation that the dates found in the inscriptions all fall in the fifty-third, fifty-fourth, and fifty-fifth great cycles. As these are taken by him to be abso- lute time periods, each begins with its fixed and determinate day; in other words, there is no sliding of the scale. According to this scheme the fifty-third great cycle began with the day 4 Ahau 8 Zotz, the fifty-fourth with 4 Ahau 8 Cumhu, and the fifty-fifth with the day 4 Ahau 3 Kankin, these dates following one another at the distance of one great cycle apart, which is correct on his assumption that 13 cycles make one great cycle, a conclusion which I shall have occasion to question. Now, it is apparent that he assumes that 4 Ahau 8 Cumhu, the day following the first numeral series noted above, is the beginning day of his fifty-fourth great cycle. This being assumed, it follows that the preceding dates, 8 Ahau 18 Tzec and 1 Ahau 18 Zotz (which precedes the former in actual time by precisely one month), must fall in his fifty-third great cycle; and as the former (8 Ahau 18 Tzec) is the ter- minal date of the initial series, therefore this initial series goes back to 4 Ahau 8 Zotz, the beginning day of the fifty-third great cycle. As the time to be counted back from 4 Ahau 8 Cumhu to reach the closing date of the initial series is, according to the first numeral series, 8 ahaus, 5 chuens, 0 days, or 2,980 days, it must necessarily fall in the last katun ofthe fifty-third great cycle, which, according to his peculiar method of numbering periods, will be the 19th katun of the twelfth cycle. Counting back into this katun (using his tables), 8 ahaus and the 5 months carries us into the ahau beginning with 1 Ahau 8 Uo, as the only day Ahau of this period falling in the month THOMAS] TABLET OF THE CROSS 743 Tzec—which the inscription requires—is 9 Ahau 8 Tzec, which requires a numeral series of 3,180 days, or 8 ahaus 15 months. As Mr Goodman concludes that the face numeral prefixed to the symbol for the month Tzec should be interpreted 18, the nearest position in which a day Ahau the 18th of the month Tzec can be found, is in the thirteenth ahau of this katun. From this date to 4 Ahau 8 Cumhu is 6 ahaus 14 chuens; hence his proposed change in the numeral series. The question therefore to be answered before we can give full assent to his conclusion is this, Are his renderings of the face char- acters reliable? That they represent numbers seems to be evident, as I show elsewhere, but the data presented in his work are not entirely satisfactory. That the initial series now under consideration contains one or more cycles, one or more katuns, one or more ahaus, and one or more chuens—or, as I term them, units of the fifth, fourth, third, and second orders—is certain; and that the terminal date is a day Ahau in the month Tzec is also true if the inscription be correct. The language used by Mr Goodman in defining the face numerals indicates that he has relied to some extent on his system of interpretation rather than on the details of the glyphs in determining their value, but this can be decided only by a careful examination of all the inscriptions in this respect, which it is my purpose to make in a supplemental paper when Maudslay’s figures of the Quirigua inscriptions are received. When the count can be based on the glyphs his scheme will not inter- fere with a correct count. For example, 4 Ahau 8 Cumhu of this series may or may not be the first day of his fifty-fourth grand cycle, for in either case the count will bring the same result; nor will the fact that there are probably 20 cycles to the great cycle change the result. However, the subject will be further discussed when we con- sider the initial series, and for the present we will accept Mr Good- man’s determination of the face numerals with the above implied reservation. I have dwelt somewhat at length on this example in order to show some of the methods of determining positively that there is an error in the original, and the seeming impossibility in some cases of cor- recting it. Occasionally this can be done by means of a connected preceding or following series; or, where a single minor change will bring all the members of the series into harmony, this change is some- times justified, but such changes as those suggested above by Mr Good- man in regard to the example under consideration, especially where the value of a sign is also in dispute, are not warranted without proof. The next date is found in glyphs C9, D9, and is 13 Ik —? Mol. Here the numeral attached to the month is not a regular number symbol (dots and bars) and is interpreted 5 by Mr Goodman. In this I am inclined to think he is wrong, as the symbol appears to be the 744 MAYAN CALENDAR SYSTEMS (ETH. ANN, 19 same as that found in glyph F9, which he interprets 20. His descrip tion of the series is as follows: Then [after 4 Ahau 8 Cumhu] follows another reckoning of 1-92 [1 ahau, 9 chuens, 2 days], succeeded by five unintelligible glyphs, to 13 Ik, 5 Mol. The com- putation and the 13 Ik are right, but the month should be 20 Chen, as will be seen by reference to the annual calendar. It will be evident pretty soon that the sculptors got their copy mixed up. The 5 Mol should have gone with another date (p. 135). The intermediate time periods are 1 ahau (of the usual form, a, figure 9), 9 chuens, and 2 days: Days. Wah aicc secs mac sone sect eee a seee cece ae See eee ena 360 ONCNNeNS Se sian eee eee oe eee eee eee ee eee 180 Mays os22 Be. She ssis aos eeaecisee tess n se Peas ee eee eee 2 Total 2 Se. 62. 2 eae ee ee eee 942 As the first date is uncertain, unless the explanation given above be accepted, we must count back from 13 Ik 20 Mol, which falls in the year 10 Akbal. I use 20 Mol, as I believe 20 to be the true interpretation of the unusual number symbol, and it is really that adopted by Mr Goodman in his calculation, though not expressed. As 20 Mol is the one hundred and sixtieth day of the year, and the count is backward, we subtract this from 542, and divide the remainder by 365, which gives 1 year and 17 days; this brings us to the year 8 Ben. Deducting 5 for the intercalated or added days, and counting back 12 days from the end of the month Cumhu, we reach 4 Ahau, the eighth day of the month Cumhu, proving that this terminal date of the preceding series is correct and that the error of that series must be in the initial date or in the numerals attached to the intermediate time periods. This result is in fact the same as that obtained by Mr Goodman, who commences his count of the days of the month with 20, transferring the last days of the columns in our table 1 to the first place, as is shown in table 4, given below, which is simply a condensation of his ‘*‘ Archaic annual calendar,” where each of the fifty-two years is written out in full. 745 TABLET THOMAS] OF THE CROSS 6L te tS) dL Wei? (OW te I L qIp uenyy) geen t@) XIOIy 81 lly A tye (OL te EE PAN ESE ts) voy 20 uBqoorgy) ney AL We ig WI 8 = @ [ LST 9 Gh 1g) xI on[ayA, UuBYy, oBNne’) 9T OSG Guns IL tell BYE Cale Ay IL. og, OUIBT eQALV qeueZiy cI (By 6 T 2 or Oy Bt Tk i OL qa LUBIN, AT UBO BO) FI 3 oy er Ge) aie SOE wong” feet) 2gaees| qt) €1 Boll 8) a Ne OIE GGT ae) Usyoord), neyy UST ral S) ralh Lire OL sou G5 tore 18: I Me XS oni ny uBy OBNB) XT I qe ae OIE ta GG ERE 8) Ait poUBT Teqa,V Qeus2iy ud OL if (Ee GG ESI) ge UL TUB AL UBB, qa 6 B® 9G 6 wh yh A ta) rele aE TOTS) = Genie Ue) wera? (9) 8 6 LoL Om iGliena Teta Oe so uBqoorgy) neyy Udy 20 L i 4 Ol) Gh 1g Lar [Ee ee eer Geers uBy oeney) XT on OAL 9 i 9 cL ¢ WE iv OE th i) we ES I 4 T8qarv QBueZiy og youre’T G Ie Gf 100 57 OM fe GREY tsit tb) AT uBqey) OL YUBA id mye 47 OE ey ms i Ye tee GY alte XIU] oh @ wont) TUT), § (Ge 48 SG 3 IT ZL (ibe 8) ie WG 42 nvyV wey 90 uUBqvoIy() G (J 0G TW BIL) IC NE ie IRS oBney) ST On TOTAL UBS I 8 [ A ken 48) Al $8 hae (NE QBUBZGT usd yeue’yT Pav 06 th AS) cal 4S; We iy OI GS I ueBqey) qa TUBAL AL qquour - aie ssoquinu Aud saRod URQRD sinad op suvod 4 LORI siBod YT f$ ATAV 746 MAYAN CALENDAR SYSTEMS (ETH. ANN.19 It will be seen from this that 13 Ik, the last day of the month Mol (year 10 Akbal) in our table 1, by the change made by Mr Goodman becomes the 20th day of the month Chen, which is in fact the begin- ning day of this month, and would in all ordinary calculations be counted the first, or 1. Although the numbering of the days of the month and of the days is not changed by this transposition, it does make a change in two important respects. First, the days which would be last in the month, if the count of the days of the month began with 1, become the begin- ning days of the following month, though counted as the 20th by Good- man’s method. Second, the position of the years in the 52-year period is changed. For example, the year 10 Akbal of the series exam- ined, which will—as can be seen by reference to table 3—be the 49th year of the 52-year cycle, becomes the 9th by Goodman’s method. In the preface or preliminary remarks to his Archaic Annual Cal- endar, this author states as follows: [have put Ik at the head of the days because it is nearest to Kan of any of the Archaic dominicals, and because the Oaxacan calendar shows a tendency toward ret- rogression in the order of the days. There is no good reason, however, why any of the other dominicals may not have been the first. In fact the frequent and peculiar use of Caban in the inscriptions and its standing as the unit of the numeral series constituted by the day symbols would appear to go far toward justifying an assump- tion that it was the initial day; but the former circumstance may be only a chance happening, and the latter may attach to the remote pre-Archaic era when the year began with the month Chen; so that neither of these considerations, nor the signifi- sant recurrence of Manik in certain places, has had weight enough to induce me to change the order originally adopted; nor will it be worth while to alter it until some style of reckoning from the beginning of the annual calendar is discovered not in harmony with the present arrangement. In regard to these statements, it may be affirmed that the reason given for placing ‘Ik at the head of the days” is wholly insufficient, as it is not, in fact, nearest Kan of any of the Archaic dominicals, being nearer to Akbal, which certainly was a dominical, than to Kan; nor, in fact, would this be any reason for the change were it true. Second, as he begins the count of the days of the month with 20, it is in fact not first in the count. It is proper, however, to add here that if Dr Brinton (The Native Calendar, p. 22) bas interpreted cor- rectly his authorities, Ik was the initial dominical day in the Quiche- Cakchiquel calendar, though it must have been in comparatively recent times, as will appear from what follows farther on. Mr Good- man’s remark that ‘‘there is no good reason, however, why any of the other dominicals may not haye been first” is certainly correct. But this statement involves the correctness of his entire calendar sys- tem so far as the determination of the position of dates is concerned. It is true, as he states in the paragraph next below that quoted, that THOMAS] TABLET OF THE CROSS 747 ‘**for all ordinary purposes the point of beginning is of no importance, since the annual calendar is only an orderly rotation of the days until each of them with the same numeral has occupied the seventy-three places allotted to it in the year,” if ‘tall ordinary purposes” be limited to finding the beginning, closing, and length of periods without regard to the absolute position in the higher Mayan time periods. To illustrate, I take the last day of the series just examined. If the dominical days be Akbal, Lamat, Ben, Ezanab, in the order given, as first declared by Seler, this day will be 13 Ik, the 20th day of Mol in the year 10 Akbal, and the forty-ninth year of the 52-year period, where the count is by true years, and the 52-year period begins with the year 1 Akbal. According to Mr Goodman’s system, using Ik, Manik, Eb, and Caban as the dominical days in the order given (20 Ik being first in the 52-year period), counting the beginning day of the months as the 20th, it would be (though absolutely the same day in time) the 20th day of the month Chen in the year 9 Ik, the 9th year of the 52-year period. It is undoubtedly true that if the days were written out in proper succession with the proper numbers attached and the months properly marked, as in my Maya Year, we might, if the series should be made of sufficient length, begin the cycle at any point where we could find a day numbered 1 and standing as the first (beginning) day of the month Pop. But the cycles of years beginning at different points would not coincide with one another unless they were exactly 52 years, or a mul- tiple of 52 years, apart. As the system has, for the periods above the year, no fixed historical point as a basis or guide, the dates are only relative, that is to say, a date though readily located in the 52-year period, unless connected with some determinate time system, may refer to an event that occurred 200, 500, or 5,000 years ago; intother words, is but a point in each of an endless succession of similar series. It is possible, after all, that Goodman and I are both in error as to the initial year of the 52-year period, though this will in no way affect the calculation of series and determination of dates. The result in these calculations will be the same with any year as the initial one, provided that the regular order of succession be maintained. If the ordinary calendar among enlightened nations had nothing fixed by which to determine relative positions in time, our centuries might be counted from any one selected year, and all calculations made would be relatively correct. Although Mr Goodman’s computations may be, as we shall doubt- less find them as we proceed, usually correct, yet there is, if I read him aright, one radical error in his theory. He has taken the appa- ratus, the aid, the means which the Mayas used in their time counts as, in reality, their time system. In other words, he has taken the 748 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 calculation as the thing calculated. He makes the statement, already quoted: It was taken for granted that a year of 365 days must necessarily enter into the reckoning; whereas, the moment the Mayas departed from specifie dates and embarked upon an extended time reckoning, they left their annual calendar behind and made use of a separate chronological one. It is the error made in this statement that vitiates the entire stupendous fabric he has built upon it, though all of his computations may be correct so far as calculation is concerned. The Maya, in order to calculate time, had necessarily, just as any other people, to use some system of notation. Maudslay, though usually so carefully conservative, seems to have been led astray in this matter, as he remarks: All the dates and reckonings found on the monuments which can be made out by the aid of these tables are expressed in ahaus, katuns, ete., and not in years; but Mr Goodman maintains that the true year was known to the Mayas, and that it is by the concurrent use of the chronological and annual tables that the dates caryed on the monuments can be properly located in the Maya calendar. Dr Férstemann and Dr Seler seem also to have missed the true signi- fication of this time counting. If the former intended to be under- stood, in suggesting an ‘‘ old year” of 360, that this number of days was at an early period in the history of the Mayan people actually counted as a year, as seems to be a fair inference from his language, it follows as a necessary consequence that the years and also the months always commenced with the same day, though not with the same day-number (Zur Entzifferung der Mayahandschriften, ry, 1894, and elsewhere). Although Dr Seler distinguishes the 360 days from the true year of 3865 days, he alludes to it as a real time period. Speaking of the ‘* katun,” he says: And hence the discussion—upon which many profitless papers have been written— whether the katun is to be considered 20 or 24 years. The truth is, it consists neither of 20 nor of 24 years—the years were not taken into account at all by the old chron- iclers—but of 20 x 360 days. His katun was therefore 7,200 days, the same as that afterwards adopted by Mr Goodman. As a Mayan date is properly given when it includes the day and day number, and the month and day of the month, this determines the year in the system and the dominical day. As dates are found in the oldest inscriptions and in the Dresden codex, the oldest, or one of the oldest codices, and these dates show beyond question a year of 365 days, and hence a four-year series, there is no reason for believing that there are allusions, either in the inscriptions or codices, to a year of 360 days. The simple and only satisfactory explanation is that the 360 is a mere counter in time notation. THOMAS] TABLET OF THE CROSS 749 It would seem, therefore, that Mr Goodman has taken the system of notation in use among the Maya—their orders of units—to be, in real- ity, their chronological system. It would be just as true to say that the system of notation adopted by most enlightened people—the units, tens, hundreds, thousands, millions, ete., used in calculating periods of time—is, in fact, their time system. The Maya never left their annual calendar behind them when embarking upon extended time reckoning, a fact which is overwhelmingly proved by the constant reference to dates in the codices and inscriptions. The only proof furnished by Mr Goodman as to the reality of his discoveries is based upon this fact. The Maya time counts have only dates of the calendar system in view. Of course the mystical or ceremonial use of the 260- day period is not denied. Were it otherwise, their counting up of high numbers would haye no more meaning than the figuring of school- boys to see what great numbers they could reach. However, addi- tional evidence of the correctness of this assertion will become more apparent when I come to the examination of the characters and num- bers which Goodman assigns to his highest Mayan time periods. But in the meantime, though pointing out his fundamental error in this respect, we must not lose sight of his real and important discoveries, which must haye a material bearing on all future attempts at interpre- tation of the codices and inscriptions. Continuing our examination of the inscription of the Palenque Tablet of the Cross, and starting now from our last date, 13 Ik 20 Mol, in the year 10 Akbal (as I have interpreted it), we take up the succeeding series, explained by Mr Goodman as follows: After half a dozen glyphs, unintelligible further than like most intervening char- acters they are to be found elsewhere in the lists of period symbols, there is another reckoning—1l-18-3-12 20 from the preceding date to 9 Ik 15 Ceh [8 left slab]. This is correct, and in connection with the previous reckoning it proyes conclusively that the preceding date should be 13 Ik 20 Chen (p. 135). 5 This ‘‘ reckoning” signifies 1 cycle, 18 katuns, 3 ahaus, 12 chuens, and 20 days. Here, however, occurs again at the left of the chuen symbol the same character as that at the left of D1 mentioned above, which we counted as 0 instead of 20, as interpreted by Goodman. We count it as 0 in this instance also: Days ICY ClOR Ae se sate sists sot es beeen oes setae Sore a 2h ew ots! 144, 000 LSP ohn eee ay Soe Se NO ae oe niacin sims 129, 600 £53 (211 OF Os es 2h i ee eee oe et 1, 080 NOR CEUICTIS epee sere eae 5 = eee See fe oat th 240 LD EN teen BOS CR ene eeas oe Oro = Soe ee ee 0 274, 920 Following our own count as given above from 20 Mol, let us see what the result will be. From the total (274,920 days) we subtract 14 750 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 calendar rounds or 265,720 days, leaving a balance of 9,200 days. Subtracting from this 205, the remaining days of the year 10 Akbal, and dividing the remainder by 365, we obtain 24 years and 235 days, or 11 months and 15 days. Referring to table 3, and counting for- ward 24 years from 10 Akbal and passing to the year following, we reach 9 Lamat. By table 1 we find that the 15th day of the 12th month of the year 9 Lamat is 9 Ik, the 15th day of the month Ceh. This is correct, and proves (what Mr Goodman also claims for his count) that our decision as to the dates and the naught symbol is also correct. We pass to the series which follows (4, left slab). This is described by Mr Goodman thus: Six unintelligible glyphs follow; then there is a reckoning of 2-1-7-11 2, succeeded by four directive signs, to 9 Ik 20 Zac. I call attention to the directive signs. Two of them are the bissextile character and its coadjutor, which I think are employed in Palenque to denote different numbers of calendar rounds. These should denote fifteen, if intended to indicate the length of the reckoning; if to express an addi- tional period, it is uncertain how many. The other two directive signs are identical with two of those used after 1 Ahau 18 Zotz to show the reckoning is from that date. This reckoning is also from that date; hence the glyph consisting of a bird’s head and two signs for 20 over it probably indicates an initial date, or a substitute for it, as 1 Ahau 18 Zotz would appear to be in this case. The month symbol is wrong here also. It should be Yax instead of Zac. The next date is at E9, F9, which, as there given, appears to be 9 Ik 20 Zac, and the series is 2 days, 11 chuens, 7 ahaus, 1 katun, and 2 cycles at E5 to F6, the symbols being of the usual form. As this will not connect 9 Ik 20 Zac with the,preceding date, 9 Ik 15 Ceh (El F1), we will reckon from 1 Ahau 18 Zotz (A16 B16), as Mr Goodman sug- gests. This date falls in the year 2 Akbal. The count 2-1-7-11 x 2, when conyerted into days, is as follows: Days DICY CLES Sat crate ott tee oie ane a ee Stee eee eee 288, 000 OLS bh oe A Risk Nee oe Se A BSL Be ee A a 7, 200 FT ADBUSGS Soo eee wee nenhe Seas ee oe eR eee ae eee 2,520 TIP CHUCH Sack fesece ae Os Oooo Eee ee oan oe ee ee 220 P26 a ele oe pt Sy RES Ao REIS OSes Atria See PS = 2 Totaleorer esac eee ee ee ee eee eee 297, 942 Subtracting from this 15 calendar rounds—284,700 days—we get 13,242 days. Subtracting from this 287, the remaining days of the year 2 Akbal, after 1 Ahau 18 Zotz, and dividing the remainder by 365, we obtain 35 years and 180 days, or 9 months. Counting 35 years from 2 Akbal, on table 3, we reach 11 Ezanab. As the next year will be 12 Akbal, by counting on table 1 nine months in this year, we reach 9 Ik, the 20th day of the month Chen. This corresponds with the inscription except as to the month, which is 20 Zac. The count as given by Mr Goodman is 20 Yax, which is identical in his system with 20 Chen according to the system I am following. His THOMAS] TABLET OF THE CROSS (Sil suggestion, therefore, that the reckoning is to be from 1 Ahau 18 Zotz appears to be correct; at least it connects this date with that follow- ing the series, when allowance for the correction mentioned is made. Although this irregularity, of taking the series step by step from a given date for a time and then skipping back to another date as the starting point, arouses suspicion of something wrong in the proceed- ing, yet it occurs more than once both in the inscriptions and codices, and hence is not necessarily an evidence of error. The two dates which precede the first series indicate two points from which the count in some of the following series is to begin. Did we fully understand the intermediate glyphs, we should probably find this explained; at any rate we must follow at present what seems to be the most proba- ble rule, trusting that future investigation may correct any errors into which we have fallen. Mr Goodman, who has sought to learn the meaning of what he calls directive signs, says in regard to those connected with this series, ‘*‘ Two directive signs are identical with two of those used after 1 Ahau 18 Zotz to show the reckoning is from that date.” There is, however, but one that is similar, and it is an oft-repeated glyph. At any rate the proper result appears to be 9 Ik 20 Chen in the year 12 Akbal, as in no possible way can 9 Ik 20 Zac, which falls in the year 11 Akbal, be reached; and the day 20 Zac in the year 12 Akbal is 3 Ik, whereas the plan of the series appears to require 9 Ik. That the count should be from 1 Ahau 18 Zotz—that is, 1 month back of 8 Ahau 18 Zotz—or that the 11 chuens in the numeral series should be 10, is shown in another way, thus: To obtain the lapse of time from the last preceding date, 9 Ik 15 Ceh, we deduct 9,200 days (third series) from 13,242 (fourth series), and from this deduct 2,982 (first series), over which, as we have seen, the count skipped; this leaves 1,060 days. Counted forward from 9 Ik T5 Ceh (year 9 La- mat), this number of days brings us to 3 Ik 20 Yax in the year 12 Akbal, just 1 month later than 20 Chen. This calculation is based on 8 Ahau 18 Tzee as the starting point; hence we must count from 1 Ahau 18 Zotz, or assume that the 11 chuens in the numeral series should be 10. That the 20 Zac is wrong seems to be evident. Basing the count on 4 Ahau 8 Cumhu and 8 Ahau 18 Tzee will bring the same result, as will be seen by subtracting 2,440 from 13,242 and counting forward from the former. The series (5 of the left slab) following the last date—9 Ik 20 Chen— as corrected, is described by Mr. Goodman as follows: *‘ The reckon- ing which follows, 3-6-10-12 x 2, from the beginning of the great cycle is correct. It is here the 5 Mol should have gone, that being the month date.” These number symbols, 3 cycles, 6 katuns, 10 ahaus, 12 chuens, 2 days, which amount to 479,042 days, are followed at F12 by 9 Ik without any accompanying month symbol. The cycle and ahau symbols in this instance are face forms. By assuming as the month 7 bo 5 MAYAN CALENDAR SYSTEMS (ETH. ANN, 19 date 5 Mol, and counting back, Mr Goodman reaches 4 Ahau 8 Cumhu— D3, F4. That the count backward from 9 Ik 5 Mol will reach 4 Ahau 8 Cumhu is true, but here again is leaping over series as though they were inserted without plan or system. Moreover, Mr Goodman’s remark that the count reaches back to the beginning of the great cycle appears to be inconsistent with his own figures unless we change his ‘“‘full counts” to naughts. The initial series which he gives is, as has been shown, 53-12-19-13-4 x 20 to 8 Ahau 18 Tzec. Now, from this date—8 Ahau 18 Tzee—to 4 Ahau 8 Cumhu, according to his own count (page 135) is 6-14 20. Let us add these together. Cycles Katuns Ahaus Chuens Days 12 19 13 4 20 6 14 20 13 0 0 2 0 This reckoning runs back beyond the beginning of his 13th cycle, and hence, by his method of stating series, past the beginning of his great cycle, by two months, using his own figures. If the 20 days in the two series had been counted as 0, his calculation would have brought him to the beginning of a great cycle according to his scheme. Although, as has been stated, he does not use the full counts in his calculations, reference is made here to his method of stating numeral series in order to guard students from being led into error thereby. In every case where he uses 20 for days, ahaus, or katuns, and 18 for chuens, the true figure is 0. Another fact to be taken into consideration in deciding whether the evidence in the last count is satisfactory is that, as Ik might fall on the 5th, 10th, 15th, or 20th of the month and any one of the months might be chosen, there are 72 (418) variations to be tried to bring it into accord with the preceding date. If it could be connected by a following numeral series with some other date, the evidence would then be entirely acceptable, but this does not appear to be the case. However, I am not entirely satisfied with the result in this case, as the omission of the month date seems to imply that the 9 Ik is to fall on the 20th day of the month. If we follow the same rule as in the two preceding series, and subtract the 4th (297,942 days) from the 5th (479,042), and from the remainder the first numeral series, taking off the one month as before, and counting from the last preceding date— 9 Ik 20 Chen as corrected—we reach 9 Ik 20 Mol, year 6 Akbal. Or, subtracting the first series from the 5th (the 4,542) and counting for- ward from 1 Ahau 18 Zotz, we reach 9 Ik the 20th day of the month by dropping the same troublesome one month. These facts lead me to suspect that the true solution of the problem has not yet been reached. Following the last date, after some five unknown glyphs are passed, comes, at F15, F16, the numeral series (6, left slab) 13 days, 7 chuens, THOMAS] TABLET OF THE CROSS 753 6 ahaus, 1 katun, equal to 9,513 days. As no date appears in the remainder of the columns of this left slab, the question arises, Is the left inscription complete in itself and this the close, or is there con- nection with that of the middle space or right slab? This question will be discussed a little farther on. However, it may be stated here that by using the last (tenth) numeral series on the right slab (7,002 ? days) and counting forward from 1 Ahau 18 Zotz 2 Akbal, of the left slab, we reach 9 Ik 5 Mol8 Ezanab, of the fifth series of the left slab; but this would seem to be an accidental coincidence. As additions to the evidence already adduced in regard to the use of face characters to represent numbers, attention is called to others on this slab in regard to which there can be no question. One of these representing the ahau, or third order of units, is seen at F10; one denoting the cycle, or fifth order of units, at F11; another repre- senting the ahau is seen in front of the anklets of the left priest at L13, and another denoting the katun or cycle is under the feet of the left priest. The inscription in the middle space begins with the date 9 Akbal 6 Xul—ineluding the two glyphs G and H aboye the head of the left priest. These are distinct, and are probably to be accepted as correct, as the inscription in the middle space of the Tablet of the Sun, which appears to be similar in several respects to that on this tablet, begins with precisely the same date, in the same relative position. The numeral series (1) which follows consists of glyphs L12 and L13, imme- diately in front of the anklets of the left priest. These are 17 days, 8 chuens, 1 ahau, which equal 537 days. It is possible, however, that the large glyph on which the left priest is standing, which serakiaeiee 9 katuns or 9 cycles, is to be included in this series. If they are katuns, then the total number of days is 65,337, from which deducting three calendar rounds (56,940 days), leaves 8,397 oO S ye be counted; if they are cycles, the total number of days is 1,296,537, from which deduct- ing 68 calendar rounds (1,290,640), leaves eo ae s. The date which follows at glyph L14 is 13 Ahau and apparently 18 Kayab ¢or Xul? or possibly Kankin, though the month symbol can not be determined with positive certainty by inspection of the photograph or of Maudslay’s drawing. The corresponding date in the Sun Tablet is 13 Ahau 18 Kankin; and what is worthy of notice is that counting forward 537 days from 9 Akbal 6 Xul, year 8 Ezanab, brings us to 13 Ahau 18 Kankin, year 9 Akbal; this is probably the correct date. Using the katuns or cycles we can make connection with none of the given dates; hence the glyph on which the priest is standing may be omitted from the numeral series. Neither 9 Akbal 6 Xul, nor 13 Ahau 18 Kankin, nor 13 Ahau 18 Kayab will connect with any of the dates on the left slab by any of the numbers given. Taking for granted that 9 Akbal 6 Xul is the date intended by the 754 MAYAN CALENDAR SYSTEMS (ETH. ANN.19 aboriginal artist to be given at this point, we next try the connections forward. The other dates and series in the middle space after 13 Ahau 18 Kankin ? (or Kayab 7), already mentioned, are the following: A date at O1, O2 over the hands of the right priest. This is too badly detaced to be determined; all that can be positively asserted is that the number of the day of the month is 3, thus rendering it certain that it must be Ahau, Chicchan, Oc or Men. The number of the day was small, seemingly 3 or 4, but evidently not exceeding 8; Maudslay’s drawing gives 8. The corresponding date on the Tablet of the Sun as given by Goodman is 8 Oc 3 Kayab, and the same date is found correspond- ingly on the Tablet of the Foliated Cross. The next numeral series (2, middle space) is found in the second and third glyphs of column R, immediately behind the shoulders of the right priest. This appears by inspection to be 6 days, 11 chuens, 6 ahaus = 2,386 days. Maudslay, in his drawing of this inscription in part 10 of his work, makes the number of chuens 13, taking for granted, as seems to be indicated, though it is somewhat doubtful, that the two outer dots have been broken away. This would increase the total number of days to 2,426, while the true number appears to be 2,386. Before attempting to make connections between the dates on the middle space and those which follow we will pass to the columns of the inscription on the right slab. The first date is found in glyphs T2, S3, viz: 11 —? 20 Pop. The day can not be determined by inspec- tion. However, it must be Caban, Ik, Manik, or Eb, these being the only days which fall on the 20th day of the month. The number pre- fixed to the month in this instance is the full-count or 20 symbol, two semicircles. Before reaching a numeral series another date occurs at glyphs S4, T4, as follows: 5 —? 14 Kayab? The day can not be determined with certainty, but is apparently Cimi, or Cib, most likely the former; the month symbol is somewhat indistinct, but appears to be that of Kayab. The corresponding date in the inscription of the Tablet of the Sun and also of the Tablet of the Foliated Cross is 2 Cib 14 Mol, but in the former it is preceded by + Ahau 8 Cumhu, whose position is occupied in the Tablet of the Cross now under consideration by the 5 —? 14 Kayab? above mentioned. There is no recognizable numeral series in the middle space of either the Tablet of the Sun or Tablet of the Foliated Cross, but it is a singular fact that the second numeral series of the middle space of the Tablet of the Cross, given in the above list as 2,386 days, is exactly the lapse of time (counting forward) from 8 Oc 3 Kayab to 2 Caban 14 Mol in the Tablet of the Sun and Tablet of the Foliated Cross, and the 537 days of the first series in this space also connects the first and second dates in the middle space of the Sun Tablet, viz: 9 Akbal 6 Xul and 13 Ahau 18 Kankin. It is possible that these three inscriptions are dependent to some extent one upon the other, or are based upon an older and lost original. THOMAS] TABLET OF THE CROSS COS Neither of the two dates preceding the first series of the right slab, as determined by inspection of the inscription, makes a satisfactory connection with any preceding or following date; the proper day, but not the proper number, and even the day of the month, is reached, but there is no complete agreement, nor can the result be followed up with proof of its correctness. If we deduct 8 days from 8,034, the first numeral series of the right slab, and count back from 5 Cimi 14 Kayab 10 Ben, we reach 13 Ahau 18 Kayab 1 Akbal, which may pos- sibly be the correct date following the first series in the middle space. But this will not connect with 9 Akbal 6 Xul by the intermediate 537 days, but with 9 Akbal 6 Chen, year 13 Ezanab. However, if we deduct 8 days from 8,034, leaving 8,026, and count forward from 13 Ahau 18 Kankin, year 9 Akbal, the second date of the middle space, as found by calculation from 9 Akbal 6 Xul 8 Ezanab, this will bring us to 5 Cimi 14 Kankin, year 5 Ben, which may be the second date of the right slab, though the month symbol appears to be that of Kayab, and is so interpreted in Maudslay’s drawing. This will change the days of the glyph T+ from 14 to 6, but these are exactly in the line of the break in the slab and haye been restored by Dr Rau. Nevertheless, as 5 Cimi 14 Kankin will not connect with any following date by the numeral series as they stand, the result is not satisfactory. The first date, 11 —? 20 Pop, if construed to be 11 Manik 20 Pop 5 Lamat, will, by counting forward with 15,217, the seventh series, bring us to 5 Kan 12 Kankin, year 7 Ben, the date of the sixth series, except that the month is Kankin instead of Kayab as in the inscription. Can it be that these supposed Kayab symbols should be interpreted Kankin ? That some of them differ materially from the others is apparent. If, however, the date is construed to be 11 Ik 20 Pop, year 5 Akbal, and series 2 and 3 (4,749 and 123) be subtracted from the first ‘series (8034), the remainder, 3,162, will, by counting forward, reach 1 Kan 2 Kankin, year 13 Akbal, the date following the first series except as to the month, which in the inscription appears to be Kayab, though uncertain. The day symbol of the first date, 11 —? 20 Pop, does not appear to be Ik, though too nearly obliterated to be determined by inspection. But it appears, on the other hand, as has been stated, that if we assume this tirst date to be 11 Manik 20 Pop, year 5 Lamat and count forward 15,217 (the seventh series), we reach 5 Kan 12 Kankin, year 7 Ben, date of the sixth series except the month, which is Kayab in the inscription, or what has usually been taken as Kayab, and is of the form given in the Dresden codex to this month symbol. And lastly, it may be stated that Maudslay’s drawing is evidently intended to indicate Caban. As neither of these results can be followed up with other satisfactory connections they must be con- sidered as merely accidental coincidences. The same remark applies also to the next date, 5 Cimi (or Cib?) 14 Kayab. Nor can any satis- factory connection be made with the next date—1l Kan 2 Kayab. By 756 MAYAN CALENDAR SYSTEMS [erH. ANN. 19 reading it 1 Kan 2 Kankin, connection can be made in the manner mentioned above. If the date of the fifth series, left slab, be con- strued to be 9 Ik 20 Mol, which it may as well be as 5 Mol, by counting forward 4,542 days we reach 1 Kan 2 Kayab 5 Akbal, the apparently correct date, according to the inscription. If this reckoning be accepted it will form a connection between the inscriptions of the right and left slabs. ‘ The second date following the first numeral series on this slab is found in glyphs S10, T10. This is 11 Lamat 6 Xul, year 10 Akbal; following this, at 512, T12, is the numeral series 9 days, 3 chuens, 13 ahaus, which equal 4,749 days, and following this series, at S14, T14, is the date 2 Caban 10 Xul, year 10 Lamat. The two last-mentioned dates make connection, as by counting forward 4,749 days from 11 Lamat 6 Xul 10 Akbal we reach 2 Caban 10 Xul in the year 10 Lamat. Immediately following the last-mentioned date, at 515, is the short numeral series (3, right slab), 3 days, 6 chuens, or 123 days, which, count- ing forward, bring us to 8 Ahau 13 Ceh, year 10 Lamat, the date which followsat T17, U1. The rule therefore holds good as to these dates and the two intervening numeral series. It would seem to follow, there- fore, that the arrangement or plan of the series on this slab, when found, should coincide with the determination as to these two series; but from this point to the end of the inscription there is no connection of dates—with possibly one exception—without some change in dates or numbers from what they appear to be by inspection, or change in the direction of the reckoning. I shall therefore note the position of the dates and series which have been mentioned in the preceding list, and then add some remarks in regard to the relation of the dates and series to one another. I do this because Mr Goodman has left unnoticed the series of the inscription on this right slab, possibly because of the difficulty and seeming impossibility of bringing them into harmony with his theory. Immediately following the last date mentioned there is at U2 a symbol denoting 9 cycles, or ninth cycle, but judging by the rule adopted by Mr. Goodman this is not to be considered a part of the numeral series (4) which follows immediately after at U8 to U4, viz, 18 days, 1 chuen, 8 ahaus, 1 katun=10,118 days. At U7, V7 is the date 8 Ezanab 11 Xul, the day somewhat indistinct, but so rendered, apparently correctly, by Maudslay. Following this at U8, U9 is the numeral series (5), 18% (or 17%) days, 10? (or 87) chuens, 16 ahaus, 14 katun. The numbers of this series in the inscription have been injured to such an extent as to render uncertain those marked as doubtful; the number of days is assumed to be 13,138, which is probably correct, but the error, if there be one, is such that it should be readily discoy- ered by means of connecting series, if these be correct. Following the last series, at U10, V10 is a date so nearly obliterated THOMAS] TABLET OF THE CROSS (ASC that it can not be determined (except the numerals) with positive cer- tainty; itappears to be 5 Ahau 3 Tzec. Glyphs V12, U13 give another date, 5 —? 20 Zotz. The features of the day symbol are completely obliterated; the prefix to the month glyph is the symbol for 20. Imme- diately following, at V13 V14, is the series (6) 16 days, 6 chuens, 19 ahaus, 1 katun (14,176 days); at U17, V17 the date 5 Kan 12 Kayab; at W1, W2 the series (7) 17 days, + chuens, 2 ahaus, 2 katuns (15,217 days); at X5, W6 the date 1 Imix 4+ Ceh (or Zip), month symbol somewhat doubtful, but one of the two named, apparently Ceh. Following this at X6, W7 is the brief series (8) 1 day, 1 chuen, 1 ahau (881 days), fol- lowed at X10, W11 by the date 7 Kan 17 Mol; this is followed at X11, X12 by the series (9) 7 days, + chuens, 8 ahaus, 2 katuns (17,367 days); following this at W14, X14 is an uncertain date—11 Cib, Cimi, or Chicchan, 14/ (or 184) Kayab? The day symboland its number are distinct and clear, but the symbol is unusual; the number prefixed to the month symbol has been partially broken away; there were cer- tainly two lines (10) and some two, three, or four balls. The month symbol is uncertain, but is apparently the same as that of the date 13 Ahau 18 Kayab? or Xul, in column L, though it has something addi- tional on top. It is possible the symbol is intended for Chen or Kankin. ; Following the last date (11 Cib?) at W15, X15 is the series (10) 2 days, 8 chuens, 16, 17, 18, or 19 ahaus. The three lines (15) prefixed to the ahau symbol are distinct, but the additional balls or dots haye been injured to such an extent as to render the number uncertain (7,002 days, counting 19 ahaus). There is no date or other series in the remaining portion of the inscription. If it be possible to determine the plan, succession, or arrangement of the series in this inscription, an important step will have been gained and a basis laid for the correct determination of the associated glyphs. The peculiarities of Mayan time system and notation so often lead to deceptive results that extreme caution is required, and a single connection or proper result is seldom sufficient evidence of a correct interpretation. Taking the list of the series as given we are at once impressed with the strong general resemblance to the plan of the series on many of the plates of the Dresden codex, where several different series are found, some reckoned in one direction and some in another, as, for example, plate 73, where there are one entire series, parts of two others, and dislocated parts of two; or plate 70, where there are, in whole or in part, some half dozen series still in a tangle which has not yet been straightened out; also other plates. Taking merely the numerical series in the order they stand and changed to days, there is certainly in the irregularly ascending scale an indication of arrangement, of and relation between the series. 19 ETH, PT 2- 15 758 MAYAN CALENDAR SYSTEMS (ETH. ANN, 19 These, beginning with the first in the middle space and following with the right slab and then with the left, are as follows: Middle space eee 537 a 2, 386? Right slab i beeaty S 8, 034 En N 4, 749 Bees 123 Mewen ee 10, 118 ee 13, 138 (eee 14, 176 rita ae 15, 217 Slee 381 eee: 17, 367 TON ee 7, 002? Left slab eee 2, 980 Cater 542 Oseee 274, 920 4222 297, 942 Oetne eis 479, 042 a 9,513 It is apparent from this list that there is an irregularly ascending scale following the order given, but so far no common divisor forming a basis of the differences has been found; moreover, the introduction at some three or four points of short periods seems to break in upon the idea of special references to the differences, as is usual in the Dresden codex. Besides this, the differences do not serve to connect dates, except possibly in two instances, while in one-third or more cases successfully traced individual numeral series do. As the exceptions alluded to above may possibly prove to be impor- tant factors in determining the relations of the series on this tablet, it will not be amiss to again notice them here. As is shown above, if we add two days to the first numeral series on the left slab, making it 2,982, and count forward from 8 Ahau 18 Tzee (2 Akbal), we shall reach 13 Ik 20 Mol (10 Akbal), the date following the second numeral series. If now we add the first numeral series as corrected—2,982—to the third numeral series (after deducting calen- dar rounds)—9,200—making a total of 12,182, and count forward this number of days from 8 Ahau 18 Tzee (2 Akbal). we reach 9 Ik 15 Ceh (9 Lamat), the date following the third numeral series. If we go back now and subtract the second numeral series—542—from the tirst—2,982—which leaves 2,440 days, and count forward this number of days from 8 Ahau 18 Tzee (2 Akbal), we reach + Ahau 8 Cumhu THOMAS] TABLET OF THE CROSS 759 (8 Ben), the date following the second numeral series. These agree- ments can scarcely be accidental, and if not, they establish two facts: First, that Goodman’s interpretation of the face glyphs giving the date 8 Ahau 18 Tee is correct, or at least brings a correct result; and, second, that the emendation of the first numeral series by adding 2 days is also correct. Other relations of dates on the left slab have been given, besides which no further connection by using the differences of the numeral series can be obtained. Turning to the right slab, if, as has been suggested, we assume the first date (11 — ? 20 Pop) to be 11 Ik 20 Pop (year 5 Akbal), and sub- tract series 2 and 3 (4,749 and 123) from the first series (8,034), the remainder, 3,162, counting forward from 11 Ik 20 Pop (5 Akbal) will bring us to 1 Kan 2 Kankin 13 Akbal, the date following the first numeral series, if the month symbol is interpreted Kankin instead of Kayab. This result, however, is not so satisfactory as that of the left slab, as the day in (11 — 4 20 Pop) does not appear to be Ik, though indeterminable by inspection; but it has been referred to in connection with the reckoning in regard to the inscription onthe left slab, as it may tend to show that these minor series are to be deducted in tracing connection of the dates. After a somewhat lengthy and careful study of the inscription on this tablet, testing the relation of the series by calculation in every possible way, I have failed to find any satisfactory evidence of connec- tion ina continuous line. The indications point rather to two or more parallel lines. There are, however, difficulties in the way of obtaining a clear understanding of the plan adopted by the original artist which Ihave been unable to overcome, so great, in fact, that were it not for other evidence, the correctness of Goodman’s theory in this respect would be left in doubt. It was probably on account of these difticul- ties that this author omitted any reference to the inscription on the right slab, the best known and most accessible to students of all the Central American inscriptions. Some indications of different lines of series are found in the overlapping of reckonings in the inscription of the left slab already given. At glyph U2 of the right slab, immediately after the date 8 Ahau 13 Ceh which follows numeral series 3 of this slab (see list of series above), is the symbol for 9 cycles, which, as we have stated, is not con- nected with any numeral series. This is, as will be found in other instances, probably intended to indicate that at this point 9 cycles have been completed from + Ahau 8 Cumhu, the date following series 1 of the left slab. The day 8 Ahau 13 Ceh is the first day of the 10th cycle as given in Goodman’s chronological calendar. It is, however, cer- tain that all the numeral series preceding it on the tablet fall short of amounting to 9 cycles. Moreover, some of them appear, as has been shown, to reach back over others, thus lessening the number to be an 760 MAYAN CALENDAR SY STEMS (ETH. ANN.19 actually counted. These facts seem to indicate that there is some omission, in truth a very large one; but with our present knowledge we are unable to solye the problem. I have already alluded to the question of connection between the left and right slabs, direct, or by means of the characters in the mid- dle space. Mr Goodman evidently follows the idea that the beginning of the inscription on the right slab (six columns) follows directly the close of that on the left slab. He does not make this plain in his notes on this tablet (op. pp. 185, 136), but when his remarks and figure on a previous page are considered (p. 96) it becomes evident, as the two upper glyphs of this figure are the last (E17 and F17) of the insecrip- tion on the left slab, and the other three the first three (S1, T1, and 52) in the inscription on the right slab. In connection therewith he remarks as follows: The reckoning here is from the beginning of a great cycle. A notation of 1-6-7 «12 (the 12 erroneously appears as 13) precedes the glyphs and is to be incor- porated with them. The reckoning shows the difference between the dates in the annual calendar. His reckoning (1-6-7 x 12) is 1 katun, 6 ahaus, 7 chuens, 12 days= 9,512 (given in the sixth series of our list of the left slab as 9,513). If it were true, as he states, that the ‘‘reckoning shows the difference between the dates of the annual calendar,” meaning the date preced- ing and that following the numeral series, this would be strong proof of connection, but unfortunately Mr Goodman is mistaken in this instance, as neither the last preceding date (9 Ik 5 Mol), nor the initial date, nor any other date of the left slab connects by 9,512 or 9,513 with either of the first two dates of the right slab, or any other date thereon. If there be any connection between the dates in the different spaces, it is between those of the middle space and those of the right slab, reading forward, and the last date on the inscription of the right slab and one of those on the left. It is evident from what has been shown that the proof of Mr Good- man’s theory, drawn from the Tablet of the Cross, is not very satis- factory, as not more than one-third of the dates thereon can be connected thereby. But where two and three series connect in suc- cession the probability of the double or treble coincidence is so extremely remote that the theory as to the numeral symbols and their use may be accepted as demonstrated. If the double connection occurred but once in the whole range of the inscriptions it would be best to conclude this to be a mere coincidence, but as this occurs again and again in the inscriptions, and even, as will be seen, a succession of three and four, the proof is too strong to be resisted. Even without this mathematical demonstration the strong, in fact, evident resem- blance of these numerical series to those of the codices is almost, if not quite, sufficient to justify Goodman’s interpretation of the numeral symbols to which allusion has been made. OF AMERICAN ETHNOLOGY TEMPLE OF THE SUN THE IP Pr PL NINETEENTH ANNUAL REPORT : HEN (( sak 2 * me a \ thee BR K WALL OF THE SANCTUARY T. BUREAU OF AMERICAN ETHNOLOGY. PL, XLI NINETEENTH ANNUAL REPORT, yy a kes Bh aren B) Ab. ‘e J 6 a We ~~ a) ~ 10 10 13 SANCTUARY SUN OF THE TEMPLE THOMAS] TIME SERIES IN THE INSCRIPTIONS 761 TABLET OF THE SUN We turn to the inscription on the Tablet of the Sun—of which we also have a photograph by Mr Maudslay, shown in our plate x~1—and to Mr Goodman*: comment, which is as follows (page 136): Initial date: 54-1-18-5-3 x 6-13 Cimi 19 Ceh. The month symbol comes after one of the glyphs of the initial directive series. A reckoning of 1-211, with three unintelligible glyphs following, points to a date which appears to be 1 Caban 10 Tzec; but as that is not the date to which the intelligible part of the reckoning would lead, both the date and direction are uncertain. Thirteen glyphs follow, some of them of recognizable purport, but the exact meaning of which in this con- nection I do not know. Then comes a restatement of the initial reckoning, 1-18-5-3 «6, from the beginning of the great cycle, followed by nine glyphs whose use here is unintelligible, though four of them are signs with whose meaning we are acquainted. Next in order comes a reckoning of 9-12-18-516 (followed by four glyphs nearly identical with a series in the preceding inscription), from 4 Ahau 8 Cumhu, the beginning of the great cycle, to 2 Cib 14 Mol. This is correct. After five incomprehensible glyphs occurs the date 3 Caban 15 Mol. In the annual calendar the last two dates adjoin each other, but whether the latter is here intended to be the succeeding day, or whether some calendar rounds are indicated by the characters preceding it, is something we are at present unable to determine. Sixteen baffling glyphs follow, and then there is a reckoning of 7-6-123-12 Ahau 8 Ceh. There are no recognizable directive signs here, but by trial we discover that the reckoning is the distance between 12 Ahau 8 Ceh and 9 Akbal 6 Xul, a date that comes after six intervening glyphs. Eight more unintelligible glyphs occur, and then a reckoning of 6-218 (the 18 should be 17), 2 Cimi19 Zotz. The directive signs are unfamiliar, but as the reckoning is backward to 9 Akbal 6 Xul, they probably denote that fact. Next is 1-817, 13 Ahau 18 Kankin, which is declared to be a 10th ahau, the reckoning being the distance from 9 Akbal 6 Nul to that date. Both of these dates are subsequently repeated for some reason, and the record ends with 8 Oc 3 Kayab, followed by ten glyphs whose meaning is not apparent. This is a puzzling inscription so far as its numeral or time series are concerned, a fact apparent from the comment which Mr Goodman makes on it. Although there are several series with sufficient data for the purpose of tracing them, but few of the dates can be connected, and these not satisfactorily. The series and dates in the order in which they come in the insecrip- tion are as follows, adopting Goodman’s interpretation of the initial series: Left slab Days Gel Gl ls, BO 13 Cimi 19Ceh (9 Lamat) 2 2 abl ieCalban2alOekzecke (Syuam at) eee ee 411 3 [eeSueDroi. (6: (Noxdate)ian(27.0;466)) seasee ees eee eee o = 9, 746 4 9 12 18 5 16 @e Ghia) (GUEBAOIS) siseeseecsssdoosee 3, 456 Middle space 9 Akbal 6 Xul (8 Ezanab) 1 (Unintelligible ) 13 Ahau 18 Kankin (9 Akbal) 8 Oc? 3 Kayab? (11 Lamat?) (62 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 Right slab 4 Ahau 8Cumhu (8 Ben) 2Cib 14 Mol (5 Akbal) 3 Caban 15 Mol (5 Akbal) 1 7 6 12 3) D2:Ahan® \8iCehve ((6iBenz)) (52)803)seen- 2 14, 843 9 Akbal 6 Xul (8 Ezanab) 2 6) 2) 182i Cini o Zotz (Zama) paeeese eee eae EA ls} 3 I 8 2) to Ahan, 18 Kankin’ (9)Ak:pal)iseesssssseo- 52 For convenience of reference the series of each division are num- bered at the left; the year to which the date refers is given in paren- thesis following the date, and the equivalent in days of the time series—after deducting the calendar rounds where greater than one round—is placed at the right. The positions of the various dates and series in the inscription are given as we proceed. In this inscription, as that of the Cross, the numbers prefixed to the periods of the initial series are face characters instead of the ordinary number symbols, except the number prefixed to the month symbol Ceh, which consists of the usual lines and dots. This initial series— 54-1-18-5-3-6— interpreted, is as follows: The fifty-fourth great cycle, 1 cycle, 18 katuns, 5 ahaus, 3 chuens, 6 days, to 13 Cimi the 19th day of the month Ceh. Mr Goodman’s interpretation of this inscription, so far as it extends, is given above. It appears that he places, as seems to be his rule, the inscription in the middle space after that in the right slab. It is possible, as is indicated by what fol- lows, that he is right in this instance. That 13 Cimi 19 Ceh, the first date, will not connect with the next date by 1 ahau, 2 chuens, 11 days (411 days), the second numeral series (in reverse order)—glyphs A13, B13—is certain, as the reckoning brings us by counting forward to 8 Caban 5 Muan, year 10 Ben. Yet, notwithstanding the radical error on the part of the original artist implied by the assumption that the last is the correct date here, there are some grounds for the assumption. As there are no more dates on the left slab, Goodman assumes that those attached to the 3d numeral series, which is precisely the same as the initial series, are the same as those which precede and follow that series, viz, + Ahau 8 Cumhu, beginning of the 54th great cycle, and 13 Cimi 19 Ceh. But this result, it must be remembered, is based upon the assumption that Mr Goodman’s interpretation ** 13” Cimi of the first given date is a correct rendering of the face numeral. In this case his determination has been reached not from the details of the face character, but from his theory that his 54th great cycle begins with 4 Ahau 8 Cumbu, as counting forward 1—-18-5-3-6 (9,746 days after deducting the calendar rounds) reaches 13 Cimi 19 Ceh (9 Lamat). This is apparent from his statement on page 49 of his work, where he gives figures of face signs for 13: [ do not know what to conclude about the last face in the list, which is the day numeral in the initial date of the Temple of the Sun, Palenque. It is more like the THOMAS] TABLET OF THE SUN 63 chuen sign than any other, but the numeral ix unmistakably 13. It is more rea- sonable to suppose that the sculptor madea mistake in the kin sign, than that the chuen symbol should have been used to represent both 13 and 15. The third number series is found (in reverse order) in glyphs C7, D7, C8, Ds, the ahau and cycle symbols—D7 and D8—being face characters. The fourth series, 9-12-18-5-16, or 9 cycles, 12 katuns, 18 ahaus, 5 chuens, 16 days, is found (in reverse order) in glyphs Cl4 to C16, inclusive. Here the days are not joined to the chuen symbolas usual, but have a separate symbol (C14), a face character with the number prefixed. The chuen symbol (D14) is also a face character. The series reduced to days is 1,388,996, from which subtracting 73 calendar rounds leaves 3,456 days to be counted. Counting forward this num- ber of days from 4 Ahau 8 Cumhu (8 Ben) the beginning of Goodman’s fifty-fourth great cycle, we reach 2 Cib 14 Mol (5 Akbal). Both dates in this instance are found after the numeral series and on the right slab—4 Ahau (P2) 8 Cumhu (O03); 2 Cib (O4) 14 Mol (P4.). Placing the dates together before or after a numeral series which denotes the lapse of time between them is unusual, but not without precedent. Using the last result, we may perhaps find the proper connection with 13 Cimi 19 Ceh, the first given date. Subtracting the third series (275,466 days) from the fourth series (1,888,996 days) leaves 1,113,530 days, a which subtracting 58 calendar rounds (1,100,840 days) leaves 12,690 days to be counted. Reckoning back this number of days 7 ,690) from 2 Cib 14 Mol (5 Akbal) we reach 13 Cimi 19 Ceh (9 Lamat) the first date of the left slab. Of course it follows that counting forward from 13 Cimi 19 Ceh (9 Lamat), the difference between the third and fourth series, we reach 2 Cib 14 Mol (5 Akbal). Subtracting the third series from the fourth in order to get back to 13 Cimi 19 Ceh is certainly proper, as the former is included in the latter. These results would seem to be correct, and if so, justify Goodman’s interpretation 13” of the face numeral joined to Cimi, and form a second connection between the inscriptions of the left and right slabs. However, using the last number, 12,690 less 411 (12,279), and counting back from 2 Cib 14 Mol, we reach 8 Caban 5 Muan (10 Ben) instead of 1 Caban 10 Tzee. As this is, as it should be, also the date reached by counting forward 411 days from 13 Cimi 19 Ceh (9 Lamat), I am inclined to believe that it is correct, and that here the original artist has by mistake given an erroneous date. It is apparent that to use 411 days in counting forward from 13 Cimi 19 Ceh, year 9 Lamat, must of necessity bring us into the year 10 Ben, therefore, as 1 Caban 10 Tzee can not be connected with any other date by sub- traction, addition, or skipping, and the date 8 Caban 5 Muan will connect both backward and forward, it may be accepted as probably correct. As there is no numeral series in the middle space, these may he leit 764 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 to be determined by the dates, or from the numeral series in the cor- responding position in the Tablet of the Cross. Be this as it may, it is certain that the first numeral series in the middle space of the latter tablet—537 days—measures exactly the lapse of time from 9 Akbal 6 Xul to 13 Ahau 18 Kankin of the Sun Tablet; and that 2,386 days, the second series in the middle space of the Tablet of the Cross, is exactly the time from 8 Oc 3 Kayab (middle space) to 2 Cib 14 Mol, second date on the right slab of the Tablet of the Sun. This result, however, would seem to be contrary to the evidence adduced of the direct connection between the inscriptions of the left and right slabs; nevertheless it is a remarkable coincidence which depends on some fact in regard to the series not yet ascertained. Possibly these form a separate succession of series. IT have been unable to find any connection between either of the dates of the right slab which precede the first numeral series and any one which follows. This series in reverse order is 3 days, 12 chuens (glyph P16), 6 ahaus (QI), and 7 katuns (R1), equal 52,803 days, or, after subtracting 2 calendar rounds, 14,843 days. Using the latter and counting forward trom 12 Ahau (Q2) 8 Ceh (R2), year 6 Ben, we reach 9 Akbal (Q6) 6 Xul (R6), year 8 Ezanab. Here also both dates follow the numeral series. Following the last-mentioned date, at Q11, R11 is the numeral series 18 days, 2 chuens, 6 ahaus, or 2,218 days. This is followed at Ql2 R12 by the date 2 Cimi 19 Zotz (year 2 Lamat), which is followed at Qi4, R14 by the numeral series 12 days, 8 chuens, 1 ahau (left portion of R14), and this is followed at R14 (right portion) and Q15 by the date 13 Ahau 18 Kankin. It will be observed that two of these dates are the same as the first and second dates of the middle space. It seems from the reckonings which follow that the number of days in the second numeral series should be 2,217 instead of 2,218. Subtracting 2,217 from the first series (14,843), the remainder—12,626 days—exactly measures the lapse of time from 12 Ahau 8 Ceh, year 6 Ben, of the first series, to 2 Cimi 19 Zotz, year 2 Lamat, of the second series. Count- ing forward 2,217 days from 2 Cimi 19 Zotz we reach 9 Akbal 6 Xul, year 8 Ezanab; this may be the first date in the middle space, and not the 9 Akbal 6 Xul which precedes the second series of the right slab, as Goodman contends, which would be a backward count as stated in the quotation on page 761; or it may bean omitted date. Counting 537 days (532 in third series right slab should evidently be 537, the number given between the same dates in the middle space of the Tablet of the Cross) from 9 Akbal 6 Xul, we reach 13 Ahau 18 Kankin, third series and last date on the right slab; or, adding together the second and third series— the 2,217 and 537, making 2,754 days—and counting forward from 2 Cimi 19 Zotz, year 2 Lamat, we also reach 13 Ahau 18 Kankin. These results seem to justify the slight corrections made in the numerals. OF AMERICAN ETHNOLOSBY, BUREAU 10 bh ie ae A) HM So rer ars ge nie em me 13 4 5 6 _- ~,' INSCRI TEMPLE OF THE FOLIATED CROSS STOGRAP?t PH( N THE BACK WALL OF THE SANCTUARY STER CAST. L o io) ra en 2 ws BUREAU OF AMERICAN ETHNOLOSY. NINETEENTH ANNUAL REPORT. PL XLII. i Sn) WSN -” at Vg ‘oes } en: SOT 1 (oree® ASS “ ! 4.) hi 1BED PANEL on = oss. INSCRIBE? "SON THE Back WALL OF THE SANCTUARY TEMPLE OF THE FOLIATED CR : _ ne f LASTER D STER CAST >HOTOGRAF THOMAS] TABLET OF THE FOLIATED CROSS 765 The data also seem to favor Goodman’s conclusions except in one or two cases where his statements are palpably erroneous. He gives 17 as the number of days in the third series right slab without reference to the fact that the inscription shows 12. I think that 17 days are to be counted here, but the inscription shows clearly 12. TABLET OF THE FOLIATED CROSS The next inscription to which attention is directed is that on the so-called Tablet of the Foliated Cross. Here we are favored with Mr Maudslay’s excellent photograph, of which a copy is given in our plate Xxuir. The numeral series and dates in the order in which they stand in the inscription, including the initial series as interpreted by Goodman (except as to the 20 days), are as follows: Left slab Days. 1 Sf 18 5 4 OF 1 Ahaud3 Mae (9 Vamat) (275.480) 2222 -. 2 eo G0 2 LALO ei Canacy iy axe (LORBen)) eee ee meat sere sas eee ee 299 3 elas Oe 2 Ahan 3s Uayeb (438) 7anain)) mae eee 12, 520 1 Ahau 13 Mac (9 Lamat) 4 (nine /omloe | (mordate)): (060996) eseeseeee seems es sae ee ae 17, 096 Middle space 8 Oc 3 Kayab (11 Lamat) Right slab 2 Cib 14 Mol (5 Akbal) 3 Caban? 15 Mol (5 Akbal) 12 6 9 3 (no date; doubtful series though distinet)..---.-. 2, 343 2, 2 9 6 4 8 Ahau3 Uo? (12 Ezanab?) or 8 Oc 3 Kayab... 17, 764 3 Gretel (6hs | GON date eee ere eee arenas, een ees, 2, 386 4 Ze As SrA aw S alos (ise tlie) Meee ete ee cee 2 604 5? 13 0 0 O (no date; probably not a counter)--.-.------ (17, 680?) As in the lists heretofore given, for convenience the series are num- bered at the left, the years are added in parentheses, the number of days are indicated by the numeral series placed to the right, and the remainder is shown after the calendar rounds have been subtracted when the total exceeds a calendar round. In place of the 20 days given by Goodman I have in each case substituted 0 days, as T thus interpret the symbol in the inscription. As the reader must have the inscription before him to find the posi- tion of the numeral series and dates and is presumed now to be suf- ficiently posted to find them from the list given above, it is deemed unnecessary to give here a list of the glyphs. Such reference to special glyphs as is deemed necessary will be made as we proceed. The numerals to the time periods in the initial series of this inscription, as in the two which have been examined, consist of face characters, 766 MAYAN CALENDAR SYSTEMS [ETH ANN. 19 except the 13 to the month Mac. For their determination we are indebted chiefly to Mr Goodman, the evidence so far as obtained being sufficient to enable us to identify some of them. The date from which this series is counted, the beginning of Mr Goodman’s so-called fifty-fourth great cycle, is, of course, 4 Ahau 8 Cumbhu, in the year 8 Ben. Counting forward from this date 9,760 days, the number after the calendar rounds are subtracted, brings us to 1 Ahau 13 Mae (9 Lamat). the first recorded date. As it is with the latter date, which is designated the ** initial date.” though it is not strictly so, that Mr Goodman begins his reckoning, we give here his comment on the inscription: Initial date: 54-1-18-54 x 20-1 Ahau 13 Mae. This date is just fourteen days later than the initial date of the preceding inscription [Tablet of the Sun]. The.directive series follows, succeeded by a reckoning of 14 chuens and 19 days to 1 Cauac 7 Yax. Eleven unreadable zlyphs come next, and then 1-14-1420, which, after four uncer- tain directive characters, is declared to be a reckoning to the beginning day score of the second cycle, 2 Ahau 3 Uayeb. It is correct. Then come two reckonings in an unfamiliar style, the first from the beginning of the great cycle, the second from 1 Ahau 13 Mac. I am positive of this, for the very next reckoning will show that there are 40,000 days to be accounted for somehow, and they can be represented only by one of these counts. That reckoning is: 7-7-7-3>16, to 2 Cib 14 Mol. Subsequent computations show that date to be the one to which 9-12-18-5x 16 led up in the preceding inscription; hence the necessity for something to explain the missing 40,000 days. As from this on the reckoning and dates of the two inscrip- tions are nearly the same, it is not worth while to repeat them; I will, however, give a synopsis showing the position of the dates in both: (1), 54-1" 18 5) 35646) 13° Cimi'coiCeh (2) 54 1 18 58 4x20 1 Ahauw 13 Mac (3) 54 1 18 6 18x19 1C@auac7 Yax (4) 54 2 20 20 18X20 2 Ahau 3 Uayeb (5) 54 9 3 7 1520) 12) Ahan 8iCeh (6) 54 9 10 2 6X6 2 Gimil 19 Zotz (7)) eb 69) 110) “80 95e-35 (So Aleball'6 kal (8) 54 9 10 10 1820 13 Ahau 18 Kankin (9) 54 9 12 1 12X10 8Oc3 Kayab (10) 54°9 12 18 5ox 18=1080. Fourth glyph—We must infer this to be an arbitrary sign, equivalent to a third ahau, or three ahaus. THOMAS| COPAN INSCRIPTIONS—STELA J 781 Fourtn Anau—l440 Days Tt will be observed that the reckoning of the days is missing here—a fact that will become important when we reach the next ahau. Second glyph—As a portion of this is obliterated we will pass it by. It is a waste of time to study illegible glyphs when the missing part is not restorable from what is left or from the context. Third glyph—Same remarks. Fiera Anau—1800 Days Second glyph—18 X40=720 X2=1,440; hence this glyph should have gone with the preceding ahau. Third glyph—A symbol which appropriately denotes the beginning of a fifth ahau in several other places in the inscriptions. I call attention to the peculiar character of the wing, or whatever it may be termed. It is not the ordinary form, signifying 20, but must have the value of 86—10x5=50 x 36=1800. Sixta AnAu—2160 Days Second glyph—The under number being 4 here, the character above the coils should represent 30, but instead it represents only 25—1825=450<4—=1800; hence this glyph should have gone with the fifth ahau. Third glyph—The 20-day sign again, qualified by a character which the connection requires to be a sign for 108—108 x 20=2160. Fourth glyph—An arbitrary sign, probably, for 6 ahaus or a sixth ahau. SreventH AnHAU—2520 Days Second glyph—18 X4=72 X35=2520. Third glyph—Two of the characters encountered above reappear here, associated with a knot which we know to be a sign for 5 or some of its multiples. As neither 10, 15, nor 20 added to the other characters would form a number that would bean even divisor of 2,520, we must consider this a sign for 5 and the character underneath it to represent 60—10+27+5=42 x 60=2520. The subfix here, consequently, not- withstanding its resemblance to the character representing 72, can have no value, but must serve merely as a pedestal, as it does under the day symbols. EicutH AHAu—2880 Days Second glyph—18 X 40=720 X 4= 2880. Third glyph—18 X 40=720X4=2880. The subfix is without value here also. Fourth glyph—Too defaced to justify any estimate of it. Ninto AnAu—3240 Days The computation, if there was one, and the equivalents are defaced beyond the possibility of recognition. ; Trento AHAU—3600 Days The ahau sign here differs from all the rest. It is the symbol used in a Tikal tablet to denote a date to be a tenth ahau. Second glyph—The two coils do not appear here, only one; but that one is qualified by a curve, signifying 5. As it can not be added without destroying the 9 element, it must serve as a multiplier—95=45 X40=18002=3600. The 2 sign here looks something like the ahaw character for 4, but the context requires it to be 2. Third glyph—The symbol that everywhere denotes a tenth ahau or an even 10-ahau reckoning, with the character that commonly constitutes its center placed beside it. 782 MAYAN CALENDAR SYSTEMS (ETH. ANN, 19 Eveventa Anav—3960 Days Second glyph—The stone is so badly mutilated that this glyph can not be restored with certainty. If the characters that are tolerably preserved be 5, 9, and 2, the other should be 44, but I distrust their identity. Third glyph—There may be two glyphs here, though I think not. The 20-day period being the factor to be raised, it requires 198 for a multiplier to bring it to the necessary total. The character to the left of it being 1, there is good reason for supposing it to represent 73, and the right-hand sign at the top being 18, it follows that there can be no multiplication of these numerals, but that they must be added; hence the remaining characters must aggregate 107. The comb sign—though dupli- cated here, as in many other places, to give it a more ornamental effect—probably represents but 20. That leaves 87 to be accounted for by the remaining character. It is a sign that occurs many times, but its central part is seldom twice alike, some- times being a single bar, sometimes two, and again something quite different. Here it has the appearance of the spire in the akbal sign, which stands for 7. On either side is a comb sign for 20, raised to twice that value bya line of dots. It is possible, therefore, that the two together may represent 80, the particular center part in this instance raising the full value of the character to 87. TweL_rro AHAU—4320 Days Second glyph—aAt first view the principal factors appear to be identical with the characters representing 108 and 18. But the ball in the center of the first is double, and there is cross hatching on both, which may modify the meaning. The character at the bottom seems to be only a beginning sign, though its form is somewhat unusual. If the right-hand sign be 18 and the subfix nothing, the other character must represent 240; but there is too much uncertainty involved to warrant confidence in this deduction. Third glyph—Here again we are nonplussed. We know the bouquet sign for 6 (the same as that over the symbol for Zac) and the ymix character for 5; but the lat- ter has a peculiar marking at the top, and we do not know how that may alter its value. The character over it may be a multiple of 20, as it has the general appear- ance of the wing sign for that number with a qualifying mark at the left part of it. For a reason that will be made evident later on, we will assume that it represents 120, and the ymix character 6—120 x 6=720 * 6=4320. THIRTEENTH AHAU—4680 Days Second glyph—Here the signs for 9, 5 and 4 are plain, indicating that the other character must be 26—9 & 5=45 K 4=180 & 26=4680. Third glyph—The chief factor here is a 260-day sign which we encounter else- where. It consists of the ahauv sign, doubled in value by the surrounding row of dots, and ineclosed in the ymix character for 5—4 x 2=8 +5=13, and then multiplied by 20, denoted by the duplicate comb sign below—13 x 20=260. There are just eight- een of these periods in 13 ahaus; hence the character to the right must represent 18. Fourth glyph—A beginning sign before a glyph that must necessarily be a symbol for a thirteenth ahau or 13 ahaus. FourreentH Anavu-—5040 Days Second glyph—There is doubt if this was intended for a single glyph, or if two glyphs were artfully or accidentally mixed up. The characters, moreover, being so nearly illegible that there is no certainty about them, it would be useless to attempt a solution of the puzzle. Third glyph—A head tha\ appears to be a compound of the chuen and ahau heads. As it probably represents an ahau, the sign in front of it must stand for 14. THOMAS] COPAN INSCRIPTIONS—STELA J 783 FirreentH AnAu—5400 Days Second glyph—The 9, 5, and 4 signs are plain here; the other character, therefore, must be 30. Third glyph—The 5-ahau character, qualified by a siga that must represent 3—the whole being a symbol for a fifteenth ahau, or 15 ahaus. SrxTEENTH AHAU—5760 Days Second glyph—A. different character qualifies the coil here. It must stand for 4-9 4=36 x 4=144 40=5760. Third glyph—The same form of the ymix character encountered at the twelfth ahau is again the central figure, but here it has a 20 sign under it, which presumably raises it to 120. If so, it requires to be multiplied by 48 to make up the total num- ber of days. The signs for 18 and 10 leave 20 to be supplied by the other character, which is the skeleton jaw, an invariable sign for 10, here doubled in value by the row of dots in the upper part. The manner of piecing out the numerals in some of the above instances has been too forced for the result to be regarded as altogether trustworthy. There are also several inconsistencies or errors; but, take it all in all, the number of occurrences in perfect accord with our assumption is too great to be attributable to accident, and we are therefore justified in believing our theory to be correct, however we may have erred in particular applications of it. We have gained a great deal more than is apparent at a first glance. Not only have a considerable number of equivalents for different ahaus and symbols for minor time periods been identified and the value of many new numeral signs established, but—more important than all this—we have satisfied ourselves that there is a plan underlying the employment of a portion of these signs which is capable of almost unlimited variation and extension. As our investigations so far appear to confirm sufficiently for gen- eral acceptance Mr Goodman’s interpretation of the symbols denoting the orders of units, or time periods as he terms them, we may now inquire how far the data bear out his announcement of various other numeral symbols. That there appears to be sufficient basis for his idea that certain face characters are used as numerals has already been noticed, though the evidence is as yet not entirely satisfactory as to the values assigned some of them. In his comment on the inscription now under consideration he goes more into detail in this direction, assign- ing number yalues to the component parts of and appendages to glyphs. In our examination of this inscription we shall notice briefly some of these ideas as we proceed. In the paragraph immediately preceding the long quotation given above he remarks as follows: We start with the assumption that every glyph following a particular ahau repre- sents it or its value in another way. The fact that there is no twentieth ahau— which, so far as the symbol that numeral is attached to is concerned, means no ahau at all—shows that one full ahau, or 360 days, is considered to have passed when the table begins. Here, at the outset, we are met with an assumption which seems to coyer half the ground to be examined. On what grounds does he base the opinion that ** every glyph following a particular ahau represents 784 MAYAN CALENDAR SYSTEMS [ETH ANN.19 it or its value in another way/” This, in the absence of proof, is but simple guesswork. However, before we examine it, uttention is called to the further assumption that what would, according to his system, be the beginning ahau of the series, which he would number 20, is omitted because it is considered as already passed. He observes in a quotation which will be found on a previous page of this paper, that ahaus are numbered 20, 1, 2, 3, etc., up to 19, but the evidence to establish the correctness of this assertion is nowhere given in his paper. I presume, therefore, that it is based upon the chronologic system that he has constructed, of which further notice will be taken before closing this paper. But how does it happen they are found numbered 1, 2, 3, ete., In an inscription when Mr Goodman tells us that in the katuns, taken in their order, they were numbered 9, 5, 1, 10, 6, 2, 11, 7, 3, 12,8,4,13% That, in telling in a numeral series how many ahaus are to be added, the numbers must be given 1, 2, 3, etc, is very evident; but if ahaus were real periods in the Maya chronology, and not simply units of the third order, as we have stated, why are they not numbered in this inscription in the order in which they come in the katun? It may readily be seen that the succession 9, 5, 1, 10, 6, ete., arose from counting by the day numbers 1-13 by divisions of four, as in the series in the Cortesian codex, the count being backward; as, for example, counting upward from the bottom of one of the other columns in table 3, or by the 360-day periods, as referred to elsewhere and as asserted by Mr Goodman. He quotes the following from Perez (page 12): There was another number which they called wa katun, and which served them as a key to find the katuns. According to the order of its march it falls on the days of the wayeb yaab and revolves to the end of certain years: katuns 13, 9,5, 1, 10, 6, 2, 11, W312) 8,4. On this he remarks as follows (loc. cit.): Poor Don Pio! To have the pearl in his grasp and be unaware of its priceless- ness—like so many others! But I must not exult too much yet. The succession of the katuns, reckoned according to this principle, is yet to be ascertained before my fancied discovery can be established by a crucial test. I score the ahaus off in the foregoing order, and, sure enough, the twentieths give the desired result: 11,9, 7,5, 3, 1,12, 10,8,6,4,2,18. Eureka! The perturbed spirit of the Maya calendar, which has endeavored so long to impart its message to the world, may rest at last. As the *‘uayeb haab” signifies the five added days of the year and is so recognized by him, how is it possible to reconcile this count, which “falls on the days of the uayeb haab,” with the count of his ahaus which only cover 360 days each and recognize no 5 added days, which only come into notice when the year of 865 days is considered, which he says the Maya left behind when they entered on a chronologic count? It seems doubtful, therefore, whether this explanation will allay ‘*the perturbed spirit of the Maya calendar.” THOMAS) COPAN INSCRIPTION—-ALTAR K 785 By reference to his comment on the ahaus of this inscription, as quoted above, it will be seen that he uses the coils and other parts of the attached and accompanying glyphs as multipliers, assigning values to them that bring out the desired number. It is unnecessary to fol- low his process, as it is given fully in the quotation. But all this is presented without proof that the values assigned are correct, or, in fact, that the characters are number symbols. Until evidence render- ing such interpretation at least probable is presented, it is nothing more than a guess. However, it must not be taken for granted that I reject all these symbols und appendages as not indicating numbers, as two or three already noticed (besides face characters) appear from satisfactory evidence to have been used as numerals; and it will be seen farther on that there are reasons for believing there are some append- ages which are also thus used. The point made above is that Mr Goodman fails to present reasons for his assertions in this respect, which necessitates going over the entire record to verify or disprove them. That the symbols in this inscription which Mr Goodman designates by the name ‘‘ahau” are to be counted as equivalent to 360 days each must be admitted, but the name ahau, it must be remembered, is, as applied here, merely an arbitrary designation, and its use is wholly different from that made of it by the natives, so far as the preserved records show. ALTAR K The inscription on Altar K contains nothing recognizable save a portion of the initial series which is given by Mr Goodman as follows: 54-9-12-16-7-8—3 Lamat 16 Yax, or fifty-fourth great cycle, 9 cycles, 12 katuns, 16 ahaus, 7 chuens, 8 days. As no photograph is given by Maudslay, we have no means of testing his drawing (plate 73, part 3). The prefixed numerals in this case are the usual dots or balls and short lines, but are not sufficiently distinct to verify Goodman’s interpreta- tion; in fact, the number prefixed to the chuen symbol looks more like 10 than 7—is 10 if Maudslay’s drawing be accepted—and the day glyph is wholly obliterated. The series and date as given by him are there- fore largely conjectural, the latter having evidently been obtained by calculation according to his system, and not from an inspection of the inscription. STELA M The initial series on Stela M,as given by Goodman, is 54-9-16-5- 18-20—8 Ahau 8 Zotz, or, changing the 18 and 20 to 0, as we have found to be correct, the fifty-fourth great cycle, 9 cycles, 16 katuns, 5 ahaus, 0 chuens, 0 days, to 8 Ahau 8 Zotz. The prefixed numerals in this series are of the usual form, balls and short lines, and agree with Goodman’s interpretation. IME) Tone 1241! IS) 756 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 STELA N Of the inscriptions on Stela N, Maudslay gives both photographs and drawings, the former somewhat indistinct, but the latter very clear. The initial series on the east side as given by Mr Goodman is as fol- lows: 54-9-16-10-18-20—1 Ahau 8 Zip, or as we write it, fifty-fourth great cycle, 9 cyeles, 16 katuns, 10 ahaus, 0 chuens, 0 days to 1 Ahau 8 Zip. This is correct, if the month symbol, which is inverted and stands at some distance from the day glyph, has been correctly inter- preted, sa the prefixed numerals are of the ordinary form and dis- ‘tinct. Mr Goodman says ‘*the month symbol is wrong; it should be 3 Zip.” This is true if we accept his theory that the count is to be from 4 Ahau 8 Cumbhu, the assumed initial date of his fifty-fourth great cycle. As an important question arises in regard to the series on the west side of this Stela, we quote the following from Mr Goodman in regard to it: At the top of the second column occurs the sign that indicates a reckoning back- ward. It is followed by seven glyphs, which I think give in another form the sub- stance of the subsequent reckoning, which is the longest that occurs in any of the inscriptions, embracing a period of 75,264 years. It is given as 14-17-19-10-18X20 from the initial date to 1 Ahau 8 Chen, the beginning of a katun, etc. The reckoning is not only wrong, but is absurd as well. The cycles run only to 13, and no such reckoning backward or forward from the initial date would reach a 1 Ahau 8 Chen. But fortunately, despite all the blundering, we can see what the intention was. 1 Ahau 8 Chen begins the 17th katun of the 8th cycle, and thence to the initial date is just 19 katuns and 10 ahaus. The fact that these are the numbers of katuns and ahaus expressed in the reckoning would lead us to suspect that it was to go backward even if the directive sign had not already so informed us, for that would do away with the odd katuns and ahaus and leave the reckoning in even katun rounds. If it were to have gone forward, the odd numbers would have been 3 great cycles, 7 cycles, 9 katuns, and 10 ahaus. A little figuring will show the difference. . . . It will be borne in mind that 3 great cycles, 8 cycles, and 9 katuns are the equivalent of a katun round—that is, the time that must pass between two occurrences of any given date as the beginning of a katun. ; In thinking of the odd 19 katuns and 10 ahaus, they blundered in respect to the total period. I think it should be 14-8-15-10-1820. If so, the reckoning goes back to the 40th great cycle; if it went forward, it would extend to the 69th. It is not material which way it be decided. The important fact is that in either case they ranged over a period of more than 75,000 years, which substantially proves my estimate of the immense reach of their chronological calendar. There are a few glyphs following the reckoning and date in the same column, but they do not assist us, nor can anything beyond the dates and a few disconnected characters be made out of the rows of glyphs around the base. The numbers of the long series mentioned are given correctly except as to the 18 and 20, which should be 0. The reading as it stands in the inscription is as follows: 0 days, 0 chuens, 10 ahaus, 19 katuns, 17 cycles, 14 great cycles, to 1 Ahau 8 Chen. This series, as it clearly stands in the inscription, seems, as has been noted on another page, positive evidence against Mr Goodman’s theory that 13 cycles make 1 great THOMAS] COPAN INSCRIPTIONS—ALTAR Q 787 eycle, or, according to the nomenclature we have suggested as correct— that 13 units of the fifth order make one of the sixth order. It would indicate (unless it can be shown that the 17 cycles is an error) that the system in use at Copan was the same as that in the Dresden codex, the count being 20. It is true that the series will not connect the first date (1 Ahau 8 Zip) with the 1 Ahau 8 Chen which follows, but the length of the series indicates, as we have so often found the case, that the count is back to some initial date. The order of the series, not- withstanding Mr Goodman’s contrary opinion, seems to indicate that the count is forward to 1 Ahau 8 Chen. Counting back from 1 Ahau 8 Chen, year 3 Ben, we reach 12 Ahau 13 Zotz, year 5 Lamat, which would be the initial date. Counting 20 cycles to the great cycle, as we are justified in assum- ing is correct, would of course put out of order Mr Goodman’s tables so far as they relate to great cycles and the numbering of the cycles, though it would not affect the order of the katuns. The date 12 Ahau 13 Zotz is, as we find by his table, the first day of the sixth katun, sixth cycle of his fifty-fifth great cycle. This, however, will be further noticed when we come to the discussion of the initial series. STELA P I pass by Stela P, as I believe Mr Goodman’s interpretation of the initial series (the only part noticed by him) to be largely guesswork, and as there are no recognizable minor series. ALTAR Q We turn next to the inscription on the top of Altar Q, of which Maudslay gives a large and clear photograph and a good drawing. This is to be read by double columns, as usual, commencing at the upper left hand. The first two glyphs give the date 5 Caban 15 Yaxkin. Passing over three characters, we reach another date, 8 Ahau 18 Yaxkin. There is no intermediate numeral series, but a reference to our table 1 will show that these two dates are but 3 days apart. At the bottom of the first column is the symbol for 12 days, 7 chuens, which is followed at the top of the third and fourth columns by 5 Ben 11 Muan. The 12-day numeral to the left of the chuen symbol should certainly be 13, notwithstanding the fact that Maudslay’s drawing gives itas 12. An inspection of his photograph shows a middle prominence which appears to be part of a ball, though he renders it without any evident reason a cross. Counting forward 7 months and 13 days in the year 1 Akbal (in which these dates fall), on our table 2, from 8 Ahau 18 Yaxkin, we reach 5 Ben 11 Muan, which is correct. At the bottom of the third column is the symbol of 17 katuns, which does not appear to bea counter, but which Mr Goodman interprets seventeenth katun. Following this at the bottom of the fourth column is 6 Ahau, and at the top of the fifth column 13 Kayab. The next date, which is 788 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 at the bottom of the fifth column, is 5 Kan 13 Uo, between which and the preceding is the counter 4 days, 3 chuens, equal 64 days. As 6 Ahau 13 Kayab falls in the year 12 Lamat, we count forward 64 days from this date, which brings us to 5 Kan, twelfth day of the second month (Uo) in the year 13 Ben. This is correct, as Kan may be the twelfth day of the month but not the thirteenth. The date glyphs in this inscription are of the usual form found in the Dresden codex, and the minor numerals the ordinary dots or balls and lines; and with the slight and evidently necessary corrections noted, the series conform to the rule. However, there is a break in the interpretation and calculation which remains unexplained, From 5 Ben 11 Muan, which is in the year 1 Akbal, as the preceding date, to 6 Ahau 13 Kayab in the year 12 Lamat, there is a forward jump of 37 years and 42 days unaccounted for. This appears to indicate that the 17 katuns passed over (bottom of third column) and possibly some other nuimber glyphs should be brought into the count. Mr Good- man merely says (page 134): An unintelligible reckoning follows [5 Ben 11 Muan], succeeded by a 17th katun sign and 6 Ahau 13 Kayab, the date probably being indicated by the one begin- ning the 5th ahau of the 17th katun of the 9th cycle. ALTAR S$ We refer next to Maudslay’s Altar S, the initial series on which, as given by Goodman, is 54-9-15-20-18-20—4 Ahau 13 Yax, or as we write. it, fifty-fourth great cycle, 9 cycles, 15 katuns, 0 ahaus, 0 chuens, 0 days, to 4 Ahau 13 Yax. These numbers appear to be correct except the katuns, Maudslay’s drawing showing 13 or 11. ‘There are two short lines and three balls or dots, but the two outer ones are darkened with lines indicating that they may possibly be loops. Mr Goodman appears to have changed the number of katuns in this case to form connection with 4 Ahau 8 Cumhu, beginning day of his fifty- fourth great cycle, without explanation. On this altar we find very distinctly shown these dates, 4 Ahau 13 Yax and 7 Ahau 18 Zip. Between the two are four glyphs, one of which indicates 5 katuns. This count (86,000 days) precisely connects the two dates. We have now noticed all the series of the Copan inscriptions which afford any means of testing Mr Goodman’s discoyeries, following his explanations so far as this was necessary. INSCRIPTION AT PrrpRAS NkEGRAS Before concluding reference to the inscriptions, | call attention to one more recently discovered by Mr Teobert Maler at Piedras Negras on the Usumacinta river. This, as copied from Mr Maudslay’s drawing, which he made from the photograph, is given in our figure 20. As Mr Maudslay has subjected it to Mr Goodman’s theory, we give here THOMAS] INSCRIPTION AT PIEDRAS NEGRAS 789 the result in his own words, after stating that the initial series as Goodman would read it is 54-9-12-2-0-16 to 5 Cib 14 Yaxkin: Ss Vi Gee ee) u 3s Oe The next three glyphs are undeciphered; then comes another reckoning: Cl is the chuen sign with the numeral 10 (two bars=10) above it, and a ‘‘full count”’ sign at the side. Whether the 10 applies to the chuens or days can only be 790 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 determined by experiment, and such experiment in this case shows that the reckon- ing intended to be expressed is 10 chuens and a ‘‘full count’’ of days—that is, for practical purposes 10 chuens only, for as in the last reckoning, when the full count of chuens was expressed in the ahaus, so here the full count of days is expressed in the chuens. : The next glyph D1 is an ahau sign, preceded by the numeral 12. This gives us: Days 12 Ahaus (12360) -...--- 4, 320 10 Chuens (1020) ..-..-- 200 4,520 4, 380=12 years > 140 Adding 4,520 days, or 12 years and 140 days, to the date 5 Cib 14 Kankin it brings us to the date 1 Cib 14 Kankin in the thirteenth year of the/annual calendar. Turning to the inscription we find at C2 (passing over the first half of the glyph) 1 Cib followed by (the first half of D2) 14 Kankin, the date at which we have already arrived by computation. Passing over the next three glyphs we arrive at another reckoning. D4 gives 10 days 11 chuens 1 ahau, and the first half of C5 gives 1 katun. Days IKatuni-22.sccceemcenee 7, 200 Ath aus eee eee 360 11 Chuens (1120) .....- 220 LOMDayS\. 2 eciseens= coe 10 7,790 7, 665=21 years 125 Adding 7,790 days, or 21 years and 125 days, to the previous date, 1 Cib 14 Kankin, it will bring us to + Cimi 14 Uo in the thirty-fifth year of the annual calendar, and we find this date expressed in the inscription in the glyphs D5 and C6.! Passing over the next three glyphs we arrive at another reckoning (E1), 3 ahaus, 8 chuens, 15 days: Days SeAhaussee eee 1, 080 8 Chuens...-.- 160 Lbidaysieee coer 15 1, 255 1,095=8 years. 160 Adding 3 years and 160 days to the last date, 4 Cimi14 Uo, brings us to 11 Ymix 14 Yax in the thirty-eighth year of the annual calendar; this is the date we find expressed in the glyphs E2 and F2 of the inscription. It is true that in the sign in the glyph E2 is not the sign usually employed for the day Ymix, but that it is a day sign we know from the fact that it is included ina 1 He counts the side number of chuen symbol, chuens. THOMAS] SUMMARY (91 cartouche, and I am inclined to think that the more usual Ymix sign (something like an open hand with the fingers extended) was inclosed in the oyal on the top of the grotesque head, but it is too much worn for identification. Passing over seven glyphs, the next reckoning occurs at F6, which gives: Days 4 Chuens...-... 80 19idayseee see 19 99 Adding 99 days to the last date, 11 Ymix 14 Yax, brings us to 6 Ahau 13 Muan in thesame year, and we find this date expressed in F7 and FS. The last glyph in the inscription is a Katun sign with the numeral 14 above it, and a sign for ‘‘beginning’’ in front of it, and indicates that the last date is the beginning of a fourteenth katun. If we turn to the table for the ninth cycle of the fifty-fourth Great Cycle, from which we started, it will be seen that the fourteenth Katun of that cycle does commence with the date 6 Ahau 13 Muan. It is simply impossible that the identity of the dates expressed in the inscription with those to which the computations haye guided us can throughout be fortuitous. SUMMARY Having now concluded my examination of the inscriptions, | may state that I am satisfied on the following points: That the significa- tion and numeric value of the symbols (each represented in two or more forms) which Mr Goodman names, respectively, day in the abstract, chuen, ahau, katun, cycle, and calendar round, are as indi- cated aboye and must be accepted as correct; that the usually large (quadruple) initial glyph represents the sixth order of units, or, as Goodman terms it, great cycle; that certain face characters and also some two or three characters not face glyphs are used as number symbols. These are undoubtedly the most important discoveries yet made in regard to the signification of the glyphs in the inscriptions; and although they seem to throw but little light on the codices, they must influence, to a considerable extent, attempts at interpretation of these records. The use of face characters for days and time periods should not be considered as something peculiar to the inscriptions, as an examina- tion of the codices will show that this change of ordinary symbols into face forms is by no means unusual. In the Troano codex the symbol for the day Eb is oftener a face form than otherwise, and those for the days Men and Oc are often changed into faces. The sym- bol for the day Ix is occasionally radically changed so as to represent a face. A remarkable change in the Chicchan symbol in order to give it a face form is seen in plate 31. In one or two instances, as on plate 23, what are presumed to be symbols for the ahau have a pre- fixed face character possibly denoting a numeral. We pass now to the consideration of some other questions which are brought up by this investigation. 792 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 MR GOODMAN’S SYSTEM OF MAYAN CHRONOLOGY First, I will explain briefly Mr Goodman’s interpretation of the ancient Mayan system of chronology. It must, however, be borne in mind that his ‘tarchaic chronological calendar” or system is distinct from the well-known Mayan calendar system comprising years of 365 days and 18 months, 52-year cycles, ete. Attention has already been called to his time periods from the day up to and including the cycle, and also to the fact that these are iden- tical with the orders of units in the Mayan system of notation, a fact which seems to negative the idea that they should be called time peri- ods. These periods, with his names and the values assigned them, are as follows: 1 day. 20 days make 1 chuen. 18 chuen make 1 ahau. 20 ahaus make 1 katun. 20 katuns make 1| cycle. 13 cycles make 1 great cycle. 73 great cycles make the grand era. If we follow him carefully throughout his work, it becomes apparen’ that. after he had arrived at the conclusion that the orders of units or steps in notation were veritable chronologic periods, it was a natural consequence that he should conceive the idea that the system must reach back to a number or period that would round out evenly as a great common multiple of all the lower factors. This is apparent from the following passage near the commencement of his paper: ' Ii, as is probable, a more satisfactory answer should be found by many in the assertion that I am in error as to such an era, and I be asked how I know that it exists, my reply would be that it is self-evident. Its existence is established by all the certainty of mathematical demonstration. The evidence of the inscription does not go hand in hand with us to the ultimate destination, but it leads us far on the journey, and leaves us only when it has pointed out an unmistakable way to the final goal, which an intellectual necessity compels us to reach before we can rest satisfied. The inscriptions show us that every separate chronological period must be rounded out to completeness before the calendar itself can be complete. We see the years, ahaus, and katuns come back to their respective starting-points, thus rounding out the periods of which they are the units. Of necessity the eycles and great eycles must do the same, else the system would be an incomplete creation, without form and void. No fair-minded person, I think, will contend that the Mayas elaborated almost to its conclusion a design not only susceptible of but inviting the most perfect finish and then willfully or blindly left it disproportioned and awry. If they did not do this—a thing alien and repugnant to human nature—then their grand era embraces 374,400 years. There are two unmistakable indices pointing to this conclusion. The moment the cycle and great cycle appear upon the scene we know by the unchange- able law governing the calendar that they must go forward until they commence 1The Archaic Maya Inscriptions, p. 6. THOMAS] GOODMA N’S SYSTEM 7938 again with the same date from which they started. Such a result in the case of the former requires 949 cycles, and in that of the latter 73 great cycles, each of which reckonings constitutes a period of 374,400 years. It is also apparent in the following expression (p. 26): The grand era is composed of seventy-three great cycles and comprises 374,400 years, or 136,656,000 days. It is the period in which the Maya chronological calen- dar completes itself, just as their annual calendar does in a period of 52 years. This number of days is the product of the factors 20 18x 20 x 20x 13x73. Now let us examine his reason for introducing the 13 and 73 iustead of carrying on the count according to the usual Maya vigesimal notation, as Dr Férstemann has done. This is easily seen. Having conceived the idea that all the factors of the calendar system are time periods and must come into harmony in the highest period, it was absolutely necessary to bring these prime numbers into the count. The 13 is necessary to the day numbering and to the 52-year period (413), and the 73 to the 365-day period (5x73), and as 4 and 5 are factors of the lower periods (as 20) the prime numbers only were necessary to complete the scheme. As the attempt to introduce both these into one period would have required the use of the very large multiplier 949 (see his use of it, p. 27), the 13 was introduced into the grand cycle. We might ask, and seemingly with good reason, why not in one of the lower orders? The answer is apparent—the records show beyond question that, up to the cycle, the multiplier, except in the case of the chuen, was 20. But in passing from the cycle to the grand cycle, but a single example has been found in the inscriptions showing a higher number than 13, and this, as has already been stated, Mr Goodman decides must be erroneous. As the introduction of the 13 somewhere is absolutely necessary to round out his grand multiple, how, we may ask, was the system com- pleted in accordance with the Dresden codex which he admits (page 3) ‘““pertains to the archaic system in the main, though reckoning 20 cycles to the great cycle”? Unless 949 is introduced as a multiplier in the next step, which can not be supposed possible, the entire scheme is destroved and the several steps reduced merely to those of notation, which in fact they are. The idea that the Mayan tribes of Chiapas, Guatemala, and Honduras had such a magnificent rounding-out system, while the Yucatec tribes, though having a system similar in other respects, failed to introduce the rounding-out factors, is, to say the least. very strange. In order to include the 365 days of the year in the great multiple, it was also necessary to introduce the prime number 73, which is not a divisor of any of the lower periods. This explains Mr Goodman’s theory of a great cycle composed of 13 cycles and a grand era composed of 73 great cycles, as he could not otherwise have a general rounding-out period. These are of course necessary to this scheme, but the crucial question is, did the Maya have any such scheme, 794 MAYAN CALENDAR SYSTEMS [BTH. ANN. 19 or ever imagine suchaone? Where isthe proof tobe found? The fact that the scheme works out nicely according to the figures is no eyi- dence that it was ever in use, ever adopted, known, or even imagined by the most advanced Mayan priest. Speaking of the grand era, his great rounding-out period, Mr Goodman says: As the existence of this period is very likely to be questioned, I will give my rea- sons more fully here for believing in such an era. The numbers 73 and 949 are as important factors in the Maya chronological scheme as 13 and 20, This results from two features of the system not hitherto touched upon, which may very properly be termed the minor and grand rounds of the periods. After 73 occurrences, and not until then, every period of the chronological calendar begins again with the same day of the same month, but (with the exception of the burner and great cycle) with a different day number. This is the minor round. Thirteen of these, or 949 occur- rences, constitute the grand round, when the periods begin again not only with the same day of the same month but with the same day number. There is no doubt that the calculation here is all right, and that 73, 13, and their multiple, 949 (7313), will be divisors of any product of which they have been multipliers. Hence there can be no question that the results he gives in the two tables following the paragraph quoted are correct, but after all he is simply taking apart the pieces he has put together. In other words, no amount of figuring in this way will furnish proof that such a scheme as his was in vogue among the Maya. That they did have a notation with the following multipliers: 20 18x 20 20, and another, presumably 20 (admitted by Mr Good- man to have been 20 in the Dresden codex) we know; but it can hardly be granted that the great scheme he has built up on this foundation is justified. There is just as much evidence, in fact much more, that the count went on after the second order of units according to the vigesimal system, than that Mr Goodman’s scheme was in yogue. That there was a count or order of units above the fifth or cycle is evident both from the codex and from the inscriptions, and I am inclined to believe, as heretofore stated, that Mr Goodman is right in interpret- ing the large initial glyph of the Tablet of the Cross, Palenque, and the other similar initial glyphs as the symbol of such count, order of units, or great cycle, as he prefers to call it. But I find no evidence in the codices or inscriptions that the count was ever carried beyond this sixth order of units or great cycle, though there is nothing in the system to prohibit it more than there is to prevent counting beyond billions in the decimal system. That this order of units appears to have been the limit of computation is inferred in part from the promi- nence and position given the symbol, and from the fact that no higher count has been found. Although there is no satisfactory evidence in the inscriptions of the numbering of these so-called great cycles, except the series on Stela N, Copan, yet it is known from the Dresden codex that they were numbered; but the limit, unless we assume that it was governed by the vigesimal system, is unknown. THOMAS] GOODMAN'S SYSTEM 795 That the symbols of this order forming the initial glyph of various series in the inscriptions differ in some of their parts and append- ages is evident, but that these elements and appendages are used to indicate numerals has not yet been established by Mr Goodman, as is evident to anyone who will examine his explanation of the ahaus on Stela J of Copan in the quotation given above, which shows his method of arriving at the numbers indicated by glyphs. There is too much guessing in the building wp of numbers by piecing together the parts to justify acceptance by those who are in search of positive results. I have stated again and again that I believe the so-called time periods to be nothing more than the orders of units used by the Maya tribe in its system of notation. That they are the same up to the cycle, or fifth order, is known from the evidence furnished by the codices and inscriptions; and that the same vigesimal system is continued to the sixth order in the Dresden codex is admitted by Mr Goodman and proved by the series on plate 31, which has been given above (page 728). As positive proof that the nineteen cycles here are to be counted it is only necessary to state that the series connects with 13 Akbal, which may be that below or that to the left above. Let the count be either way, it begins and ends with this date. The great time series on Stela N of Copan heretofore mentioned, which Mr. Goodman brushes aside as *‘ not only wrong but absurd as well,” deserves more consideration than has been given it. The attached numerals are of the ordinary form—balls and short lines and are quite distinct in Maudslay’s photograph and drawing. It is absolutely necessary to Mr Goodman’s theory as to the Maya time system that this series be effectually disposed of. And yet, so far as any evidence bearing on the case can be found, there is no other reason for rejecting it than that it conflicts with a theory. This series as given in the inscription is as follows: 14-17-19-10-0-0, or, written out, 14 great cycles, 17 cycles, 19 katuns, 10 ahaus, 0 chuens, O days. This is an immense stretch of time, amounting to 42,908,400 days, or 117,557 years and 95 days, counting 20 cycles to the great cycle, as I believe is correct, or over 75,000 years, counting 13. The great cycle symbol is in this case a face character, as are the cycle, katun, and ahau symbols. The chuen symbol, which has the days attached, is of the usual form. The day which follows is 1 Ahau 8 Chen. If we assume that the 1 Ahau 8 Zip which terminates the initial series and is found in the column on the east side of the Stela is to be connected by the long series with the 1 Ahau 8 Chen in the column on the west side (the series being in the same column), it is true, as Good- man remarks, that the numeral series as given will not make the con- nection. But this fact is by no means conclusive evidence that there is an error in the series; for, in the first place, taking into consideratior 796 MAYAN CALENDAR SYSTEMS [BTH. ANN. 19 the fact that there is an inscription running around the base which may or may not be a part of the whole, it is by no means certain that the aboriginal artist intended to connect these two dates by this numeral series; and, in the second place, it is possible and eyen prob- able that this long series was intended to connect the following date with some preceding initial date, as Mr Goodman insists is true with regard to series in several other inscriptions. Nor is it a rare oceur- rence that the first following date does not connect with the terminal date of the initial series. We think, therefore, that it is more reason- able and more in accordance with the rule in other inscriptions to conclude that this numeral series was intended to connect the date which follows with some initial date, and this, unless the count was forward, which Mr Goodman does not admit, would be far back of 4 Ahau 8 Cumhu, the first day of his fifty-fourth great cycle, to which he has commonly referred. As will be seen by reference to the quo- tation given above from his remarks on this series, he accepts as correct the 14 great cycles, places the date 1 Ahau 8 Chen in his fifty-fourth great cycle, and carries back the count from that date, reaching the fortieth great cycle. It is evident, therefore, on his theory, that it was not the intention to connect the two dates 1 Ahau 8 Zip and 1 Ahau 8 Chen by this series, as both, according to his own showing, fall in the fifty-fourth great cycle. As proof that this is his view, we quote his words: “I think it should be 14-8-15-10-18 x 20. If so, the reckoning goes back to the fortieth great cycle; if it went forward it would extend to the sixty-ninth.” As he says (p. 148) that the latest date of the inscriptions is ‘*55-8-19-2-18 x 20,” and in another place that Mayan count always related to past time, it is clear that he carries this count back 14 great cycles from the fifty- fourth. It follows, from the conclusion reached in the preceding paragraph, and from Mr Goodman’s scheme, that, counting back from 1 Ahau 8 Chen, the ‘* 8-15-10-18 x 20” of the series ‘* 14-8-15-10-18 x 20,” as he corrects it, should bring us to+ Ahau 8 Cumhu, the commencement of his fifty-fourth great cycle; but it does not bring this result. It must also be admitted that, counting back, the 17-19-10-0-0 of the series as it stands in the inscription will not bring us to 4 Ahau 8 Cumhu. But it must be borne in mind, as has been stated, that counting 20 cycles to the great cycle or sixth order of units (as there are good reasons for believing is the proper method) would break up the order of Goodman’s tables so far as they relate to the great cycles and the numbering of the cycles, though it would not affect the order of the katuns. The cycles, katuns, and lower periods would follow in regu- lar order, the initial days of each depending on the day with which the count begins. As 17 is given as the number of cycles, it seems clear (unless evidence to the contrary be presented, which Mr Goodman THOMAS] GOODMAN’S SYSTEM 1S) fails to do) that the theory of 13 cycles to the great cycle is erroneous and that the count follows the vigesimal system, as in the Dresden codex. It is significant, however, that by simply changing 1 Ahau 8 Chen to 13 Ahau 8 Chen, counting back 17-19-10-0-0 we reach + Ahau 8 Cumbu. Moreover, if the Dresden codex, which, so far as appears, follows the same time system that is found in the inscriptions, can haye cor- rectly 19 cycles, where is the evidence to be found that 17 cycles would necessarily be erroneous in the inscriptions? Mr Goodman’s objection seems to rest wholly on his theory of the chronologic system. This is insufficient to justify belief in such a radical difference between the systems of two records which in all other respects are so nearly alike. Following Mr Goodman’s interpretation of numeral symbols, an additional fact bearing on this question, we find in certain details of the great cycle and katun symbols. According to him, the comb- like figure similar to those on the katun symbol has the value of 20, If it plays any part in making up the numerical value of the katun, it may reasonably be assumed that it performs a similar office in connec- tion with the great cycle symbol, of which it is a usual accompaniment. It is true that Mr Goodman has furnished no proof that this particular character is a numeral symbol denoting 20, but in accordance with his theory it should have the same value in connection with the great cycle glyph as elsewhere. In this series we have the only evidence in the inscriptions of which I am aware that the great cycles were numbered, 14 being the highest number given. But this numbering is just as the numbering of our thousands or millions; we say 10 thousand and 10 million. In the Dresden codex four of these periods are noted in some four or five series. These are the highest counts, so far as is known, that the Maya reached, their notation seeming to have spent itself in the sixth order of units. We conclude, therefore, that, though the data are not suft- cient to settle all these points by absolute demonstration, as all the evi- dence obtainable is against the theory of 13 cycles to the great cycle and in favor of 20, andas the only evidence as to the numbering of the great cycles indicates that they go above 13, it is safest to assume that the vigesimal system was followed throughout after the count rose above the chuen or second order of units. It is often justifiable to advance into the field of speculation in order to clear away so far as possible obstructions to advancement and to fix the limits of investigation, but the result of speculation can not safely be used as a factor in mathematical demonstration, and Mr Maudslay has candidly stated the necessity for further investigation in this respect. We have noticed the numbering of the ahaus by the day numbers, 798 MAYAN CALENDAR SYSTEMS [ETH. ANN.19 thus, 9, 5, 1, 10, 6, 2511, 7, 3,12, 8, 4, 13) 95 5, 1, ete: Selecting, in’ a continued series of days in proper order, with the day numbers attached, any day Ahau, for instance 1 Ahau, and counting forward 360 days (Goodman’s ahau period), we find that the next 360 day period begins with 10 Ahau; that the third period begins with 6; the next with 2; the next with 11, and so on in the order given above. But the same is true if we select any other day, as 1 Akbal in our table 1, or begin at any point in the continued series, counting 360 days to each step. As Mr Goodman holds that each ahau begins with the day Ahau, it follows, according to this system, that the katuns, which contain just 20 ahaus, must begin with the same day. By this it results that katuns begin with day numbers running in the order 11, 9, 7, 5, 3, 1, ete. This is apparent if we write out the ahau numbers—the 9, 5, 1, 10, etc. —in a continuous series and take each twentieth one. As there are twenty katuns in a cycle, the latter must also, according to this system, begin with the day Ahau. Writing the numbers 11, 9, T, 5, 3, 1, ete., in a continuous series, and taking each twentieth one, the result willl be the’ series 11. 110)°95 (8.7%, 6 5; 45.3, 9) 1 13. 19° 1d ete: If the correct count be, as Mr Goodman asserts, 13 cycles to the great cycle, the latter will all begin with the same day and same day number, but if 20 be the correct count, then the order will be 11, 4, iO), BB PE el 1 7G Wek WO Gy bk, 2h ee: But after all, this kind of figuring is a mere source of amusement except where the knowledge conveyed may aid to more certain and rapid counting. It is as though we were to take the days of our almanac in regular order as named, beginning the first hundred with Sunday; the second hundred would begin with Tuesday, and. so on. By taking these and placing them in consecutive order we could pick out every tenth one as the beginning of the thousands. This might amuse us, and might under possible circumstances be an aid to us in counting time, but it would be no explanation of our calendar system, and would not be a part, but a result thereof. That these ahaus or 360-day counts always began, as Mr Goodman asserts, with a day Ahau, is not proved; moreover, there is no reason for believing the assumption to be correct, but there are on the con- trary, good reasons for believing it to be incorrect. It may be true, as will seem to be the case from what follows, that Ahau was more usually selected as an initial date than any other day, is, in fact, the initial day in most of the inscriptions and is also prominent in the Dresden codex, because, perhaps, some great event took place or was supposed to have taken place onaday Ahau. But it can be demonstrated that the initial day of some of the series in the Dresden codex where the 360-day period is one of the counters is Kan, which, in these, is necessarily the begin- ning of the ahau count. It is true, however, that the ahau or 360-day period must, if the succession be continuous and unbroken, begin on THOMAS] GOODMAN'S SYSTEM AS, : ° the same day, a fact to which I have heretofore called attention (see The Maya Year, pages 47 and 53). But the series may be arbi- trary; that is, the engraver or painter may have chosen to begin one series with one day and another with another day. This, however, goes to the yery root of the subject, as Mr Goodman’s system abso- lutely requires that the ahaus or 360-day counts shall all begin with the same day, and as worked out by him with a day Ahau. Dr Seler, impressed by the result of Dr Férstemann’s investigations, has been led to believe that most of the series of the Dresden codex have 4 Ahau 8 Cumhu as their initial date, or the day to which they refer. While I admit that this is undoubtedly the day which seems to be most prominent in this codex, my investigations do not lead me to indorse his conclusion. Now, it is true that the series on plates 46-50 of the Dresden codex, of which there are in reality 39 sectional, or 3 complete, have Ahau as the initial day, but the initial days of the three series are not all 360 days or an even multiple of 360 days apart, as they should be if Mr Goodman’s theory be correct. But the series are all exact multiples of 260, showing that they are based on a 260-day period. The long series on plates 51-58 does not commence with the day Ahau, whether we consider the upper line or lower line of days the proper one to count back from. It is also apparent that in this case the series is based primarily on the 260-day period. As the least common multiple of 260 and 360 is 4,680, it does not appear possible to bring those series based on the 260-day period into harmony with the Goodman theory except where the total number of days is a multiple of 4,680, unless we suppose that there are two series of non- coincident factors running through them. It is true that we may use the week of our calendar in counting 100-day periods by allowing for the supplementary days, as is undoubtedly done in some of the series of the codices and inscriptions; but the theory that the ahaus are time periods which can not overlap (thus indicating two starting points not consistent with the idea of uniform unbroken succession) is the point aimed at in the above references to the series of the Dresden codex. Another point in connection with the series on plates 51-58 difficult to account for on this theory is that the first day of the chuens (suppos- ing the numbers in the lower order of units to represent the day of the chuen) is Muluc throughout. It is true that the number in the lower order of units may commence anywhere in the chuen, but if these are fixed time periods and the chuens (but not true months) as well as the ahaus commence with Ahau it seems that such important series as this one would reveal this fact somewhere in the reckoning. In the inscription at the end there are two symbols of the usual type, one indicating 1 katun, the other 13 ahaus=11,880 days, while the sum of the series is 11,960, or 80 days more. The series on plates 71-73 has, if we may judge by the numbers S00 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 in the lower order of units, Ben as the first day of the chuens. and 5 Eb as the first day of the series. While these examples do not furnish positive proof in regard to the question at issue, they at least, in connection with what has been presented concerning the plan and object of these reckonings, do indicate that the so-called time periods are merely orders of units and not chronologic periods always coming in regular order from a fixed point in time.’ Never- theless, it must be admitted that most of the initial series in the inscriptions, as will clearly appear when their reckoning is presented, begin with Ahau, which fact must receive a satisfactory explanation before this question can be considered settled. Another fact to be borne in mind is that according to Mr Good- man’s idea, if a katun begins with Ahau, all the chuens or 20-day periods must commence with the same day, though not the same day number, and this would continue indefinitely. The same thing, how- eyer, would be true in this scheme were any other day selected as the initial date; all that will apply in any respect to Ahau will, until the year count comes into play, apply in every particular to any other day, a statement which admits of positive demonstration. The only reason for preferring Ahau, if there be any, is historic, or rather mythologic, as many of the series cover too great lapses of time to be historic. If the two ahau symbols in the inscription in the Temple of Inscrip tions of Palenque, referred to above on page 774, be counters in the time series with which they are connected, they certainly occupy the katun place. As they present the true ahau form, it may be possible that they bear some relation to the name of the period for which they stand. This, however, is at best but a mere guess, and the names are of but minor importance in the discussion. INITIAL SERIES Taking up now the initial series of the inscriptions, I shall give the beginning day of each and briefly discuss its bearing on Goodman’s theory of the Mayan time system. The list so far as noticed by this author is as follows, using his notation, but substituting naught for full count: Pali nue Inscriptions. (1) Tablet of the Cross—53-12-19-13-0 to 8 Ahau 18 Tzec. This connects, by counting back, with 4 Ahaw 8 Zotz, the beginning day of Goodman’s fifty-third great cycle. Here the numerals pretixed to the time periods are face characters for which we must take Mar Good- man’s rendering (see what has been said above on pp. 773-760). 1 After this paper was in print I discovered the connections of the high series ranning up through the serpent figures on plates 61, 62, and 69. These prove beyond question that 20 cycles (or 20 units of the fifth order) are counted to the great evecle (or unit of the sixth order), and that the initial date of these is in some instances Kan. It is my intention to discuss these series in the supplemental piper mentioned above. THOMAS] INITIAL SERIES 801 (2) Tablet of the Sun—54+1-18-5-3-6 to 13 Cimi 19 Ceh. This con- nects with + Ahau 8 Cumhu, the beginning day of the fifty-fourth great cycle. Here also the prefixed numerals are face characters. (3) Tablet of the Foliated Cross—d4-1-18-5—0 to 1 Ahau 13 Mae. This connects with 4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle. Here also the prefixed numerals are face characters. (4) Temple of Inscriptions—54-9-0-0-0 to 138 Ahau 18 Yax. This as given by Mr Goodman connects with 4 Ahau 8 Cumhu, but has certainly been interpreted almost wholly by pure guesswork. The glyphs are nearly obliterated, but enough remains to show that the prefixed numerals were of the ordinary form, balls and short lines (see notes below). (5) Inscribed Steps, House C—55-3-18-12-15-12 to 8 Eb, 15 Pop. This, as given by Mr Goodman, connects with + Ahau 3 Kankin, the first day of his fifty-fifth great cycle, but he admits that the prefixed numerals, all of which are face characters and badly damaged, have been determined otherwise than by inspection. Copan Inscriptions (6) Stela A—54-9-14-19-8-0 to 12 Ahau 18 Cumhu. This con- nects with 4 Ahau 8 Cumhu, initial day of the fifty-fourth great cycle. The prefixed numerals are of the ordinary form, balls and short lines, and are quite distinct. (7) Stela B—54-9-15-0-0-0 to 4 Ahau 13 Yax. This connects with 4 Ahau 8 Cumhu, initial day of the fifty-fourth great cycle. The pre- fixed numerals are of the ordinary form, balls and short lines, and are distinct. (8) Stela C—First inscription: 554-13-0-0-0-0 to 6 Ahau 18 Kayab. This does not connect with the first day of either of Goodman’s great cycles (fifty-third, fifty-fourth, fifty-fifth). The only counter of the initial series has the prefixed numerals of the ordinary form, quite distinct. Second inscription: 557-13-0-0-0-0 to 15% (9%) Ahau 8 Cumhu? This makes no connection with the beginning day of either of Good- man’s great cycles. The prefixed numerals to the single counter are of the ordinary form and distinct. For further notice of these series, see reference to Stela C on a preceding page and remarks below. (9) Stela D—54-9-5-5-0-0 to 4 Ahau 13 Zotz. This connects with 4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle. The pre- fixed numerals are in this case peculiar, being complete forms. (10) Stela F—54-9-14-10-0-0 to 5 Ahau 3 Mac? (according to Good- man). This also connects with the first day of the fifty-fourth great eycle, using the series as given by Goodman; the series is, however, wholly made up by this author, as there is nothing in the inscription and no glyphs obliterated or otherwise to indicate it, the date fol- lowing immediately after the great cycle symbol. 19 pre, PT 2 16 802 MAYAN CALENDAR SYSTEMS [ETH. ANN, 19 (11) Stela [—54-9-12-8-14-0 to 5 Ahau 8 —?, the month symbol being unusual; Mr Goodman says it should be Uo. This connects with 4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle, if we adopt Mr Goodman’s interpretation of the month symbol. The pre- fixed numerals are of the ordinary form and are very distinct. (12) Stela J—West side: 54-9-12-12-0-0 to 1 Ahau 8 Zotz (as given by Goodman). This connects with 4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle, according to the counters as here given. The prefixed numerals are of the ordinary form and are mostly dis- tinct, but there is great uncertainty as to the order in which the glyphs are to be taken. East side: 54-9-13-10-0-0 to no recognized date; Goodman says it should be 7 Ahau 13 Cumhu, presumably reached by counting from 4 Ahau 8 Cumhu, first day of his fifty-fourth great cycle, but in this case he has made a mistake, as the connection is with 7 Ahau 3 Cumhu. The prefixed numerals are of the ordinary form and are distinct, but the order in which the glyphs come is very doubtful (see remarks below). (13) Altar K—54-9-12-16-7-8 to 3 Lamat 16 Yax. This connects with + Ahau 8 Cumhu, the first day of the fifty-fourth great cycle. The prefixed numerals are of the ordinary form, but some of the glyphs are defaced and some of the numbers do not appear to agree with those given by Goodman (see remarks below). (14) Stela M—54-9-16-5-0-0 to 8 Ahau 8 Zotz. This connects with 4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle. The prefixed numerals as given in Maudslay’s drawing (the photograph is not given) are of the ordinary form and correspond with the numbers given here. (15) Stela N—54—-9-16-10-0-0 to 1 Ahau 8 Zip (Goodman says that the month numeral is wrong here and that it should be 3 Zip). This will connect + Abau 8 Cumhu, first day of the fifty-fourth great cycle, with 1 Ahau 3 Zip, but not with 1 Ahau 8 Zip. The prefixed numerals are of the ordinary form, are quite distinct, and agree with those given. (16) Stela P—54-9-9-10-0-0 to 2 Ahaul3 Pop. This connects with4 Ahau 8 Cumhu, first day of the fifty-fourth great cycle. The prefixed numerals are unusual face characters, and the result appears to have been reached by Mr Goodman by appeal to his chronological system. (17) Altar S—54—9-15-0-0-0 to 4 Ahau 13 Yax. This connects with 4 Ahau 8 Cumhu, the first day of the fifty-fourth great cycle, accord- ing to Mr Goodman’s figures here given. However, the pretixed numer- als, which are of the ordinary form and distinct in Maudslay’s drawing (the photograph is not given), do not appear to agree with Goodman’s figures (see remarks below). As I do not haye Maudslay’s photographs and drawings of the Quirigua inscriptions I will omit them from consideration here. Examining these different series and noting Goodman’s explanations THOMAS] INITIAL SERIES 8038 and comments, we soon perceive that the data on which to base a decision in regard to his interpretation of these initial series are rather meager. In six of them the prefixed numerals are face characters, so that the result depends entirely on the correctness of Goodman’s inter- pretation, in regard to which the proof is as yet entirely lacking. A more thorough examination of all the inscriptions containing face numerals, including those of Quirigua, photographs of which are not yet at hand, is necessary before this question can be decided. There are two, I believe, in which connection can be made between the terminal date of the initial series and dates which follow. But this is not positive proof of correct rendering’ where the series runs into high numbers, as do all the initial series. This will be under- stood by the statement that one, two, or more calendar rounds may be dropped out of the aggregate and yet the result will be the same if the prefixed numerals are changed to accord with this result; in other words, the same remainder in days will be left in the one case as in the other. This is possible, but it is not possible to change the time periods so as to give the same result where the sum is less than a calendar round, as one of the higher periods embraces all and more than all the given lower periods. However, we may accept his inter- pretation where the terminal date of the initial series connects with the date which follow. The uncertain and somewhat suspicious ele- ment in the investigation is the evidence in some cases and indication in others that Mr Goodman has obtained his series not from the characters, but from his system. In these cases it is evident that connection of the terminal date by the series with the initial date proves nothing more than the correctness of his calculation. For this reason none of these are considered as evidence of the general use of a certain initial, except where there is connection with a following date through a following series. The two or three instances in which this is the case have been specially referred to. As bearing on this point, the following facts are noted: The initial series in the Temple of Inscription (4 in the above list) is so nearly obliterated, as appears from Maudslay’s photograph, that it is impossible to determine the prefixed numerals or the terminal date. The 4(katuns) is the only distinct number in the series. Enough of the day number, given by Goodman as 13 Ahau, remains to indicate that his rendering is wrong. There are (as is also shown in Maudslay’s drawing) two short lines denoting 10, but the dots or balls are obliter- ated; there is, however, the little loop remaining at one end. Asa rule which has no known exception, unless this be one, there are never more than two balls between these end loops, usually but one (see the quotation on this from Maudslay given above). As there would have to be three to give the 13, either Mr Goodman is wrong or the inscription is irregular. This series must therefore be excepted from those offering evidence in favor of this author’s theory. S04 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 The series on the inscribed steps (5 of the list) Mr Goodman admits has been determined otherwise than by inspection, and hence it must be excluded. Series 6 and 7 of the above list (Stelee A and B) must be accepted as evidence, as the prefixed numerals are of the ordinary form, are distinct, and make connection with the initial date of Goodman’s fifty-fourth great cycle. The two inscriptions on Stela C (8 of above list) present one unusual feature, and one which seems to bear very strongly against Mr Goodman’s theory of 13 cycles to the great cycle, in fact is almost positive evidence against it. Here, following Mr Maudslay’s drawing—for his photograph is not sufficiently plain for satisfactory inspection—we notice that but one time period is given, 13 cycles, and that this is followed without any intervening glyphs by the date 6 Ahau 18 Kayab. The day symbol is a face character, but is so ren- dered, and seemingly correctly, by Goodman. ‘This will not make connection with the initial date of either of the three great cycles given by him. The fact that the numeral in this case (balls and short lines) prefixed to the cycle symbol is 13 appears to stand in direct contradiction of this author’s theory, as ‘‘full count” is nowhere else given in ordinary numerals or even in a face character, but always in one of the symbols for full count. We never find in ordinary numer- als 20 days, 18 chuens, or 20 ahaus, etc., nor has Mr Goodman in any case rendered a face character by either of these numbers. The other inscription on this stela is also unusual in the same respect, the numeral series consisting of only one time period—13 eycles—which is followed immediately by the date 15% Ahau 8 Cumhu. The 15 prefixed to Ahau is evidently an error. Mr Maudslay, though giving 15 in his drawing, concludes, from a subsequent examination, that it may be 9 or 5. However, it will not connect with the first day of either of Mr Goodman’s great cycles, whether we use the one or the other number or any other Ahau 8 Cumhu. These two initial series taken together present another fact difficult to account for on Mr Goodman’s theory. They have precisely the same counters—13 cycles—but reach different terminal dates. This could not be true if the dates are in the same great cycle, and if in different ones they would necessarily be precisely one or two great cycles apart, as Mr Goodman limits the inscriptions to the fifty-third, fifty-fourth, and fifty-fifth. In his comment on these series he virtually confesses his inability to determine the number of the great cycle by the details of the glyph. The inscriptions on the east and west faces of Stela J are placed irregularly, in one case in three columns and transverse lines, and in the other in diagonal lines; the order, therefore, in which the glyphs are to be taken is very uncertain. According to Maudslay’s drawing of Altar K (no photograph is given), the initial series of the inscription as given by Goodman does THOMAS] INITIAL SERIES 805 not appear to be correct. The drawing shows 12 or 14 cycles and not 9, unless the two short lines are to be considered as one, which can only be determined by inspecting a photograph or a cast. The initial series of Altar S (17 of the above list) as given by Mr Goodman does not correspond throughout with that of the inscrip- tion as given in Maudslay’s drawing (there is no photograph). He gives 15 katuns, whereas the inscription shows only 13, the prefixed numerals being ef the ordinary form. Although the evidence presented is not sufficient to establish Mr Goodman’s theory of a distinct Mayan time system, it, together with the very frequent references in the Dresden codex to the day 4 Ahau 8 Cumhu (which always falls in the year 8 Ben), indicates that this date was considered one, perhaps the chief, initial point in the time series. Dr Forstemann has called attention to its use in this codex in his Zur Entzitferung der Mayahandschriften and in a letter to me. Neither of the high series running up the folds of the serpent figures of plates 61 and 62 appear to begin or end with Ahau. The black series in the right serpent of plate 62 over 3 Kan 17 Uo (the 16 is an evident error) reaches back, if counted from this date with 20 cycles to the great cycle, to 12 Chicchan 8 Xul; or, counted with 13 cycles to the great cycle, it reaches 10 Chicchan 18 Pax.’ But it is noticeable that at the bottom of the plate (62) at the right of these serpent figures and extending into plate 63 are five short series with 4 Ahau 8 Cumhu as the given date in each. The red loops here seem, as I have shown on another page, to indicate connecting series, as some of them con- nect with the dates immediately above. The series in the upper left-hand portion, accompanied by loops, terminate with 4 Ahau 8 Cumhu, but go back to 9 Ix counting either or both series of the column, that with the loops and that above 9 Ix. The series running through the middle and lower divisions of plates 72 and 73 starts with 4 Eb. The two high series at the right of the upper division of plate 52 go back to 4 Ahau 8 Cumhu. It will be seen from this discussion that while 4 Ahau 8 Cumhu is a notable initial date, it is not the only one with which series running into years commence, and that Ahau is not the only initial day in long series. There is, however, one noticeable difference between the initial series in the inscriptions and the series in the codices; in the former the symbol of the highest or sixth order of units is a marked character which has no parallel in the latter, but it must be remembered that in the latter the distinction between the orders of units is made by the position of the ordinary counters and not by distinet symbols, as in the former. One fact which must be borne in mind in connection with this point is that Ahau can not be the first day of a year or month in Mr Goodman’s system, nor in any Mayan system. It follows, there- 1See footnote on page 800. 806 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 fore, that neither of his large periods—cycle and great cycle—can begin with the first day of a year. This, however, is true of most, if not all, of the series of the Dresden codex, which goes far toward proving that Mr Goodman’s supposed time periods are not really such in a true sense, but are simply time counters or orders of units; other- wise we must suppose that the Maya had two time systems coincident only at certain points, which is what Mr Goodman assumes. Why the calendar used should be called ** Archaic,” as compared with that of the codices, is not altogether apparent from the inscrip- tions examined. As given and explained by Mr Goodman, it was as complete and perfect in all its details as that which would be designated more recent. The months, years, and 52-year periods, the method of numbering the days, and hence the 4-year series and all the peculiari- ties of the system, were precisely the same as those of the codices. As it is a rule in the progress of human culture to advance from the imperfect and crude to that which is more nearly perfect, that the archaic Maya calendar system might be expected to exhibit imperfec- tions which were gradually remedied by experience. Dr Férstemann, reasoning on this very justifiable assumption, concluded (though we must admit he fails to present satisfactory evidence) that primarily their years consisted of only 360 days, and that the next step in advance was to a year of 364 days, the final correction resulting in the year of 365 days. Mr Goodman says (page 3) that the Cakchiquel time system included two different years, the calendar year consisting of 366 days; and the chronologic year of 400 days (it was 400 days). His scheme includes not only a 360-day period, but carries with it the 365- day period or true year, as this is one of his essential factors, and more- over is apparent in almost every inscription and must be admitted as a part of the chronologic system of the oldest inscribed records which have been discovered, be our theory as to their time system what it may. IDENTITY OF SYSTEMS AND CHARACTERS OF THE DIFFERENT TRIBES That there are found in the inscriptions on the now ruined structures of Tabasco, Chiapas, Yucatan, and Central America forms for the months and for some of the days, as well as some other peculiarities in symbols, not observed in the codices, is true. But considering what has been given by early writers concerning the names and order of the days and months among the different tribes, the agreement in the forms and order of the days and months as shown by the inscriptions is remarkable. Take the day Ahau for example; although we meet here and there a face form, yet the usual symbol at Palenque, Tikal, Menche, and Copan is the same as that found in all the codices. The same is true of Ik, Akbal, Kan, Ben, Ezanab, Imix, and some others. And each holds the same relative position throughout, which indicates THOMAS] IDENTITY OF SYSTEMS AND CHARACTERS 807 a sameness and uniformity at variance with the idea of any difference in system, or any great difference even in nomenclature. Several of the month symbols, as Pop, Zip, Zotz, Xul, Yaxkin, Mol, , Yax, Kayab, Cumhu, and in fact nearly all, are substantially the same as those found in the Dresden codex, which is the only codex in which the months have as yet been discovered. This similarity would seem to indicate that the names among the different tribes have not always been correctly given by the early writers. In fact, the codices and inscriptions show greater uniformity in regard to the time system and time symbols than is to be inferred from the historical record. Each section introduces some glyphs not found in other sections, and there is more or less variation in the ornamentation and nonessential features, but the typical forms of the time symbols are generally essentially the same. ‘ The evidence, when carefully examined in detail, presents some facts which seem to demonstrate the correctness of the above conclusion, and to show that the testimony of the early authorities indicates a greater difference in systems than is indicated by the inscriptions. The names and order of the days of the month used by the Maya (proper), Tzental, and Quiche-Cakchiquel tribes, as based on the his- toric evidence, are as follows: | Maya Tzental Qui.-Cak. 1 | Imix Imox Imox 2 | Ik Igh Tk 3 | Akbal Votan | Akbal 4 | Kan Ghanan | Kat 5 | Chicchan | Abagh | Can 6 | Cimi Tox Camey 7 | Manik Moxie Queh 8 | Lamat Lambat Canel 9 | Mulue Molo Toh 10 | Oc Elab Tai 11 | Chuen Batz Batz 12 | Eb Euob He 13 | Ben Been Ah 14 | Ix Hix Balam 15 | Men Tziquin Tziquin 16 | Cib Chabin Ah mak 17 | Caban Chic Noh 18 | Ezanab Chinax Tihax 19 | Cauae Jahogh Cooe 20 | Ahau Aghaual Hunahpu S08 MAYAN CALENDAR SYSTEMS [BTH. ANN. 19 The names in italics are the supposed dominical days. Some of the names in these lists are but equivalents in the different tribal dialects, but this does not apply to all, as is evident from the efforts of Dr Brinton and Dr Seler to bring them into harmony. Although uniformity in the form of the day symbols does not prove identity in the names in the different tribal dialects, it tends in this direction, if allowance be made for the variation necessary to express the same idea, and undoubtedly indicates unity of origin. Take, for example, the day Votan in the Tzental calendar, which stands in the place of Akbal in the other calendars. The symbol of this day is remarkably uniform in all the inscriptions where it appears. The same is true in regard to Kan, Lamat, and Ezanab, which never appear as face characters. As it is admitted that Votan or Uotan is not equivalent to Akbal, Kat to Kan, nor Canel to Lamat, how are we to account for the uniformity of the symbols in the several regions that these tribes are known to have inhabited ¢ However, the widest variation between the historic evidence and that of the inscriptions is in reference to the names of the months. In regard to these, as given historically, it may be stated that those of the Maya (proper) and the Tzental-Zotzil and Quiche-Cakchiquel groups differed throughout, morphologically and in signification, so far as the latter has been determined, no name in one being the same, save in a single instance, as that in another. As compared with those in the Maya calendar, which have already been given, those of the Tzental were 1, Tzun, 2, Batzul, 3, Sisac, etc.; those of the Quiche, 1, Tequexepual, 2, Tziba pop, 3, Zac, 4, Ch’ab, ete., differing in like manner throughout. So widely different, in fact, are they, that Dr Brinton and Dr Seler made no attempt to bring them into harmony. Now, in contrast with this, the symbols are not only comparatively uniform in the inscriptions, as is shown by the figures given in Mr Goodman’s work, but, with very few exceptions, correspond with those in the Dresden codex. There are also indications that the names were the same as those found in the Maya calendar. For example, the symbol of the month Pop is characterized by an interlacing figure apparently intended to denote matting; in Maya, Pop signifies ** mat.” The name of the fourth month, Zotz, signifies ‘ta bat,” and the sym- bol, which is always a face form, has an extension upward from the tip of the nose, presumably to indicate the leaf-nosed bat. But as conclusive evidence on this point, if Mr Goodman is correct in his interpretation, the month is designated on one of the Stelae at Copan by the full form of a leaf-nosed bat. So general is the uniformity of the month glyphs, both in the Dresden codex and in the inscriptions that Mr Goodman has not hesitated to apply to all the names of the Maya calendar, and to place side by side those of the inscriptions and those of the codex. ‘‘ There is not,” he says, ‘‘an instance of THOMAS) IDENTITY OF SYSTEMS AND CHARACTERS 809 diversity in all their calendars; their dates are all correlative, and in most of the records parallel each other.” Of course there are spo- radic variations and imperfect glyphs which often render determina- tion by simple inspection uncertain, but it is generally aided by the connecting numeral series. The change of day symbols from the typical form to face characters is found in the codices as well as in the inscriptions, as is shown by an examination of the Troano codex, where it is of frequent occurrence. The occasional variations of the symbols for the days Chicchan, Cimi, and Ix, in the latter codex, are so radical that identity is ascertained only by means of the positions they occupy in series. It is upon this uniformity Mr Goodman chiefly bases his theory of an archaic calen- dar. Following the quotation given in the preceding paragraph he says (pp. 145-146): From this is deducible the important fact that—whether a single empire, a federa- tion, or separate nations—they were a homogeneous people, constituting the grandest natiye civilization in the Western Hemisphere of which there is any record. Yet when the Spaniards arrived upon this theater of prehistoric American grandeur, there was not only no powerful nation extant but no tradition or memory of former national greatness. The very sites of the ancient capitals were unmentioned, name- less, unknown. This obliviousness could not result from the passage of a few score or a few hundred years. It could only come in the wake of a period that had outlasted the patience and retentiveness of even aboriginal minds. Next, Dr Otto Stoll, the distinguished comparative linguist, who has made a special study of the Maya dia- lects, states that the Cakchiquel language, one of the most nearly affined to that of the Tzentals, who at present occupy the central seat of the extinct empire, is yet different enough to require a period of at least two thousand years to account for the divarication. This points toa remote date of separation, though indefinite. Thirdly, we find in the Yucatec chronicles a definite indication singularly in keeping with Dr Stoll’s estimate. All the Xiu chronicles begin with a record of the migration of their ancestors, in two great bodies, about two hundred and forty years apart, from some region to the westward. From long and careful study of the annals I haye come to the conclusion that these migrations took place respectively about 353 and 113 years before the beginning of ourera. That this migration could have come from the Archaic nation only is proved by the identity of the graphic system of the Yucatees with that of Palenque, Copan, Quirigua, and other cities of the central region—a system found nowhere to the north, south, or west of it. Even to this day the Yucatec language is more closely allied to that of the Tzentals and Zotzils of that same region than to any of the other numerous Maya dialects. That the Yucatec calendar and chronological system differ in several respects from those of the Archaic cities is not a final or even grave objec- tion to this theory, but only what under the circumstances might be expected. The Xius found the Cocoms and Itzas, older offshoots of the Maya race, already in pos- session of Yucatan, and appear always to have acted a subordinate part to them in subsequent history. It is not unlikely, therefore, that they changed their methods of computing time so as to conform to those of their superiors; or the change may have been made for some reason not evident to us; but that they did change their methods there can be no doubt, and that, too, shortly after their contact with the other nations. Two of their chronicles distinctly state that at a time equivalent to about the 257th year of our era ‘‘ Pop was put in order.’’ The statement can refer 510 MAYAN CALENDAR SYSTEMS (ETH. ANN. 19 only to a rearrangement of their calendars, for the calendars themselves had heen in existence for unknown centuries; hence, these records probably denote the time at which they changed their chronological methods to conform to those of their neigh- bors. Our best hope of correlating the calendars lies in the discovery of some record made by the Nius in their new home previous to this change. The difficulty in this theory lies in the fact that precisely the same calendar system continued down to the coming of the Spaniards, at least in some of the districts. This is proved by the codices, some of which we know were in use down to that time, though possibly understood only by the priests, and the radical differences in the month names seems to have been of comparatively recent date. The same general system, allowance being made for differences in names and forms of symbols, was also found, as has already been mentioned, among the Aztec, Zapotec, and some other stocks. In fact, except for the differences in the names of the months and of some of the days, the change of dominical days by the people among whom the Troano codex was written, and some difference in counting the months which seems to have obtained among some of the Cakchiquel, the calendar system was uniform among the Mayan tribes from the first notice we have of it to the coming of the Spaniards. The idea, therefore, advanced by Mr Goodman of an ** Archaic calendar,” which ceased to be in use about the time of the Niu migration, between sixteen hundred and two thousand years ago, appears to be without valid basis. Finally, on this point I think I will be justified in the statement that if the archaic Mayan chronologic system was so complete and perfect as it is believed by Mr Goodman to have been, it was the most system- atic, orderly, and complete time system ever known to the world, not only outranking in this respect the oriental systems, but even those of modern civilization. We are therefore compelled from our examina- tion of the subject, while commending as exceedingly valuable his real discoveries, which have been noticed, to reject his theory in regard to the ancient Mayan chronologic system, so far as it differs from that generally received, believing that he has mistaken the notation used by this ancient people in counting time for a veritable time system. One somewhat startling result of Mr Goodman’s theory in regard to the Mayan time system is the conclusion reached by him in refer- ence to the range of time over which the history of the Maya people has extended. This is shown in the following extract from his work: Let us, finally, consider for a moment the possibilities of duration for that Maya empire. The Mayas were a primitive, pure-blooded, united people. No ancestral prejudices or racial jealousies could spring between them. Whatever tendencies there were dependent on the inserutable laws of nature must all have been in common. They were strong in numbers, and stronger still by their great and solitary enlighten- ment. They occupied a territory that is practically a fortress. To the east, south, and west there is not area enough to harbor savage foes in numbers that would have been formidable even if coalesced, and to the north, if necessary, they could oppose their united forces. No other great nation ever occupied so secure a position. Hence THOMAS] IDENTITY OF SYSTEMS AND CHARACTERS $11 the question of danger from outside sources is practically eliminated from the prob- lem of their national existence. Their unity of origin, the simple numeral worship indicated by their monuments, the civic spirit to be inferred from the absence of all warlike insignia in the inscriptions, point unmistakably toa happy, contented, peace- ful state of internal affairs, akin to brotherhood. Under such conditions, how long might not a nation endure? We go back ten thousand yearsand find them then ciy- ilized. What other tens of thousand years may it have taken them to reach that stage? From the time of the abrupt termination of their inscriptions, when all sud- denly becomes a blank, back to that remote first date, the apparent gradations in the growth of their civilization are so gradual as to foreshadow a necessity for their 280,800 recorded years to reach the point of its commencement. Manifestly, we shall haye to let out the strap that confines our notion of history. The field of native nationality in America promises, when fully explored, to reveal dates so remote that it will require a wider mental range to realize them (page 149). This conclusion is reached by the following process of reasoning: That the concluding date (he always calls it ‘‘initial date”) of the initial series **could have but a single purpose—that of recording the date at which the monument was erected.” The fact that some of the stele have different ‘‘initial dates” on opposite sides is explained by the statement that ‘‘in these instances one date is reckoned from the other, the latter one undoubtedly designating the time of dedica- tion.” This, however, is a supposition not sustained by satisfactory evidence. As to the two on Stela C, he confesses he can give no expla- nation of them without radical changes in each. By a comparison of the dates in the various inscriptions he arrives at the conclusion that the lapse of time between the earliest and latest of these was 8,383 years. Adding to this 2,348 years, the time preceding 1895 A. D., at which he thinks the record closed (page 148), ‘*we shall arrive at the time when that ancient Maya conqueror trod his enemies under foot, 10,731 years ago, the oldest historical date in the world”; that is to say, the monument on which the earliest date is recorded was erected 8,836 years before the Christian era. To obtain the enormous stretch of 280,800 years, mentioned in the above extract, he counts back according to his theoretic time system to the beginning of the grand era. Of course, such startling result, based upon the kind of testimony offered, can hardly be accepted as historic. The inscriptions showing what may be called ‘initial series” exist; they show the counters up to the sixth order of units, or the great eycle, but all else upon which his great structure is built consists of speculation. There is no basis for his grand era, his 73 great cycles, or his fifty-third, fifty-fourth, and fifty-fifth great cycles. That the great cycles were numbered, just as we number thousands and mil- lions, is undoubtedly true, but 14 is the highest numbering of which we have any positive evidence in the inseriptions or codices, which indicates that the count would have ended at 20, following the vigesimal system if carried higher. Notwithstanding these criticisms Mr Goodman seems to be right in 812 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 his conclusion that, at the time the inscriptions were chiseled and the codices formed, the Maya people were in a much more homogeneous state and tribal distinctions much less marked than when described by the early Spanish writers. Dr Brinton says that ‘*in all the Mayan dialects the names [ot the days] belonged already at the time of the conquest to an archaic form of speech, indicating that they were derived from some common ancient stock, not one from the other, and that, with one or two possible exceptions, they belong to the stock and are not borrowed words.” Though we can not say positively to what tribes the inscriptions of the different districts are to be respec- tively attributed, we can safely assert that they are Mayan, and that those at Palenque are in what is or was the country of the Tzental and Chol tribes; those at Menche (or Lorillard City) in the Lacandon country; those at Copan and Quirigua in the habitat of the Quiche and Cakchiquel or possibly Chol peoples; and those at Tikal in that form- erly occupied by the Itza tribes. The great similarity in the time and numeral symbols and the time systems shown by the inscriptions in these different localities would seem, therefore, to justify Mr Goodman’s assertion ‘‘that—whether a single empire, a federation, or separate nations—they were a homogeneous people,” and thus, though these records have so far failed to furnish any direct historic data and seem likely to fail to furnish any by further investigation, they do form indirectly a firm basis in our attempts to trace the past history of this people. The next step is to determine the age of the records, for, as appears from what has been shown, the history as derived from the carly Spanish writers can not be fully relied on, and the traditions can be trusted only so far as they agree with the monuments and the lin- guistic evidence. That Mr Goodman’s conclusion in reference to their age can not be accepted is evident from the quotation given aboye. One conclusion which appears to be justified by the foregoing facts is that the Maya of Yucatan represent the original stock, or that they have retained with least change of any of the tribes the names and time system of the calendar, except as to the dominical days. NUMERAL SYMBOLS IN THE CODICES Before closing this paper I will, for the benefit of those who have recently taken up the study of the Maya manuscripts and inserip- tions, refer to some symbols found in the codices which probably rep- resent numbers. The study of these may, if followed up by further investigation in the light of Mr Goodman’s discoveries, lead to fruit- ful results in attempts at interpretation of the codices. In THE DRESDEN CODEX The katun symbol in the ordinary form shown at a, figure 10, is very frequently used in this codex, sometimes, as already shown, as one of the counters in a numeral series connecting dates, as for THOMAS] NUMERAL SYMBOLS IN THE CODICES $13 example, on plates 61 and 69. These, which have been heretofore alluded to, are precisely of the form found in the inscriptions. The series as given on plate 69 is 15 katuns, 9 ahaus, 4 chuens, 4 days, the days having a special symbol not joined to that of the chuens. The preceding date is 4 Ahau 8 Cumhu, and that which follows 9 Kan 12 Kayab. The reckoning in this case reaches, as has been shown, the day and day number (9 Kan), but the 7th day of Cumhu instead of the 12th of Kayab. Nevertheless, there can be no question that this is a series precisely after the form of those given in the inscriptions. In these two series are also seen the ahau and chuen symbols of the usual forms, the days, as has been stated, usually having a separate symbol, generally the so-called kin symbol, as the lower character in the symbol of the month Yaxkin. The ordinary numerals found at the side or top of these symbols are frequently replaced by one or more little ball or cup-shape characters, such as are shown in figure 21. Others of like form attached to other period symbols are shown at A3, B3, and A4, figure 16. In the latter, ordinary numerals are also present. The first (figure 21) is from the upper division of plate 73, and the others are from plate 69. Are these characters numerals? If so, what is the value of each? As they can not together represent in any instance more than 20, and as many as three are found in some instances attached to one symbol, it is evident that, ae ao if they are number characters, each must indicate 1, 2, piate 73, 3, 4,5, or 6, not more. As the latter three have also Rery co ordinary numerals attached, but odd numbers, it may be i inferred that the value is 2, 4, or 6. There is, however, other evidence bearing on this question, which is seen in the symbol shown at A3, figure 16. This is certainly the equivalent of the **calendar round” symbol of the inscriptions, and as the largest number of full calendar rounds in the time series immediately below is 5, the value of each of these little characters would seem to be 2. As a chuen symbol in the same connection is followed by the symbol for day in the abstract sense, each having these little characters attached, the evi- dence in favor of the theory that they are numerals is very strong. In the middle of the lower half of plate 70 a katun symbol is followed by an ahau symbol, each having these little characters attached with- out other numerals. So far, however, I have been unable to connect dates by means of these counters, if they be such; but this is not decisive, as there are not sufficient recognized data in any case for a fair test. On plate 71, second column, near the top, is a face glyph used as an ahau symbol; as positive proof that it is such, it has inserted in it a small ahau symbol of the usual type. There are several other characters in this codex which appear to be used as number symbols, 814 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 as the bird head with 10 prefixed, center of plate 70; the Imix-like character with 19 prefixed, lower left-hand corner of plate 71. In regard to this character, which is contained in two groups—one on plate 51, shown at A5, plate xnrv, the other on plate 52, shown at C4, plate xurv, as given in the codex, Mr Goodman’s figures containing supposed restorations—he remarks as follows (p. 93): The resemblance between the last glyph in the list and the character occurring on plates 51 and 52 of the Dresden codex removes all doubt of the latter being a directive sign. It is employed so curiously in one instance that it is well worth while giving both examples of its use in order to illustrate the peculiarity. The reckonings it follows are from 4 Ahau 8 Cumhu (which, coincidently, is the beginning of the 54th great cycle of the Archaic era) to 12 Lamat in both cases, but with different intervals. The reading on plate xr is this: [See plate xziva]. Here the meaning, plainly enough, is: From 4 Ahau 8 Cumhu to the 12 Lamat; that is, 8 days from the former (or initial) date. The reading on plate 52 is more complicated. There are two 4 Ahau-8 Cumhu dates followed by this reckoning: [See plate xirv)]. The 12 Lamat is not distinct, as here, but there can be no question of its identity, the reckoning being of exactly the same character as the other. The reading here is: 4 Ahau 8 Cumhu, 4+ Ahau 8 Cumhu, to the 12 Lamat; that is, 8 days, 1 chuen, and 5 ahaus from the 2 former (or initial) dates. The peculiarity here is that the direc- tive sign indicates the reckoning to be from two dates—the only instance of the kind that has come under my observation. In regard to the group on plate 51 (our plate xiv) it may be safely assumed that the upper date is 4 Ahau 8 Cumhu, and it is true that count- ing 8 days from this date brings the reckoning to 12 Lamat, but the long series immediately below seems to be intended to connect the latter date with the 12 Lamat which is below this long series precisely as in the preceding case, the series here ascending to the left. The assump- tion, therefore, that the Imix symbol isa directive signis very doubtful; moreover, the Lamat symbol precedes it. Férstemann suggests that it signifies an ahau-katun=8,760 days. Mr Goodman’s interpretation of the group on plate 52 (our plate XLIv), will scarcely stand the test of careful examination. In the first place, the assumption that 12 Lamat stands at the head of the group is not warranted. The remnant of the obliterated glyph gives no color to it, nor is there anything in the arrangement of the series in the diyi- sion to suggestit. Moreover, the two dates—each + Ahau 8 Cumhu—do not pertain to the column, but to the two long series at the right imme- ediately under them. This is evident from inspection, but positive proof is found in the fact that, if we use the black numerals of the series, the 4 Ahau 8 Cumhu over the right column connects with the 12 Lamat below, and when we use the red counters we reach, in the same series, the 1 Akbal below. Using the red counters in the left column and counting from the 4 Ahau 8 Cumhu above, we reach 7 Lamat below. The black numerals of this column, which, as they stand, differ only LO days from those of the right column, reach Ezanab, NINETEENTH ANNUAL REPORT PL. XLIV BUREAU OF AMERICAN ETHNOLOGY ee a wih vee : 4% . JPN Be vee Ig 290005 | 2g 2000] (2280 XK meee e CLEFT S ye eed =F IEE i) : ' ‘ a DRESDEN CODEX AND 52 (8), UPPER DIVISION OF PLATES 51 (4) THOMAS] NUMERAL SYMBOLS IN THE CODICES 815 but the day number is 9 and not 3, as it should be; a dot over the 10 chuens will, however, make the connection. It is evident, therefore, that Mr Goodman’s explanation of the two dots before the Imix-like symbol of the group is only a supposition, and his theory as to the use of this symbol is without convincing support; nevertheless, it is prob- ably anumeral character. F6rstemann’s suggestion is that it signifies a ‘“‘katunic cycle,” Goodman’s calendar round. It is true that the troublesome question arises, Are we to assume that the glyphs which have been noticed are always to be considered number symbols, wherever found? This would appear to carry the idea of number symbols to the extreme. See, for example, the ahau symbols on plates 72 and 73. To assume this would imply that the various prefixes to these symbols are numeral signs, as Mr Goodman contends, haying assigned values to most of the types found on the plates referred to. Possibly he may be right (see page 67 of his work). A puzzling character found in this codex is the red circle or loop with bowknot on top (figure 22). Whether these are intended as symbols of connection or not, the series connected with them appear in a majority of cases to form links between other series or to join one or more of what we may term side dates not following in the line of the series. They appear, however, in one series to have some other use; at least, as will be seen when the series is noticed, the numerals inclosed appear to be used ina different way from those in other loops. The first we notice are those in the lower left-hand corner of plate 70. Counters connected with the left loop are + (supposed) chuens, 6 days, the latter number being inclosed in the loop. The date below is 4 Ahau 8 8 Cumbhu, and at the top of the long series over the loop ® \ is9 Ix. If we count backward from + Ahau 8 Cumhu neetaee a 4 chuens, 6 days, or 86 days (which does not carry us ures from plate beyond the commencement of the year), we reach 9 Ix. eee oo The numerals connected with the rightloop are 10chuens, 8 days, or 208 days, the date below + Ahau8 Cumhu and the day above 4 Eb. Reckoning backward as before, we reach the 4 Eb above. The rule also holds good for the counters connected with the loops above, near the middle of the same plate, where those of the left loop are 1 ahau, 12 chuens, 6 days, and those of the right 4 ahaus, 10 chuens, 6 days, the date below each being 4 Ahau 8 Cumhu and the day above each 9 Ix. The reckoning indicated by the series belonging to the loops in the lower left-hand corner of plate 63 is not quite so satisfactory. The series of the left loop is 11 chuens, 15 days, the date above 3 Chic- chan 13 Kankin; that of the middle loop 17 days, the date above 13 ) 816 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 Akbal 6 Cumhu; that of the right loop 7 (or 2) ahaus, 14 (or 2) chuens, 19 days, the day above 3 Chicchan (or 13 Akbal); the date below each, 4 Ahau8 Cumhu. Counting the series of the left loop backward, we reach 3 Chicchan 13 Yaxkin. This is correct except as to the month, which in the codex is certainly Kankin. The reckoning in case of the mid- dle loop reaches 13 Akbal 11 Kayab, whereas the month date in the original is 6 Cumhu. The series attached to the right loop has been corrected by the insertion of a red 2 between the ahau and chuen numerals. The long series above has also been corrected, which indi- cates some material error here. However, the series will not connect with either of the two days aboye, following or rejecting the correction. Attention is called to the fact that the numerals inclosed in the loops here in each case exceed 13, the highest day number, as the question of the use of the numerals will come up in a series to be noticed. The series belonging to the red loop on plate 58 (using the original black numerals, there being a correction or different series in red) is 1ahau, 7 chuens, 11 days; the date below 4 Ahau 8 Cumhu, the nearest date of the long series to the right is 13 Mulue —? Zac. The reckon- ing backward reaches 13 Mulue 2 Zac. The native correction is a red 12 inserted between the ahau and the chuens. This has probably been inserted to bring the reckoning to the Mulue of the right column above the lower date. The series in the upper division connects with 13 Oc to the right. That in the middle division of plate 48 connects with the 3 Lamat over it. Of the two series in the upper division of plate 31, that of the right loop connects with the date above, but that of the left does not. The series attached to the red loop on plate 24, if we consider the red symbol inside as naught, connects with 1 Ahaw 18 Kayab at the right. The series connected with the thirteeen loops, upper divisions of plates 71-73, appears to be the usual form of most other series of the codex, but in this case the numbers in the loops do not form part of the counters, but denote the day numbers of the days reached, counting forward (from left to right) from 9 Ix (plate 71), with an interval of 2 chuens, 14 days. ‘This series is explained in my Aids to the Study of the Maya Codices (Sixth Ann. Rep. Bur. Eth., pp. 337-338). It may, however, be called a connecting series, as by the numbers in the loops—though they are day numbers and never exceed 13—it is joined to the series concluding in the upper division of plate 71. It will be observed that in each case except the last the day from which the reckoning is made is 4 Ahau, and when the month is given + Ahau 8 Cumhu. It would seem, therefore, that special importance was, for some reason, attached to this date by the people of the country and era when the codex was written. This, it must be admitted, bears somewhat in favor of Dr Seler’s and Mr Goodman’s idea of the impor- tance of Ahau in the Mayan time count. THOMAS] NUMERAL SYMBOLS 817 Iy OrHerR Copices in regard to these it may be stated in brief that in the Cortesian codex plates 31 to 38 contain frequent repetitions of the ahau symbol, used apparently as a counter, ordinary numerals being generally attached. These, however have, in addition to the numerals, other appendages not seen in the inscriptions (at least not in the same form) as, for example, the cross-hatched adjunct seen on plate 34. It is true some of the forms given by Goodman show cross-hatching, and of these the Cortesian character may be an equivalent. On plate 34 in the lower division and elsewhere are symbols (with numerals attached) which apparently occupy the place of days and chuens, or of the first and second orders of units. However, I am unable to determine either their relation to any of the numerous dates on the plate or their use. Mr Goodman gives to the cross-hatching in some instances the value of 9, but in others he uses it as a multiplier, usually as 20X20 (see pp. 100, 101 of his work). Possibly he would decide that these ahau symbols are simply intended to refer to the beginning of the first, third, tenth ahau, etc., according to the number prefixed. I am inclined to believe there can be little doubt that they are counters with the usual value assigned to the ahau, whatever may be their relation to the dates on the plate. On plate 35, lower division, and possibly elsewhere, is what appears to be a counter in which the chief element is the Cauac character. The ordinary chuen symbol occurs quite frequently on the plates referred to, but never with more than one set of numerals. Other symbols with numerals attached which may possibly be counters are found on the same plates, but I have been unable to test the supposi- tion. In the Troano codex what appear to be ahau symbols are found on plates 20 to 23, 31, T* to 10*, and also elsewhere. On the latter two plates are also what appear to be katun symbols. In a few instances these two symbols have numerals attached. Scattered through the codex are quite a number of other symbols with numerals attached, which appear to be counters or number glyphs. On the so-called title- page of this and the Cortesian codices are quite a number of glyphs which I take to be number symbols. Some of these I presume from the form to be chuens, but they are in groups usually with numerals attached, and as in three instances these numerals are 19, I take them to indicate days, and the number of chuen symbols in a group to indicate the number of chuens, as the two numbers attached to the chuen glyphs in the inscriptions indicate the days and chuens. IT am also rather inclined to the belief that on this title-page the fourth line of characters from the top denotes ahaus. The red oval symbols below with numerals attached are also probably number glyphs, 19 ETH, pr 2——_17 818 MAYAN CALENDAR SYSTEMS [ETH. ANN. 19 but they must indicate days or some higher order of units than chuens, as the numerals in some cases are 19. However, I have not suc- ceeded in finding any relation between these series and accompanying days. Whether I have succeeded in showing satisfactorily the real discoy- eries made by Mr Goodman and in indicating clearly their true value must be determined by the use which other workers in this field will make of what has been here presented. That these discoveries have opened up new lines of investigation in regard to the signification of the codices and inscriptions will be admitted. Believing that the advance made thereby may be profitably carried into the study of the codices in connection with Dr Férstemann’s discoveries, I have added some suggestions in regard thereto in the hope that other workers in this field may be induced to pursue the subject. WORKING TABLES. As an aid to readers I have followed Mr Goodman’s example in pre- senting tables, chiefly after those in his paper, carrying the cycles up to twenty. Calendar rounds | Calendar rounds 1 18, 980 21 398, 580 4] 778,180 | 61 1,157,780 2 37, 960 | 22-417, 560 42 797, 160 62 1,176, 760 3 56,940 | 23 436,540 | 3 816,140 3 1,195, 740 4 75, 920 24 455,520 || 44 $35,120 64 1,214, 720 5 94,900 | 25 474,500 || 45 854, 100 65 1, 233, 700 6 113,880 26 493,480 || 46 873,080 | 66 1,252, 680 7 182,860 27 «+512, 460 47 892,060 | 67 1,271,660 | § 151,840 28 531, 440 48 911,040 | 68 1,290,640 9 170,820 29 550, 420 49 930, 020 69 1,309, 620 10 189, 800 30 569, 400 50 949,000 | 70 1,328, 600 | a1 208,780 | 31 588,380 51 967,980 | 71 1,347,580 | 12 227,760 32 607, 360 52 986,960 | 72 1,366,560 | 18 246, 740 33 626, 340 53 1,005,940 | 73 1,385,540 14 265,720 | 34 645, 320 54 1, 024, 920 74 1,404,520 15-284, 700 35 664,300 || 55 1,043,900 | 75 1,423,500 16 303,680 | 36 56 1,062, 880 76 1,442,480 17 322, 660 37 702, 260 57 1,081, 860 77 1,461, 460 18 341,640 | 38 * 721,240 || 58 1,100,840 | 78 1,400,440 19 360,620 | 39 740,220 59 1,119, 820 79 1,499,420 | 20 379,600 | 40 759, 200 60 1, 138, 800 80 1,518,400 | THOMAS] WORKING TABLES 819 Ahaus Katuns "Cycles 1 360 1 7, 200 1 144, 000 2 720 2 14, 400 2 288, 000 3 1, 080 3 21, 600 3 432, 000 4 1, 440 4 28, 800 4 576, 000 5 1, 800 5 36, 000 5 720, 000 6 2, 160 6 48, 200 6 864, 000 7 2,520 7 50, 400 7 1,008, 000 8 2, 880 8 57, 600 8 1, 152, 000 9 3, 240 9 64, 800 9 1, 296, 000 10 3, 600 10 72, 000 10 1,440, 000 11 3, 960 iil 79, 200 11 1,584, 000 12 4, 320 12 86, 400 12 1,728, 000 | 13 4, 680 13 93, 600 13 1, 872, 000 14 5,040 | 14 100, 800 14 2,016, 000 15 5, 400 15 108, 000 15 2, 160, 000 16 5, 760 16 115, 200 16 2, 3804, 000 17 6, 120 a7, 122, 400 17 2,448, 000 18 6, 480 18 129, 600 18 2,592, 000 19 6, 840 19 136, 800 19 2,736, 000 20 7, 200 20 144, 000 20 2, 880, 000 — ] PRIMITIVE NUMBERS BY W J McGEE 821 CONTENTS Place of numbers in the growth of knowledge -.---------------------------- Characteristics of primitive thought Primitive counting and number systems Numeration)=- =-ss--=—-- = Notation and augmentation Germs of the number-concept Modern vestiges of almacabala PRIMITIVE NUMBERS By W J McGerr PLACE OF NUMBERS IN THE GROWTH OF KNOWLEDGE The gateway to knowledge of aboriginal character is found in aboriginal conduct; for among primitive folk, habits of action are more trenchant than systems of thought. Yet full knowledge of aboriginal character may be gained only through study of both the activital habits and the intellectual systems of the aborigines; for in every stage of human development, action and thought are concomi- tant and complementary. In dealing with aboriginal customs connected with numbers (simple counting, numeration, calendar systems, etc.), the working ethnolo- gist is confronted by the elusive yet ever-present fact that primitive folk commonly see in numbers qualities or potencies not customarily recognized by peoples of more advanced culture. Accordingly it seems especially desirable to trace the thoughts, as well as the customs, of primitive number-users, and this may be done with a fair degree of confidence in the light of homologies with the early stages of mathe- matics and related knowledge among peoples of advanced culture. Fairly close homologies with the numbers of primitive peoples are atforded by the early stages of chemistry and astronomy. Chemistry grew slowly out of alchemy as natural experience waxed and primeval mysticism waned; and in earlier time astronomy grew out of astrology in similar fashion. The growth of chemistry is fairly written, and that of astronomy less fully recorded in early literature; and in the history of both sciences the records are corroborated and the sequence established by vestigial features—for such features are no less useful in defining mental development than are vestigial organs and functions in outlining vital evolution. Now on scanning the long way over which modern knowledge came up, it becomes clear that the beginning of chemistry marked the third step in the development of science, and that the beginning of astron- omy marked an earlier step; and it also becomes clear that another 825 826 PRIMITIVE NUMBERS [ETH. ANN. 19 step, taken amid the mists of unwritten antiquity, was marked by the beginning of mathematics. In the absence of records, the rise of mathematics may be traced partly (like the growth of the next younger sciences) by vestigial features and functions; and these vestiges indi- vate that, just as scientific chemistry came out of mystical alchemy and as scientific astronomy sprang from mystical astrology, so rational mathematics grew out of a mystical system which long dominated the minds of men and slowly waned under the light of natural experience concentrated among the Arabs of past millenniums. In Arabia this mystical system preceded the simple and essentially natural, though happily conventional, system of enumeration and notation long known as algorithm (or algorism)—i. e., that inchoate form of arithmetic which permitted numerical treatment of quantities, and thus gave a foundation for science. The mystical system is even more clearly rep- resented in algebra, in which the conventional symbols now used to express natural values were originally employed as indices of magical potencies, like the characters inscribed on amulets and talismans; indeed the literature of science yields definite records of that long- abandoned side of algebra known as almacabala (sometimes written almachabel) from the Arabic word for learning and the Hebraic (or older) term for mystical or magical attainment of purpose,’ the whole constituting a jumble of occult or semi-occult redintegration such as appeals strongly to the ill-developed mind. Accordingly the step- ping stones to modern science may be enumerated as (1) almacabala, (2) astrology, (8) alchemy, leading respectively to mathematics and astronomy and chemistry, the oldest branches of definite knowledge. While the transition from almacabala to mathematics is indicated somewhat vaguely by the records and more clearly by vestiges among the peoples influenced by Arabic culture (including all the Aryans and their associates, who make up the intellectual world), the sequence is established by parallel developments displayed by other lines of cul- ture. The import of these parallelisms becomes clear in the light of principles pertaining both to science in general and to anthropology in particular; and some of these principles are worthy of enumeration: 1. In all science it is necessarily (albeit often implicitly) postulated that knowledge grows by successive increments through experience and its assimilation, through observation and comparison (or general- ization), through discovery and invention, or’ in short, through natural processes. In the natural (or chiefly inductive) sciences and in recent decades this postulate is commonly made consciously and deliberately; in the more abstract (or chiefly deductive) sciences the postulate is less frequently made consciously, though a notable example of recognition 1“ Cabala, or ‘practical cabala,’ as described by Hebraic authors, is the art of Snpihine eRnowe edge of the hidden world in order to attain one’s purpose in accordance with the mysticism expounded in the ‘Sefer Yezirah’ (Book of Creation), in which the creation of the world is ascribed to a com- bination and permutation of letters of the alphabet.’’—The Jewish Encyclopedia, Vol. 1, 1891, p. 548. MCGEE] UNIFORMITY OF HUMAN DEVELOPMENT 827 of the experiential basis of mathematics was recently afforded by the president of the American Mathematical Society.' 2. In all departments of definite knowledge, but especially in the sev- eral branches of anthropology, it is implicitly, if not explicitly, postul- ated that knowledge is diffused and its acquisition stimulated through association and interchange among individuals and peoples; indeed, this postulate affords the warrant, and forms the basis, for education. 3. In anthropology as in other sciences it is necessary to recognize a volume or body of knowledge proper to each people, made up of the combined intellectual possessions of all the individuals, increasing with successive experiences, decreasing only through disuse or neglect, and in greater part perpetuated by record and tradition if not by direct heritage. 4. In ethnologic research, as measurably in other lines of inquiry, it is desirable and fair to assume that (7) mental capacity and (4) the sum of knowledge, either in the individual or in the group, are in the long run practically equivalent. 5. In ethnologic inquiry it is convenient to assume that the course of development is approximately uniform (or about as nearly similar as are environmental conditions) in each separate or independent group of men. This assumption, which was recognized first by Powell under the law of activital similarities, and later by Brinton under the formula “unity of mind,” is rapidly crystallizing in the minds of anthropolo- gists; it is, indeed, but a corollary of the primary postulate on which all science rests, namely, that knowledge grows by natural means; and latterly the postulate (which is but a generalization of invariable experi- ence), with its corollaries and applications, has been formulated as one of the cardinal principles of science, namely, the responsivity of mind.? The recognition of the foregoing principles yields a means of out- lining intellectual development in general, and hence of defining the grades, or growth-stages, of given intellectual stocks (or peoples); for when once the general scheme of development indicated by the several examples is perceived clearly, the relative positions of each of the examples are evident. The relations of the natural stages in intellee- tual development may be illustrated by comparison with the growth- stages of aged sequoia groves of prehistoric birth, whose beginnings no man recorded and no living man saw, but whose history may be read clearly in terms of younger groves in other counties; for the towering groyes of the big-tree species and the upshooting forests of human ideas may well be likened in individual and collective growth, save that the vegetal species is decadent and shrunk into scattered 1“Eyen pure mathematics, though long held apart from the other sciences, must be founded, I think, in the last analysis, on observation and experiment.’’—R. S. Woodward, Science, new ser., vol. x111, 1901, p. 522. 2Proc. Washington Academy of Sciences, vol. 11, 1900, pp. 1-12. 828 PRIMITIVE NUMBERS [ETH. ANN. 19 patches, while the mental growth is luxuriant and spreading exuber- antly from province to proyince throughout the lands of the earth. In both cases the interpretation in terms of growth-stages is established by conformity with natural law: did the grove receive extranatural impulse at any stage, or did knowledge arise otherwise than through interactions of nature, the interpretation would fail; but in the absence of evidence against the uniformity of nature, the equivalence of corres- ponding stages must be recognized alike for the figurative forests of ideas and the material forests of wood and leafage. Now the acceptance of these principles, and the recognition of the general course of intellectual development, afford a means of tracing the unrecorded history of Aryan culture and of interpreting the meager records of Arabia’s mathematical pioneering in terms of the culture of other peoples still below, or just rising above, the plane marked by the birth of writing—i. e., the beginning of scriptorial culture. Especially useful for comparison are various practically independent Amerind peoples, some low in prescriptorial culture, others grap- pling with the rudiments of definite graphic art, and still others just within that phase of scriptorial culture marked by conventional calen- dric and numeral systems; hardly less useful are several African peo- ples representing various early stages of development; of much significance, too, are the Australian tribes, of culture so low that numerical knowledge is inchoate only, together with different Polyne- sian tribes whose culture curiously reflects their distinctive environ- ment; while useful suggestions as to the origin of numerical concepts may be drawn from various subhuman animals. True, the lines of mental growth maturing in mathematical systems must vary with environmental conditions, and doubtless with hereditary traits per- sistently reflecting both ancestral and proto-environmental factors; yet, if knowledge be not an extranatural product rather than a reflex of nature (as brilliantly conceived by Bacon) the lines must be so far conformable as to render the comparisons trustworthy and sufliciently accurate for practical purposes—just as the retracing of the history of an isolated grove by comparison with the growth-lines of other groves must be inexact in detail, though trustworthy in general and sufli- ciently accurate to meet practical needs. CHARACTERISTICS OF PRIMITIVE THOUGHT In tracing the lines of intellectual growth maturing in modern enlightenment, it is needful to note certain habits of mind character- istic of all primitive men, yet measurably distinct (in degree if not in kind) from those common to civilized and enlightened men; and for present purposes, as for practically all others, it will suftice to define primitive peoples as those who have not yet acquired and assimilated MCGEE] PRIMITIVE MYSTICISM $29 the art of writing, i. e., as those who remain in prescriptorial culture; for the longest single step in the development of mind and the widest chasm dividing humanity is that marking the transition from the lowly stage of unaided thinking to the stage of mechanically extended memory and mentation. Mysticism of primitive thought—All primitive men are mystics. Believers in extranatural potencies, inexpert observers, and incon- stant reasoners, their vague faith veils or counterfeits realities and clothes its own figments with all manner of attributes, oftener incon- gruous than germane. In their simple (and presumptively primeval) aspect, the fear-born figments are grotesque shadows or fantastic dupli- cates of actual things moved by capricious or malicious motives, like those of human kind; in somewhat advanced thought the figments are more complex, and are incarnated chiefly in self-moying things and invested with enlarged and intensified autonomy; while in the higher stages of primitive culture the figments are idealized into mystical potencies conceiyed to actuate the objects and powers of the universe in accord- ance with impulses and motives such as those observed to control human action. And this lowly faith, with its imputation of animistic impulses and agencies to all nature, is far more than mere abstraction; in all its aspects the belief is profound and paramount; it is an ever- present possession, passing often into complete obsession, whereby action and thought are habitually and wholly controlled. In every phase of primitive culture the mystical potencies imputed to natural things are held to be the chief factors of failure or success in the ceaseless strife for existence. So these potencies are invoked by fasting, propitiated by sacrifice, celebrated by feasting, and expa- tiated and glorified by individual and collective ceremony, as well as by the marvelously persistent tradition of prescriptorial culture. The first effect of recurrent ceremony is to crystallize the animistic con- cepts and concentrate the imputation of potency on the more conspic- uous objects of current experience, and hence to lead to the deification of strong and swift beasts, venomous serpents, rapacious birds, turbu- lent waters, destructive volcanoes, and other impressive things; though since the successful men and tribes give more thought to joyous glorification and less to anxious propitiation than their unsuccessful contemporaries, the beneficent potencies tend to survive and the maleficent mysteries tend to die out of the darksome—but ever bright- ening—faith of primitive men. Yet throughout the whole domain of lowly culture the mystical potencies are dominant factors of thought. In all aspects of primitive faith the controlling mysteries are con- ceived as associated with symbolic objects and actions; and by reason of this notion both mysteries and symbols are zealously enshrouded in ever deeper mysticism. So, fetishism and shamanism grow apace; not only ceremonial objects, but places and persons and forms of utter- 8380 PRIMITIVE NUMBERS [ETH. ANN. 19 ance become secret or sacred, as when the plaza is forbidden to all save priests, and when the Word is deemed a symbol of the Life of the speaker. So, too, esoteric observances, impressive insignia, and imposing formalities are established, and systems of rank or caste grow up as tangible expressions of the intangible structures of control- ling subjectivity. Cumulatively strengthened by reaction of symbol on mystery and of mystery again on symbol, the pervading mysticism is exalted above all other motives in primitive thought; and the artis- tic concepts, the industrial devices, the social relations, and the themes and forms of speech all pass under the control of the unreal potencies which shadow the primitive thinker. Throughout primitive culture invocation habitually carries a reverse of incantation, so that the normal course of fiducial development is attended by persistent magic, sortilege, thaumaturgy; while in the higher stages necromancy and soothsaying, spells and enchantments, conjury and exorcism, oracles and ordeals, and divination by lot or chance become characteristic. In the higher strata, too, expressions supplement or supplant the objective symbols of lower plane, and the jargon of jugglers and the farrago of fakirs take the place of fetiches and idols; and it is particularly significant that words and verbal for- mulas come to be regarded as superpotent expressions of mystical power, and that even the letters of early times were credited with creative powers in practical cabala. Some sayage tribes regard their language as sacred, some haye hieratic languages, and among all known tribes personal names are considered magical or tabu in one way or another; while just within the lower strata of scriptorial sculpture (as illustrated by the Arabs and Hindoos and other Eurasians of a few centuries ago, and attested by literary and linguistic and objective vestiges), shibboleths and numerical formulas become rife, and the inscribed talisman and abracadabra and mystical number, and even- tually the magic square, form favorite symbols of occult power. The growth of writing and the attendant decadence of tradition sounded the knell of primitive mysticism; for one of the leading functions of lowly faith in the actual economy of thought was the maintenance of long series of mnemonic associations, and when this function was assumed (and better performed) by mechanical devices the strongest support of the crude philosophy fell away. Yet the mode of thought crystallized by uncounted generations of habit was too firmly fixed for easy dropping, and innumerable vestiges in the line of Aryan culture, as well as the examples afforded by other lines, demonstrate the potency of primeval mysticism and the tenac- ity of its hold on the human mind eyen beyond the yerge of modern enlightenment. Lgoism of primitive thought—All_ primitive men are egoists. Knowing little of the external world, tribesmen erect themselves or MCGEE] PRIMITIVE EGOISM 831 their groups into centers about which all other things revolve accord- ing to the caprice of their all-potent mysteries; they act and think in terms of a dominant personality, always reducible to the Ego, and an Ego drawn so large as to stand for person, place, time, mode of action, and perhaps for raison d’étre—it is Self, Here, Now, Thus, and Because. Science shows that the solar system hurtles through space, presumably about an unknown center; it showed before that the sun is the center of our system; but the heliocentric system was expanded out of an antecedent geocentric system, itself the offspring of a demo- centric system, which sprang from an earlier ethnocentric system born of the primeval egocentric cosmos of inchoate thinking. In higher culture the recognized cosmos lies in the background of thought, at least among the great majority, but in primitive culture the egocen- tric and ethnocentric views are ever-present and always-dominant factors of both mentation and action. The prominence of self-centred thinking in lowly life is exemplified by kinship organization, the universal basis of primitive society. In the lowest of the great culture stages, the recognized kinship is maternal, and in the next higher (but still prescriptorial) stage it is nominally paternal, though increasingly modified by adoption and other conventional devices; yet the organization is maintained by bonds and interrelations which can not better be illustrated than by analogy with the planetary assemblage: Each individual rotates inde- pendently, may be attended by satellites, and revolves primarily about the head of the family yet ultimately about the patriarch of the group, and each exerts a definite attractional influence (albeit proportional to individuality —or perhaps intellectuality—rather than mass) on all his associates. The relative social positions are expressed and kept in mind by habitual conduct and form of speech; each member of a fam- ily, each family of a clan, and each clan of a tribe has a fixed place in the group to which he or she is kept by thon’s own memory and con- strained by the consensus of associates; and among most primitive peoples no individual can speak to or of a companion without refer- ence to the currently accepted view of his circumscribed cosmos—a man can not say ‘* brother,” but must say ‘*my elder brother,” or use some other term implying the relative position of several individuals to himself, and among each other as reckoned through himself; and in many tribes the terms of relationship used by women differ from those employed by men. The ever-present view of a self-centered cosmos finds expression throughout primitive language, as well as in the lowly faith with which it is bound up and in the social organization by which it is maintained. Primitive speech is essentially associative, abounding in numbers and genders, persons and cases, moods and tenses, in a complex structure reflecting the egocentric habit of thought. This structure 832 PRIMITIVE NUMBERS [ETH, ANN. 19 is crystallized in a characteristically and often chaotically elaborate grammar, well suited to the formulation and utterance of a limited number of ideas representing a few main classes (or lines) of thought, and well adapted to maintaining the associative thought habit; so that primitive languages are essentially structural or morphologic, only incidentally lexie. With the multiplication of ideas accompanying cultural advance, the bonds of linguistic association break under their own weight, and discrete yocables multiply at the expense of unwieldy collocations; and with the attainment of writing, the function of lin- guistic association largely disappears, and speech becomes essentially lexic, only incidentally morphologic. Concordantly with self-centered language, primitive arts and indus- tries are conspicuously egoistic. The most strikingly inchoate esthetic thus far critically studied is the totemic face-paint borne by the ma- trons of clans, apparently as beacon-signals analogous to the face-marks of yarious animals,’ while the tattoo-marks denoting marriage among the women of many Amerind tribes are clear vestiges of the more primitive beacons; and the autobiographic winter count of the warrior and the closely related calendar of the shaman are commonly egocen- tric, never more than ethnocentric—for if the motives of the primitive scribe perchance transcend self, they never outpass the clan or tribe, or at most the confederacy. Similarly the industrial devices of early culture are held to absorb and retain a part of the personality of, and indeed to become subjective appendages to, their makers and users; while in advancing culture the subjective personality of the device passes over into the industries in such wise as to engender guilds and crafts, and ultimately to grow into the ‘ tional apprenticeship. Concordantly, too, egocentric thought finds expression in primitive belief; for the individual long retains his personal tutelary or fetish, endowing it with characters revealing his own subjectivity; and it is art and mystery” of conyen- with exceeding slowness that he rises first to the recognition of family fetishes and clan totems, and eventually to the inheritance, or perhaps as among the Kwakiutl Indians to the conjugal acquisition, of those symbols of potency, and much later that he rises to that recognition of alien tutelaries which expands with piratical and amicabic «ccultu- ration, and ends in pantheism. So in every line of human activity self-centered thinking is crys- tallized by custom, and the thought and custom interact with cumu- lative effect in dominating the primitive mind well into the upper strata of prescriptorial life. The persistence of the cumulative effect is clearly indicated by numberless vestiges of egocentric cosmology clinging often to the higher phases of Aryan culture. 1Cf. The Seri (ndians: Seventeenth Annual Report of the Bureau of American Ethnology, 1898, part 1, p. 168. MCGEE] PRIMITIVE COUNTING 833 In short, it can not be too often stated or too strongly emphasized that primitive thought is unlike the finer product of contemporary intellectuality. While the differences are many, the most conspicuous are those connected with the pervading mysticism and prevailing egoism of primitive thinkers, both magnified in their influence by the fewness of concurrent intellectual stimuli and motives; so that pre- seriptorial culture may justly be regarded as the outgrowth and out- showing of that mysticism-egoism which arose early in the unwritten past, which began to decline with the birth of writing, but which still retains some hold on the minds of men. PRIMITIVE COUNTING AND NUMBER SYSTEMS NUMERATION Simple counting is an accomplishment common to men and many lower animals. The special appreciation of numbers sometimes dis- played by horses, dogs, and pigs may be due to human association, while the geometric sense of the bee may be considered mechanical merely; yet the well-known ability of the crow to count (or at least to discriminate units) up to six or seven, the similar faculty of the fox, and the habits of wasps in providing fixed numbers of spiders for their unborn progeny, as well as various other examples, demonstrate a native capacity for numerical concepts on the part of birds and mammals and insects. Apparently similar is the numerical capacity of various lowly tribes of different continents: Numerous Australian tribes are described as counting laboriously up to two, three, four, or six, sometimes doub- ling two to make four or three to make six, and in other ways reveal- ing a quasi-binary system; though both Curr and Conant opine that ‘*no Australian in his wild state could ever count intelligently to seven.”’ Certain Brazilian tribes are also described as counting only to two, three, or four, usually with an additional term for many; while the Tasmanians counted commenly to two and sometimes to four, and were able to reach five by the addition of one to the limital number.” The analogy between the counting of the tribesmen and that of the animals is not so close as the bare records suggest, since the descrip- tions of the tribal reckoning relate to systems of vocal numeration rather than to actual ability in discrimination and enumeration; more- over, most of the tribesmen reveal the germ of notation in the use of sticks, notches, knetted cords, and the like to make tangible the numerical values—something which lower animals never do so far as is known. Actually the savages, even those of lowliest culture, 1The Number Concept, by L. L. Conant, 1896, p. 27; The Australian Race, by E. M. Curr, 1886, vol. I, p. 32. 2The Aborigines of Tasmania, by H. Ling Roth, 1890, p. 147. 19 ETH, PT 2 1s 8384 PRIMITIVE NUMBERS [ETH. ANN.19 habitually think numerically up to or above three, as 1s shown by the plurality of plurals and by other features of their speech: and the meagerness of their numeration no more negates numerical capacity than does the absence of such systems among counting crows and foxes and wasps. Nevertheless, the comparison is instructive. In the first place, it indicates roughly corresponding ability to count on the part of higher animals and lower men; it also defines the origin of vocal numeration at the bottom of the scale of human development; and it is especially significant in demonstrating that neither the animals nor the men (1) either cognize quinary and decimal systems, or (2) use their own external organs (toes, fingers, ete.) as mechanical adjuncts to nascent notation—unless the binary numeration of certain Austra- lian tribes is really bimanual, as W. E. Roth implies." Many primi- tive peoples count by fingers and hands, sometimes with the addition of toes and feet, and thereby fix quinary, decimal, and vigesimal sys- tems; but the burden of the evidence derived from animal counting and from the numeration of lower savagery seems to demonstrate that these systems are far from primeval. Simple number systems of mystical or symbolic character abound among the better-studied tribes of middle-primitive culture, including the aborigines of North America. The most widespread of the mys- tical numbers is four. It finds expression in Cults of the Quarters in North America, South America, Asia, and Africa, and is suggested by certain customs in Australia;” it is crystallized in the swastika or fylfot and other cruciform symbols on every continent, save perhaps Australia; and it is established and perpetuated by associations with colors, with social organization, and with various customs among numerous tribes. In much of primitive culture the hold of the quatern concept is so strong as to dominate thought and action—so strong as to seem wholly inex- plicable save through the interwoven mysticism and egoism of the lowly mind. The devotee of the Cult of the Quarters is unable to think or speak without habitual reference to the cardinal points; and when the quadrature is extended from space to time, as among the Papago Indians, the concept is so strong as to enthrall thought and enchain action beyond all realistic motives. To most of the devotees of the quatern concept—forming probably the majority of the middle primitive tribes of the earth—the mystical number four is sacred, perfect, and all-potent, of a perfection and potency far exceeding that of six to the Pythagoreans and of the hexagram to Paracelsus and his disciples; they are unconscious or only vaguely conscious of any other numerical concept; and many investigators fail to discover the reverse of the quartered shield and so trace the mystical figure to the subcon- scious self which it invariably reflects. Yet careful inquiry shows | Ethnological Studies among the North-West-Central Queensland Aborigines, 1897, p. 2. 2Curr, The Australian Race, vol. 1, pp. 339, 340. MCGEE] THE SENARY-SEPTENARY SYSTEM 835 that the cardinal points are never conceived apart from the ego in the ceuter: that the subjectively prepotent part of the swastika is the inter- section or common origin of the arms; that the four colors of bright- ening sunrise and boreal cold and blushing sunset and zephyr-borne warmth must have a complementary all-color in the middle; that the four winds are balanced against some mythic storm king (able to par- alyze their powers in response to suitable sacrament) in or near the middle of the world; that the sky falls off in all directions from above the central home of the real men; that the four termini of Papago time relate to the end of the period conceived always with respect to the beginning; that the four worlds of widespread Amerindian mythology comprise two above and two below the fate-shadowed one on which the shamans have their half-apperceived existence; that the four phratries or societies are arranged about the real tribal center; and that in all cases the exoterically mystical number carries an esoteric complement in the form of a simple unity reflecting the egoistic per- sonality or subjectivity of the thinker. It is easier to represent the quatern concept graphically than verbally—indeed it has been repre- sented graphically by unnumbered thousands of primitive thinkers in the cruciform symbols dotting the whole of human history and dif- fused in nearly every human province, or in the form of the equally widespread but less conspicuous quincunx. The exoterically quatern and esoterically quincuncial concept appears to mark a fairly definite phase of human development; a somewhat higher stage is marked by the use of six as a mystical or sacred num- ber. In this stage the mythology remains a Cult of the Quarters, though the cardinal points are augmented by the addition of zenith and nadir, while a third upperworld and a third underworld may be added to the tribal cosmology. The ramifications of the concept are still more extended than those of the quatern idea, and lead to even more patent incongruities—particularly when the attempt is made to graph- ically depict the essentially tridimensional concept on a plane. Now the senary concept, like its simpler analogue, is always incomplete in itself: the six cardinal points must be reckoned from a common center, the three underworlds and the three upperworlds are reckoned from the middle world of actuality, and the six colors (for example, of corn, as among the Zuii, according to Cushing and others) are habit- ually supplemented by a central all-color; so that, in this case, as in that of the quasi-quaternary system, the exoterically perfect number is esoterically perfected through the unity of subjective personality, i. e., the ever-present ego.’ It is significant that the six-cult is much 1 The perfecting of the mystical numbers four and six by the addition of unity has been recognized by many investigators, notably by Powell (On Regimentation, in the Fifteenth Annual Report of the Bureau of Ethnology, 1893-94, 1897, p. cxvii and elsewhere), Morris (Relation of the Pentagonal Dodeca- hedron . . . toShamanism: Proceedings of the American Philosophical Society, vol. Xxxv1, 1897, pp. 179-183), and Cushing (ibid., p. 185 and elsewhere). 836 PRIMITIVE NUMBERS (ETH. ANN.19 less extensively distributed through history and throughout the world than the four-cult, though it may be traced in different continents; and it is peculiarly meaningful in establishing that marvelous prepotency of the number cult which, among many tribes, carried the nascent numeral system past the point at which nature strove, through the obvious organic structure of the hand and through simple algorithmic order, to implant the quinary system. Indeed, if further evidence than that of bestial and savage counting were required to show that finger numera- tion and the quinary system were not primeval, it would be afforded by the development of the senary-septenary system in so many lands. The quaternary and senary cults illumine the binary systems pre- vailing among tribes still lower in the scale of intellectual development. Especially helpful is the light on the Australian aborigines, who are found thereby to exemplify what might be called a Cult of the Halves; for they are controlled by a binary concept of things expressed not only by their numeration, but even more clearly by their social and fiducial systems, which, in turn, shape their everyday conduct and speech. ‘*The fundamental feature in the organization of the central Australian, as in that of other Australian tribes, is the division of the tribe into two exogamous intermarrying groups,” say Spencer and Gillen;' and all other students of native Australian society have either been overwhelmed by an apparently irresolvable nebula of overlapping classes and subclasses and superclasses, or have been led to a related conclusion. Indeed the Gordian knot of entangled relationships con- stituting Australian society is easily cut by the student who places himself in the position of an individual blackfellow, and projects from self dichotomous class-lines occasionally uniting and bifureating in other individuals, after the manner of the dichotomous lines of Aris- totelian classification and the Tree of Porphyry; for the social classes, and the conduct involved in their maintenance, are fixed by a bifureate series of ordinances, ostensibly descended from the mystical olden time, and put in the form of tabus and equally mystical mandates by the shamans. In like manner the obscure pantheon of the Australians seems to be arranged in nearly symmetric pairs; and even the indi- vidual shade (or mystical double of the person) is conceived as bipartite, as among the Arunta, who designate the ghostly attendants Iruntarinia and Arumbaringa, respectively.* Although typically developed among the Australian aborigines, the binary philosophy is by no means confined to the Austral continent and primeval culture; it existed among the Tasmanians, it reappears in Africa, persists in China and Mongolia, and may clearly be traced in America, e. @., in the **sides” forming the primary basis of society in the Seneca and other Amerind tribes; while no fiducial system is 1 The Native Tribes of Central Australia, by Baldwin Spencer and F. J. Gillen, 1899, p. 55 2Op. cit., p. 613, MCGEE] AUSTRALIAN NUMERAL SYSTEM 837 wholly free from the persistent dualism springing from binary inter- pretations of nature. Yet the mystical Two is no more complete in itself than the mystical Four and Six of higher culture; the primary classes or ‘‘sides” are perfected in the tribe both in Australia and in America, the Iruntarinia and Arumbaringa are conjoined in and non- existent apart from the personality they are held to shadow, and the mandates and prohibitions of Australian (and indeed of most other) laws are perfected in permissive, or normal, conduct; in Australia indeed the central factor is so well developed that Lumbholtz was led to note a ternary concept as expressing a definite ‘‘idea of the Trin- ity” among the southeastern tribes;' so that the exoterically binary system of thought is esoterically, or in subconscious fact, ternary. The dichotomous fiducial and social structure clarifies the Australian numeral system. The abundant numerations recorded by Curr and others strongly suggest the simple binary system traced by Conant. A common form is goona, barkoola, barkoola-goona, barkoola-barkoola (1, 2. 2-1, 2-2) sometimes followed by ‘* many” or ‘* plenty” and more rarely by barkoola-barkoola-goona (2-2-1), though usually the table does not go beyond the fourth term, which may itself be replaced by ‘““many.” Now, examination of the numerous records shows (1) that none of the terms correspond with fingers; (2) that a very few of the terms correspond with the word for hand, such terms being three, four, one, and two in (approximate) order of frequency; (3) that a somewhat larger number of terms, chiefly three, one, and two, cor- respond with the words for man; (4) that a considerable number of threes and ones, with a few fours and twos, suggest affinities with obscure roots used chiefly in terms for man, tribe, wild dog, I, yes, etc.; and (5) that there is a strong tendency to limit the formal numer- ation to three. It is particularly noticeable, too, that certain per- sistent number-terms are used sometimes for two and sometimes for three among numerous slightly related tribes—i. e., the term is more definitely crystallized than the concept, which oscillates indiscrimi- nately between two and three, betraying a confusion impossible to arithmetic thought. Similarly the Tasmanian numerations are binary, and without reference to finger or hand, though five sometimes appears to connote man. These features clearly indicate that the Australa- sians do not count on their fingers, and are without realistic notion as to the number of fingers—indeed the Pitta-Pitta of Queensland are able to count their fingers and toes only by the aid of marks in the sand,” while the abundant Australian pictographs reveal habitual uncertainty as to the number of fingers in the human hand (save where the picture is developed from a direct impression). Suggestively analogous in form and meaning are certain South 1 Among Cannibals, 1889, p. 129. 2 Ethnological Studies, by Walter E. Roth, p. 26. 838 PRIMITIVE NUMBERS (ETH. ANN, 19 American number-systems—e. @., that of the Toba, whose ordinary numeration ends with six (the term meaning also ** many” or ** plenty”), though Barcena has traced it to ten. The terms are somewhat vari- able, and of such form as to imply actual or vestigial connotive char- acter; as recorded by Quevedo’ they are nathedac, cacayni or nivoca, cacaynilia, nalotapegat, nivoca cacainitia (2+-3), cacayni cacaynilia (23), nathedac cacayni cacaynilia (1+2% 8), nivoca nalotapegat (2X 4), nivoca nalotapegat nathedae (2X4-+-1), cacayni nivoca nalotapegat (2x4+-2). Now, it is noteworthy (1) that none of the terms connotes finger, hand, or man; (2) that there are alternative terms for two in both simple and composite uses; (3) that two is the most prominent factor in the composite part of the series; (4) that one of the terms for two and the term for three are closely similar, and distinguished only by inflection; (5) that the term for four apparently connotes equality (nalotath=equal) and declaration (na-pega=they say; sena- pega= I say, ete.); and (6) that the system is definitively not quinary or decimal. There are suggestions, both in the combinations and connota- tions of the terms, of two threes of ill-defined numeric character, corresponding respectively to the numeric two and three; and that four is an essentially mechanical square. There are also many indica- tions that the system is inchoate so far as the strictly numerical aspect is concerned. In the dearth of knowledge concerning the original or collateral meanings of the Australian and South American number-terms, it is dificult to formulate the fundamental concept or to give it graphic expression; but a suggestion of great inherent interest is found in the Shahaptian numeration, in which, according to Hewitt, the first two integer-terms are denotive or arbitrary merely, while the term for three means Middle or Middle onz—not middle finger or middle of the hand, but apparently a general (or semi-abstract) Middle like that of the Zuni ritual; and the suggestion is enforced by corresponding expressions in Serian, Iroquoian, and some other Amerindian tongues. The Zuni expression for the middle finger, as rendered by Cushing, is particularly suggestive, viz, ‘* Counter-equally-itself-which-does ”;* and the persistent tendency to double as well as to divide is illustrated by the Hai-it terms (incorporated by Dr Thomas, postea, p. 871) for two, four, and eight, viz, pen, tsoo'-7k, and pen'-tsoo-7h (2X 4), and still more clearly by the absence of the numeral nine—indeed this brief vocabulary displays a curious combination of the binary and quinary systems. In the light of these analogies the Australian thought-mode, with its numerical and social and fiducial expressions, and measurably also that 1Arte de la Lengua Toba, por el Padre Alonso Barcena * * * con Vocabularios * * * por Samuel A. Lafone Queyedo, Biblioteca Lingiiistica del Museo de la Plata, vol. 11, 1898, p. 41. *Manual Concepts, Am. Anthropologist, yol. v, 1892, p. 293. MCGEE] CORRESPONDENCE IN THE THREE SYSTEMS 839 of the Toba and perhaps other South American tribes, assume definite and harmonious shape in a binary-ternary system, in which things are conceived in pairs related subconsciously to an initial or central inter- pretative nucleus—that is, to the dominating Ego of primitive ideation. The three number-systems pertaining to prescriptorial culture are essentially distinct from modern Aryan numeration, and indeed from the whole of Arabic algorithm and arithmetic, in motive as well as in mechanism. Primarily, they are devices for divination or for con- necting the real world with the supernal, and it is only later or in minor way that they are prostituted to practical uses; yet by reason of the magical potency imputed to them they dominate thought and action in the culture-stages to which they belong and profoundly affect the course of intellectual development—indeed, like other figments (or pure abstractions, dissevered from the actualities of nature), their office is first to stimulate and later to enchain mentation. In mechanism the three systems correspond substantially, even if they are not actually correlative, for each rests on an exoteric base in the form of a small even number, and each is really controlled and per- fected by a half-apperceived unity, itself the reflection of the Ego, whereby the base is raised esoterically to the next higher odd number. The systems differ only in the value of the exoteric base, which is a measure of the intellectual capacity normal to the culture-stage to which it pertains. The two higher systems have graphic equivalents which shape and intensify their mystical potency (for the mechanical conditions attending graphic representation always interact with pri- mary concepts in primitive thought); but the lowest and presumptively primeval system is without known graphic symbol. NoraTION AND AUGMENTATION Resting as they do on inconstant and largely subjective bases, and per taining as they do to prescriptorial culture (or at the best to inchoate ideographic representation), the primitive number systems are not susceptible of algorithmic notation. Concordantly they are insuscep- tible of treatment by the methods of rational arithmetic; though the two higher systems (and probably the lowest also) lend themselves to combinations made in accordance with a method or law which may be styled augmentation—a process tending to perpetuate itself, and, while neither addition nor multiplication, tending to generate both. This curious law of augmentation is of much significance; in the first place, it represents a process apparently lost (along with the observa- tional basis of arithmetic) from the recorded history of mathematics; and, in the second place, it seems to explain the interrelations and evo- lution of the magica) number-systems; again, it would seem to con- stitute the germ of the fundamental arithmetic processes, and hence to explain the transition from magical to rational numbers; and finally 540 PRIMITIVE NUMBERS [ETH. ANN. 19 it is of no small interest as a source of those vestigial features of almacabala still persisting in Aryan culture, still cropping out in “lucky numbers” and in other fantastic forms. The augmentation of the widely dittused quaternary-quinary system is made clear by aid of its mechanical symbolism, which combined with the egoistic concept to shape the system. The commonest (and nearly world-wide) symbol is the cruciform figure +, or the quincunx, in Now, magnification of the peripheral powers or objects is readily and intuitively represented by adding a line or dot to each of the four extremities of the symbol, whereby it is converted into the simple swastika in its prevailing forms, @,or-+ Actually the figure is sometimes developed (as among some Pueblo peoples, according to Cushing) by laying down four billets or arrows radiating from a fetishistic Middle toward the east, north, west, and south, and then adding, as the ritual proceeds, shorter transverse sticks touching the extremities of the four cardinal billets, the whole being done in such a manner as to harmonize ritual and symbol, and impress the former by the objective representation in the latter. In any case, the symbol is raised from its original value of 44+1 to 8+1; and the graphic rep- resentation accords with the shadowy concept lying behind the number system in which the mystical Middle is persistent, and can be counted but once howsoever the value be augmented. Similarly the periph- eral potencies may be multiplied by the addition of dots, as in a common form of the swastika noted by Wilson, rH or che or by the deyelop- ment of the ‘‘meander,” ch. which thus represent, respectively, 12+-1, 20-+-1, and 20-+-1; and the augmentation may proceed indefinitely, by either mechanical or mental addition, though always in accordance with the primary principle that the Middle is reckoned but once. The mechanical conditions accompanying the development of the figure tend to maintain its symmetry, i. e., the supplementary trans- verse billets, or sticks, are naturally so laid as to form counterparts in relation to the primary billets and to the center; but, as pointed out by Wilson (after Max Miiller and Burnouf), the additional billets com- pleting the swastika proper may be turned either to right or to left, i. e., the development of the figure may be either clockwise or counter- clockwise. The question has even been raised whether distinct names should be applied to the alternative forms; but in view of the fact that the habitual motions of primitive peoples are predominantly centrip- etal, or toward the body, while the predominant motions of advanced peoples are centrifugal, it seems safe to infer that the clockwise swas- tika represents the higher cultural plane (just as writing toward the right represents a higher plane than the archaic mode of writing ! The Swastika; Report of the United States National Museum for 189, p. 767. MCGEF] SENARY-SEPTENARY NOTATION 841 toward the left), and accordingly that this form would be normal if the form itself were normal to advanced culture; but that since the symbol pertains in all essential respects to the lowly culture charac- terized by centripetal hand-movement, the counter-clockwise form and it is would seem to be more properly considered the norm: drawn herein. While the concept of the senary-septenary system is much more complex than that of the quaternary-quinary system, the law of aug- mentation is similar; and it is significant that the similarity accom- panies (and presumptively results from) analogous efforts at graphic representation. Commonly the concept is directional, as in that form of the Cult of the Quarters in which zenith and nadir are reckoned as cardinal points; and the mechanical symbol is complicated, and event- ually modified, through the difficulty of depicting tridimensional rela- tions on the bidimensional surface. Among the pueblo peoples this difficulty is overcome by bisecting two of the quadrants in a simple cruciform symbol in such manner as to produce the asymmetric figure Me; but the ever-acting mechanical tendency operates to produce the regular figure 44 as the applications of the systems are extended. In either case, augmentation is effected by doubling or further increas- ing the peripheral extremities in such manner as to produce simple hexagrams, at first irregular, 4g, and eventually regular, &: or &. The value of successive augmentations is expressed by the figures 6+1, 12+1, 18+1, ete., i. e., by successive additions (mechanical or mental) to a once-reckoned Middle. Now, comparison of these two number systems, especially as illumined by the Pueblo method of depicting the fifth and sixth direc- tions, indicates that the higher is produced from the lower simply by the superposition of a binary system on the quaternary system; and the inference, coupled with the ‘patent fact that the higher base is the measure of increased intellectual capacity, seems to define the course of development of both systems. True, it is difficult for the arith- metical thinker to see how the mathematical pioneer missed the now- plain road from the indefinite quaternary-quinary notion to the defi- nite quinary concept; but the fact can not be gainsaid that the road was missed by many primitive tribes of especially mystical cast of mind, and that it was found and followed only by the ancestors of the practical Arabs with their decimal system, the barefoot Mexicans with their vigesimal system, and a few other peoples of exceptionally vigorous mind. The failure to find so plain a way may be ascribed largely to the complete domination of primitive thought by mystical concepts; and it would seem to repeat the demonstration by other facts that throughout much of preseriptorial culture little if any use 842 PRIMITIVE NUMBERS [ETH. ANN.19 was made of nature’s abacus, the ever present human hand—for a habit of finger-counting could hardly fail to fix the quinary system in the minds of. counters able to grasp so high a number as five without aid of extraneous symbols. The growth of the senary-septenary system out of the quaternary- quinary arrangement forcibly suggests the genesis of the latter; for just as the hexagram of the higher system represents the swastika of the lower system plus a trigram of the binary-ternary system super- posed by almacabalic augmentation, so the swastika itself merely represents two superposed trigrams. This view of the growth of the three systems in the order of passage from the simple to the complex is supported by all that is known of the relative intellectual capacity ot their users; and it would seem to be established by the occasional advances from the binary-ternary system to the quaternary-quinary plane by some of the Australian numerations, as well as by various vestiges of the binary-ternary system along various culture lines, notably the Mongolian and Aryan. The presumptively primeval system apparently arose spontaneously (perhaps along lines noted later) and became fixed through habitual mental effort shaped less by purpose-wrought symbols than by per- sonal or subjective associations. Analogy with the higher systems would indicate that the number-concept outlined vaguely through the dull mentation of the Australian blackfellows might be symbolized by any regular trigram uniting the perceived pair of objects and the unapperceived Ego, i. e., connecting the objective impression with its subjective reflex; but the inequality of all social pairs in the tribal organization, the ever-varying relative potencies of the good and evil mysteries, the unequal rank of the two ghostly Doppel-ichen, and divers other indications, would suggest that a better figure for the concept would be an irregular trigram. Yet howsoever the system be represented graphically by the student (for apparently the black- fellow had no notion of notation), the law of augmentation common to the two higher systems prevailed, as is shown both by certain of the Australian number-terms and by the Mongolian vestiges—i. e., the augmentation proceeded by successive additions to a once-reckoned middle, yielding the values 2-+-1, 4+1, 6-+-1. It is questionable whether any enlightened student will ever enter sufliciently into the prescriptorial thought represented by any consid- erable number of distinct primitive peoples to grasp and record all the stages and substages in the growth of number systems; yet the records already extant would seem to indicate the lines of growth in fairly adequate fashion. ‘The records are consistent in indicating that primitive peoples used integral numbers rather as symbols of extra- natural potencies than as tokens for natural values; that they com- bined the symbols through mechanical devices by aid of a simple rule MCGEE] FEAR IN PRIMITIVE LIFE 843 tending to develop into algorithmic processes; and that the mechanical arrangements employed to represent the numerical combinations tended to develop into geometric forms and symbols—the several proc- esses being characterized by the method of reckoning from an ill- defined unity counted but once in each combination. GERMS OF THE NUMBER-CONCEPT The course of intellectual development defined by the three pre- scriptorial number-systems (2-3, 4-5, 6-7) naturally leads interest toward the inception of the number idea among lower men—some- thing which must always remain obscure, save as illumined by analo- gies with lowest men and higher animals. Now, the more intelligent fera! animals and the lowest known savages are fairly comparable in their capacity for counting; they are also alike in another respect of such consequence as to shape the character of both—their lives (as Ernest Seton-Thompson so well shows for the animals) are lived in the shadow of tragedies unto often early and always tragic death. This great fact of inevitable tragedy overlays all other facts woven in the web of nascent mind; the most firmly fixed habit of lowly life is that of eternal vigilance; the everpresent thought is that of ever-present danger; the dominant motive is that of mortal fear. No line of intellectual development can be fairly traced without full recognition of the ceaseless terrors of feral life; and the primeval interpretations of environment by animals and men alike manifestly reflect their tragic experiences: The fear-born cunning of the fox engenders that care for a way of escape without which he ventures on no advance; his every intuition is molded by living realization of a two-side universe—the danger side in yan, the safety side in rear— with self as the all-important center; and only religious adherence to experience-shaped instincts enables him to survive and permits his tribe to increase. The ‘sagacious crow, even in semidomestication, constantly betrays his notion of a two-side cosmos in frequent back- ward lances as he surveys the novel or forbidden field in front; and he is an arrant mystic, crazed with abject terror by night, replete with flippant joy by day, and given to the formless fetishism of hoarding uncanny things in well-hidden shrines.‘. In like manner nearly all animals, from the fiercest carnivores to the timidest herbivores, mani- fest constant realization of three overshadowing factors in nature as they know it—factors expressed by Danger, Safety, Self, i. e., by Death and Life to Self, or in general terms, the evil of the largely unknown and the good of the fully known coordinated in the vaguely defined subject of the badness and the goodness; and the chief social activities of animal mates and parents are exercised in gathering their 1Wild Animals I have Known, by Ernest Seton-Thompson, 1898, pp. 72. 83. S44 PRIMITIVE NUMBERS (ETH. ANN. 19 kind into the brightness of the known, and educating their native dread of all outer darkness. So, too, the more timid tribesmen of dif- ferent continents betray, in conduct and speech, a dominant intuition of a terrible Unknown opposed through self to a small but kindly Known. ‘This intuition is not born of intertribal strife, since it is strongest in those innately amicable family groups who (despite an implication of their designation) typify lower savagery, and since it is slowly modified with the rise of self-confidence among vigorous and ageressive tribes in whose minds the good grows large with the wax of conscious power; it is merely the subjective reflection of implacable environment—yet it is vaguely personified as a grisly and horrent bestial power, flaunting specters of death by toothand claw, by serpent venom and swallowed poison, by pitiless famine and insidious disease, by wracking storm and whelming flood, by hydra-headed chance against half-felt helplessness; and oyer against this appalling eyil there is a less completely personified good refiecting the small nucleus of confident knowledge with its far-reaching penumbra of faith. Accordingly, the lowest men and the higher animals seem much alike in their interpretation of nature—both rest their deepest convictions on a two-side cosmos connected in and through a largely passive Self. A yague yet persistent placement of the two ever-present sides with respect to Self is clearly displayed in the conduct of animals and men—the evil side 1s outward, the good side at the place or domicile of the individual and especially of the group, as is shown by the homing instinct of the wounded carnivore, by the haste of the fire-crazed horse to meet the flames in his familiar stall, by human and equine nostal- gia, and by the barbarian longing for burial in native soil. Moreover, both animals and men reveal indications of instinctive placement of the sides in the individual organism; and the indications consistently point to persistent intuition of face and back as the essential factors of self. Yet there is a significant diversity in the assignment of the sides of the organism to the sides of the good-bad cosmos: In general it appears that among the lower and the more timid the back stands for or toward the evil, the face toward the good, and that among the higher and more aggressive the face is set toward the danger; thus, defenseless birds and sheep huddle with heads together, savages sleep with heads toward the fire, and timid tribesmen tattoo talismans on their backs, while litters of young carnivores lie facing in two or more directions, self-confident campers sleep with feet to the fire, and higher soldiery think only of facing the foe. The interesting and significant growth of self-confidence need not be followed; it suffices to note that the primeval concept of the organic ego, as revealed in the conduct of animals and men, appears to be that of a face-back (and not bilateral) unity, with the two sides set toward the two aspects of a cosmos con- ceived in fear-born philosophy. MCGEE] THE CULT OF THE HALVES $45 The passage of the primeval concept of a Face-Back Ego into that notion of two cardinal points suggesting a Cult of the Halves is happily represented among those Polyne sian tribes who, according to Chur- chill, have a system of geographic coordinates dominated by two cardinal directions, primarily seaward and landward, and secondarily northward and southward, respectively; while the language and cus- toms connote a corresponding pantheon, capriciously malevolent on the sea side and steadily benevolent on the land side. This system of orientation is especially significant as a link in the chain of conceptual evolution, and equally as an explanation of the persistence of quasi- binary systems throughout Polynesia and Australasia with their shore- lands of antithetic potencies; and no less significant are the facts in their bearing on the question of the habitat of primeval man, or of the orarian prototype already inferred from other facts.” Although varving from tribe to tribe in its relation to the meridian, this nascent orientation is no fleeting figment, but a deep-laid instinct so firmly rooted as to control every serious thought and direct every vital indus- try; indeed the Samoans and related navigators have developed their orientations into one of the most marvelous instincts in the whole range of animal and human life, viz, a cognition of definite albeit invis- ible sailing paths, whereby they are able to traverse the open Pacific, far beyond sight of land, with a degree of safety nearly equal to that afforded by chart and compass. The Polynesian orientation at once illumines the unformulated Cult of the Halves, and opens the way to an explanation of the Cult of the Quarters; for each point of the shore is necessarily defined by sea in front and land in rear, and also by strands stretching toward the right and toward theleft. Moreover,assemblages of Polynesiansand Austral- asians, like the Iroquoian tribal councils, find it convenient to arrange themselves in coordinate groups or ‘‘sides,” so placed laterally as to face a speaker at the end of the plaza or prytaneum; and there is good reason for opining that the collective habit was soon strengthened, even if it was not initiated, by the slight asymmetry of the human body whereby the left brain receives blood a little more directly than the right and gives proportional excess of strength and cunning to the right hand. The initial inequality was doubtless too slight to yield more than barely perceptible physiologic advantage to the dextral fore- limb, as Brinton and Mason and others have shown; yet it may well have sufticed to set in operation a chain of demotic interactions leading to the survival of the right-handed and the extinction of the left-handed 1 Personal communication. While United States consul at Samoa, Mr Churchill collected volu- minous linguistic and other data well worthy of publication, though not yet issued. Conformably, Lesson and Martinet note that in Tahiti north and south are distinguished by denotive terms bear- ing a suggestive relation to tempestuous and milder winds, while east and west are without denotive designations, and are indicated only by descriptive phrases (Les Polynésiens, vol. 11, 1881, p. 314.) 2The Trend of Human Progress: American Anthropologist, new series, vol. 1, 1899, p. 423. 846 PRIMITIVE NUMBERS [ETH. ANN.19 throughout the earlier eons of human development. A clue to the demotic process is easily found in widespread horror of left-handed- ness. especially among primitive peoples; the clue becomes definite in the light of systematic infanticide among many tribes, whereby all manner of natal deformity is eliminated; it becomes conclusive in the light of the customs of those American tribes who habitually eliminate the sinistral offspring as monsters betokening the wrath of the powers. So, apparently initiated by slight physiologic difference and unques- tionably intensified by demotic selection, right-handedness became even more predominant among primitive men than among their less super- stitious descendants; the dexter and dextrous hand came to be exalted in scores of languages as ‘‘ The One That Knows How” or ** The Wise One,” while the sinister hand was degraded by linguistic opprobrium unto a symbol of evil and outer darkness. Naturally and necessarily the bilaterally symmetric division of the Ego into Right and Left fell into superposition with the antecedent Face-Back concept, and pro- duced a quatern notion such as that expressed in the Cult of the Quar- ters. Happily this transition is crystallized in the language of the Pitta-Pitta of Queensland, which possesses directional inflections indi- cating Front and Back reckoned from the Ego; and it is especially significant (in connection with the bimanual count inferred by W. E. Roth) that the inflection for Front applies also to (right?) Side.* It is evident that the passage from the Cult of the Halves to the Cult of the Quarters marked a considerable intellectual advance, both in extension and in intension; and it is evident, too, that the transition must have introduced novel and distinctive thought-modes, susceptible of growth into habits and hence of crystallization into instincts. Con- cordantly, men in several stages of culture as well as certain higher animals are found to display habits and instincts reflecting some such system of coordinates as that formulated in the Cult of the Quarters. The habits are especially prominent among the many primitive folks who ceremoniously yenerate the cardinal points, systematically orient the doorways and other st ructural features of their houses, and main- tain social relations in terms of direction. ‘The instincts are particu- larly conspicuous among horses and kine and swine with their remarkable direction-sense, and most notable of all in the mule with its curiously concentrated hereditary intelligence, and the carrier- pigeon with its carefully cultivated homing-sense. In the present state of knowledge it would be impracticable to trace confidently the entire course of development of the direction-sense in animals and men, partly because so few naturalists have sought, like Ernest Seton- Thompson, to interpret the habits and instincts of lower animals, partly because so few anthropologists have really entered the esoteric life of primitive peoples; yet it is easy to perceive the general trend 1 Ethnological Studies; p. 2. MCGEE] MYSTICAL NUMBERS S84 of the developmental lines from an obscure beginning in higher ani- mality to a conspicuous culmination somewhere in that lower humanity in which the direction-sense is fixed by generation on generation of direction-worship. And it is not to be forgotten that the quatern con- cept, born of unrecorded myriads of experiences and nurtured by unwritten eons of ceremonies, is much more than an idle fancy of kiva and camp-fire. Intensified by the strongest motives of primitive life, it doubtless attained maximum strength before writing arose to divide its functions; yet despite the decadence of millenniums, it still survives in one, if not both, of the two strongest instincts of higher humanity— the instinct of orientation, with the correlative instinct of right- handedness. On the whole, it would seem safe provisionally to trace the begin- nings of the number-concept in the light of common attributes of animals and men, and especially in the strong light afforded by the late-studied workings of primitive minds; and when this is done, the lines of natural development seem clearly to define a crude philosophy, or rather a series of intuitive thought-modes, whence all almacabalic and mathematical systems must necessarily have sprung. MODERN VESTIGES OF ALMACABALA The character of almacabala, and the strength of its hold on the haman mind, are illustrated by numberless vestiges, mainly mystical numbers and cognate graphic symbols. The entire series of mystical numbers may readily be ascertained by juxtaposing the three almaca- balic number systems and the products of their augmentation under the almacabalic rule. They are as follow (the super-mystical numbers accentuated): 2-3—3, 5 75 9) ete. 45— 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, etc. 6-7— Th, 65 Ie ay Sil, Bi, ZY Cehe GbR TS ye bhai The vestigial uses of the binary-ternary system are innumerable. Two persists as the basis of the semi-mystical Aristotelian classifica- tion, which still exerts strong influence on Aryan thought; 2 is the basis, also, of the largely-mystical Chinese philosophy in which the complementary cosmologic elements, Yang and Yin, are developed into the Book of Changes’; and it finds expression, either alone or in its normal union, in most Aryan cults. The mystical 3 pervades nine- tenths of modern literature and all modern folklore; it finds classic expression in the Graces and the Fates; it is particularly strong in Germanic and Celtic literature, cropping out in the conventional Three Wishes and Three Tests (a survival of the ordeal), and also as a cus- tomary charm number; and in these or related ways it persits in half 1 Chinese Philosophy, by Paul Carus, 1898, p. 3 et seq. S45 PRIMITIVE NUMBERS [ETH. ANN, 19 the families and most of the child-groups even of this country and of today. The concept survives, also, in all manner of trigrams— triangles, triskelions, hearts, ete.—of mystic or symbolic character. The quaternary-quinary system survives conspicuously in the form of graphic devices, especially the world-wide cruciform symbol, which has taken on meanings of constantly increasing nobility and refine- ment with the growth of intelligence. Hardly less conspicuous are the classic and later literary survivals in the Four Elements—air, earth, fire. water—of alchemistic philosophy, the Four Winds of astrology and medieval cartography, the Four Iddhis of Buddha, and the Four Beasts of Revelation, with their reflections in the ecclesiastic writing of two millenniums; while the survivals in lighter lore are innumerable. The system persists significantly also in its augmentals, especially 9, 13, 25, 49,and 61. The numerical vestiges are naturally for the most part quaternary, since the quinary aspect is merged and largely lost in algorithm. The senary-septenary system survives as the bridge connecting almacabala and mathematics. In the graphic form it became Pythag- oras’s hexagram of two superposed triangles, the equally mystical hexagram of Brianchon, with which Paracelsus wrought his marvels, and the subrational hexagram of Pascal, while the current hexagram of the Chinese is apparently a composite of this and the binary as well as algorithmic systems. In the numerical form, 6 and more especially 7 play large rdles in lore and in the classic and sacred literature revived during the Elizabethan period; even so recently as the middle of the century the hold of the astrologie 7 was so strong as to retard general acceptance of the double discovery of the eighth planet, Neptune; and equally strong is the hold on the average mind of certain senary-septenary augmentals, particularly those coin- ciding with the augmentals of the lower systems. In idealized (or reified) form, the number 7 has exerted marvellous influence on thought and conduct, especially in the medial stages of human development; according to Addis, ‘*The common Hebrew word for *swear’ meant originally ‘to come under the influence of the number 7°”'; and this is but a typical example of reverence for the magical number among various peoples. In tracing vestiges in the form of augmentals, it is clearly to be borne in mind that their significance, like that of the primary num- bers, is mystical rather than quantitative, so that certain augmental numbers possess greater vitality than others of corresponding arith- metic grade. This is especially true of the almacabalic doubles, nota- bly 9 as the first augmental of 5, and 13 as that of 7; for in these and other cases the first augmental is commonly of opposite sign, in alma- cabalic sense, from its basis—thus, 5 and 7 are beneficent or ** lucky,” 1The Documents of the Hexateuch, part 1, 1893, p. 35. oO MCGEE] MYSTICAL NUMBERS 84 while 9 and especially 13 are maleficent or ‘‘unlucky” numbers. More- over, there is a further mystical intensification in squares of the bases (perhaps growing out of mechanical or arithmetical superposi- tions on the mystical notions); and the charm seems to be still further augmented by coincidences between the several systems. It is partly through this mystical accentuation of the always mystical augmentals that such numbers as 9, 13, 49, and 61 become conspicuous as factors and vestiges of almacabala. Nine survives as a mystical number in the Muses of classical mythol- ogy, in Anglo-Saxon aphorisms emphasizing the vitality of the cat and the effeminacy of the tailor, and as a recurring tale in all of the super- abundant Celtic lore such as that currently recorded by Seumas Mac- Manus; it even survived in the schoolbooks of the early part of the century in the more curious than useful arithmetic process of ‘‘ cast- ing out the nines;” and throughout the last decade of the nineteenth century the newspaper-writing jugglers with nines found (and dif- fused) much mystery-tinged amusement in almacabalic analyses of the numbers 1890-1899. Glaringly prominent in the mythology of recent centuries is the bode clustering about the ill-omened first augmental of ‘‘ lucky ” 7— indeed it is probable that nearly half of the enlightened citizens of the world’s most intelligent country habitually carry the number 13 in their minds as a messenger or harbinger of evil. The almacabalic double of 13 (which is at the same time an augumental of 5) has largely lost its mystical meaning in Europe and America, apparently through friction with practical arithmetic; but it retains no little hold on the oriental mind, and finds expression in twenty-five-fold collectives in India and China, and in a rather frequent organization of Tibetan tribes into 25 septs or formal social units. Eminently conspicuous in Europe and America is the mystical number 49, especially when expressed as 7X7; for, in the belief of a large element of European population, the seventh son of a seventh son needs no training to fit himself for medical craft, while scanners of advertising columns of American newspapers may daily read anew that the seventh daughter of a seventh daughter is a predestined seeress. Few of the larger mystical numbers have survived the shock of occidental contact; but they abound in the Orient. The coincidental- augmental 61 prevails in Tibet, where Sven Hedin found a lama, 1 out of 61 of co-ordinate rank, who professed survival for sixty-one millerniums, through a succession of exoteric deaths and esoteric rein- carnations at uniform periods of sixty-one years;' and this odd value is explained by the designation of the sixty-first figure in the Mongo- lian hexagram—‘ The Right Way” or ‘‘In the Middle” ’—which at 1Through Asia, by Sven Hedin, 1899, vol. 1, p. 1132. 2Chincse Philosophy, p. 12. 19 ETH, PT 2——19 850 PRIMITIVE NUMBERS [ETH. ANN. 19 the same time connects the Book of Changes with the nearly world- wide Cult of the Quarters and its mystical Middle. The numbers 63 and 65 are also mystical in Chinese philosophy, though their potency would seem to be dwarfed by the mechanical-arithmetical structure of the octonal square to which they have been adjusted evidently during recent centuries. Among the Hindu more or less mystical numbers abound, and many of these are found on analysis to correspond with conventional almacabalic augmentals and coincidentals; while the Budd- histic rituals and series of aphorisms often run in measures of fives, with an initial or final supernumerary—the feature being apparently fixed by a mnemonic finger-count superposed on the almacabalic sys- tem, much as the octonal count is superposed on the mystical figures in the Chinese hexagram. Suggestive vestiges of the mystical number-groups persist widely in the form of irrational and functionless supernumeraries, such as the thirteenth loaf in the baker’s dozen, the twenty-first skerret in the coster’s score, the thousand-and-first night of Arabian tale, and the conventional oyerplus in the legal ‘‘ year and a day.” It is possible that the supernumerary habit was crystallized in some cases by sim- ple object-counting so conducted as to include an additional object as a tally; but there are many indications that the habit originally sprang from almacabalic augmentation, in which the sum is always one more than the multiple of the even-number basis. Moreover, the super- numerary habit is especially characteristic of countries and culture- stages in which mystical number-jumbles are rife. Certain of the graphic vestiges of the quaternary-quinary system are of special significance; for just as the hexagrams of the senary- septenary system bridged the way from mystical almacabala to rational geometry, so the mechanical development of symbols exoterically quatern but esoterically quinary carried intelligence across the chasm dividing the morass of almacabala from the algorithmic forelands rising into the firm ground of arithmetic. True, the passage was made easier by the coincidental structure of the hand, that natural abacus which undoubtedly served to fix the quinary system in all minds trained up to the contemplation of fives; yet the way was apparently so long from the habitual perception of lowly twos and fours to the ready grasp and combination of fives that mechanical struc- ture was even more efficient than organic structure in guiding progress. The graphic number symbols of the Mexican codices illustrated and discussed by Dr Thomas and others epitomized the growth of a vigesi- mal system crystallized by the coincidence of manual and pedal strue- tures, while both the terms and the gestures of the Zuni finger-count analyzed by Cushing point the way in which binary prepossessions passed into quinary practices despite the obstruction of the senary MCGEE] SIGNIFICANCE OF VESTIGES 851 concept.1. The most conspicuous and persistent graphic vestiges are those of the barbaric Roman notation, which barred arithmetical prog- ress for ages, and even to-day saps vitality by its crude extravagance in form and function. In certain aspects this notation may be consid- ered binary, or rather dichotomous, and a reciprocal of the bifurcate classification of Aristotle with the Tree of Porphyry,’ although, as has been well shown by Cushing, the integers of the ystem stand for fingers and represent in their combinations the ordinary inger-counts employed throughout the lower medial strata of cultural development. In reality the system is neither perfectly binary nor fully quinary, and still less is it susceptible (by reason of the indefiniteness® as well as the inelasticity of the notation) of development into a complete decimal system; yet its survival as a mere enumerative system opens a vista through the millenniums to a thought-plane in which men man- aged to exist without arithmetic, without number systems save of the crudest, without numerical bases of ratiocination, without traceable germs of ideas now fundamental in daily thought. The Chinese number symbols also show traces of genesis and development from the lowly plane of finger-counting; but to the Aryan mind the most strik-| ing vestiges of essentially prescriptorial thought relating to numbers are those conserved in the Roman notation. The various vestiges, verbal, proverbial, and graphic (vestiges far too many for full enumeration), at once illumine prerational numera- tion and seem to establish that course of development of number- concepts suggested by the customs of people still living in the lower culture-stages. Conversely, the definition of almacabala serves to explain certain 2urious vestiges of primitive thought prevailing even today and in the highest culture; and the vestiges and developmental outlines combine to form a useful means of tracing the general course of intellectual progress from the obscure beginnings in lower savagery toward the present culmination in modern enlightenment. 1Manual Concepts, American Anthropologist, vol. v, 1892, pp. 289-317. [t is to be observed that throughout this luminous discussion, than in which his genius never shone more brightly, Cushing confined himself to the middle strata of development in which numerical concepts are quinary, and in which counting is habitually manual, and made no reference to the lower strata of numerical conceptuality represesented by peoples less advanced than the Zufi. 2The Foundation of Science, The Forum, vol. xxv, 1899, p. 177. 8Thus a prodigal publisher may burden his title-page with the cabala mpcccci; if a shade less prodigal of ink, he may substitute the sign mpcp1; orif still more economical of ink and no less inconsiderate of the convenience of readers, he may recast the formula as McMI. NUMERAL SYSTEMS OF MEXICO AND CENTRAL AMERICA BY CYRUS THOMAS Bes We ba a “i ail a i CONTENTS Page IPHimMabyeUUMIberseme oases series e. asc iste see eee eee ee eee een cileieaiciee 859 INumpersiapov.erlOsasesreasacce cise cise e -See eRe Reece ee meee ence eoseecacen 882 DISCHESIOMIaMGKCOMpArInONser ene oo Se ee eee eee eee eee eee cenee 919 INumibersimsihes Micxicanicodices!s--ss5se eee eee reese eee eeee ener eee eeae 934 The mystical and ceremonial use of numbers..................--..--------- 948 898 FIGURE 23. 24, mS ycoboletors Calli (house) pe eeee ree een Sane eee ee eee eae . Symbol for Itzquintli (dog). From Fejervary codex, plate 6 -_.- . Symbol for Ocelotl (tiger). From Fejervary codex, plate 6 ...... . Symbol for 400. Mendoza codex, plate 20, figure 16 --........-. . Symbol for 4,000. Mendoza codex, plate 28, figure 24 ._._..__-- . Symbol for 20 jars of honey. Mendoza codex, plate 38, figure 21 - . Symbol for 100 hatchets. Mendoza codex, plate 39, figure 20 -__. 2. Symbol for 20 baskets. Mendoza codex, plate 19, figure 2 .--.-.-- . Symbols for 20 days. Mendoza codex, plate 19, figures 10, 11, ILLUSTRATIONS SymbolstottheMexitcantd ays sess eee eee an ae eee Syn bolitoreatl(waten) ssscec masa eee meee ere ee eee meee eo Feo eee aie eee eee ee ee ae ree nensciae see . Symbol for 8,000 sheets paper. Mendoza codex, plate 25, figure 11 - . Symbol for 8,000 pellets copal. Mendoza codex, plate 38, figure 35- 36. . Symbol for 1,800. Codex Telleriano-Remensis, plate 25.........- . Symbol for 4,008. Vatican codex 3738, plate 7, figures 2 and 3. ._. . Symbol for 5,206. Vatican codex 3738, plate 10-.....-..-....--- . Symbol for 19,600. Vatican codex 3738, plate 123...........---. . Diagram of figures on plates 11 and 12 of the Borgian codex ---_- Symbol for 200 cacaxtles. Mendoza codex, plate 44, figure 34 -_-- Page 937 938 938 938 938 945 945 945 946 946 NUMERAL SYSTEMS OF MEXICO AND CENTRAL AMERICA By Cyrus THomas PRIMARY NUMBERS Tt 1s well known that the vigesimal system of numeration prevailed among the Mexican and Central American tribes, at least among all which had adopted the so-called ‘‘ native calendar”’—that is, the cal- endar specially referred to in my paper entitled Mayan Calendar Systems, published in this volume. Numerous short notices and inci- dental mentions of the general system and completer notices of the systems of particular tribes are to be found in the early Spanish authorities and in the works of more recent writers. As, however, most if not all of them are limited in scope, relating to the system of but one tribe or people, or referring only to certain points, and as no paper devoted specially to the subject of numeral systems has appeared in English, it is deemed expedient to, present this paper as a supple- ment to those which have preceded it. Moreover, it is believed that a résumé of the subject in the light of the recent advance in our knowl- edge of Mexican and Central American archeology will be acceptable to those devoting attention to the study of prehistoric Mexico and Central America. As my paper on the calendar systems* related to the time system and symbols of the Mayan tribes, and incidentally to the numeral sys- tem as used by them in counting time, attention will here be paid to the numeral system in its more general application among the Nahu- atlan, Mayan, and other tribes of Mexico and Central America which used the vigesimal system. T have shown in the paper on calendar systems that in counting time 1 1 This expression will be used throughout to refer to the paper mentioned aboye, published in this volume. 859 S60 NUMERAL SYSTEMS (ETH. ANN. 19 the units used by the Mayan tribes were as follow, the day being the primary unit: unit of the 5th order = 20 units, of the 4th order = 144,000 days. unit of the 6th order = 20 units of the 5th order = 2,880,000 days. 1 unit of the Ist order = 1 day. 1 unit of the 2d order = 20 units of the Ist order = 20 days. 1 unit of the 8d order = 18 units of the 2d order = 360 days. 1 unit of the 4th order = 20 units of the 8d order = 7,200 days. i 1 As this notation has been fully explained and discussed in the pre- ceding paper, I pass at once to an examination of the general numeral system of the Mayan tribes. The notation given above dif- fered from that of general application in the change of the second step from 20, as it should be according to the regular yigesimal system, to 18, probably to facilitate counting with the month factor. ; As 20 is the basis of the higher counts, attention will be directed first to the steps leading up to this number. The oldest records to which we can appeal for knowledge of the system in use among the Mayan tribes are the inscriptions and codices. From these we can, however, learn only the method of wrztiéng numbers, not the number names; yet the method of writing will indicate to some extent the process in oral counts. Although the symbols commonly used for this purpose are now well known from the frequent notices of them which have been published, it is necessary for our present purpose that they be presented here. 1 5 Chy ae e ———— ——— Dye abe i ees [pe ees _——— yd ONC Sipecniome ———— b= Aree caate Gi mensions im Sees o> 5 0 — From these it is seen that the count as expressed in symbols is from 1 to 4 by sing dots, or the unit repeated; but that to indicate 5 the method is changed, and a single short line is used instead of five dots. Though frequently horizontal, it is not necessarily so, but is found both in the codices and inscriptions in a vertical position; oftener, even, in the latter than in the former. The next four num- bers, 6, 7, 8, and 9, are formed by adding to the single line one, two, three, and four dots or units, but 10 is represented by two parallel lines. That these lines must be parallel, or substantially so, whether horizontal or vertical, seems to be requisite in the Mayan hiero- glyphic writing. Dots are added to the two lines to indicate the num- bers 11, 12, 13, and 14; three parallel lines are used to represent 15, THOMAS] MAYAN NUMERALS 861 and dots are added to these to form the numbers 16, 17, 18, and 19, where the use of symbols of this form stops, 19 being the highest number for which they appear to have been used in Mayan writing. The higher numbers were, as has been shown in my paper on calendar systems, represented by other symbols, or by relative position. Sub- stantially the same plan of writing numerals is seen in the Roman system, the line being used instead of the dot, thus: I, II, I, LV, V, V1, VU, VIII, 1X, X, XI, ete., to XIX, 19. Attention is called to this because of another resemblance which will be noticed hereafter. Now it is apparent that if these symbols, taken in the order in which they stand, indicate the method followed in actual or oral counting, this method must have been as follows, from five upward: 5 and 1; 5 and 2; and so on to 2 fives; then 2 fives and 1; 2 fives and 2; and so on to 8 fives; then 3 fives and 1; 3 fives and 2, to19. If this theory be true, we should expect to find terms in the language to correspond with the symbols; evidence that these existed in Mayan count appears to be wanting, yet, as favoring the theory, we do find, as will appear, that the Nahuatl and some other surrounding languages contained terms corresponding precisely with this method of counting. It is, however, somewhat strange that the Borgian codex, which is probably the oldest of the existing Mexican codices, does not use the short line for 5, but counts with single dots as high as 26, and in fact no one of these codices appears to use it in counting time from date to date, though it is used in them for other purposes. The Mayan terms from 10 to 20 follow not this quinary system but the decimal order, as will be seen. The terms used for numbers up to 20 in the Maya (or Yucatec) dialect are, according to the usual orthography, as follow: 1 hun. 6 uae. 11 bulue. 16 uaclahun. 2) ca. 7 yee. 12 laheca. 17 uuclahun. 3 ox. 8 uaxac. 13 oxlahun. 18 uaxaclahun. 4° can. 9 bolon. 14 canlahun. 19 bolonlahun. 5 ho. 10 Jahun. 15 holahun. 20 hunkal, or kal. It is scarcely necessary to state that the orthography is varied slightly by different authors, the Spanish 7 being used by some for / in hun, ho, and lahun, and k substituted for ¢ in wae, wuc, and waxae. Tt is apparent from these terms that the numbers from 12 to 19 are formed by adding 2, 3, 4, etc., to 10. The terms for 6, 7, and 8 appear also to be composite, as the terminal c or / seems to indicate either the same radical throughout, or the same suffix, though no satisfac- tory explanation of this point, which will be again referred to, has been presented. As additional data bearing on these questions, the names of the numbers up to 10 in the different Mayan dialects as given by Stoll? are added here, the Spanish 7 being used by him instead of /. 1 Zur Ethnographie der Guatemala, 1884, pp. 68-69. 862 NUMERAL SYSTEMS [ETH. ANN, 19 Dialect 1 2 8 4 5 1 | Huasteca jun tzab ox tze bo 2 | Maya jun ca ox can jo 2a) Peten jun ca ox can jo 3 | Chontal jumpé chapé uxpé chompé jodp 4 Tzental jun cheb oxeb chanéb jooéb 5 | Tzotzil jun chim oxim chanim joom 6 | Chanabal juné chabé oxé chané joé 7 | Chol jum cha ux chum joo 8 | Quekehi jun eaib oxib cajib 06b 9 | Pokonchi jendj quiib ixib quijib joéb 10 | Pokomam jandj quiém ixiém quiejém joém 11 Cakchiquel jun cai oxi caji yuod 12 | Qu’iché jun quiéb vuoxib cajib joéb 13 | Uspanteca jun quib oxib quejéb joéb 14 | Ixil tingyual cdvual éxyual cdjvual évual 15 | Aguacateca | jun cab ox quidj 0 | 16 | Mame jun cave 6xe quidje jévue | | Dialect 6 7 8 9 10 1 | Huasteca akak buk vuaxik belléuj laju 2) Maya, uak utik uaxdk bol6n lajun 2a) Peter uak uuk uaxdk bol6én | lajun 3 | Chonta. (2) (2) (2) (2) (2) 4 Tzental uakéb uukéb uaxakéb | balunéb | lajtin 5 | Tzotzil uakim uukim uaxakim baluném lajuném 6 | Chafiabal uaké juké uaxaké | baluné lajuné 7 | Chol yvuok juk uaxok | bolén lujim 8 | Quekchi vuakib vuktib vuakxakib | -beléb | lajéb 9 | Pokonchi vuakib vuktib vuaxakib | belejé lajéb 10 | Pokomam vuakim vukim vyuaxakim | belejém lajém 11 | Cakchiquel vuaki vukti vuajxaki | belejé lajuj 12 | Qu’iché vuakib | vuktib vuaxakib | belejéb lajuij 13 | Uspanteca vuakakib vuktib yuajxakib | belejéb lajuj 14 | Ixil vuajil vijvual | vuaxajil | behtivual livual 15 Aguacateca ukak vuuik vuidijxak bélu | laju 16 | Mame yudk uk vuacxék | belejuj | lajiij THOMAS] MAYAN NUMERALS 863 Before commenting on the list, the names in some other dialects of this stock not included by Stoll and some variations from the orthog- raphy of his list will be noted. Pupuluea! | Chuhe? Jacalteca® Subinat 1 hun 1 hun 1 hune 1 hun 2 kai 2 chaab 2 caab 2 cheb 3 oxi 3 oxe 3 oxuan 3 oxé 4 kiahi 4 changue + canek 4 chaneb 5 yoo | 5 hoe 5 houeb 5 hoe 6 vahatzi 6 vuaque 6 cuaheb 6 guaqueb 7 vuku 7 uke 7 huheb 7 huqué 8 (?) 8 vuaxke 8 yuaxaheb 8 guaxaqueb 9 belehé 9 yuangue 9 baluneb 9 baluné | 10 lahu 10 lahne | 10 lahuneb 10 lahuneb | 20 hunvinack) 20 hun e’al 20 hun e’al 20 tab Membreno gives the following numerals of the Honduras Chorti, which are added here for comparison: Chorti (Honduras) * 1 yuté. 4 canté. 2 chajté. 5 guajté. 3 ushté. 12. astoraj. Huasteca—Alejandre (Cartilla Huasteca) gives for 6, acac; for 7, buc; for 8, huaxic; for 9, velleuh. Maya—The only variation from Stoll’s orthography (the Spanish 7 and the 4 being considered equivalents) is the terminal ¢ for / in the names for 6, 7, and 8; this can, however, scarcely be considered a variation. Tzental—Charencey (Melanges, p. 44) has given as the Tzental names of numbers what are in fact the Tzotzil names, as is evident from the yocabularies of Stoll and Guardia and also the Vocabulario Tzotzil-Espanfiol edited by Charencey. Tzotzil—The Vocabulario Tzotzil-Espanol gives for 1, ghum, for 6, vuaquim; for 8, vuaxaquin; and for 20, tod. Cakchiquel—Guardia (op. cit., p. 23) gives vakakib for 6, but on page 42 vuacaqi. 1Ricardo Fernandez Guardia, Lenguas Indigenas Cent. Am. Siglo, vol. xv111, pp. 35-36. Probably a mere idiom of the Cakchiquel Pupulueca, near Volean de Agua, Guatemala. 2 Stoll, Sprache der Ixil-Indianer, p. 146 (h substituted for j). Apparently an idiom of the Chafiabal. 8Ibid. This author associates this dialect with the Mam group; however, in its numerals it approaches the Maya very closely. 4Guardia, op. cit., pp. 79-80. The number names are closely related to those of the Chafabal and Tzental dialects, if not identical with the latter. His substituted for the Spanish j. 5 Alberto Membreno, Hondurenismos, p. 264. S64 NUMERAL SYSTEMS (ETH. ANN. 19 Quiche—As Brasseur’s orthography (Gram. Lang. Quiche, p. 141) differs considerably from Stoll’s, we give his list here: 1 hun. 4 cah, or cahib. 7 vukub. 10 Jahuh. 2 cab, or caib. 5 00, or oob. 8 vahxakib. 20 huvyinak. 3 ox, or oxib. 6 yakakib. 9 beleh, or beleheb. Charencey follows this list, except in 8, which he writes varah. Quekchi (KCak’chi, or Cakgi)—Pinart (Vocabulario Castellano- Wak’chi, page 7) gives for 2, hab; for 4, kaaib; for 5, joob; for 6, gquakib; for 7, gukub; and for 8, guajxakib. Charencey (Melanges, page 64) gives for 1, hoon, for 2, cad; for 3, oi; for 4, cagi; for 5, joob; for 6, wakki; for 7, wuku; tor 8, wakshaki; for 9, belojem; and for 10, /ajegem. Mam—As Stoll gives another list (Sprache der Ixil-Indianer, p. 146) which differs somewhat from that given above, and as both vary from that given in Salmeron’s Arte y Vocabulario, page 156, this and Stoll’s second list are given here (7 being changed to /): Salmeron Stoll | | Salmeron Stoll | ] hum hun if vuk vuuk 2 k’ abe caabe | 8 vuahxak vuahxak 3 oxe ox 9 belhuh belhoh 4 k’iahe chyah | 10 | Jahuh lahoh 5 hoe hue | 20 | vuink’im yuinqui | 6 | vuak’ak kak | | | When the names in these lists are examined, the following points appear worthy of attention in attempting to trace their origin and determine their signification. It requires but a cursory examination to see the very close agreement, morphologically, throughout; a fact which may reasonably be assumed as indicating that they had come into use while the ethnic group was still homogeneous, and before the tribal distinctions had become marked. This conclusion agrees with the inference drawn in our paper on calendar systems from a study of the hieroglyphics. As the names of the days in all the Mayan dialects are believed by Dr Brinton to belong ‘‘to an archaic form of speech, indicating that they were derived from some common ancient stock and not one from the other,” the close agreement in the numeral terms may perhaps justify the same conclusion in regard to them, espe- cially as it is generally true that the origin of the names of the lower numbers lies back of history. This similarity also agrees with the uniformity, in the different sections oceupied by the Mayan tribes, in the method of writing the numerals up to 20. The Chontal, Chattabal, Quekehi (or Kak’chi) and Txil names, and those in some of the other dialects, appear to be furnished with THOMAS] MAYAN NUMERALS 865 suffixes. These, in the numbers exceeding 1, are, in a large number of as for example where the terminal letter is > or 7—additions, apparently indicating the plural. In other cases, where they are joined to the name for 1, they play a different réle; for example, the suffix wwa/ in the Ixil dialect signifies turn or repetition, or, per- haps more correctly, step in counting, a sort of reflective from a vaguely defined unity connotative of direction and time; thus the name for 1, wngvual, may be rendered ‘‘one time”; for 2, cavual, ‘two times,” etc. The plural sign may be taken as evidence that the name still holds a trace of or reference to the process of counting, and has not yet reached what we may term the abstract or purely simple form. The pé in Chontal, ¢ in Chanabal, and 7 (or ah) in Pokonchi and Poko- mam, are also suffixes, though possibly merely phonetic. The replac- ing of 7 by / (or j), or the dropping of the letter entirely, as in /ahun, lahuh, lahu, ete., is, of course, understood to be a mere dialectic variation. It has been stated above that the terminal } or 7}, and in some cases cases the m, are construed as suffixes denoting the plural. This conclusion is strongly supported by Charencey (Mélanges), but Stoll (Die Maya- Sprachen der Pokom-gruppe) gives a different interpretation. ** By agreement,” he says, “‘with the Ixil, an isolated 4, complete as 72d, is attached to the numerals 1-10 [not to 1]; it is undoubtedly to be explained as the better understood form 7), which appears in vz-7d, ‘my head,’ of the Aguacateca, as well as in the reflexive pronoun of the Pokonehi, Quiche, ete.; 77-7 would therefore have meant origi- nally ‘three human beings.” Nevertheless this would still carry the idea of plurality and would properly receive a plural termination. According to the same authority the suffix aj in jen-a7, Pokonchi for 1, ‘‘ was chosen as the object, in which at any rate we may recog- nize the personal suffix a, so that jen-a7 very probably meant origi- nally ‘a man.’ This conelusion appears to me doubtful, notwith- standing Dr Stoll’s thorough knowledge of the Mayan languages. The names for the numbers 6, 7, and 8 in this list, as stated above, appear to be compound words, the terminal / or ¢ indicating a suflix, or the radical with a prefix; as yet no generally accepted explanation of these terms has been offered. Charencey (Mélanges, page 156), fol- lowing Brasseur, makes the following suggestion in regard to wac—6: “This corresponds to our expression ‘hors, pardela, superflu, surabun- dant,” in other words, over or beyond, that is, above or more than 5. Perez gives as the signification of the verb wac, wacah, *‘to take out one thing which is placed in another and united with it.” If this be assumed as the origin of the name, it would seem to refer to count- ing on the fingers, turning them in while counting the first five and then opening them out in counting the next five. Although the literal signification of the names for 6, 7, and 8 may not be 5 + 1, 19 ETH, Pr 2 20 866 NUMERAL SYSTEMS [ETH. ANN. 19 5 + 2%, and 5 + 3, yet, judging by the Maya method of writing the numbers, shown above, and the Mexican terms, lam inclined to believe that this is the implied meaning, the words being doubtless archaic; and I will give on a later page an additional reason for this opinion. As the names and method of counting in other languages may throw some light on the subject, the following lists of numerals up to LO are added. The first is the Nahuatl or Mexican (using the term in its lim- ited sense—Aztec as given by Charencey), the signification so far as satisfactorily determined being added. Nahuatl 1 ce. 2 ome. 3 yel or ei. 4 naui. 5 macuilli (‘‘ hand taken’’). 6 chiqua-ce or chicua-cen (literally 5 and 1). 7 chic-ome (literally 5 and 2). 8 chicu-ei or chicu-ey (literally 5 and 3). 9 chico-naui or chiue-naui (literally 5 and 4). 10 matlactli (‘‘ the two hands’’). The term for 5, macuilli, is a composite word from ma7t/, hand, and cu7, to seize or take—that is to say, the five fingers of the hand have been taken (Siméon, Dic. Lang. Nahuatl). The name for 10 is also composite from mazt/, hand, and ¢/actl, bust or torso of the man; in other words, the two hands. It is apparent that the names for 6, 7, 8, and 9 are formed by adding the names for 1, 2, 3, and 4 to ch? or chico, which here takes the place of macuill7, 5. The signification of this term is ‘tat the side, in part, by fraction, a moiety,” etc.; the name is apparently formed from ch7co and zhuan or huan, **near another.” It is probable, therefore, that the correct interpretation is, one at the side, two at the side, ete., the 5 or hand being understood, the reference being evidently to the process of counting on the hands. The following lists are those of related tribes belonging to the group called by Dr Brinton the ‘* Uto-Aztecan family.”* Some of these, as the tribes of the Shoshonean group, had not adopted the vigesimal system nor the ‘‘native calendar”; nevertheless, it is best to bring the material concerning them together, that all which seems to have any bearing on the questions that arise may be before the reader. That the boundaries of the use of the vigesimal system and *‘‘ native calendar” in the southern half of North America were not governed entirely by the lines of linguistic or ethnic stocks is well known, and hence they must have been governed, in part at least, by some other influence. Possibly a careful study of the numeral systems of the ' This is used here provisionally, though the Bureau of American Ethnology will, according to the rule established by Major Powell, adopt the name Nahuatlan. THOMAS] 867 NAHUATLAN NUMERALS different tribes may throw some light on this question; hence we have thought it best to present sufficient examples, so far as our data will allow, to give a definite idea of geographic and tribal differences in the group. Examples from other stocks or families of Mexico and Central America are also given, the stock names being from Brinton. Nahuatlecan branch Pipil! Alagiiilac? 1 ce 1 se 2 ome or ume 2 umi 3 yae, yel 3 jel 4 nahue, nayui nagui 5 maquil, macuil 5 makuil 6 chicuasin, chicuas=5 +1 6 tschikuasi=5 +1 7 chicome=5+2 7 tschikume=5 +2 8 chicuei=5+3 9 chicunahue=5—4 20 tschikwei=5 + 3 matakticumi=(10—1)? matakti sempual 10 mahtlati 11 mahtatici=10-+-1 12 mahtatiome=10-+-2 20 cempual | 1Stoll, Ethnog. Repub. Guatemala, p. 21. Squier, Notes on Cent. Am., p. 352. 2 Brinton, The So-called Alaguilac Language of Guatemala, p. 376. Sonoran branch Coral Opata? Cahita? = | 1 ceaut or zeaut 1 se or seni 1 senu 2 huapoa or huah- | 2 gode 2 uoi poa | 3 yeide or vaide 3 yahi, or bei’bey 3 huaeica | 4 nago 4 naequi 4 moacua or maocoa | 5 mazirs or marizi 5 mamni 5 anxuvioramauri | 6. bussani | 6 busani 6 a-cevi=(5)+1 7 seni-bussani, or) 7 uobusani 7 a-huapoa=(5)+2 | seni gua bussani 8 uonaequi=2 4? 8 a-huaeica or ahu- =1+6? | 9 batani veica=(5)+3 8 go nago=2x4? 10 uomamni=2*5? 9 a-moacua or ama- 9 kimakoi 11, uomamni aman ocoa=(5)+4 10 makoi senu=10-+-1 10 tamoamata (moa-| 20 seuri, orseneurini | 20 tacahua, or senu- mati, ‘‘hand’’) tacua= “the body” 1Conant, Number Concept, p. 166,and Charencey, Melanges, pp. 15-17. 2 Pimentel, Cuadro, Vocab. Opata, vol. 11, p. 273. 3Tbid., Charencey,and Mélanges, pp. 15-17,and Eustaquio. Buelna, Arte Lengua Cahita, p. 199. 868 NUMERAL SYSTEMS (ETH. ANN. 19 Sonoran branch—Continued 20 Pima! | youmako, or hu- | 1 mac 2 houak, or kouak, or keéko 3 vaik, or vaiko kick? or kiik 4 pouitas, huitas, or 5 khekhtaspe tehu-ut, or tsautep 6 wawa, or bubak kikig 7 umu-tchiko, or hu- mukt 8 wistima kuko-wistima 9 10 20 Tarahumari? bire, pile, or sinepi oca, or oka, or | guoca beica, baica, or beiquia nagueoca, or naguo mariki, or marika, or mariqui pussaniki, orusani- qui kichao, or qui- chauco ossanagroc, oka- nako, or osana- guoco kimakoé or qui- macoiqui makoé, or macoi- qui osamacoi Tepehuan ® 1 uma, or huma, or homad 2 gokado, or gaok 8 yeicado, or baech 4 maukao 5 chetam 1Charencey, Mélanges, pp. 15-16, and Hale, Trans. Am. Eth. Soc. (per Gatschet). eit. *Charencey, loc Miguel Tellechea, Compend. Gram. Tarahumar, p. 7. 8Charencey, loc. cit., and Brinton, American Race, p. 337. Shoshone branch 1 Conant, Number Concept, p. 165. 2Gatschet, Forty Vocabularies, Wheeler's Report, vol. vit (number 19). Cahuillo! Kauyuya? 1 suphi 1 sople 2 mewi 2 vuy 3. mepai 3) pa 4 mewittsu 4 yuitehiu 5 nome-kadnun 5 namu-kuanon 6 kadnun-supli=5-+1 6 kuan-sople=5+1 7 kan-munwi==5-+-2 7 kuan-vuy=5+2 8 kan-munpa=5+3 8 kuan-pa=5+-3 9 kan-munwitsu—=5-+-4 9 kuan-vuitchiu=5-+-4 10 nomatsumi 10 nami-tehumi THOMAS] NAHUATLAN NUMERALS Shoshone branch—Continued Gaitchaim! Kechi (of San Luis Rey) 2 1 sopul 1 suploj 2 vue 2) whii 3 pahe 3 paa yosa 4 witcho 7 se-ula 5 maha-ar 6 auva-khanuetech 6 suploj-namehon=1-++5 5 nummu-quano (numma, ‘“‘hand’’) 1Gatschet, Forty Vocabularies, Wheeler's Report, vol. vir (number 20). 2Tbid. (number 22). Southern Pai- California Shoshone! Pavant? utes Painter Shoshone ® 1 shoui 1 soos 1 shui 1 shum- 1 simitich, uue or tchi- mouts 2 wali 2 wyune® 2 vay 2 voahay 2 hwat, or wat 3 pahi 3 piune 3 pay 3 pahi 3 pite, or manu- git 4 wachoui 4 watsuene 4 vatchue 4 voats- 4 watsuet, agve or hwat- chiwit 5 manek 5 manigin 5 manigi 5 manegi 5 managet, or tehu- manush 6 nawa 6 navyiune 6 navay 6 napahi 6 naviti, or natak- skweyu 7 moquesi 7 tatsuene 7 mukui- 7 tatsuu 7 tatsuit she 8 naantz 8 niwatsu- 8 nant- 8 voshu® 8 nywat- ene chui suit 9 you- 9 surromsu- 9 yuvibe 9 kvanik 9 shimero- weep ene men 10 mat-j]| 10 tomsuene 10 mashu!] 10. shuyvan 10 shimmer shoui 1Gatschet, Forty Vocabularies, Wheeler’s Report, vol. vit (number 6). 2Tbid. (number 5). 8Tbid. (number 12). 4Tbid. (number 11). 5Tbid. (number 10) and Charencey, Mélanges. 6Termination wne, probably from onee, ‘‘ to stand up.” “I 0 NUMERAL SYSTEMS (ETH. ANN, 19 Shoshone branch—Continued = = = Comanche! Chemehueyi? Capote Uta® Hopi* | Takhtam & 1 semmus 1 shooy | 1 soois 1 shukhga | 1 aukpeya 2 waha || 2) vay. | 2 w yune 2 lei 2) yurm 3 pahu 3 pay 3 piune 3 pahhio 3 pahe 4 hagar-so-| 4 vatchue 4 watssuline 4+ nale 4 voat- wa cham 5 mawaka 5 manuy | 5 manegin® 5 tchibute | 5 ma-hat- cham 6 nahwa | 6 navay | 6 naveune 6 navai 6 pa-ahaye 7 tah-acho- 7 mukui-j| 7 navechiune 7 tsenggee | 7 voatch- te she : geve 8 nahua-| 8 nantchui}| 8 wahwatssu-| 8 nanal 8 yoa-otch wachota une 9 semmon-| 9 yuepa | 9 sooroosiiiine 9 peve 9 ma-ak- ance ove 10 shurmun | 10 mashu 10 towumsuiine | 10 pakte 10 yoa-ham- | atch | 1Charencey, Mélanges, pp. 15-17. 2Gatschet, Forty Vocabularies, Wheeler's Report, vol. vit (number 13). 8 Ibid. (number 15). 4Tbid. (number 17). 6 Tbid. (number 18). 6 Probably ‘‘all.”’ Kechi (San Diego)! Tobikhar=? Kij or Kizh? Wihinacht! 1 tehoumou 1 pugu 1 puku 1 sifgwein 2 echyou 2 vehe 2 wehe 2 wahéiu 3 micha 3 pahi 3 pahe 3 pahagu 4 paski 4 vatcha 4+ watsa 4 watsikweyu 5 tiyerva 5 mahar | 5 maharr 5 napaiu 6 ksoukouia 6 pavahe 6 paboi 7 ksouamiche 7 vatcha-kabya 8 scomo 8 vehesh-vatcha 9 seou-motchi 9 mahar-kabya 10 touymili 10 vehes-mahar 1 Charencey, Mélanges, pp. 15-17. 2Gatschet, Forty Vocabularies, Wheeler’s Report, vol. vil (number 21). THOMAS] NUMERALS OF CALIFORNIA TRIBES The five following lists from California dialects obtained and fur- nished by Prof. W J McGee are inserted here as the most appropriate place to introduce them: = wttk’-te. 2 pen. 3 shé-poo/-i. 1 keng’-e. o-tee’-ko. 3 to-long’-ko-shoo. bo 1 yélk. boéng’-dy. 3 sha/-pin. bo chich. 2 wo. 3 pai. 1 shan-tee. kti-wik. bo 4 5 6 on On Hai’it dialect} tsoo/-ik. fii tii-poo/-ik. mi/-wttk. 8 pen/-tsoo-ik. ttim-bak’. 9 (lacking). Mi/witk dialect * o/-yee-sa. v ma/-sho-ki. 8 kai/-win-ti. tem/-o-kii. 9 woo/-e. Yet/tripih (Tulare) dialect* hat-pin/-ik. 7 nim/-cheet. hit-shin-ik. 8 chitt-da-pe. mon/-ic. 9 nan-eep. Tatatl (Kern River) dialect * ni/-now. 7 niéim/-tsin. mii’-ee-tsing. 8 nip/’-n-sing. nap/-ai. 9 la/-i-kee. Maricopa dialect? 3 ka/-mok. 4 shtm-pitip. ka-nek/-kié-koo. 10 20 10 20 30 10 20 30 10 20 30 mii/-tsiim. pen/-i-ma-tsiim. ni/-ii-cha. na/-a. na/-ii-nii-ii-chi. tree’-o. bong/-Oy-tree-o. shi/-pin-tree-o. iim-hai-tsing. wom/-m-hai-tsing. pai’-m-mai-tsing. 5 sti-rtp. Three other lists from California dialects, two collected by Stephen Powers and one from Major J. W. Powell’s Comparative Vocabularies (Contributions to North American Ethnology, vol. m1) are added here. One of these—the Konkau—appears to be substantially the same as the Haiit of Professor McGee’s lists. Konkaua Nishinam a Nakum 0d 1 wuk-teh 1 wut-teh 1 chut 2 pe-nim 2 pen 2 penneh | 3. sha-pwi 3 sa-pwi 3 cha-pwi | 4 ch’u-yeh 4 chui, or chuch 4 chui | 5 ma-cha-neh 5 mauk 5 ma-wuk | 10 ma-cho-ko 10 ma-chum 10 ma-suk a Powers, Contrib. to N. A. Eth., vol. 111, p. 313. b Powell, Comp. Voecab., ibid., pp. 594-596. 1 Obtained at Nevada, California, October 3, 1898, and verified at Forest Hill and Colfax. 2 Obtained near Jamestown, California, October 18, 1898. 8 Obtained at Tule River agency, October 25, 1898. 4 Obtained at Tule River agency, October 25, 1898. 5 Obtained at Ashfork, Arizona, from girl en route to San Diego, California. NUMERAL SYSTEMS Zapotecan family * Zapotec? Mixtec® (ETH. ANN.19 Chuchon* (or Chocha) 9 10 1To conform to the rule proposed by Major Powell, wh single term terminating with an in forming family names, this family will be called the Zapotecan. tobi, tubi, or chaga topa, tiopa, or cato chona, or cayo tapa, or taa caayo, gayo, orgoyo xopa, or goxopa caache, gaache or gooche xoono, xono, or goxono caa, or gaa chii, or gochii ao - w to a bt | 8 9 10 11 ec (ce?) or ek wui, uvui, or uhui uni gmi, or kmi hoho ino ucha una ce usi usi-ce ngu 2 yuu-rina,® or yuu 3 ni-rina, or nyi 4 nuu-rina, or fuu 5 nau-rina, or nau 6 njau-rina, or nhau 7 yaatu-rina, or yaatu 8 nh-rina, or nhi vo} naa-rina, or naa te-rina, or te 2Cordoya, Arte del Idioma Zapoteco (reprint), p. 176, and Vocab. Castellano-Zapoteco. 8Charencey, Mélanges, p. 44. 4N. Leon, Introd. to Cordova, Arte del Idioma Zapoteco, p. 1xxii. 5 Leon says that rina appears to be a sign of the numeral adjective. This is merely a subdialect of ich has been generally accepted, to use a the Chuchon, Popoloca! (of Oaxaca) Trike? | Mazateca® 1 gou, or ngu 1 ngo 1 gu 2 yuu 2 nghui 2 hé 3 nii, or nyi 3 guandanha 38 ha 4 noo, or nuu 4 kaha 4 ni-kti 5 nag-hou, or nau 5 huhtha 5 ut 6 tja, or nhau 6 guatinka 6 ht 7 yaata, or yaatu 7 chiha 7 yi-tu 8 gnii, or nhi 8 tonha 8 hi-i 9 na, or naa 9 htinha 9 fi-ha 10 tie, or te 10 chia 10 te 20 kaa 11 chainha 20 ka 12 chuuiha 20 hikoo, or kooha 1N. Leon, Introd. to Cordova Arte del Idioma Zapoteco, p. 1xxii. zateca, p.43 (under the name Chocha). 2 Belmar, Ensayo sobre la Lengua Trike, 1897, p. 10. 8 Belmar, Lengua Mazateca, p. 40. Francisco Belmar, Lengua Ma- THOMAS] OTHOMIAN AND ZOQUEAN NUMERALS OTHOMIAN FAMILY Othomi" 1 unra, n’nra, or ra. 6 rahto, or rathto=1-+-5. 2 yooho, or yoho. 7 yoto, or yohto=2+5. 3 hit. 8 chiato, or hiahto=3-4-5. 4 gooho. 9 guto, or gytho=4+5. 5 kuto, gyto, kuta, or qyta. 10 reta. Matlaltzincan or Pirinda® (2 vocabularies ) 1 indawi. yndahhuy,?* or rahui. 2 inawi. ynahuy, or nohui. 3 inyuhu. ynyuhu. 4 inkunowi. yneunohuy. 5 inkutaa. yneuthaa. 6 inda-towi=1 to 5. yndahtohuy. 7 ine-towi=2 to 5. ynethohuy. 8 ine-nkunowi=2 4. ynencunovi. 9 imuratadahati=10—1? ynturahtadahata. 10 inda-hata. yndahatta. 20 yndohonta. ZOQUEAN FAMILY Zoque* 1 tuma. 6 tutay, or tuch tan. 2 metza, or metsan. 7 cuyay, or wueus-tuch tan. 3 tucay, or tuan. 8 tucututay, or tuduchtan. 4 macseuy, or makchtashan. 9 mactulay, or makchtuchtan. 5 mosay, or morshan. 10 macay, or makeh-kan. Mixe or Mije° 1 tuck, or tuue. 7 mirsh-tuk, miish-tuk, westuuk 2 metzk, or metsk. huextuue. 3 tegeug, or tukok. 8 tuk-tuk, or tuktuuk. 4 madarsk, maktashk, or mactoxe. 9 machk, tastuuk, or taxtuuc. 5 m’kosssk (?) mokoshk, or macoxe. 10 tards-tuk, makh, or mahe. 6 tech-teuchch, or tuduuk. 20 ypx. Pupuluca (of Tepeaca)® 1 tuub. 5 mokoxko. 9 taxtujtujko. 2 mesko. 6 tujtujko. 10 mako. 3 tuo. 7 juxtukujtujko. 20 ipxe. 4 maktaxko. 8 tukujtujko. oO ca | ist) or 1Conant, Number Concept, p. 165; p. 153. Charencey, Mélanges, p. 84; Ymolina, Arte del Idioma Othomi, 2One under the first name by Conant, Number Concept, p. 166; the other under the second name by Charencey, Mélanges, p. 84. %Charencey regards the yn as a “‘simple prefix,’ whether merely euphonie or not he fails to state. 4Charencey, Mélanges, p.72; E. A. Fuertes, manuscript in Bureauof American Ethnology archives; Grassierie, Lengua Zoque, in Vocab. 5E. A, Fuertes, manuscript in Bureau of American Ethnology archives; Grassierie, Lengua Mixe, p. 332; Stoll, Ethnog. Guatemala, p. 28. ‘Ibid. Belongs to the Mixe group. 874 NUMERAL SYSTEMS [ETH. ANN. 19 TARASCAN OR MICHOACAN FAMILY Tarasco* 1 ma. 6 cuimu.? 11 temben-ma=10+-1. 2 tziman. 7 yun-tziman=(5)+2. 12 temben-tziman=10-+2. 3 tanimu. 8 yun-tanimu=(5)+3. 20 macquatze, or maka- 4 tamu. 9 yun-thamu=(5)+4. tori. 5 yumu. 10 temben. CHIAPANECAN FAMILY Chiapanec*® 1 tige, tique, tiqui, ticao, tighe, or tiche. 8 mahumihi, or hahu-mihi. 2 hao, jomi, or humihf. 9 helimihi. 3 haui, jami, or hemihi. 10 henda. 4 ahau-mihi, ahu-mihi, or haha. 14 henda-mahua. 5 aomihi, haomo, or haumihi. 15. henda-mu. 6 amba-mihi, or hamba-mihi. 20 hahua, hahue, ahué, or hahoy. 7 hendi-mihi. TOTONACAN FAMILY Totonaca* tani: 4 tati. 7 tushun. 10 kau, or cauh. 2 tuyun. 5 kitsiz. 8 tsayan. 3 tutu. 6 tehashan. 9 nahatsa. Totonaca (Starr)* 1 tla-ka-tin. 4 la-ka-ta-te. 7 la-ka-to-hon. 10 la-kal-xao. 2. tla-ka-to. 5 la-ka-ki-tsis. 8 la-ka-tsai-yun. 20 la-ka-po-shan. 3 tla-ka-to-to™. 6 la-ka-cha-shun. 9 la-ka-na-has. Akal’man ( Vera Cruz)® 1 tam. 9 naxatze. 2 thoi. 10 kau. 3 thut. 11 kautam=10-+1. thaate. 12 kauthoi=10+2. 5 kis. 20 pusham. 6 tchashan. 30 pushamkau=20--10. 7 taxun. af 40 thoipusham=2> 20. <} 8 tsaxen. As the origin of the names for 1 to 4 is a question belonging largely to the deductive domain because of the very meager data bearing on the subject, it will not be discussed at any length here. The reader is, however, referred for an examination of the subject in its broad and general aspect to a paper by Professor W J McGee, entitled The Beginning of Mathematics, in the American Anthropolo- — es 1 Anales de Museo Michoacan, entraga 1, p. 59, 1888. 2 Cu, to join or mix one thing with another ’’—N. Leon, Anales de Museo Michoacan, entraga 1,106. Basalenque, Arte del Idioma Tarasco, p. 48, says cu refers to the hand. Charencey, Mélanges, p. 44; R. F, Guardia, Lenguas Indigenas Cent, Am. en el Siglo, yol. Xvut, p. 86. 4Grundriss, vol. 11, p. 293. 6 Notes on Ethnog. South Mexico. ®A.S. Gatschet, quoting Pinart, American Antiquarian, yol, rv, p. 237 (April-July, 1882). THOMAS] ORIGIN OF NUMBER NAMES 875 gist, October, 1899, and to the preceding paper in this volume. This author points out that while the count of many primitive peoples has been by the fingers and hands, giving rise to the quinary and dec- imal systems, and sometimes by the toes and feet also, leading to the vigesimal system, yet the evidence derived from the method of count- ing by tribes in the lowest status seems to demonstrate that these sys- tems are far from primeval. He suggests that numbers of the lower scale, beginning with 1, rep- resenting the Ego, were the outgrowth of mysticism; 2, growing out of the lateral or the fore and aft aspects, being the first pausing point, and 4, the Cult of the Quarters, the second pausing point, beyond which a number of systems never advanced; to this the Ego being added gave the number 5. However, for a more complete and clear understanding of the author’s suggestions on this interesting subject the reader is referred to his papers. That the quinary system, or counting on the fingers and hand, could not have taken its rise until 5 had been reached by some other process appears to be self-evident, and is proved by the numerous systems in which 5 is not reached, and by others in which it does not form a basis. It would seem necessary, therefore, in order to obtain a satisfactory explanation of the origin of the primary numbers, to look for some other solution than the supposed method of counting on the fingers. The hand would not be likely to come into use in this respect until 5 had been reached and the attempt made to rise above that number; then the advantage of using the five fingers of the hand, or the hand as rep- resenting 5 as a basis would be perceived. Pebbles, sticks, or any other objects, would answer just as well for this purpose as the fingers until some reference to 5 was desirable, except that the latter were always convenient objects and were best adapted to use in sign language. When 5 was reached, and the advantage of using the hand became apparent, it would be used for the numbers below 5 as well as those above, but the inquiry here is, were the fingers considered so essential in counting 2 to 4, before 5 had been reached, as to bring evidence of the fact into the nomenclature? This can be determined only by obtaining the signification of the names of numbers in those dialects of tribes which have not reached 5 in their numeral systems.’ Orozco y Berra, speaking of the Mexican names for the numbers— ce, 13 ome, 2; yet, 3, and nahui, 4—says, ‘*no one has given a reason for the origin of these names.”” Chavero® contends that, although 1Conant (Number Concept, pp. 24-25) says: ‘‘ Itseemsmost remarkable that any human beingshould possess the ability to count to4,and not tod. The number of fingers on one hand furnishes so obvious a limit to any of these rudimentary systems, that positive evidence is needed before one can accept the statement. A careful examination of the numerals in upwards of a hundred Australian dialects leaves no doubt, however, that such is the fact. The Australians in almost all cases count by pairs; and so pronounced is this tendency that they pay but little attention to the fingers.’’ The last sentence of this quotation appears to answer the author's cause of wonder expressed in the first sentence; the fingers were, it seems, considered by the Australians as no more essential in the process of counting than any other convenient objects. *Anales Mus. Mex., pp. 2, 34. 3 Op. cit., p. 33. 876 NUMERAL SYSTEMS [ETH. ANN. 19 the Mexicans counted on the fingers.and hands, 4 was the first basis, the four fingers completing the first count, 5 being formed of 4+-1. He remarks as follows: **In the Hindu system the principal number of the system is 10, which is formed of 5+-5; to it the number 5 is essential; but in the Nahua system the essential number is 4, hence the 20 is formed of 5 times 4, as 5 is formed of 4+1.” The same author says that among the manuscript notes of Ramirez he has found one that says, ‘‘the Nahoas formed the number 5 with the four fingers of the hand, completing the sum with the thumb, as 4++1.” However, it must be admitted that, in this dialect, in forming the numbers above 5 until 20 is reached, 5 is the basis, and its name is derived from the term for hand. Charencey, ‘referring to the dialects of his so-called Chichimecan family, which corresponds substantially with Brinton’s Sonoran and Shoshonean branches of his Uto-Aztecan family, says that ‘*in almost all the idioms of this family, if not all, the name of the number 2 enters into composition in the word which signifies 4.” This is very apparent in the Shoshonean branch, as is seen in the following examples: Tribe 2 4 — — = = ————— ~ | Cahuillo mewi | mewittsu Kauyuya | vuy vuitchiu Kechi (San Luis Rey) whii witcho Shoshone (Gatschet’s number 5) | wat watsuet | Southern Paiute | vay vatchue California Paiute | voahay yoatsagve | | Chemehuevi vay vatchue | Hopi lei nale | Tobikhar | vehe vatcha It is less apparent, however, in the Sonoran branch, as will be seen by reference to the lists given above. This fact seems to bear evidence in favor of Professor MeGee’s suggestion in regard to the primary steps in the development of num- ber systems—viz, that 2 and 4 were the first pausing points. An exam- ination of other systems outside the scope of the present paper will furnish many items of evidence in this direction. Hubert Bancroft* gives the following definitions of the Maya names of the first five numbers: Awn, paper; ca, calabash; ov, shelled corn; can, serpent, or count; and /o, entry; it is apparent, however, that the meanings given can have no reference to the use of the terms as number names. However, as the origin of the names of the primary 1 Mélanges, p. 16. 2Native Races, yol. 11, p. 753. THOMAS| ORIGIN OF NUMBER NAMES 877 numbers below 5 is not deemed of special interest in the present dis- cussion, which relates more directly to the systems, we begin with 5.1 fo or jo, the name for 5 in all the Mayan dialects (except the Huas- teca) when the affixes are omitted, is without any signification except as a numeral, so far as is now known, that seems to be appropriate to this use. Bancroft gives *‘ entry,” as is stated above, but this, though one signification of the term, has no apparent application here. If a guess be permissible, I would offer the following suggestion: In Stoll’s list for 5 we notice that the name for this number in Cakchiquel is wuoo, and for 15 in Quekehi is wwolahu, and in Cakchiquel wuolahuh (substituting the / for j). Now, as 6 is wae, ewak, or vuok, 7 wuk, vuky, or vuuk, and 8 waxak, uaxvok, ov vuarak, is it not possible that ho or ois an abbreviation of a word beginning with w or wu, as vol, which, in addition to its signification (as a verb) **to make round,” *‘to will,” also, according to Brasseur, signifies *‘ filled wp,” *‘full, entire,” ete. ¢ Henderson, manuscript Maya-English dictionary, gives as another meaning ‘‘all in one,” **the gross amount,” and Beltran, Arte del Idioma Maya, states that in composition it signifies ‘‘todo junto,” oe which is substantially the same signification as that given by Brasseur. The term was also used, according to all the authorities, in counting round or solid things, as bundles of cotton, ete. As Perez informs us that the ancient form of the word was /o/, it is possible that in 1It is to be hoped, however, that Professor MeGee, or some one who has given thought to the sub- ject, will carry forward these investigations, as the working out of the beginnings of counting, and the origin of the lower number names, will have an important bearing on some of the problems of ethnology and linguistics not yet completely solved. The field most likely to yield fruitful results is of course to be found in the languages and customs of the lower savage tribes. The more the rela- tion of 2 and 4 to one another is studied the more important becomes Professor McGee's suggestion that these numbers represent the first two steps in many primitive counts. Thestatement by Conant, quoted in the preceding note, that ‘‘the Australians in almost all cases count by pairs,’”’ seems to be exactly in line with this suggestion. Curr, to whom Conant refers as ‘the best authority on this subject,’ believes that where (among the Australians) a distinet word for 4 is given, investigators have been deceived in every case. This would seem to explain the supposed use of pairs; the 2 was used in naming the 4. This tendency, as indicated above in the text, is found in various dialects in widely separated countries. As a few examples we note the following: | Jiviros | Bakairi toya (Si . 1 x * Be poves(south (South |(South Amer- Torres Straits 5 America)) ica) | 2 cayapa eatu asage okosa 4 cajezea = 2 with | encatu asage-asage | okosa-okosa plural termina- | , | tion | | Mosquito (Central Watchandies (South 5 Tee ey prea America) Africa) Karankawa (Texas) = eae a ais 2 wal utauara haikaia | 4 wal-wal atarra-utarra hayo hakn=2x2 | Many examples might be presented, but these will suffice to show how widely spread they are, Australia and South America being the regions of most frequent occurrence, and few examples being found in Polynesian dialects. { 878 NUMERAL SYSTEMS [ETH. ANN. 19 these facts an explanation of the /o, the name for 5, is to be found. I offer this suggestion merely as a possible explanation, without as yet giving it my own positive acceptance. The Mexican or Nahuatlan term for 5—macu/l/i/—is as is shown above, a compound word signifying **hand taken,” that is to say, one hand completed, referring to counting on the fingers. The same is also true in regard to the name in the allied Pipil and Alaguilac dialects. The name for 5 in the Opata and Tarahumari is apparently the same as the Mexican term modified by dialectic requirements. The Cahita name—manni—is from mama, the general term for hand. Although Gallatin (Trans. Am. Eth. Soe., vol. 1, p. 53) considers Auto or gyto, the name for 5 in Othomi, as uncompound, this seems to be somewhat doubt- ful; however, its signification is unknown to me; the same is true of the Matlaltzincan or Pirinda. The word for 5 in Tarascan—ywinu— appears to be simple, but Iam unable to determine the signification; it is not, however, the usual Tarascan word for hand. The m7h7 in aomih?, the Chiapanec name for 5, is a suffix common to a number of numeral terms in this dialect. This leaves ao, hao, or mao, written variously as the radical. The name for 5 in some of the dialects of the Shoshonean group appears to indicate *‘all,” doubtless referring to all the fingers of the hand; for example, in the Chemehuevi, Capote Uta, Shoshoni, Pa Vant, Southern Pa Uta, and Uinta Uta dialects. In some others the term appears to be derived from the name for “hand.” It seems, therefore, that the name is usually based on the count on the hand, and implies the complete count of the fingers of one hand. Examining now the terms for the numbers 6 to 9, we will begin with those of the Mexican proper or Aztec dialect: chicua-cewe sass -ae eat 6. Chiclmels2. = acc smene sees 8. ehic-onie.= 432.2425 fee ile chico-nauli-see-- eee ee 9. These, as is shown above, signify or are equivalent to 5+1, 5+2, 5-+-38, and 5-+4, the count being by additions to 5 or to one hand, and the names being compounded of chéco, *‘at the side, in part,” ete., thuan or huan, ** near another,” and the terms for 1, 2, 3,and4. These evidently refer to the process of counting on the fingers of the hand, and the system is a true quinary one up to 20. It would seem from this that Chavero’s theory that the Mexican or Nahuatlan count was based on + instead of 5 can scarcely be maintained. The closely allied Pipil and Alaguilac dialects form the names for 6, 7, and 8 in the same way, but in the latter the name for 9 evidently has reference to 10. In the Cora the numbers 6, 7, 8, and 9 are clearly based on 5, and the names are compound, being composed of @ and the names for 1, 2, 3, and4. Charencey (Mélanges, p. 17) says, “*le @ prétixe suivi du chittre THOMAS] ORIGIN OF NUMBER NAMES 879 de Punité de 1 45 indique les nombres depuis 5 inclusivement jusqwa 10 exclusivement, @est le remplacant de chic Azteque.” This, how- ever, does not give us the signification of the term. In Opata, Cahita, and Tarahumari, where there is a somewhat close agreement in the number names, especially in the first two, the method of counting from 5 to 9 appears to vary to some extent from the quinary system. If we may judge from the termination 7/7 in pussaniki, the Tarahumari name for 6, the count has reference to 5, as seems also to be true with regard to the name for 7 in Cahita; but the name for 7 in Opata, if correctly given, is apparently equivalent to1+6. In the three dialects the name for 8 is equivalent to 2x 4; and the 9 refers to LO, Ava, the prefix in Opata, being interpreted “antes” by Pimental. The 10 in these dialects refers to the hand. The name for 1 in Tarahumari, as given in the list—d7re or pile—is considered by Charencey as abnormal, who says that s?nep7 is given in one place. This would bring the dialect into harmony with the others. Of the dialects belonging to the Shoshonean branch, we notice that the Cahuillo and Kauyuya are regularly quinary, 6, 7, 8, and 9 being formed by adding 1, 2, 3, and 4 to 5. The Kechi of San Luis Rey appears to follow the same rule. The numbers 6 to 10 in the Tobikhar appear, so far as can be determined by the names, to be formed irreg- ularly. The name for 7 includes that for 4; 8 is 2x4; the name for 9 includes that for 5; and 10 as given is 2X5; but in counting the numbers above 10 another term—Awrura—is used for 10, possibly an equivalent for ‘‘man,” as 20 is hurura-vehe=2 hurura. However, a more perfect knowledge of the language may show the count to be quinary. The method of forming the numbers 6 to 9 in the dialects of the Zapotecan family can not be determined with positive certainty from the names alone, except in the Mazateca, where, if Belmar (Lengua Mazateca) be correct, it follows with great regularity the quinary system even into the higher numbers. For example, 6, /7, is a con- traction of t-n-gu, or 5+1; 7, y/-ti, of vi-n-ho or 5+2 (4), ete. Judging from this and the slight indications in the Chuchon, Popoloca, and Trike, these idioms appear to follow the same system. For example, in the Trike, as we learn from Belmar’s ‘‘ Ensayo sobre la Lengua Trike,” the anka in guatanka, 6, same as ango, signifies ‘** another,” or “other,” and the 2, nghui, when changed to the ordinal by the pretix ¢s7, becomes ¢s/-guaaha. That the same rule is followed in the Zapotec seems evident from the fact that above 10 the quinary-vigesi- mal system is followed as distinctly as in the Nahuatl, 15 having a dis- tinct name and the count therefrom to 20 being based on it. In the Othomi the numbers 6 to 9 are formed regularly according to the quinary system. In Pirinda 6 and 7 are formed by the addition SSO NUMERAL SYSTEMS (ETH. ANN. 19 of 1 and 2 to 5 or its equivalent; 8 is 2X4, and 9 is based on 10. In Mixe 6, 7, and 8 are formed by adding 1, 2, and 3 to 5, but 9 is based on 10; and the same rule appears to be followed in the Zoque. In Tarasco the regular quinary order appears to prevail, though the term for 6 seems to refer to the process of counting, as the ew in cudmu, according to Basalenque (op. cit.), refers to the hand. Passing over the other idioms of the Shoshonean group, of which the signification of the numeral terms has not been specially studied by linguists, we return to the terms for 6, 7, 8, and 9 in the Mayan dialects. It will be noticed that in all of these dialects, except the Chuhe, the name for 9 begins with he, ba, or bo, and that most of them, omitting the terminal 4, add to complete the name the term for 10, lahun, lahu, ete., in more or less varied form. Thus, in Pokonchi, is be-lehe and 10, /ehe; in Pokomam, 9, be-lehem, and 10, lehem; in Ixil, 9, be/raual, and 10, /avual, ete. It is evident, therefore, that in these idioms the term for 9 is based on that for 10, the /ehe, Jun, Ju, and /on being mere abbreviations of dahun, lahu, ete. As be in the various dialects signifies ‘‘road, journey, way,” ete., this is probably next to.” In Chuhe, however, the name for 9, vv-angue, shows that here the term used here and is to be interpreted ‘‘on the way to, this number, contrary to the rule which prevails in the other dialects, is formed by the addition of 4, ch-angue, to some equivalent of 5, thus conforming to the quinary system. It is somewhat singular, however, that the name for 19 is ban-lahne, the ban being doubtless an abbrevia- tion of balun. The « in the name for 8 in all the idioms seems to furnish the key to the problem of the numbers 6, 7, and 8, as it indicates that 3—oa, ur, or dz—is combined with some equivalent of 5 represented by w and pu, as in u-ae-ae and wu-ar-ak, to form the 8. Up to the present no suggestion as to the signification of this prefix has been presented other than what is contained in the quotation from Charencey in regard to wac, 6, given above. Of the correctness of the above sug- gestion in regard to the name for 8 there would seem to be but little doubt. If this be accepted, it follows as reasonably certain that the names, except the one for 9, correspond with the mode of counting indicated by the written number symbols; that is, with the quinary system. The numbers 6, 7, 8, and 9 in the Maya (Yucatec) dialect may therefore be written out as follows, the 5 being inclosed in parentheses to indicate that it is represented by some substitute: 6 u-ac=(5)+1. 8 u-ax-ac=(5)-+-3. 7 u-uc=(5)+2. 9 bo-lon=on the way to 10. The name for 5 is not represented even by an ultimate abbreviation in the names for 6, 7, and 8, unless it be by the w and ww. THOMAS] NUMERALS OF VARIOUS TRIBES 8$1 Before passing to the numbers aboye 10, some few examples of methods of counting by peoples bordering on or within the geo- graphic limits embraced in this paper, and with whom some of the tribes we have mentioned must have come into contact, will be pre- sented, as some of them are exceptional. The first of these is a list of numerals given by Gallatin;' the par- ticular tribe referred to is unkn own. San Antonio, of Texas 1 pil. 7 puguantzan co ajti ¢ pil=4+2--1. 2 ajté. 8 puguantzan ajte=4%2. 3 ajti c pil=2+1. 9 puguantzan co juyopamauj=4-+5. 4 puguantzan. 10 juyopamauj ajte=5 <2. 5 juyopamiuj. 20 taiguaco. 6 ajti ¢ pil ajte=(2+1) 2, or chicuas. The numbers to 10 in use among the Mosquito tribe of Honduras are as follows: Mosquito” kumi. 8 matlalkabe pura wal=6+2. 2 wal. 9 matlalkabe pura niupa=6—-3 3 niupa. 10 mata-wal-sip=fingers of the second 4 wal-wal=2+-2 or 2X2. hand. 5 mata-sip=the fingers on one hand. 20 twanaiska-kumi=20> 1. 6 matlalkabe. 40 twanaiska-wal=20 2. 7 matlalkabe pura kumi=6-+1. Dr Brinton® gives lists of numerals in three of the dialects of the > Xinea stock as follows: 3 uala + jiria 5 puj 5 tacal 7 pujud 5 tepuc 9 uxtu 10 pakil 3 ualar 4 iriar 5 pijar 7 puljar 8 apuj Sinacantan | Jupiltepeque | Jutiapa 1 ica 1 ical LW eical 2) th 2 piar 2 _piar* 3 guarar + iriar 5 . pujar 6 tacalar 7 pulluar S apocar 9 gerjsar 10 paquilar 1Trans. Am. Ethn. Soc., vol. 1, table a, p.114. “Conant, Number Concept, p. 121. Membreno, Hondurefiismos, p. 210, under the name ‘* Zambo del Cabo.” 3 Xinea Indians of Guatemala, Proc. Am. Phil. Soc., 1885. 4 Dr Brinton remarks that the termination arin this dialect reminds one of the Ixil termination vual, indicating turn or repetition, as ungvual, one time, cavual, two times, etc. SEE —— $82 NUMERAL SYSTEMS [ETH, ANN. 19 The four following lists are from R. F. Guardia (Lenguas Indigenas Cent. Am. Siglo., pages 101 and 110). The tribes are classed with the Chibcha group, a South American stock, but are, or were, located in Guatemala and Porto Rico. Cabecar Viceyta Lean y Mulia Terrava 2 2. = 1 estaba 1 etabageme | 1 pani 1 crara 2 boctebs 2 buttebd | 2 matiaa 2 crubu 3 manalegui 8 manac | 3 contias 3 cromia 4 quetovo 4+ quiet | 4 chiquitia 4 cropquin 4) exquetegu) 5 exquetegu | 5 cumasopni 5 croshquin | 6 sehen 6 sehen 6 comasampepani=5-+-1 | 6 cloter i Cure, 7 curge 7 comasampematiao=5+2) 7 crococ 8 (?) 8 (?) | 8 comasampecontiac=5+-3) 8 croquon Ss) eh 18) | 9 comasampechigui- 9 croshcap | tias=5-+-4 | 10 dope 10 dop 10 comassopnas 10 crodobob 11 quinsho erosa| 20 ynste 20 ynste 20 comascoapssub 20 zac vbu Another list in the last idiom—Terrava—given by Thiel, differs so considerably from the preceding that it is given here: 1 krari. 4 krobking. 7 k6égodeh. 9 schkawdeh. 2 krowu. 5 kraschking de. § kwongdeh. 10 dwowdeh. 3 krommish. 6 terdéh. II NUMBERS ABOVE 10 Our examination of the number names and the method of counting from 10 upward will be contined chiefly to the systems of some of the more important civilized tribes of Mexico and Central America, and those of other tribes will be alluded to only where occasion may call for comparison. The first example to be presented is that of the Nahuatl or Aztee method of counting, this being selected because it follows strictly the quinary-vigesimal system, and presents clearly the characteris- tics of that system, and because of its importance. The signification of the terms or the equivalents of their parts in figures will be given in connection with the list so far as known. 1Vocabularium der Sprachen der Boruca—Terraba—und Guatuso—Indianer in Costa-Rica, Archiv fiir Anth., Band Xvt1, p, 620. THOMAS) bo oh be ee bh SN ion) a co oO 40 ios CO iM) NAHUATL NUMBERS Nahuatl * matlactli=2 hands. matlactli once=10+1, or 2 hands-++1. matlactli om-ome=10-+2. matlactli om-ei=10+3. matlactli on-naui=10-+-4. caxtolli. caxtolli once=15—1. caxtolli om-ome=15+2. caxtolli om-ei=15+-3. caxtolli on-nau=15—-4. cempoalli?=1 counting or complete count. cempoalli on-ce=20—1. cempoalli om-ome=20+ 2. cempoalli om-ei=20—-3. cempoalli on-naui=20—-4. cempoalli om-macuilli=20 cempoalli on-chiqua-ce=20+5—+-1. cempoalli on-chic-ome=20+ cempoalli on-chic-uei=20--5-3. cempoalli on-chico-naui=20+5+4. cempoalli om-matlactli=20—10. cempoalli om-matlactli once=20-+-10+1. cempoalli om-matlactli om-ome=20—+-10+2. cempoalli. om-matlactli om-ei=20+10+3. cempoalli om-matlactli on-naui=20+10+4. cempoalli on-caxtolli=20+-15. cempoalli on-caxtolli on-ce=20+15+1. cempoalli on-caxtolli om-ome=20-+15+2. cempoalli on-caxtolli om-ei=20+-15+3. cempoalli on-caxtolli on-naui=20+15-+4. ompoalli=2 20, or two twenties. D. The count follows the same order as that from 20 to 39, the only variation being in the names of the multiples of 20, that is to say, 60, 80, 100, etc., which are as follows : 60 ei-poalli, or epoalli=3 x 20. nauh-poalli=4>< 20. macuil-poalli=5 x 20. chiqua-cem-poalli=6 20, or literally (5+1) x20. chic-om-poalli=7 x 20, or literally (5+2) x 20. chic-ue-poalli=8 20, or literally (5+3) x 20. chico-nauh-poalli=9 x 20, or literally (5+4) x20, chico-nauh-poalli chiqua-c=920-+5—1. chico-nauh-poalli ipan caxtolli on-nau=9 x 20-+-15+4. matlac-poalli=10 20. matlactli on-cem-poalli=11 20, or (10+-1) x20. matlactli om-om-poalli=12 x 20. matlactli om-ei-poalli=13 x 20. matlactli on-nauh-poalli=14 x 20. 1Siméon, Dic. Langue Nahuatl, p. xxxiii. 2Cempoalli signifies one entire or complete count, from ce, one, and poa or poua, to be counted or estimated. 884 NUMERAL SYSTEMS (ETH. ANN 19 300 caxtol poalli=15 x 20. 320 caxtolli on-cem-poalli=16 20, literally (164-1) x20. 340 caxtolli om-om-poalli=17 20. 360 caxtolli om-ei-poalli=18 x 20. 380 caxtolli on-nauh-poalli=19> 20, 399 caxtolli on-nauh-poalli ipan caxtolli on-nau=19 20+-15+-4. 400 cen-tzontli. 800 ome-tzontli=2 400. 1,200 ei-tzontli, or e-tzontli=3 x 400. 1,600 nauh-tzontli=4>< 400. 2,000 macuil-zontli=5 x 400. 2,400 chicua-ce-tzontli=6 x 400, literally (5-+1)>400. 4,000 matlae-zontli=10>% 400. 6,000 caxtol-tzontli=15 > 400. 8,000 cen-xiquipilli, or ce-xiquipilli=1 xiquipilli, or 18,000. 16, 0001 on-xiquipilli=2> 8,000. 24,000 e-xiquipilli=3> 8,000. 120,000 caxtol-xiquipilli=15 x 8,000. 160, 000 cem-poal-xiquipilli=20>% 8,000. 320,000 om-poal-xiquipilli=2 20 8,000. 3, 200,000 cen-tzon-xiquipilli=400> 8,000. 64, 000,000 cem-poal-tzon-xiquipilli=20 x 400 8,000. The signification of caxto/l7, the term for 15, does not appear to be given. Centzontli, the name for 400, is from ce, 1, and fzontl7, herb, hair, and signifies one handful, bundle, or package of herbs, or one wisp of hair, ‘tau figuré une certaine quantité comme 400,” says Siméon (op. cit.). Aiquipilli, the name for 8,000, signifies a sack, bag, or wallet. Clavigero” says ‘*They counted the cacao by wiqguipill7 (this, as we have before observed, was equal to 8,000), and to save the trouble of counting them when the merchandise was of great value [quantity ?] they reckoned them by sacks, every sack having been reckoned to contain 3 xiguipill/, or 24,000 nuts.” It is apparent from the list given that this system was strictly quinary-vigesimal throughout, the higher bases—400 and 8,000—being multiples of 20. The retention of the quinary order in the higher numbers is evident from the use of 15 in counting 35 to 39, 55 to 59, ete. The complete maintenance of the vigesimal feature is also shown by the fact that the count from 20 to 400—that is, 20 20—so far as the multiples are concerned, is by 2, 3, etc., up to 19x 20 plus the addi- tions 1, 2, 3, ete, to 19. In its systematic uniformity it is one of the most perfect systems that has been recorded, though its nomenclature is somewhat cumbersome. Another point to which attention is called, as there will be occasion to refer to it further on, is the method of counting the minor intermediate numbers. It will be observed that the count above 40 as well as that from 20 to 40 is by additions to the hase, thus: 40+-1 for 41, 40+2 for 42, and so on: and the same rule is Thus Clavigero, Hist. Mex 2Cullen’s Trans., vol. 1, O86. THOMAS] ZAPOTEC NUMERALS 885 true for the count from 60,80, etc. This is mentioned because it will be found in some systems that 41 is not formed by adding 1 to 40, but is formed by counting the one on the next score—that is to say, one on the third score. This difference, slight as it seems to be, is neverthe- less an important characteristic in comparing the numeral systems. The Maya method of writing numbers to 19, as shown above, is pre- cisely in accord with the Mexican count. The second example of the quinary-vigesimal system I present is that in use among the Zapotecs, as given by Cordova in his Arte del Idioma Zapoteco. This is so burdened with alternates that it will be best understood by presenting the regular series first and the alter- nates, so far as is necessary, in a separate list. The equivalent figures placed to the right show my interpretation of the terms. However, the correctness of the interpretation can be easily tested by considering the numbers up to 10 heretofore given in connection with those above 10 here presented. Zapotec 10 chii. 11 chii-bi-tobi=10+1. 12. chii-bi-topa, or chii-bi-cato=10+2. 13 chii-No, or chii-bi-chona=10+3. 14 chii-taa=10+-4. 15 chino, or ce-caayo-quizaha-cal le=15, or 20—5. 16 chino-bi-tobi=15+1. 17 chino-bi-topa, or chino-bi-cato=15+ 2. 18 chino-bi-chona=15-+-3. 19 chino-bi-tapa=15--4. 20. cal le. \ 21 eal le-bi-tobi=20-+1. 22 cal le-bi-topa, or cal le-bi-cato=20+-2. 23 cal le-bi-chona, or cal le-bi-cayo=20+3. 24 cal le-bi-tapa, or ete=20+-4. 25 cal le-bi-caayo=20-+-5. 26 cal le-bi-xopa=20+6. 27 cal le-bi-caache=20-+7. 28 cal le-bi-xono=20+8. 29 cal le-bi-gaa=20-+9. 30 cal le-bi-chii=20+10. 31 cal le-bi-chii-bi-tobi=20+10+1. 32 cal le-bi-chii-bi-topa=20+10-+ 2. 33 cal le-bi-chii-bi-chona, or cal le-bi-chiifio=20+10+3. 34 cal le-bi-chii-bi-tapa, or cal le-bi-chii-taa = 20+-10+4. 35 cal le-bi-chino=20-+15. 36 cal le-bi-chii-bi-xopa=20+10+-6. 37 cal le-bi-chii-bi-cache=20-+ 10+-7. 38 cal le-bi-chii-bi-xono=20+10-+8. 39 cal le-bi-chii-bi-caa=20+10-+9. 40 toua. 41 toua-bi-tobi=40+1. 50 toua-bi-chii=40-+ 10. 51 toua bi-chil-bi-tobi=40+ 10+1. So to 54. 886 NUMERAL SYSTEMS [ETH. ANN, 19 At the next step there is a change in the method, or, as will be seen when the alternates are given, the regular method is abandoned and the second method of counting adopted. Thus, instead of saying for 55 toua bi-chino=40+15, they say ce-caa quiona, or ce-caayo quiona= 5from 60. The term guéona appears to be a variation of cayona, 60. 55 ce-caa quiona, or ce-caayo quiona= 5 from 60. 56 ce-caayo quiona-bi-tobi=5 from 60--1. The correctness of this interpretation seems to be confirmed by the alternate ce-tapacaca quizahachaa-cayona=4 from 60. 57 ce-caayo quiona-bi-tobi=5 from 60+-2. The alternate in this case is 3 from 60, ete. 60 cayona. 61 cayona-bi-tobi=60+-1. So to 70. 70 cayona-bi-chii=60-+10. 71 cayona-bi-chii-bi-tobi=60+10+-1. So to 74. At the next step—75—the order changes as at 55, for, instead of say- ing cayona-bi-chii-bi-caache=60-+10-+ 5, they say ce-cad-tad, or ce-camyo- taa=5 from 80. 75 ce-caayo-taa=5 from 80. 76 ce-caayo-taa-bi-tobi=5 from 80-+-1, or ce-tapa-quizahachaa-taa=4 from 80. So to 79. 80 taa. 81 taa-bi-tobi=80+1. 90 taa-bi-chii=80-+-10. 95 ce-caayo-quioa=5 from 100. 96 ce-caayo-quioa-bi-tobi=5 from 100+1, or ce-tapa-quizahachaa-cayoa =4 from 100. 100 cayoa. 101 cayoa-bi-tobi=100+1. 120 xopalal-le=6 20. 121 xopalal-le-bi-tobi=120-+-1. 130 xopalal-le-bi-chii=120-+-10. 135 ce-caayo-caachelal-le=5 from 140. The rule given above is followed throughout. 140 caachelal-le=7 20. 150 caachelal-le-bi-chii=140-+-10. 160 xoonolal-le=8 x 20. 170 xoonolal-le-bi-chii=160-+-10. 180 caalal-le=9 x 20, 190 caalal-le-bi-chii=180+ 10. 200 chiia=10X 20? 210 chiia-bi-chii=200+-10. 220 chiia-cal-le=200+-20. 240 chiia-toua=200+40. 260 chiia-cayona=200 +60, THOMAS] ZAPOTEC NUMERALS 887 280 chiia-taa=200-++80. 300 chinoua (probably 15> 20) 400 tobi-ela, or chaga-el-la=1>< 400. 500 tobi-ela-cayoa=400+-100. 800 topael=2400, or catoela=idem. 1,000 catoel-la chiia=2 400—-200. 1,600 tapa-ela=4> 400. 4,000 chii-ela=10> 400. 8,000 chaga-coti, or tobi-goti=1 > 8000. Cordoya adds at this point: ** Hasta aqui es toda la quenta de los yndios, y de aqui arriba van contando do ocho en ocho mil arriba esta declarado.” Of the alternates above alluded to it is only necessary to mention the following: 15 ce-caayo-quizaha-cal le=5 from 20. 17 ce-chona-quizaha-cal le=3 from 20. 18 ce-topa-cal le, or ce-topa-quizaha-cal le=2 from 20. 19 ce-tobi-cal le, or ce-tobi-quizaha-cal le=1 from 20. The alternates for the numbers 35 to 39 follow the method of count- ing from 55 to 59,75 to 79, and 95 to 99 mentioned below, thus: 35 cecaatoua, or cecaayotoua=) from 40. 36 cecaayotoua-bitobi=5 from 41; or cetapa caca quizah chaatoua=4 from 40. So to 39. A thorough knowledge of the language, enabling us to furnish a complete explanation of the terms and particles added and interjected in forming the intermediate numbers in the higher counts, would be more satisfactory. However, it is believed that the number equivalents given in the list will be found correct. o Tt is apparent from the list that the system is vigesimal and to some extent quinary-vigesimal (note the names for 15, 55, ete.) The most notable feature, however, is the intermediate position it seems to hold between the Aztec and the Maya systems. The tendency toward the quinary method and the use of a special term for 15 ally it on the one hand to the Aztec system, while, on the other hand, in the reference in counting to the next higher score, which will hereafter be shown as a feature of the Mayan systems, it resembles them. It is possible, how- ever, that a more thorough knowledge of the language and the system may show that the names for 15, 40, ete., which have been assumed to be simple, uncompounded terms, are in fact composite. While c/7n0 is the usual term for 15, the alternate is cecaayo-quizaha-calle, which is equivalent to 5 from 20, showing direct reference to 5. It is possible, therefore, that chino is composite. As tow, the name for 40, contains the first syllable of fopa—name for 2—it may also be, and probably is, composite; this supposition seems strengthened by the fact that cayona, the name for 60, appears to be based on cayo, 3; and faa, name for 80, S88 NUMERAL SYSTEMS [ETH, ANN.19 on fapa ov taa, 4; and cayoa, name for 100, on caayo, or 5. The simi- larity of the name for 20—ca//e—in this language and cal or ka/, the term for the same number in most of the Mayan dialects, is noticeable, though apparently accidental. The next numeral system referred to is that of the Mazateca, a tribe speaking a dialect of the Zapotecan family. This, if correctly given by Francisco Belmar, in his Ligero Estudio sobre Lengua Mazateca,' presents one of the most complete examples of the quinary system to be found in Mexico or Central America. In order that the formation of the names may be more apparent, the list from 1 to 10, which has been heretofore given, is repeated here. Mazateca 1 gu. 2 ho. 3 ha. ni-hu. 5 “i. 6 ht. 7 yi-tu. 8 hi-i. 9 fi-ha. 10 te. 11 te-n-gu=10-+1. 12 te-n-ho=10+2. 3 te-n-ha=10+3. 14 te-ni-hu=10+4. 15 te-=10-+5. 16 te-Q-n-gu=10+5-+-1. 17 te-ti-n-ho=10+-5-+-2. 18 te-Q-n-ha=10+-5+3. 19 te-t1-Ni-hu=10+5-+-4. 20 ka. 21 ka-n-gu=20+1. 22 ka-n-ho=20+2. 23. ka-n-ha=20+3. 24 ka-ni-hu=20+4. 25 ké-f=20-+5. 26 ka-hu (ka-t1-n-gu)=20+5-+-1. 27 « 20. 41° yicha-ngu=40+1. So to 45. 46 yicha-hti (yicha-t-ngu)=40-+5+1. So to 49. 50 yichite (or ichite)=40+-10. 51 ichite-ngu=40+-10+-1. So to 55. 56 ichite-hti (ichite-Q-ngu)=40+10-+-5-+1, So to 59. 60 ichite-ko-te=50-+-10, or literally 40+-10+-10. 61 ichite-ko-te-ngu=50-++-10--1. So to 65. ; 66 ichite-ko-te-hti (ichite-kote-ngu) !=50-+-10+5-++1. So to 69. 70 ichite-koho-kaA=50-+-20. 71 ichite-koho-ka-ngu=50+20-+-1. So to 75. 76 ichite-koho-ka-hti (ichite-koho-ka-t-ngu )=50+-20-+-5-+-1. Belmar does not give any explanation of the /oho in these names; however, it seems—though one signification of jo is two—to play no other role here than io in the name for 60, ete. 80 ichite-koho-kate=50-+-20+-10, literally 40+-10-+20+-10. 90 ichite-koho-yicha=50-+-40. 95 ichite-ko-ho-yicha-i=50+40+5. 100 t-cha=5 x 20. 110 t-cha-te=5« 20-+-10. 200 ho-ticha=2x5 x20. 300 ha-ticha=3 x5 20. So to 900. 1,000 te-Gcha=10> 100, literally 105» 20. 2,000 ho-mi (ho-te-ticha)=2 10 100. So to 9,000. 10,000 te-mi (k4é-tcha)=? There seems to be some mistake here in Belmar’s parenthetical explanation; if 4@ is 20 and “vicha 100, kd-tcha would be 2,000, which, as shown above from his own list, is (ho-te-ticha). the equivalent of fe-vwcha, 1,000, then 10,000, unless varying from the rule, should be ¢e-te-vicha, ov hd-i-ticha=20*5xX100; the latter is probably what was intended, as we judge from the following numbers: As m7 is given as 20, 000 30, 000 100, 000 110, 000 130, 000 Although ka-mi (ké-te-ticha)=20 10 100. kate-mi (kAte-te-ticha) =380 10 100. So to 90,000. ticha-te-Gicha=100 x 10 100. tichate-te-icha=110 10 100. ficha-kate-te-tcha= (1004-30) x10 100. this numeral system carries out the quinary count to an unusual extent, yet it is clearly quinary-vigesimal. It isa little strange, 1Jn this, as in the three following numbers (not given here), Belmar, whose list I follow, seems, probably by a slip of the pen, to have failed to give the complete name; it certainly should be ichite-kote--ngu. S90 NUMERAL SYSTEMS [ETH. ANN. 19 however, that 10 should have what appears to be a simple integral name. The name for 20 is also simple, but that for 40—y7/-cha—is composite, signifying 2 times 20. The intermediate minor numbers in this system are always added to the preceding base and not, as in so many others, on that which follows, nor are they subtracted from a higher base or number, as we have found to be the case in the related Zapotec. Some of the number counts which appear to follow somewhat closely the quinary-vigesimal system having been presented, the next method of counting to which attention is called is that used by the Maya. As this system is the one in which most interest centers because of its relation to the numerals found in the codices and inscriptions, we shall dwell upon it more fully than we have upon the others, beginning with the numerals used by the Maya proper (Yucatecs). We take as our basis the series as given by Beltran in his Arte del Idioma Maya, placing at the right the interpretations or equivalents of the terms. Maya 10 lahun. 11 bulue. 12 lah-ca=11--2. 13. ox-lahun=3-+-10. 14 can-lahun=4-+-10. 15 ho-lahun=5+10. 16 uac-lahun=6+ 10. 17 uue-lahun=7 +10. 18 uaxac-lahun=8~+10. 19 bolon-lahun=9+-10. 20 hun-kal=one 20, or kal. 21 hun-tu-kal=1-+20, or 1 to 20. 22 ca-tu-kal=2-+20. ox-tu-kal=3+-20. can-tu-kal=4+-20. ho-tu-kal=5-+-20. 6 uac-tu-kal=6+ 20. St Ww bo to Si < 27 uuc-tu-kal=7-+20. 28 uaxac-tu-kal=8+ 20. 29 bolon-tu-kal=9+20. 30 lahu-ca-kal=10+-20. 31 bulue-tu-kal=11-++ 20. 32 lahea-tu-kal=12+-20, literally 104-2+20. 3 oxlahu-tu-kal=13 +20, literally 3+-10+-20. 34 canlahu-tu-kal=14+-20. 35 holhu-ca-kal=15-+-20., 36 uaclahun-tu-kal=16+-20. 37 =uuclahu-tu-kal=17+ 20. 38 uaxaclahu-tu-kal=18+ 20. 39 bolonlahu-tu-kal=19-+-20, literally 9+10+20. 40 ca-kal=2 20. Up to this point the forms are quite regular, except that of 11, which has a name as yet uninterpreted by the linguists. With this THOMAS] MAYA NUMERALS 891 exception, the numbers from 10 to 19 are formed by the addition of 1, 2, 3, ete., to 10, the decimal system applying here. Twenty has a distinct name—/a/. From 21 to 39 the numbers are formed by the addition to 20 of the numbers from 1 to 19; and 40 is twice 20. Before alluding to the change which occurs in the next step, atten- tion is called to /ahwn, the name tor 10. Dr Brinton! says it is appar- ently a compound of /ah and Aun, and gives as the probable significa- tion, ‘* it finishes one (man).” As to its derivation, I think he is cor- rect, as /ah, as a substantive, signifies ‘* end, limit, all, or the whole,” and jun *‘ one.” The signification of the term would therefore seem to be *‘ one finish,” or *‘ ending,” or ‘‘ all of one count,” but not ** one man.” Henderson, in his manuscript Maya-English Dictionary, under lah, says, ** whole hands,” and this is doubtless the true rendering when used in this connection. A@/, 20, as a verb signifies ** to fasten, shut, close,” as a substantive, ‘‘a fastening together, a closing or shutting up.” Calling 20 a score, for the sake of simplicity, the count from 21 to 39 may be illustrated thus: Awn-tu-kal, 1 on the score, or first score; ca-tu-kal, 2 on the score, ete. Here the addition is to the score already reached, but the additions to 40—ca-ha/—or second score are counted differently, for +1, instead of being Awn-tu-cakal, is hun-tu-yorkal, the latter—yorkal or oxkal—hbeing the term for 60, or third score (3 x 20). As it is evident that this can not signify 1 added to 60, there has been a difference of opinion as to the true meaning of the expression and as to its correctness. Perez, as quoted by Dr Brinton, says, in an unpublished essay in the latter’s possession, that Beltran’s method of expressing the numbers is erroneous; that 41 should be hwn-tu-cakal ; 42. ca-tu-cakal ; 83, ox-tu-cankal, ete. Nevertheless, as Dr Brinton has pointed out, the numerals above +0 are given in Perez’s Dictionary of the Maya Language according to Beltran’s system, which appears from other evidence to be correct. Léon de Rosny” suggests that hwn-tu-yorkal should be explained thus: 60—20+1. However, the correct rendering appears to be 1 on the third score, or third 20. It is possible that an old and a new reck- oning prevailed among the Mayas, as apparently among the Cakchi- quels. According to Stoll* the latter people had an old and a more recent method of enumerating, which may be represented as follows: \ Old New | 41 hun-r-oxe’al ca-vinak-hun 42 cai-r-oxc’al ca-vinak-cai, ete | 1 Maya Chronicles, p. 88. *Numération des Anciens Mayas, in Compte-Rendu Cong. Internat. Américanistes, p. 449; Nancy, 1875. 3 Zur. Ethn. der Guatemala, p. 136. 892 NUMERAL SYSTEMS [ETH. ANN. 19 Perez says that fw is an abbreviation of the numeral particle ¢/, but Rosny! says, ‘Je crois que ce nest point, comme il [Bancroft] le sup- pose, la simple conjonction ‘et,’ mais une phrase des mots ¢/-u, ‘dans son, lui, sien’; ~ est un pronoun appele par les grammairiens Espanols ‘mixte’ et qui forme la copulation, comme en Anglais 1’ s du genitif.” Dr Berendt adopts the same opinion, which is probably correct. As Beltran’s method seems to have been followed in all the Maya lexicons down to and including Henderson’s manuscript dictionary, it is followed here. 41 hun-tu-yoxkal=1 on or to the third 20, or third score. 42 ca-tu-yoxkal=2 on or to the third 20, or third score. 43 ox-tu-yoxkal=3 on or to the third 20, or third score. So to 49. 50 lahu-yoxkal*=10 on the third 20, or third score. 51 bulue-tu-yoxkal=11 on the third 20, or third score. So to 59. 60 oxkal=3 x20. 61 hun-tu-cankal=1 on the fourth score, ete. 70 lahu-cankal=10 on the fourth score, ete. 71 bulue-tu-cankal=11 on the fourth score, ete. 80 cankal=4 20. 90 lJahu-yokal=10 on the fifth score. 100 hokal=5~ 20. 101 hun-tu-uackal=1 on the sixth score. 110 lahu-uackal=10 on the sixth score. 119 bolonlahu-tu-uackal=19 on the sixth score. 120 uackal=6xX20. 130 lahu.uuckal=10 on the seventh score. 140 uuckal=7 X20. 150 lahu-uaxackal=10 on the eighth score. 160 uaxackal=8 x 20. 170 lahu-bolonkal=10 on the ninth score. 180 bolonkal=9 20. 190 lahu-tu-lahunkal=10 on the tenth score. 200) lahunkal=10 20. 210 Jahu-tu-buluckal=10 on the eleventh score. 220 buluckal=11 x 20. 230 lJahu-tu-lahcakal=10 on the twelfth score. 240 laheakal=12 20. 250 lahu-tu-yoxlahunkal=10 on the thirteenth score. 260 oxlahukal=13 20. 270 lahu-tu-canlahukal=10 on the fourteenth score. 280 canlahunkal=14 20. 290 Jahu-tu-holhukal=10 on the fifteenth score. 300 holhukal=15 20. 310 Jahu-tu-uaclahukal=10 on the sixteenth score. 320 uaclahukal=16 x20 330 lahu-tu-uuclahuka =10 on the seventeenth score. 340 uuclahukal=17 X20. 1Op. cit. 2The reason for the omission of f# in 50 70, and 90 is not apparent. rHOMAS] MAYA NUMERALS $93 350 lahu-tu-uaxaclahukal=10 on the eighteenth score. 360 uaxaclahukal=18 x 20. 370 lahu-bolonlahukal=10 on the nineteenth score. 380 bolonlahu-kal=19 x 20. 390 lahu-hunbak=10 on 1 bak. 400 hun-bak=one 400. 500 ho-tu-bak [hokal-tu-bak?]=100+-400? 600 lahu-tu-bak [lahun-kal-tu-bak?]=200+-400? 700 holhu-tu-bak [holhu-kal-tu-bak?] =300-+400? 800 ca-bak=2> 400. 900 ho-tu-yoxbak [hokal-tu-yoxbak]=100 on the third bak, or third 400. 1,000 lohu-yoxbak, or hunpic (modern). 2,000 capic (modern). 8,000 hun-pic (former and correct use of the term). So far I have followed Beltran’s list, as it is that on which the numbers as given by subsequent writers and lexicographers are based, but it carries the numeration only to 8,000. The names for 500, 600, and 700 appear to be abbreviated; I have therefore added in brackets the supposed complete terms. These, however, as will be seen by comparison, follow the rule which prevails from 20 to 39, that is, the additions are to the last preceding basal number, and not toward that which is to follow; the first rule holds good from 41 to 399, but the second is followed after passing 800 or ca-bah, as 900 is ho-tu-youbak, or, complete, hokal-tu-yorbah, which is equivalent to 100 on the third bak. The use of hunpic for 1,000 was adopted after the arrival of the Spaniards. One reason mentioned by Beltran for the change was to prevent confusion and to facilitate the numbering of the century in giy- ing dates. The proper native expression for 1,000 was /ahu-yoxbak, or, complete, /ahunkal-tu-yorbak, equivalent to 200 on the 3d_bak. Capic—2,000—is in accordance with modern usage; according to native usage 2,000 would be hobak, or 5400. In counting the minor num- bers above 400 the particle catac, *tand,” was inserted, thus: 450, Aunbak catae lahuyorkal. Wowever, in counting the added hundreds, fw, and not catac, was inserted, as is seen above in 500, 600, and 700; hence, as Beltran indicates, the latter was only prefixed or preposed to the minor numbers. Bak as a numeral is supposed to be derived from the verb dak, bakah, **to roll wp,” *‘to tie around,” and hence presumably refers to a bundle or package. /%c signifies ** cotton cloth,” also a kind of petti- coat, which appears to have been the original meaning; as this article of dress was occasionally used as a sack the numeral term probably refers to it in this sense; and Henderson, in his manuscript dictionary, gives as one signification **a bag made out of a petticoat.” This inter- pretation corresponds with the Mexican term for 8,000. The count from 400, or one bak, when carried out regularly, would be 2 bak, 3 bak, and so on to 19 bak; 20 bak, or 8,000, forming a new 894 NUMERAL SYSTEMS (ETH. ANN. 19 basis to which the name p/¢ or hun-pic, one pic, was applied. Above this number the count continued by multiplication, thus: ca-pic =2>8,000. ox-pie =38,000. can-pic=4 < 8,000. and so on to bolonlahun-pic, or 19 pie. For 20 pic, or 160,000, another simple term—ca/a)—is introduced; and for 20 calab, or 3,200,000, another simple term—/7nch7/—is intro- duced; and for 20 kinchil, the term a/av. The series of primary or basal terms are therefore as follows: 20 units =1 kal = 20. 20 kal =1 bak = 400. 20 bak =! pic = 8,000. 20 pic =lcalab = _ 160,000. 20 calab =1 kinehil= 3,200,000. 20 kinchil=1 alan =64,000,000. In reference to the signification of ea/a>, Dr Brinton*' writes as fol- lows: ** Ca/ab seems to be an instrumental form from ca/, to stutt, to fill full. The word ca/am is used in the sense of excessive, overmuch.” His note (1) is as follows: ‘**(Ca/; hartar o emborrachar la fruta.’ Diccionario Maya-Espanol del Convento de San Francisco, Merida, MS. I have not found this word in other dictionaries in my reach.” As Perez, Brasseur, and Henderson give as one meaning of ca/ah, ** inti- nitely, many times,” itis probable that this was the sense in which it came into use as a numeral adjective, a more definite meaning being after- ward applied. Henderson gives as another signification ‘*a buckle,” but this may be modern. Zofzceh, which is sometimes used in place of hkinchil, signifies ** deer skin,” but the latter term has received no sat- isfactory interpretation. As c/7/ is interpreted by the lexicographers “knapsack, granary, barn,” it is possibly the clue to the signification. The highest term—a/au—remains unexplained. As pic has been used in post-Columbian times to denote 1,000, #7nch7/ has been used to sig- nifty 1,000,000. Before commenting further on this system it will be best to present the data at hand relating to the count aboye 10 by other tribes of the Mayan group, and by some tribes of surrounding stocks. Huasteca® 10 lahu. 17 lahu-buk=10-+-7. 11 lahu-hun=10+1. IS lahu-huaxik=10+-8, 12 lahu-tzab=10+-2. 19 lahu-belleah=10-+ 9. 13. lahu-ox=10+ 3. 20 hum-inik=1 man. 14 lahu-tze=10+-4. 80 hum-inik lahu=20 (or 1 15 lahu-bo=10-+-5. man) +10. 16 lahu-akak=10-+-6. 40 tzab-inik=2 20. 1Maya Chronicles, p. 45. 2Stoll, Zur Ethnog: Guatemala, pp. 68-70,and Marcelo Alejandre, Cartilla Huasteca, p. 158 (fh is sub stituted forj, Alejandre uses the terminal c, but to be uniform with Stoll, I have substituted *), THOMAS] HUASTECA AND QUICHE NUMERALS $95 Huasteca—Continued 50 tzab-inik lahu=2 20+10. 800 huaxik-boinik=8 x 100. 60 ox-Inik=3 x 20. 900 belleuh-inik=9 100? 70 ox-inik lahu=3x20+10. 1,000 hum xi. 80 tze-inik=4 20. 2,000 tzab xi=21,000. 90 tze-inik ca-lahu=4 20+10. 3,000 ox xi=3 1,000. 100 bo-inik=5 x 20. 4,000 tzaboinik xi? (tze xi?) 200 tza-boinik=2 100. 5,000 boi xi=5x 1,000. 300 ox-boinik=3 106. 6,000 akak xi=6 1,000. 400 tze-boinik=4 100. 7,000 buk-inik xi? (buk xi?) 500 bo-boinik=5 100. 8,000 huaxik xi=8 1,000. 600 akak-boinik=6 x 100. 9,000 belleuh-hinik xi? (belleuh xi?) 700 bu-unik=7 x 100? It is apparent that from 100 upward the count is in accord with the decimal system, though the 5 times 20 to make the 100 is retained. 4X7, the term for 1,000, appears to be modern, or, what is more probable, it is the term formerly used for 8,000, but changed, as p7e in Maya, to 1,000; it is probably derived from 7/7 or w77/, ‘“‘hair.” Several of the terms taken from Alejandre’s list appear to be doubtful, to wit, those for 700, 900, 4,000, 7,000, and 9,000. Possibly the name for 700 isa shortened form of buh boinik and that for 900 of bellewh boinih, but this explanation will not apply to the other three, as tzahboiniha/, to conform to the system, would be 200% 1,000 or 200+1,000. The proper term according to the rule would seem to be fzeav?. I am unable to offer any other explanation of the terms for 7,000 and 9,000 than that 777’ has been improperly inserted. No data are available for determining the method of counting the minor additions from 41 to 59, 61 to 79, ete. The next system of numeration to be considered is that of the Quiche, to which special attention is called for the reason that it is given somewhat fully by Brasseur, who seems to have studied it care- fully, and who furnishes explanations drawn from his knowledge of the language. It therefore affords a good basis of comparison with the systems of other dialects of the same family, especially with that of the Maya proper. Quiche! 10 lahuh. 17 vuk-lahuh=7+10. 11 hu-lahuh=1+10. 18 vahxak-lahuh=8+10. 12 cab-lahuh=2+10. 19 beleh-lahuh=9+10. 13. ox-lahuh=3+10. 20 hu-vinak=1 man. 14 cah-lahuh=4+10. 21 huvinak-hun=20+1. 15 o-lahuh=5+10. 22 huvinak-cab=20+2. 16 vak-lahuh=6+10. This continues to 39, the minor numbers 3-19 being placed after the huvinak or 20. However, it would have been more satisfactory if the author had written out more fully these added numbers to 39, thus 1 Brasseur de Bourbourg, Grammaire Langue Quiche, pp. 141-146 896 NUMERAL SYSTEMS [ETH. ANN.19 enabling us to see whether there are any contractions of the terms for 11 to 19 as given above. 40 cayinak=2 men or 2 20. From this the w/nak for 20 is replaced by gal, which is really the proper term in Quiche for the number 20, and corresponds with the kal (20) of the Maya dialect. 41 hun-r-oxqal=1 on the third score, or third 20. 42 cab-r-oxqal=2 on the third score, or third 20. 48 oxib-roxal=3 on the third score, or third 20. This continues to 59 by prefixing the numbers 4-19 to vorqgal. The latter term is composed of the possessive 77 sincopated to 7, and ox-qgal, 3x20. The counting, therefore, is precisely as in the Maya dialect; that is to say, from 21 to 39 the minor additions (1-19) are made to the first score, or 20, but from 41 to 59 they are counted as so many on the following or third score. This method is followed, as will be seen, up to 399. 60 ox-qal=3 20. 61 hun-ri-humuch=1 on the fourth score. 62. eab-ri-humuch=2 on the fourth score. 63 ox-ri-humuch =3 on the fourth score 80 humuch. The name /wnuch is composed of han, 1, and much, a measure of quantity, a little mass or pile comprising 4 qal of cacao nuts. 81 hun-r-oqal=1 on the fifth score. 82 cab-roqal=2 on the fifth score. 83 oxib-roqal=3 on the fifth score. So to 99. 100 o-qal=5 20. 101 =hu-ri-vakqal=1 on the sixth score. 102. cab-ri-vakqal=2 on the sixth score. 103 oxib-ri-vakqal=3 on the sixth score. So to 119. 120 vak-qal=6 x 20. 121 hun-ri-yukqal=1 on the seventh score. 122 cab-ri-vukqal—2 on the seventh score. 123 oxib-ri-vukqal=3 on the seventh score. So to 189, 140) vuk-qal=7 20. 141 hun-ri-vahxakqal=1 on the eighth score. 142 cab-ri-vahxakqal=2 on the eighth score. 143 oxib-ri-vahxakqal=3 on the eighth score. 160 yahxak-qal=8x 20. 161 hun-ri-belehgqal=1 on the ninth score. So to 179. 180 beleh-qal=9 20. ‘ 181 hun-r-otuk=1 on the tenth score, or literally 1 on the fifth 40. So to 199. THOMAS] QUICHE NUMERALS 897 Here is a change in the order from lahwh-gal, or 10 X 20, as it would be regularly, to otuwk, or 5 tuk, which seems to give indications of modern influence. Brasseur gives the following explanation: ‘* From the number 180 following they say hun-rotuh, 181, 1 toward 200, which is represented by the word ofwi (this name for 200 is composed of 00,5, and tuk, which appears to signify a tuft of a certain herb, which has, independently of its ordinary sense, that of 40. This makes, therefore, for the entire word, 40 multiplied by 5; that is to say, 200).” Tuc in Maya signifies as a verb ‘*to count heaps, or by heaps” (Hen- derson, manuscript dictionary, and Beltran, Arte). The succeeding numbers, as will be seen by the list, follow in the count the regular order, though with abbreviated names. 201 hun-ri-hulah=1 on the eleventh score. So to 219. Fulah in this instance stands for hwlahu-qal,; that is, 11x 20. 220 hulahu-qal=11> 20. 221 hun-ri-cablah=1 on the twelfth score. So to 239. Cablah, abbreviation of cablahuh-qal. 240 cablahuh-qal=12 20. 241 hun-roxlah=1 on the thirteenth score. So to 259: Foxlah, abbreviation of rorlahuh-qal. 260 roxlahuh-qal=13 x 20. The retention of the 7 here, contrary to the general rule, is without apparent reason unless it be for the sake of euphony. Oxlahuhqal would seem to be the proper term, as ozlahuh is given tor 13, oxgal for 60, and omuch-orlahuhgal for 660; however, the name for 300 is rolahuhgal. 261 hun-ri-cahlahuhqal—1 on the fourteenth score. So to 279. 280 cahlahuh-qal=14 20. 281 hun-r-olahuhqal=1 on the fifteenth score. So to 299. 300 rolahuh-qal=15 20. 301 hun-ri-vaklahuhgqal=1 on the sixteenth score. So to 319. 320 vaklahuh-qal=16 20. 321 hun-ri-vuklahuhqal=1 on the seventeenth score. So to 339. 340 vuklahuh-qal=17 x 20. 341 hun-ri-vahxaklahuhqal=1 on the eighteenth score. So to 359. 360 vahxaklahuh-qal=18 20. 19 ETH, PT 2 22 898 NUMERAL SYSTEMS (ETH. ANN. 19 361 hun-ri-belehlahuhgqal=1 on the nineteenth score. So to 379. 380 belehlahuh-qal=19 20. 881 hun-r-omuch=1 on the 400, or 1 on the fifth much. So to 399. 400 omuch=5>80, or 54> 20. 401 omuch-hun=400+1. Ete. 500 omuch-ogal=400+100. 600 omuch-otuk=400 +200. 700 omuch-olah, or omuch-olahuh-qal=400+15 x 20. 720 omuch-vaklahuhgal=400-- 16 >< 20. 780 omuch-belehlahuhqal=400-+-19> 20. At this point Brasseur remarks ;: ‘*From here onward they count from 400 to 4,000 with the term go, that is to say, 400, in this manner; cago, two times four hundred; and they begin to count from 781, hun-ri-cago, as if they said, one on (or toward) the eight hundred; cab-ri-cago, two on eight hundred.” It would seem, therefore, from this remark, that this change in the count commenced only with the last 20 required to make up the 800. But as soon as the count rose above 800 it was based on the 400 next above, that is to say, the third 400, thus: 801 hun-r-oxogo=1 on the third 400. 840 cavinak-r-oxogo=2 20 on the third 400. 860 oxqal-r-oxogo=3 20 on the third 400. Brasseur gives as the equivalent of Awn-rovogo *‘es decir 399 para 1200.” Though the term may indicate a number which is the same as 1200—399, it certainly does not indicate any such process of obtaining thisnumber. The first number expressed is Av, or 1, and this is related in some way to 3400, or, the third 400. Brasseur’s explanation is therefore unsatisfactory. The count evidently proceeds in the same way as that of the minor numbers above the second score both inthe Maya and Quiche dialects, that is, 1, 2, etc., on the next higher score; here it is on the next higher go or 400. 880 humuch-r-oxogo=80 on the third 400. 900 oqal-r-oxogo=5 x 20 on the third 400. 920 vakqal-r-oxogo=6 20 on the third 400. 940 yukqal-r-oxogo=7 x 20 on the third 400. 960 yahxakqal-r-oxdgo=8 x 20 on the third 400. 980 belehgal-r-oxogo=9X 20 on the third 400, 1,000 otuk-r-oxogo=5 X40 on the third 400. 1,200 roxogo=3 > 400. Here the prefixed 7 (for 77) is retained for no apparent use unless possibly for euphony. 1,600 cahgo=4>x 400. 2,000 roogo, or rogo=5> 400. 2,400 vakago—6 400. 2,800 yukugo=7 400. 8,000 otuk-vahxakgo=5 X40 on the eighth 400. THOMAS] 10 11 12 13 14 15 40 41 3,200 3,600 4,000 4,400 4,800 5,000 5,200 5,600 6,000 6,400 6,800 7,000 7,200 7,600 CAKCHIQUEL NUMERALS 899 vahxa-go=8 x 400. beleh-go=9 x 400. Jahuh-go=10 400. hulahuh-go=11 400. cablahuh-go=12 400. otuk-oxlahuh-go=200 on the thirteenth 400. oxlahuh-go=13 x 400. cahlahuh-go=14 >< 400. roolahuh-go=15 x 400. vaklahuh-go=16 x 400. vuklahuh-go=17 400. otuk-vahxaklahuh-go=200 on the eighteenth 400. vahxak-lahuh-go=18 400. belehlahuh-go=19 400. Upward from this point to 7,999 the count is based on 8,000, for which the word chuwy—which, according to Brasseur, denotes the bag or sack containing 8,000 cacao nuts, corresponding exactly with the Mexican aqguipilli—was used. 7,601 7,602 16,000 24,000 80,000 88,000 hun-ri-hu-chuyy=1 on the first 8,000. cab-ri-hu-chuvy=2 on the first 8,000, ete. ca-chuyy=2 8,000. ox-chuyy=3 < 8,000, ete. lahuh-chuvyy=10> 8,000. hulahuh-chuvy=11 8,000. *“Y asi de los demas hasta el infinito’’ (Brasseur). In the other dialects of the Mayan family the lists of numerals above 10, so far as obtained, are as follow: Cakchikel lahuh. 16 yuaklahuh=6-+10. huvilahuh ?=1-+10. 17 vuklahuh=7+10. eablahuh=2+10. 18 yvuahxaklahuh=8+10. oxlahuh=3+10. 19 belehlahuh=9-+10. cahlahuh=4+ 10. 20 huvinak=1 man. vuolahuh=5~+ 10. Stoll*® gives the old and new methods of counting among the Cakchi- quels from 40 to 80, as follow (4 being substituted for 7); the number equivalents are our additions: ca-vinak=2 men Old New 40 ca-vyinak=2 men. hun-r-oxe’al=1 on the third score. 41 ca-vinak-hun=2 men and 1, or 2x 20+1. cai-r-oxe’al=2 on the third score. 42 ca-vinak-cai=2 20+2. oxi-r-oxc’al=3 on the third score. 43 ca-vinak-oxi=220+3. cahi-r-oxc’al=4 on the third score. 44 ca-vinak-cahi=2 20+-4. yoo-r-oxe’al=5 on the third score. 45 ca-vinak-yuoo=2 20+-5. on the third 46 ca-vinak-vuaki=220-+6. yuakaki-r-oxe’al=6 score. 1Stoll, Zur Ethhnog. Guatemala, p. 136. 2The v7 in this name is apparently incorrect; it is possibly a misprint for n. 3Soce. cit. 900 ‘ 80 mala (page 68), translated from American Philosophical Society, bers, his g being changed to @ to NUMERAL SYSTEMS (ETH, ANN, 19 Old New yuku-r-oxe’al=7 on the third score. 47 ca-vinak-vuku=220-+-7. vuakxaki-r-oxe’al=8 on the third 48 ca-vinak-vuahxaki=2 20-+8. score. belehe-r-oxe’al=9 on the third score. 49 ca-vyinak-belehe=2 x 20+-9. lahuh-r-oxe’al=10o0nthethird score. 50 ca-yinak-lahuh=220+-10. hu-lahuh-r-oxe’al=11 on the third 51 ca-vinak-huvilahuh=220+11. score. cab-lahuh-r-oxe’al=12 on the third 52 ca-vinak-cablahuh=220+12. score. ox-lahuh-r-oxe’al=13 on the third 53 ca-vinak-oxlahuh=2X20+13. score. cah-lahuh-r-oxe’al=14 on the third 54 ca-vinak-cahlahuh=220+14. score. vuo-lahuh-r-oxc’al=15 on the third 55 ca-vyinak-vuolahuh=220+-15. score. yuak-lahuh-r-oxe’al=160n the third 56 ca-vinak-vaklahuh=220+16. score. vuk-lahuh-r-oxe’al=17 on the third 457 ca-vinak-vuklahuh=2x20+17. score. yuakxak-lahuh-r-oxe’al=18 on the 58 ca-vinak-vuahxaklahuh=2x20+18. third score. beleh-lahuh-r-oxe’al=190nthethird 59 ca-vinak-belehlahuh=2 x 20+19. score. oxe’al=3 X 20. 60 ox-vinak, or oxe’al=3X 20. hun-ru-humu’ch=1 on the fourth 61 ox-vinak-hun=3x20-+1. score. ; humu’ch. 80 cah-vinak, orhumu’ch =4 20, or 80. Dr Brinton, in his Grammar of the Cakchiquel Language of Guate- a manuscript in the Library of the gives the following additional num- correspond with Stoll’s list: 100 oc’al=5X 20. 101 hun-ru-vake’al=1 on the sixth score. 120 vake’al=6 x 20. 121 hun-ru-vuke’al=1 on the seventh score. 140 vuke’al=7 X20. 160 vakxak-c’al=8 x 20. 180 beleh-c’al=9X 20. 200 otue=5x 40. 300 volahuh-c’al=15 x 20. 400 omuch=5x 80. 500 omuch-oe’al=5 x 80+-5 X20, or 400+100. 600 omuch-otuk=400+-200. 700 omuch-volahuh-e’al=400-+-15 x 20. 800 cagho=2 gho or 2400. 900 oxe’al-r-oxogho? This is a mistake or misprint for 900 1,000 8,000 oc’al-r-oxogho=100 (or 520) on the third 400. otue-r-oxogho=200 (or 540) on the third 400. hu-chuvy. THOMAS] POKONCHI NUMERALS 901 The following list of Pokonchi numerals is from Stoll’s Maya- Sprachen der Pokom-Gruppe (p. 51): Pokonchi 10 lahe-b. 11 hun-lah=1+10. 12 cab-lah=2+10. 13 ox-lah=3-+10. 14 cah-lah=4+10. 15 ho-lah-uh=5+10. 16 vyuak-lah=6—10. 17 vuk-lah=7+10. 18 vuaxak-lah=8+10. 19 beleh-lah=9-+10. 20 hun-inak=1 20, or 1 man. 21 hen-ah ru-ca-vuinak=1 on the second score, or on the second 20. 22 quib ru-ca-vuinak—2 on the second score, or on the second 20. 30 laheb ru-ca-vuinak=10 on the second score, or on the second 20. 40 ca-vuinak=2 20. 50 laheb r-oxe’al=10 on the third score. 60 ox-c/al=3 Xx 20. 70 laheb ru-cah-vuinak=10 on the fourth score. 80 cah-vuinak=4 20. 100 ho-e’al=5 x 20. 200 ho-tue=5 x40. Stoll interprets the henah ru-ca-vuinak of the above list by ‘*1 sein 2x 20;” that is, 1 of, or belonging to, 220 or the second 20. This is exactly the same as saying one on the second score. The 7 for which ‘*sein ” stands is the third person, singular, possessive pronoun, as in rupat, ** his house.” In Quekchi (or K’ak’chi), from which the next example of numbers above 10 is taken, we follow the ‘* Vocabulario Castellano-ICak’chi ” of Enrique Bourgeois, as published by A. L. Pinart (pp. 7-8), always, however, changing the Spanish 7 to /. Kak’ chi 10 laheb. 16 guac-lahu=6-+10. 11 hun-lahu=1-+10. 17 guk-lahu=7+10. 12. kab-lahu=2+10. 18 guaxak-lahu=8-+10. 13 ox-lahu=3-+10. 19 bele-lahu=9+10. 14 kabahu, or kaa-lahu=4+10. 20 hun-may. 15 ho-lahu=5+10 Why may or ma? is used here instead of kal, the proper term for 20, is not apparent, as it is a term applied in counting a particular class of objects. Charencey’ remarks as follows in regard to it: Ainsi le Cakgi posseéde au moins cing termes pour rendre notre nom de nombre 20, suivant les objets auquels il se rapporte. Ainsi, l’on dira huvine, s'il s’agit de comp- ter des graines de cacao ou de pataste (cacao sauvage); huntaab, pour les couteaux et instruments de fer ou de métal; hunyut, pour les plumes yertes; hwmai, s'il s’agit 1 Mélanges, pp. 65-66 902 NUMERAL SYSTEMS [ETH. ANN. 19 de compter les poutres, les bestiaux, les fruits et objets comestibles. De méme le Quiché employait cette particule mai ou may, lorsqu’il s’agissait du comput de Vespace de vingt ans; de vinak, alors que l’on youlait supputer les mois, ete. 21 hun-x-kakal=1 on the second score. 22 kaib-x-kakal=2 on the second score. 23 oxib-x-kakal=3 on the second score. 24 kaaib-x-kakal=4 on the second score. 25 hoob-x-kakal=5 on the second score. 26 guakib-x-kakal=6 on the second score. 27 gukub-x-kakal=7 on the second score. 28 guahxakib-x-kakal=8 on the second score. 29 beleb-x-kakal=9 on the second score. 30 laheb-x-kakal=10 on the second score. 31 hun-lahu-x-kakal= 11 (or 1 + 10) on the second score. 32 kab-lahu-x-kakal=12 (or 2+10) on the second score. 33 ox-lahu-x-kakal=13 on the second score. So to 39. 40 kakal=2 x20. 41 hun-r-oxkal=1 on the third score. 42 kaib-r-oxkal=2 on the third score. So to 49. 50 laheb-r-oxkal=10 on the third score. 51 hun-lahu-r-oxkal =11 (or 1+10) on the third score. 52 kab-lahu-r-oxkal= 12 (or 2+-10) on the third score. So to 59. 60 oxal=3 20. 61 hun-x-kakal?=1 on the fourth score. 62 kaib-x-kakal?=2 on the fourth score. So to 69. 70 laheb-x-kakal?=10 on the fourth score. 71 hun-lahu-x-kakal?=11 (or 1+10) on the fourth score. 72 kab-lahu-x-kakal?=12 (or 24-10) on the fourth score. So to 79. The kakal in the last five numerals unquestionably denotes 4 20, or 80, the proper term for which is kagkal. As kakalis the term for 40, or literally 220, there must be either a distinction in the pronuncia- tion not indicated in the vocabulary or an error in the printing. The data at hand do not furnish the means of determining the signification of the inserted z as in hunvkhakal; it seems evident that it plays the same role as 7 before 0, as in vorhal. 80 kaakal=4x 20. 81 hun-r-okal=1 on the fifth score. 82 kaib-r-okal=2 on the fifth score. So to 89. 90 laheb-r-okal=10 on the fifth score. 91 hun-lahu-r-okal=11 (or 1+10) on the fifth score. So to 99. 100 hokal=5 x 20. 120 guackal=6X 20. 200 hotue=5 40. 400 hun-okob=1 400. 800 kaib-okob=2» 400. THOMAS] MAM NUMERALS 9038 The list of numerals above 10 in the Mam dialect given below is from the Arte y Vocabulario en Lengua Mame, by Marcos Salmeron, published by Charencey (page 156). 60 70 80 90 100 200 300 400 500 600 700 900 Mam lahuh. hum-lahuh=1+10. kab-lahuh=2+10. ox-lahuh=3-+10. kiah-lahuh=4+10. o0o-lahuh=5+10. vuak-lahuh=6+10. vuk-lahuh=7+10. vuahxak-lahuh=8+10, belhuh-lahuh=9-+10. yuinkim or huing (Stoll) =1 man. yuinak-lahuh=1 man, or 20+10. ka-vuinak=2 20. hum-t-oxkal-im=1 to the third score. kabe-t-oxkal-im=2 to the third score. oxe-t-oxkal-im=3 to the third score. kiah-t-oxkal-im=4 to the third score. hoe-t-oxkal-im=5 to the third score. vuakak-t-oxkal-im=6 to the third score. vuk-t-oxkal-im=7 to the third score. vuahxak-t-oxkal-im=8 to the third score. velhuh-t-oxkal-im=9 to the third score. lahuh-t-oxkal-im=10 to the third score. ox-kal=3 & 20. lahuh-tu-hu-much-im=10 on the fourth score. hum-muex=1 much, or 180. lahuh-t-okal-im=10 on the fifth score.’ okal=5 x 20. ochuk=5 x 40. oloh-kal=15 x 20. o-mucx=5 & 80. omucx-okal=400+-100, lit. (580) + (5x20). omucx-ochuh=400-+-200, lit. (680)+(5x40). omucx-oloh-kal=400+-300, lit. (680)-+(15 20). lahuh-tuki-okal. Stoll® gives a method of counting above 40 in this idiom so different from that presented above that his brief notice is presented here: 40 50 60 70 80 90 caunak=2 20 ?, or 2 men. caunak-t-iqui-lahoh=40+10. ox-c’al=3 & 20. ox-e’al-t-iqui-lahoh=60-+10. hu-much=1 80. hu-much-t-iqui-lahoh=80+10. 1Salmeson gives t-oxkal, which is an evident error. *Sprache der Ixil-Indianer, p. 146. 904 NUMERAL SYSTEMS [ETH. ANN. 19 This, as will be seen, adds to the preceding 20 instead of counting on the following 20, and is presumed to indicate the more modern method of counting. 10 11 12 13 14 15 16 17 18 19 bo o bo to bt owe bo to Cole bo ~1 O 2th tb tw om Txil la-vual. hun-layual=1+10. cab-layual=2+10. ox-lavual=3-+10. ca-lavual=4+10. o-lavual=5-+-10. yuah-lavual=6-+-10. vuh-lavual=7—10. vuaxah-layual=s-+ 10. bele-lavual=9-+ 10. vuink-il, or yuinquil. vuinah-un-ul=20-+-1. vuinah-cab-il=20+-2. yuinah-ox-ol=20+3. yuinah-cal=20+4 (cal for cah-il). vuinah-61=20-+5 (ol for o-ol). yuinah-vyuah-il=20-+-6. vuinah-vuh-ul=20+-7. yuinah-vuaxah-il=20+8. yvuinah-belu-vual = 20+-9, yuinah-lavual = 20-++10. ea-vuink-il = 2 20. ox-c’al-al=3 & 20. layual-i-much=10 on the 80. ung-much-ul=ome much, or one 80. layual-t-oe’al=10 on the fifth score. o-c’ al-al=5 & 20. oe’ alal-t-uec-ungyual=100-+-1. lavual-i-vuahe’al=10 on the sixth score. yuah-e’ al-al=6 x 20.” layual-i-vuhe’al=10 on the seventh score. vuh-e’al-al=7 X 20. lavual-i-ynuaxahe’al=10 on the eighth score. yuaxah-e’al-al=8 x 20. lavual-i-belee’al=10 on the ninth score. bele-c’al-al=9 x 20. layual-i-lac’al=10 on the tenth score. la-c’al-al=10 20 (or cayual-ciento=2>100—Spanish).. hunla-e’al-al=11 x 20. layual-i-cabla-c’al=10 on the twelfth score. eabla-c’ al-al=12 20. oxla-n-e’al-al=13 20 (same as oxlahune/alal). eala-n-c’ al-al=14 x 20. ola-n-c’al-al=15 x 20. 1Stoll, op. cit., pp. 50-52. 2Stoll gives by slip of the pen 4X20.” 905 THOMAS] IXIL NUMERALS 3820 yvuahla-n-e’al-al=16 20. 340 vuhla-n-c’al-al=17 x 20. 360 vuaxahla-n-c’al-al=18 20. 380 belela-n-c’al-al=19 x 20. 400 yuinkil-an-c’al-al=20> 20. 420 vuinah-un-ul-an-c’al-al=(20+1) «20. 440 vuinah-ca-vual-an-c’al-al=(20+-2) x 20. 460 vuinah-ox-l-an-c’al-al=(20+3) 20. 480 yuinah-ca-l-an-c’al-al=(20-+4) 20. 500 vuinah-o-l-an-c’al-al=(20+5) «20. 520 yuinah-yuah-il-an-e’al-al=(20+6) x 20. 540 yuinah-vuh-l-an-c’al-al= (20-+-7) «20. 560 yuinah-yuaxah-il-an-e’al-al=(20-+8) x 20. 580 vuinah-bele-l-an-c’al-al=(20+-9) x 20. 600 yuinah-la-yual-an-e’al-al= (20-+-10) 20. 620 yuinah-hun-la-yual-an-e’al-al= (20-+-1+-10) « 20. 640 vuinah-cab-la-yual-an-c’al-al=(20+ 2+-10) «20. 660 vyuinah-ox-la-vual-an-e’ al-al=(204-3-+-10) * 20. 680 vuinah-ca-la-vual-an-e’al-al= (20-+4+-10) x 20. 700 yuinah-o-la-yual-an-e’al-al=(20+5+10) x 20. 720 vuinah-vuah-la-vual-an-e’al-al= (20-+-6+10) x 20. 740 vuinah-yuh-la-yual-an-e’al-al= (20+7-++-10) x 20. 760 vuinah-vuaxah-la-yual-an-e’al-al=(20-+8-+10) 20. 780 yuinah-bele-la-yual-an-e’al-al=(20+-9-+10) « 20. 800 ea-vuinkil-an-e’al-al= (220) x 20. Aguacateca ! Jacalteca ! | Chuhe! = 10 lahu 10 lahuneb 10 lahne 11 hunla 11 hun-lahuneb 11 uxlche (?) 12 cabla 12 cab-lahuneb 12 lahchue (?) 13 oxla 138 ox-lahuneb 13 ux-lahne | 14 quayahla 14 can-lahuneb | 14 chanlahne 15 ola 15 ho-lahuneb 15 holahne 16 vuakla 16 vuah-lahuneb | 16 yuaklahne 17. ~vukla 17 vuh-lahuneb 17 uklahne 18 yvuahxakla 18 yuahax-lahuneb 18 yuaxlahne 19 belela 19 balun-lahuneb 19 banlahne 20 hunak 20 hun-e’al 20 hun-e’al 21 hunak-hun | 21 hun-es-cavuinah | 40 chayuinal 22 hunak-cab 30 Jahun-s-cayuinah | 60 hoix-yuinak (?) 23 hunak-ox | 40 ca-vuinah 40 caunak | 60 ox-e’al 60 ox-e’al | 100 ho-e’al 80 hun-much 1 Stoll, Sprache der Ixil-Indianer, p. 146. 906 NUMERAL SYSTEMS [ETH. ANN.19 13 14 16 17 Tzotzil (a) Chanabal (a) | Chol (b) lahunem buluchim lah-chaém=10+2 ox-lahuném=3+ 10 chan-lahuném= 4+10 ho-lahuném=5+ 10 uak-lahuném=6+- 10 10 +10 +10 tom 10 11 13 14 vuk -lahuném=7+- ity uaxak-lahuném=8 | 18 balum-lahuném=9 | 19 20 cha-vuinik=2 20, 40 or 2 men ox-vuinik=3 x 20 60 chan-vuinik=4 20, 80 ho-vuinik=5 x 20 100 lahuné buluché, or baluche lah-chane (¢)=10+-2 | ox-lahuné=3-- 10 chan -lahuné=4+-10 ho-lahuné=5+-10 uak-lahuné=6--10 huk-lahuné=7-+-10 uaxak -lahuné=8-+ 10 bala-hune=9+-10 huntahbe cha-vuiniké=2 20, | or 2 men ox-vuiniké=3 X 20 chan-vuiniké=4x | 20 ho-vuiniké=5 x 20 17 18 19 20 40 100 aStoll, Ethnog. Guatemala, pp. 69-70. bStoll, op. cit. eShould not this be lah-chabe? mahe. mahe-tuue=10-+1. Mixe? lahum humpé e luhum- pé=1+10 chapé e luhum- pé=2+10 uxpé e luhumpé= 3+10 chumpé e luhum- pé=4+-10 ho-lumpé=5+10 [ho e luhumpé] nuokpé e luhum- pé=6-+10 hukpé e luhum- pé=7-+10 uaxokpé e luhum- pé=8+-10 bolompé e luhum- pé=9--10 hun-e’al=one 20 cha-c’al=2 20 ux-c’al=3 X20 chun-e’al=4 20 hoo-e’al=5 X 20 mahe-tuduuc=10+6 or mahe-moex-tuue=10+5-+1. mahe-huextuuc=10+-7 or mahe-moex-metzc=10-+-5+-2. mahe-tuctuuc=10-+8 or mahe-moex-tucoc=10-+5-+3. mahe-taxtuuc=10-++-9 or atuue ci ypx=1 from 20 or one more to 20. 12 mahe-metze=10+2. 13. mahe-tuede=10+3. 14 mahe-mactz=10+4. 15 mahe-moex=10-+45. 16 17 18 19 20 ypx. 21 ypx-tuuc=20+1. 22. ypx-metzc=20-+2. 23 ypx-tucde=20-++3. 1 Raoul de la Grasserie, Langue Zoque et Langne Mixe, 332, 833, THOMAS] MIXE AND ZOQUE NUMERALS 907 24 ypx-maxtaxc=20-+-4. 25 ypx-mocoxc=20-+-5. 26 ypx-tuduuc=20-+6 (literally 20+-5+-1). 27 ypx-huextuuc=20-+-7 (literally 20-+-5+-2). 28 ypx-tuctuuc=20-+8 (literally 20+5+3). 29 ypx-taxtuuc=20-+9 or atuuc ca ypxmahc=1 from 30 or 1 more to 30. 30 ypx-mahe=20+-10. 31 ypx-mahc-tuuc=20+-10-+1. 32 ypx-mahc-metzc=20-+10-+4-2. 33 ypx-mahe-tucbe=20+10-+3. 40 huixticx (?) [metz-ipx?] 60 tucd-px=3 20. 80 mohcta-px=4> 20. 100 mocd-px=5 x 20. 120 tuduu-px=6 20. 140 huextuut=7 20 ? 160 tuctuut=8 x20 ? 180 taxtuut=9> 20? 200 maiqu-ipx=10> 20. 300 yucmocx=20 15 ? 400 tuue-moii=1 moin. 500 tune-moifi co mocopx=400-+-100 or 400-+5 20. 600 tuuc-moifi co maiquipx=400-+ 200 or 400+10 20. 700 tuue-moii co yaemocx=400+-300. 800 metzc-moii=2>400. 900 metze-moii co mocopx=2 > 400+100. 1,000 metze-moif co maiquipx=2 400+ 200. Zoque * 2S : oon = ears : ong | 10 makch-kan 10 macay 11 makch-tuman=10+1 TET (22) | 12 makch-kues teut-kan 12 macueste-cuy | 13 (2) 13 mac-tucay=10+3 20 i-itpshan 20 ips-vote, yps-vote, or yps-vate (literally yps or ips=20) 30 i-ips-comak-kan 30 yps co mac=20+10 40 wheus-tu-gi-ipshan 100 mos-ips=5 x 20 50 wteus-tu-gi-comak-kan=40-+10 | 300 yet-ips 60 tugi-ipshan=3 20 2,000 mosmone 70 tugips-comak-kan=60+-10 10,000 tzuno-comos-mone | 80 mak-tapshan=4> 20 12,000 tzuno-comac-mona 90 mak-tapshan-coma-kan=80+10 13,000 tzuno-coma, vestec-mone 100 mossiipshan=5 x 20 16,000 vestee-tzunu 200 magi-ipshan=1020 20,000 vestectzuno-comac-mone | 30,000 tucuy-chuno coyet-mone 300, 000 yps-coyu covestec-tzuno 1This list of numerals must be accepted with some reserve; it is partly (1) from E. A. Fuertes’ manuscript in the Bureau of American Ethnology archives and partly (2) from the Vocabulary in Grasserie’s Langue Zoque. 908 10 1] 12 13 14 16 16 17 18 19 20 21 22 30 31 32 33 40 41 42 The wad 10 11 20 40 60 80 100 200 400 500 600 700 800 900 1, 000 4, 000 NUMERAT. SYSTEMS Trike} chia. cha-nha=10-—1. chu-tiha=10+2. cha-ntinha=10+-3. chi-giha=10+4. chindénha=15x1? chindnhi-ha=15~+1. chin6én-huiha=15+2 chindn-guandnha=15+3, chinén-gaha=15-+-4. hikoo or kooha. hikoo-nia-nha=20—1. hikoo-ghuiha=20+-2. hikoo-chiha=20-++-10. hikoo-chin=20+11 (liter- ally 20+10+1. hiko o-chuuiha=20+12 (literally 20--10+2),. ikoo-chantnha=20+13 (literally 20—10+ 3.) ghuixiaiha=2 x 20? ghuixiadi-ngoha=40+-1, ghuixiad-ghuiha=40-+.2. 100 [ETH, ANN.19 ghuixiad-chiha=40-+-10. ghuixiad-chanha=40+ 11 (literally 40+-10+ il g¢huixiad-chuuiha=40+- 12 (literally 40--10+- 2). guandnxiaha=3 < 20? guanonxia-hia-nha=60 +1. guanonxia-ghuiha=60—- 9 guandénxia-chiha=60+ 10. guandnxia-chinia-nha= 60+-10+-1. kdéaxihaa=4 X20? kdaxia-ngoha=80-++1. kéaxia-chiha=80-+-10. kAaxia-chan=80+11 (literally 80+-10-++1). haitht-chia=5 x 20. in the names for 40, ete., appears to be an equivalent of 20. Cahita * uo-mamni=2 5. uomamni aman-senu=10+1 or 2x5-+1. senu, senu-tacaua=one 20 or 120. uoi-tacaua=2 20. vahi-tacaua=3 x 20. naequi-tacaua=+4 x 20. mamni-tacaua=5 x 20. Also, uomamni ama yepa- uo-mamni-tacaua=10> 20 (literally 2x5 20). uo-mamni uosa-tacaua= (25) x (220)? uo-mamni uosa aman mamni-tacaua=400+-100. uo-mamni aman vahi-si-tacaua=(25) x (320) uo-mamni vahi-si aman mamni-tacaua=600-+-100. uo-mamni naequi-si-tacaua= (25) x (420). uo-mamni naequi-si aman mamni-tacaua=800+-100. uo-mamni mamni-si-tacaua=(2*5) (5x20). naequi UoMmMamni mamnistacaua. The author adds the following paragraphs: Some nations [?] say senutacaua or sesavehere for 20, others say sesavehere for 10, and follow up the count thus, 11 sesavehere aman senu, 12 sesavehere aman uoi, ete.; for 20 they say uvosavehere, which is 2 times 10. 1 Francisco Belmar, Ensayo sobre Lengua Trike, p. 10. 2Arte Lengua Cahita (anon.), edited by Eustaquio Buelna, pp. 199, 200. THOMAS] OTHOMI NUMERALS 909 The Yaquis say for 5 sesavehere, and counting from 5 to 5 [more] say wosavehere 10, vahivehere 15; these also say for 20 senutacaua or naequivehere, and for 25 say sesavehere, and for 100 say mamnitacaua or tacauavehere, which is 20 fives. He explains the ** numeral adverbs” sesa and wosa thus: se-sa, ** one time,” wo-sa, **two times;” for example, sesavehere, one time 5, wo7- wehere, two times 5, ete. Othomi! 10 réta or rata. 30 n-rihte-ma-réta=20+10, 11 réta-ma-ra=10-+1. 40 yohte=2 20. 12 réta-ma-yooho=10-+2. 50 n-yohte-ma-réta=40+10. 13 réta-ma-hiu?=10—3. 60 hit-rahte=3 20. 14 réta-ma-gooho=10—4. 70 hitrahte-ma-réta=60-++10 (liter- 15 réta-ma-qyta=10+-5. ally 320+10). 16 réta-ma-rahto=10+-6. 80 gooho-riahte=4> 20. 17 réta-ma-yohto=10-+7. 90 gooho - rdhte - ma’ - réta=80+-10 18 réta-ma-hidhto=10-+8. (literally 420-+10). 19 réta-ma-gyhto=10-+-9, 100 n-ranthbe, or n-ranéhbe. 20 n-rdhte. 1,000 n-ram-oo. Tarasco* 10 temben. 11 temben-ma=10-+1. 12 temben-tziman=10-+2. 13. temben-tanimu=10+3. 14 temben-thamu=10-+-4. 15 temben-yumu=10+-5. 16 temben-cuimu=10-+6. 17 temben-yuntziman=10-++7. 18 temben-yuntanimu=10-++8. 19 temben-yunthamu=10-+-9, 20 maequatze or makatari. 30 maequatze ca-temben=20+-10, 40 tziman-equatze=2 20. 50 tziman-equatze ca-temben=40+-10 (literally 2 20-++10). 60 tanime-equatze=3 x 20. 70 tanimequatze ca-temben=60-+-10. 80 thamequatze=4> 20. 90 thamequatze ca-temben=80-+-10. 100 yumequatze=5 20. 200 temben-equatze=10 20. 300 temben-equatze ca yumequatze=200—-100 (literally, 10 20--5 20). 400 ma-yrepeta=1 400. 500 ma-yrepeta ca-yum-equatze=400+-100. 600 ma-yrepeta ca-temben equatze=400—-200 (literally, 400-+-10 20). 700 ma-yrepeta ca-temben yumequatze=400+-300, or in full, mayrepeta ca-temben-equatze yumequatze=400+ 1020-5 x 20. 800 tziman yrepeta=2> 400. 900 tziman yrepeta ca-yumequatze=800+-100 (literally 2><400+-5 20). 1,000 tziman yrepeta ca-temben-equatze = 800 —- 200 (literally, 2 > 400-+- 1020). 1Luis de Neve Ymolina, Arte del Idioma Othomi, pp. 152, 153, and Eléments de la Grammaire Othomi (anon.), p. 14. 2htu in Ymolina’s Arte (probably a misprint). 3mo in Arte. 4Arte y Diccionario Tarascos, by Juan Bautista de Laguna, edited by Nicholas Léon, pp. 59-61. 910 NUMERAL SYSTEMS [ETH. ANN.19 2,000 yum-yrepeta=5 x 400. 3,000 yun-tziman yrepeta ca-temben-equatze=7 400+-10 x 20. 4,000 temben yrepeta=10 400. : 5,000 temben-tziman yrepeta ca-temben equatze=12> 400--10> 20. 6,000 temben yum-yrepeta=10400-+5>400 (written in full, temben yrepeta ca-yum-yrepeta. ) 7,000 temben yuntziman yrepeta ca-temben equatze=17 400-10 20. (literally, (10+-7) x400-+-10 20). 8,000 ma-equatze yrepeta=20 x 400. 9,000 ma-equatze tziman yrepeta ca-temben equatze=(20-+-2) x400-+-10> 20. 10,000 ma-equatze yum yrepeta=8,000-+-200 (literally, ma-equatze yrepeta ca-yum yrepeta=20 400-+5 400). 20,000 tziman equatze yrepeta ca-temben yrepeta=2 > 20 4004-10 400. 30,000 tanim equatze temben yrepeta cayum yrepeta = 70400-- 2,000 (literally, (8 20+-10) x400+-5 x 400). 40,000 yum-equatze yrepeta=5 x 20 400. 50,000 cuim-equatze yrepeta ca-yum-yrepeta=6 x 20 < 400-+-5 x 400. 60,000 yun-tanim-equatze yrepeta(?)=?. 70,000 yun-tham-equatze yrepeta ca-yum-yrepeta(?) =?. 80,000 temben-equatze yrepeta, ca-temben-yrepeta=10 20> 400 (‘*ca-tem- ben yrepeta’’ surplusage?). 90,000 temben ma-equatze yrepeta, ca-temben yum yrepeta. 100,000 temben-tanim-equatze yrepeta(?)=?. 200,000 makararhi-equatze yrepeta ca-cuim-equatze yrepeta=?. 300,000 makatarhi-equatze ca-temben yuntham-equatze yrepeta=?. 400,000 tziman katarhi equatze ca-yuntanim equatze yrepeta=?, 500,000 tanim katarhi-equatze ca-tziman equatze yrepeta=?. 600,000 tanim katarhi-equatze catemben yum-equatze yrepeta=?. 700,000 tham-katarhi-equatze ca-yuntanim-equatze yrepeta=?. 800,000 yun-katarhi-equatze ca-ma-equatze yrepeta=?. 900,000 yum-katarhi-equatze ca-temben-tham-equatze yrepeta=”. There appear to be several errors in this list which can not be cor- rected with satisfactory certainty without a somewhat thorough knowl- edge of the language. The name for 60,000 as it stands in the list is equal to 8x 20 400, giving as the product 64,000, It is possible that this is the number intended. The proper expression for 60,000 appears to be yun-tziman-equatze-yrepeta temben-yrepeta=T X 20 X 400+-10 X 400. The name for 70,000 as it stands in the list signifies 9 20 400+-5 Xx 400=74,000. As it is not probable that this is the number intended, the error must be in the name. If we write yan-tanim-equatze yrepeta =64,000 and add temben yum-yrepeta, the abbreviated name for 6,000, we shall get the required number, but the positive evidence that this form is correct is lacking. We observe that the first terms in the names for 10,000, for 20,000, for 80,000, and for 40,000 are, respectively, ma, 1; tziman, 2; tanim, 3; and yum, 5. Following this rule, the correspond- ing terms in the names for 50,000, 60,000, 70,000, and 80,000 should be euim, 6; yun-tziman, 7; yuntanim, 8; and temben, 10. The correc- tions suggested for 60,000 and 70,000 (as 80,000 has temben) will con- form to this order. These high round numbers have, however, a modern look inconsistent with original Mexican number systems. THOMAS] OPATA AND TOTONACA NUMERALS One Opata' 10 makoi. 11 makoi-seni-begua?=10-+1. 12 makoi-go-begui=10+2. 13 makoi-ba-begua=10-+3. 14 makoi-nago-begui=10-+-4. 15 makoi-mari-begui=10+5. 16 makoi-bussani-begua=10-+6. 17 makoi-seni-gua-bussani-begui=10+-7 (literally 10-+-1+-6). 18 makoi-go-nago-begui=10--8 (literally 10+24). 19 kiseuri=before or next to 20. 20 seuri, or seneurini=1 man (?). 21 seuri-seni-begui=20-+1. 30 seuri-makoi-begua=20+-10. 40 gode-urini=2 x 20. 50 godeurini makoi-begua=40-+-10 (literally 2 20+-10). 60 vaide-urini=3 x 20. 100 makoi-urini? (error; should be mari-urini=5 x 20?) . Tarahumari* 10 macoi-qui. 11 macoi-guamina-bire=10+-1. 12 macoi-guamina-oca=10-+-2. 13 macoi-guamina-beiquia=10-+3. So to 19. 20 osa-macoi=2 10. 30 beisa-macoi=3 x 10. 40 naguosa-macoi=4 10. Notwithstanding the evident resemblance of the numerals of this idiom up to 10 to those of the Nahuatl, itis clear from this short list, which is all we are enabled to offer from the data at hand, that the higher number names are based on the decimal system. As the mode of counting used by the tribes of the Shoshonean group, so far as they have been obtained, is based on the decimal sys- tem, it is unnecessary to present more than one or two examples, which will be introduced farther on. Before closing this chapter a few other examples, including two from northeastern Asia, will be presented for comparison. The first of these is the Totonacan count above 10. Unfortunately we have only the round numbers. Totonaca * 10. cauh. 20 puxam. 30 puxam-a-cauh=20-+-10. 40 ti-puxam=2> 20. 50 ti-puxam-a-cauh=2 > 20+-10. 60 toton-puxam=3 20. 100 quitziz-puxam=5 20. 200 co-puxam=10 20. 400 tontaman. 1,000 ti-taman-a-co-puxam=2 400-+-10 20. 1 This incomplete list is gathered from the Vocabulario Opata in Pimentel’s Cuadro, vol. II. 2The signification of begud in this connection unknown to the writer. 8 Miguel Tellechea, Compendio Grammatical idioma Tarahumati, p. 7. 4Conant, Number Concept, p. 205. 912 NUMERAL SYSTEMS (ETH. ANN.19 For numbers in a different dialect see Akal’man in the preceding chapter. Squier’ gives the numerals of a Nicaraguan tribe that he names Nagranda (Subtiabanss?), which show that the system was regularly vigesimal. Nagranda 10 Guha=10. 41 11 Guanimba=10-+1. 42 12 Guanapu=10-+ 2. 43 18 Guanasu=10+3. 50 14 Guaracu=10+4. 51 15 Guanisu=10-++5. 52 16 Guanmahu=10-+6. 17 Guanquinu=10+-7. 60 18 Guanuha=10+8. im 19 Guanmelnu=10+-9. 80 20 Dino, imbadino, or’ badifio=1 x 20. 90 21 ’Badifioimbanu=1X20+1. 100 22 ’Badifioapunu=1X 20-+-2. 23 ’ Badinoasunu=120+-3. 200 30 ’Badinoguhanu=1X20+10. 400 31 ’Badihoguanimbanu=1 20+ 1000 10-1. 2000 32 ’ Badifloguanapunu=1 x 20+10+2. 33 ’Badifoguanasunu=120+10+3. 4000 Apudiiio=2 20. Apudinoimbanu=2 20-+1. Apudifioapunu=2 20+-2. Apudifioasunu=2 20+3. Apudinoguhanu=2> 20+-10. Apudifioguanimbanu=220+1. Apudifoguanapunu=2 x 20+ 10+-2. Asudifio=3 x 20. Asudifioguhanu=3 x 20+10, Acudifiio=4 20. Acudifoguhanu=4 20-+-10. Huisudifio or guhamba=5 x20 or great ten. Guahadifiio=10X 20. Difioamba=great twenty. Guhaisudifio=10 5X 20. Hisudifioamba=five great twen- ties. Guhadifoamba=ten great twen- ties. As we shall have occasion to refer to one example from a California dialect not pertaining to the Uto-Aztecan family, we give it here. 8 9 10 11 12 Hichném* pu-weh. 20 opeh. : 30 mol-meh. ke-so-peh. pu-pukh. pu-i-tal=(1+5)? 40 50 o-pi-dun=(2-+-5)? 60 ken-uh-sol-mi-nun. 70 hel-pi-suh-pu-tul=(10—1)? hel-pis-oh. 80 hel-pis-i-pu-tek =10-+-1. 90 hel-pis-0-0-po-tek =10+-2. 100 pu-al-yek. mis-u-o-pal-yuh=(10 on second score)? o-pal-yuh=2 20. mis-u-mol-mal-yuh=(10 on third score )? mol-mal-yuh=3 X20. mis-u-kas-a-pal-yuh=(10o0n fourth score)? kas-a-pal-yuh=4 20. mus-u-pu-al=(10 on fifth score)? pu-ol. The number equivalents which we have added are given merely as suggestions. 40,10 from 60, ete. Those for 30,50, 70, and 90 should possibly be 10 from We can only say that the equivalent, though pos- sibly not the signification of m7/s-v, must be 10,and that the count relates to the next higher score. 1 Nicaragua, vol. 1, p. 326. 2 Compar. Vocabularies, by J. W. Powell, in Contrib. to N. Am. Ethn., vol. 11, pp. 487, 488. THOMAS) The two Asiatic examples are the Tschukschi and the Aino. 10 20 30 40 100 200 1, 000 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 300 400 500 MISCELLANEOUS LISTS Tschukschi } migitken=both hands. chlik-kin=a whole man. chlikkin mingitkin parol=20+10. nirach chlikkin=2 x 20. milin chlikkin=5 20. mingit chlikkin=10 20, i. e., 10 men. , miligen chlin-chlikkin=5 x 200, i. e., five (times) 10 men. Aino?* wambi. choz. wambi i-doehoz=10 from 40, or 10 on the second score. tochoz=2 x 20. wambi i-richoz=10 from 60, or 10 on the third score. rechoz=3 X 20. wambi [i?] inichoz=10 from 80, or 10 on the fourth score. inichoz=4 20. wambi aschikinichoz=10 from 100, or 10 on the fifth score. aschikinichoz=5 X 20. wambi juwanochoz=10 from 120? juwano «hoz=6 20. wambi aruwanochoz=10 from 140? aruwano choz=7 20. wambi tubischano choz=10 from 160? tubischano choz=8 & 20. wambi schnebischano choz=10 from 180? schnebischano choz=9 x 20. wambi schnewano choz=10 from 200? schnewano choz=10 20. aschikinichoz i gaschima chnewano choz=4 x 20+10 20. toschnewano choz=2 (1020). aschikinichoz i gaschima toschnewano choz=100+400. Miscellaneous Lists. 913 The following lists are added here chiefly as a means of comparison. Some of them have not as yet been satisfactorily classified by linguis- One or two of the dialects belong to that part of South America near the Isthmus of Panama, but are given because it appears tic affinity. that the tribes speaking them used the ‘‘native calendar.” The localities where they are spoken are given in connection with the names of the dialects. 1Conant, Number Concept, p. 191. “Ibid, pp. 191-192. 19 ETH, PT 2 23 914 NUMERAL SYSTEMS Moreno ( Honduras)! (ETH. ANN. 19 The number names in this dialect present a curious admixture of Moreno and Spanish. 1 aba. 2 biama. 3. irua. 4 gadri. 5 sene (Sp.). 6 sis (Sp.). set (Sp.). 8 vit. 9 nef (Sp.). 10 dis (Sp.). 50 100 300 uns (Sp. ). dus (Sp.). tres (Sp.). seis (Sp.). ven (Sp.). drandi (Sp.). biaven=2 20. biavendis=2 20+10. san (Sp.). iruasan=3 < 100. For the purpose of showing the evident relation of the Moreno num- ber names to those of the Carib group, those of the latter up to 5 are added here, from Rafael Celedon’s Gramatica Catecismo i Vocabulario de la Lengua Goajira (p. 29). lam not aware to what Carib dialect these belong, as this is not stated by Uricoechea, who wrote the intro- duction in which they are given—probably to that of the Magdalen district west of lake Maracaibo. Carib Sumo (Honduras )* tiascobas=(5+-3) 1 abana. 2 biama. 3 irhua, or eleua. 4 biamburi. 5 nacobo-aparcu, or abana-huajap (one hand). as. 2 buu’. 3 baas=(2+17?). 4. arunca. 5 cinea (Sp.). 6 tiascuas=(5-+-1?). 7 tiascabo=(5-+-2?). The author follows: gives the names cincuenta. sesenta. setenta. ochenta. cien. mil. for 50, 60, 70 32). tiascarunca=(5-+-4?). salap. salap-nica-buu’/=10+2. muiaslic. muyasloimincosala=20+-10. muyas-leibu=20x2. muy-as leibas. muy-as lelarunca. . 80, 100, and 1,000 as muy-as leisinca (‘‘sinea’’ Sp.). muy-as leitiascobas. muy-as leiarunca, muy-as leisala. 1 Alberto Membreio, Hondurenismos, p. 200. 2Tbid., pp. 225 { THOMAS] MISCELLANEOUS LISTS 915 These are clearly erroneous. We venture to correct them so far as possible as follows: ! 50 muyas leibu-mincosala? =40-+-10. 60 muyas leibas=20 3. 70 muyas leibas-mincosala? =60—-10. 80 muyas leiarunca=20 4. 100 muyas leisinca=205. 1,000 (muyas leisala may possibly be an abbreviation for muyas leisinca sala=100 10). Sumo (Nicaragua) ' 1 asia. 13 2 bo. 14 3 bas. 15 4+ arunca. 16 5 cinea (Sp. ). 17 6 tlascoguas=5-+1. 18 7 tiascobo=5+2. 19 8 tiascobas=5+3. 9 tiascoarunca=5—+-4. 20 10 salap. 30 ‘11 salapminitcoguas=10--1, 40 12 salapminitecobo=10+2. 100 salapminiteobas=10-+3.. salapminitcoarunca=10—-4. salapminitcocinca=10+5, salapminitcotisaguas=10+-5-++-1. salapminitcotiascobo=10+45+-2. salapminitcotiascobas=10-+5+-3. salapminitcotiascoarunca=10-+- 5x4. miyaslty. miiyasliiyminitcoslap=20 x 10. miiyaslityminitcobo=20 2. miiyasliiyminitcocinca=20 x5. Paya (Honduras)? 1 as. 8 oguag. 2 poe: 9 tais. 3) maig. 10 uca. 4+ ca. 12 ucarapoe=10+2. 5 aunqui (sp.?). 20 wauea. 6 sera. 100 ispoe.? 7 taoag. 1,000 areapissas. Jicaque de Yoro (Honduras)* 1 pani. 5 comasopeni. 2 mata. 10) comaspu. 3 condo. 11 quesambopani=10+1. 4+ diurupana. 12 quesambobomata=10-+-2. Jicaque del Palmar ( Honduras )* 1 pfani. 6 peve-dro. 2 pmata. 7 ashafaffani=6+1?. 3 abrucua. 8 ashafamata=6-+2. 4 urubana. 9 ashafaabruca=6+3. 5 pevebane. 10° commeayu. Guajiquiro (Honduras) * 1 eto. 7 pela sai=2 2) pee: 8 lagua sai=- 3 lagua. 9 erio sai=4+5. + erio. 10 ishish lo sai=(2>5?). 5 sal. 11 ishish eta sai=10-++1. 6 eta sai=1-+5. 1Alberto Membreno, Hondurefismos, p. 223. 2 [bid., p. 231. S[bid., p. 239. 916 20 PH 30 NUMERAL SYSTEMS Similaton (Honduras)? eta. + herea. pe. 5 say. lagua. 6 issis (doubtful, 10?). Guaymi (Veraguas) * crada (krati). erobu. cromo. crobogo (kroboko). coirigue (krorigue) . croti. crocugu. crocuo. croegon (krohonkon ). crojoto. crododi-eradi=10+1 (krojoto ti krati). crododi-crobu=10-+2 (krojoto ti krobu). crododi-cromo=10+3. crododi-crobogo=10+-4. gre. grebbi-cradi=20-+-1. grebbi-crojoto=20+10 (grebi-krojoto). grebbi-crojoto-dicradi=20+10+1. gregueddabu=20 2 (gregue krobu). gregueddabu-dicradi=40+ 1. gregueddabu-dicrojoto=40+-10 (gregue krobu ti krojoto). greguedamo=20 3 (gregue kromo). greguedamo-dicrojoto=60+10 (gregue kromo ti krojoto). gregueddabugo=20 4 (gregue kroboko). gregueddabugo-dicrojoto=80+10 (gregue kroboko ti krojoto). greguetariguie=20 5 (gregue krorigue). Guaymi Sabanero | Panama) * edaite. gdabogue or gdabu. gdamai. gdabaga or gdatare. datiga or gdabaga. edaderegue or gdabo. gdadugue or gdain. gdaapa or gdatiga. gdaica or gdatadi. gdataboco=5 X 2 or gdatabu. Count from 10 to 19 by adding 1, 2, ete., to 10. giriete. giriete-gdaite=20-+1. guiriete-gdataboco=20-+-10 (girite?). [BTH. ANN.19 1 Alberto Membreno, Hondurenismos, p. 256. 2A, L. Pinart, Coleecién de Lingilistica y Etnografia Americanas, tomo Iv, p. 23. parentheses are from Pinart’s Vocabulario Castellano-Guaymie, appendix, p. 5. ‘A. L. Pinart, Coll. Ling. y Etnog. Am. tomo Iv, pp. 52-53, and Vocabulario Castellano-Guaymie, Murire dialect, p. 48. The words in THOMAS] MISCELLANEOUS LISTS 917 40 guiribogue=20X 2 (giribogue?). 50 guiribogue-gdataboco=40+ 10. 60 girimai=20X3. 70 girimai-gdataboco=60+-10. 80 giribaga=204. 90 giribaga-gdataboco=80-+-10. 100 giritiga=205. Dorasque (Panama) * 1 que. 5 calamale. 2 como. 6 catacale. 3 calabach. 7 catacalobo. | + calacapa (calapaca?). Other lists with dialectic variations are as follow:* kue, umai. 6 kulpaka, katakala. 2 kumat, komo, umaidos. 7 katakalobo. 3 kumas, kalabac, umaitres. 10 kulmalmuk. kupaki, kalapaka. 20 sermalmuk. 5 kulmale. Cuna (Panama) * 1 cuenchique. 12 ambegui caca pocua=10+-2. 2 pocua. 20 tulabuena. 3 pagua. 30 tulabuena caca ambegui= 4 paquegua. 20-+10. 5 atale. 40 tulapocua=20 2. 6 nercua, or nericua. 60 tulapagua=203. 7 cublegue. 80 tulapaquegua=20 4. 8 pabaca. 100 tula atale=205. 9 paquebague. 1000 tula guana (guala?) buena. 10 ambegui. ‘ 11 ambegui caca cuenchique= 10+1. Choco (Panama) * 1 haba, aba. 2 ‘ome: 3 ompea. 4+ kimari, kimane. 5 huasima, juasoma. 6 huasimara-ba, juasoma-aba=5-+ 1. 7 huasimara-nome, juasoma-ome=)+2. S$ huasimara-ompea, juasoma-ompea=5+3. 9 huasimara-kumari, jJuasoma-kimane=5-+-4. 10 huasimani manima, ome juasoma=d x2 or 2X5. 11 oma juasoma aba=2%5+1. 15 ompea juasoma=35. 20 kimari, or kimane juasoma=4 5. 1A. L. Pinart, Coll. Ling. y Etnog. Am. tom. Ivy, p. 52. 2A. L. Pinart, Vocab. Castellano-Dorasque (Chumul, Gualaca, and Changuina dialects) . $A. L. Pinart, Vocab. Castellano-Cuna, pp. 6-7. +A. L. Pinart, Vocab. Castellano-Chocoe, pp. 2 918 100 200 There NUMERAL SYSTEMS (ETH. ANN. 19 Chibcha (near Bogota, Colombia) * ata. boza. mica. muyhica. hyzea. ta. cuhupea. suhuza. aca. ubchihica. ghicha ata=10+1. qghicha boza=10-++2. qhicha ta=10+6. qhicha (or complete) quihicha ubchihica; also giie and giieta (sig. “ foot ten”’). gletas asaquy ata=20—-1. guetas asaquy boza=20+-2. giietas asaquy qhicha ata? (giietas asaquy ubchihica=20+10). guetas asaquy qhicha ubchihica? (giie bozas=20 2). gue bozas asaquy ata=202-+-1. giie bozas asaquy qhicha ubchihica? (should be gie micas=20X3). giie micas asaquy ata. gue hizca=205. gue ubehihica=20 10. is apparently some error in the names for 30, 40, and 60. The term asaqguy is merely to indicate addition: ** asaguy, que quiere decir, i mas, con el nombre de las unidades.” As gite bozas asaquy ata denotes 41, the name for 40 should be giie bozas=20X2, as 100 is denoted by gite hizea=20*5. The proper term for 30 is probably giietas asaquy ubchihica (or ghicha)=20-+-10. The following is a specimen of the numerals used by the Huave (of Tehuantepec) from Burgoa, Geog. Descrip., tom. m, fol. 396, as quoted by Hubert Bancroft, Native Races.* cS 60 SI OD OT CO anoeth. 10 agax-poax. izquieo. 11 agax-panocthx? areux. 12 agax-pieuhx. apequiu. 3 agax-par. acoquiau. 14 agax-papeux. anaiu. 15 agax-pacoigx. ayeiu. 20 nicumaio. axpecanu. 30 nieumiaomecaxpo. axqueyeu. 100 anoecacocmian. Rama (island in Bluefields lagoon) * saiming. 4 kunkun-beiso. puk-sak. 5 kwik-astar. pang-sak, 1E. Uricoechea, Gram., Vocab., ete., de la Lengua Chibcha. 2 Vol. 111, p. 758. There are seeming errors in this list. ‘Brinton, American Race, p. 367. THOMAS] DISCUSSION AND COMPARISONS 919 Bribri ( Talamancan tribe, Costa Rica) } eet: 5 skang. 2 ‘but. 6 terl. 3) mnyat. 7 kugu. 4 keng, ka. $8 osehtan, pai, pa. Brunca ( Talamanecan tribe, Costa Rica) * 1 etsik. 5 kehisskan. 2 bug. 6 teschan. 3 mang. 7 kuehk. 4+ bachkan. 8 ochtan. Carrizo (near Monelova, Coahuila) * 1 pequeten. 4 naiye. 2 acequeten. 5 miaguele. 3 guiye. DISCUSSION AND COMPARISONS Before I discuss these lists and attempt to draw conclusions from them, there is one point which deserves notice. It is this: To what extent can these number lists be considered reliable? I do not by this inquiry wish to question the veracity of any author whose works I have quoted or used, but to refer to the method by which the lists were obtained, especially the portions relating to the high numbers. Did the Maya, Aztec, and other tribes make use in actual count or computation of thousands, tens of thousands, hundreds of thousands, and even millions as given in these lists, or have they been filled out, in part, by the authors according to the systems found in vogue? That implicit reliance can be placed on the judgment and accuracy of the more recent authorities who, as is known, derived their information direct from the natives, as Stoll, Gatschet, ete., is conceded, but the lists given by these authors seldom if ever reach beyond the thousand. Most of the lists from the tribes of Mexico and Central America, which run into high numbers, are given by the early authors (chiefly Spanish) or are based on their statements. When the Mexicans spoke of caxtol-tzontli=15 tzontli (6,000); ceni- poal-wiquiplli=2Ww xviquipilli (160,000); and cem-poal-tzon-xiquipilli= 20 times 400 wiquipilli (64,000,000—see list), did they have in thought the actual numbers given as equivalents of these terms, or merely measures?! When, for example, they said, ** 15 tzontli” (tzontli signi- fying bundle or package) did they intend to signify 15400, or simply 15 bundles or packages? In other words, did the reference Q 1 Adolph Uhle, in Compte Rendu Cong. Americanistes, Berlin, 1888, p. 474. 2Tbid., p. 475. 8’Uhle, Die Lander am untern Rio Bravo del Norte, p. 120, quoted by Brinton, American Race, p. 93. ee ae ‘ 920 NUMERAL SYSTEMS [ETR. ANN. 19 pass from the number to the measure! To illustrate, if we say 3 barleycorns make 1 inch; 12 inches 1 foot; 3 feet 1 yard; and 1,760 yards 1 mile, do we in speaking of 1 mile have in view the 190,080 barleyeorns! When the Mexicans spoke of xiguip/lli they alluded, according to Clavigero, to sacks or bags. He says, as above quoted, “They counted the cacao by xiguipilli (this, as we have before observed, was equal to 8,000), and to save the trouble of counting them when the merchandise was of great value [probably quantity] they reckoned them by sacks, every sack having been reckoned to contain 3 xignipilli, or 24,000 nuts.” Now, are we to suppose that in counting the sacks the number of nuts was kept in view! Did the merchant who purchased a Zz0nt/¢ of sacks (400) have in mind or pur- pose buying 9.600.000 nuts! This will suffice to make clear the thought intended to be presented, and will, it seems, justify the ques- tion—have the high numbers in these lists been added in accordance with the computation of the recorder, or were they in actual use among the native Mexicans! As contact with Europeans and their decimal system for nearly four centuries has modified to a greater or less extent the original native method of counting, it is doubtful whether direct reference to the sur- Viving natives of the present day would settle the question. The Maya pic has, as we have seen, been changed from 8,000 to 1,000, and the signification of other numeral terms has been changed in similar man- ner, Our only appeal is therefore to the native records, and here, possibly from our inability to interpret the Mexican symbols, we are limited to the Mayan codices and inscriptions. Here, however, as has been clearly shown in another paper, and as has been proved by Forstemann and Goodman, the evidence is clear that the Maya, or at least the priests or authors of the Dresden codex and the inscriptions, could and actually did carry their computations to the millions, in terms where the number element was necessarily retained, where the primary unit—in these instances the day—had to be kept in view. Of course they made use of the higher units to facilitate counting. as we do at the present day. If the Maya were capable of counting intel- ligently to this figure, it is not unreasonable to suppose that the more advanced among the surrounding tribes may have made similar, though possibly not so great, progress in their numerical systems. That the Mexicans had symbols for high numbers is asserted by the early his- torians, and is evident from their remaining codices, but no means of testing these, as the Maya manuscripts and inscriptions have been tested, has yet been found; however, the explanation of symbols carrying the count to the tens of thousands has been given. Notwithstanding this conclusion, it is apparent that the influence of the European decimal system has been felt in some of the native THOMAS] DISCUSSION AND COMPARISONS 921 counts herein given. This, for example, is probably true of the Tuas- tecan count, where the simple term 77 is used to denote 1,000, and also in the count from 200 to 900 in this system and in some others. All the preceding lists showing the count from 10 upward which belong to the Mexican and Mayan groups, except that of the Tarahu- mari, pertain to the vigesimal system and in method of counting bear a strong general resemblance one to another, yet when they are closely examined minor differences are found which have an important bear- ing on the question of the origin and relationship of these systems. Of these variations we notice the following: The Nahuatl count follows strictly the quinary-vigesimal system, as has been already stated, 5 and 15, as well as 20, being basal numbers. The count is always from a lower number, that is to say, the minor numbers are always added to a number passed; thus +1 and 42 are formed by adding 1 and 2 to 40, and not by counting the 1 and 2 on the next or third score, as we have seen was the rule among some of the Mayan tribes, as the Maya proper or Yueatee, the Quiche, Cakchiquel, Pokonchi, Quekchi, Mam, Ixil, and probably most. of the southern tribes of the group, but not among the Huasteca, who formed the northern offshoot. The count of the latter, though, like the others of the Mayan group, fundamentally vigesimal to 900, is, like the Nahuatl, by additions of the minor numbers to x number passed as 20-+-10 to form 80 and 2X 20+-10 to form 50. The numeral system of the Mayan tribes generally differed from the Nahuatl, Zapotec, Mazatee, Trike, Mixe, and Zoque systems—all of which are regularly quinary-vigesimal, and generally add the minor numbers to the pre- ceding base—in being more nearly decimal-vigesimal, and in adding the numbers above 40 to the following base, as 1 on the third score, or third 20, to form 41. In the Mayan dialects the count is never based on 5 except, as has heretofore been suggested, from 6 to 8, and in one dialect from 6 to 9 So far, therefore, as these differences are concerned, they tend toward grouping together the systems of the Nahuatlan, Zapotecan, and Zoquean tribes, as contrasted with the Mayan: but the term Nahuatlan is used here as referring only to the stock in its limited sense—the Aztecan branch—as the rule does not hold good throughout, when we pass into the Sonoran branch. However, the grouping on these points is interesting as it is in harmony with other data. In one peculiarity, however, the Zapotec count differs from the Nahuatl and approaches the Mayan systems. From 55-59, 75-79, and 95-99 the numbers are obtained by subtraction from the next higher base—thus, for 55 they say ce-caa guiona or ce-caayo quiona, that is, 5 from 60. For 56-59, 76-79, and 95-99 they have two methods of counting—thus for 56 they say ce-caayo quiona-bi-tobi; that is, 5 from 922 NUMERAL SYSTEMS (ETH. ANN. 19 60-+-1, or ce-tapa quizahachaa-cayona, which is 4 from 60, ete. The Mazateca, Mixe, Zoque, and Trike appear to follow throughout the Nahuatl method of adding the minor numbers to the preceding base. The Othomian, Tarasean, and Totonacan systems are similar to the Huastecan—that is to say, are decimal-vigesimal—and form the higher numerals by adding the minor numbers to the preceding base. Extending our inquiry northward to the Sonoran and Shoshonean branches of the Nahuatlan family, we notice the gradual change to the decimal system. For example, in the Cahita count the quinary- vigesimal rule prevails; 6, 7, and 10 are based on 5; 8 on 4; 11 to 19 on 10, or, rather, twice five. From 20 upward the count is vigesimal, 10 when used retaining throughout its form of 2x5. The contact, however, in this region with the decimal system is clearly indicated by the following statement of the author of the Arte Lengua Cahita, given above: ‘‘Some nations say senutacaua or sesevchere for 20; others say for 10 sesavehere and follow up the count thus: 11, sesavahere aman senu,s 12, sesavehere aman uot, ete. For 20 they say wosavehere, which is two times 10. The Yaqui say for 5 sesavehere, and counting from 5 to 5 say uosavehere. LO [=2 x Dil vahivehere, 15 [=3 x 4)] These also say for 20 senu tacauda | LX 20] or nacquivehere [4x 5], and for 25 sesawehere (this particular count is of this nation only), and for 100 say mamnitacaua [5x20] or tacauvehere, which is 20 fives.” In the paragraph which follows he states in general terms that some of the tribes count by fives, others by tens, both using the same term, vedere, pretixing the ‘*numeral abverbs” sesa, ‘Sone time,” wosa, *‘two times,” ete. The ‘*nations” alluded to are probably the Cahita tribes, such as the Tehu- eco, Zuaque, Mayo, Yaqui, and other related or neighboring tribes. This change in the application of a given term in closely related dia- lects is not only interesting, but somewhat remarkable; and added to the fact that the closely related Tarahumari of the same section use the decimal system, indicates that the latter and the vigesimal system here came into contact. Do the data furnish evidence as to which was the spreading or aggressive and which the yielding one? Without entering into a discussion of the question the following facts are presented for the benefit of those desiring to look further into this subject. The similarity of the number names of the Cahita and Tarahumari to those of the Nahuatl is too apparent to pass unobserved even by the mere cursory glance. Include the allied Opata and take for example the numbers | to 5 and 10, as follow: ] 2) 3 1 5 10 ——— — { | ee | . F Opata se go-de | vei-de nago marizi makoi | : . * . : . | Cahita se-nu | uoi vahi, or bei | naequi) mamni uo-mamni 1. , : : | . farahumari | bire | oca bei-ca naguo|) marika makoe Nahuatl | ce ome yei navi macuilli matlactli THOMAS] DISCUSSION AND COMPARISONS 923 The resemblance between the names in each column, except b7re, 1 in Tarahumari (for which Charencey says he finds the alternate s/ncp7, which would be in harmony with the others), and womamnd (2X5), 10 in Cahita, is at once apparent. This, however, is merely in accordance with the recognized aftinity of the first three idioms with the Nahuatl. It seems, however, that we look in vain to the Nahuatl names for the vehere (vehe-re) as it can not be derived from macutlli (5), matlactli (10), or poall/ (20), nor from the names for 5, 10, or 20 in the Opata, Cahita, or Tarahumari. The name for 20 in Opata is w77 (se-wr7), which signifies ‘‘man;” in Cahita, ¢acawa,; in Tarahumari, osa-macor (2 x 10). In these languages the only number name which resembles it is that for 3, which is not a divisor. Turning to the Shoshonean group we notice the following facts. Whether they are sufficient to justify a decision on the point is very doubtful; this, however, is left for the reader to determine. The following list of the names for 2, 5, 10, and 20 is from Gatschet’s Forty Vocabularies.’ | 2 a | 10 20 Southern Paiute | vay | manigi | mashu | voyha-mashu | California Paiute | voa-hay | manegi | shuvan voaha-vanoy Chemehuevi vay | manuy mashu voyha-mashu | Takhtam vurm? ma-hatcham | yoa-hamatch | vyoayva-hamatch | Kauvuya vuy namu-kuanon) nami-tehumi | yuys-nami-tehumi Tobikhar ve-he mahar | vehes-mahar | hurura-yehe In these our term appears in exact and (supposed) modified form, but only as the name for 2 even in the composite forms. This is seen in the Tobikhar, as appears from the following list: Tobikhar pu-gu. 8 vehesh-vatcha=2 4. 2 ve-he. 9 mahar-kabya=5-+4. 3 pahi. 10 vehes-mahar=2%5 (2 hands?). 4 va-tcha. 11 puku-hurura=1-+-10. 5 mahar. 12. vehe-hurura=2--10. 6 pa-vahe=2X3?. 20 hurura-vehe=102. 7 vatcha-kabya=4-+3?. 30 hurura pahi=10%3. There is an apparent leaning toward the quinary system in one or two of the dialects, but this has little bearing on the question. When the count rises above 10 it seems that the term used to desig- nate this number is changed. The same thing is true in regard to numbers in several other idioms of this group. It is possible that we have in this fact an indication of change from an older and more 1 Wheeler Report, vol. vu. 924 NUMERAL SYSTEMS [ETH. ANN, 19 purely original method of counting to one more recent. It is, in fact, doubtful whether the lists more recently obtained from the natiyes give throughout the true original method of counting and the ante- Columbian names. There is nothing, however, in the number names of the Shoshonean dialects above 10 to indicate any system other than the decimal. It appears, therefore, from the data presented, that the vigesimal system prevailed in Mexico and Central America from southern Sonora to the southern boundary of Guatemala, and to some extent as far as the isthmus. There seem to have been but few, if any, tribes in this area as far south as the southern boundary of Guatemala that did not make use of this system; at least the data obtainable bear out this conclusion. North of the northern boundary of this area this system is found, according to Conant,’ ‘‘in the northern regions of North America, in western Canada, and in northwestern United States”; however, the only examples he gives are the systems of the **Alaskan Eskimos,” ‘‘Tchiglit,” ‘* Tlingit,” ‘‘ Nootka,” and “Tsimshian.” As a general rule the systems of the tribes of the western part of the United States, from the southern boundary to the Columbia river, were decimal or quinary-decimal; however, instances of the vigesimal system appear here and there in this area. As one example we call attention to the numerals of the Hachnon dialect of the Yukian family obtained by Mr Stephen Powers at Round Valley reservation, California, given in the preceding chapter. That a count referring the minor numbers to the next higher base, which is, as we have seen, confined in the southern regions almost exclusively to the dialects of the more southern sections, chiefly to those of the Mayan group, should be found in California is, to say the least, interesting; however, it is not the only example from this section, as willappear. It is somewhat singular that two other idioms of the same family, the vocabularies of which are given by Mr Powers, follow the decimal instead of the vigesimal system. Other examples of this system are found south of the Columbia river, as in the Pomo dialect (Round Valley reservation, California);* the Tuolumne dialect (Tuolumne river, California); * and the Achomawi dialect.” The first, third, and fourth of these the Konkau and Nishinam dialects. appear to refer the count to the following score, while in the last (Achomawi) it is applied to the preceding score. The Tuolumne sys- tem is somewhat doubtful, as there are but two numbers (20 and 100) on which to base a decision. According to Major Powell’s classifica- tion (7th Ann. Rept. Bur. Ethnology), the Pomo are included in the 1 Number Concept, p. 195 4 Powers, op. cil., p. 596. 2 Powers, Tribes of California, p. 502. STbid., p. 606. $Gibbs, op. cit., p. 548. THOMAS] DISCUSSION AND COMPARISONS 995 Kulanapan family; the Achomawi in the Palaihnihan family, and the Konkau and Nishinam in the Pujunan family. Without referring to other examples it may be stated in general terms that while the yigesimal system has not been found in-use east of the Rocky mountains, except in Greenland and among some tribes in the northwestern cis-montane portion of British Columbia, it pre- vailed to a considerable extent on the Pacific slope from Mexico north- ward to the Arctic ocean, and it may also be added that it is found among the eastern tribes of Siberia and was the method adopted by the Aino. Conant’ says that the Tschukschi and Aino systems are ‘‘among the best illustrations of counting by twenties that are to be found anywhere in the Old World.” These have been given in the preceding chapter for comparison. The count of the minor numbers in the Aino is based, as will be seen, on the following score, as in the Mayan group. Whether the equiva- lents added are correctly given is somewhat doubtful, as the proper interpretation of the name for 30 may be 10 on the second score; that for 50, 10 on the third score, etc., as we have indicated in parenthesis. In the Tschukschi the addition is to the preceding score—thus 30 is formed by adding 10 to 20. These and additional facts of the same character tend to show that in North America the vigesimal system of counting, like some other customs, was confined almost exclusively to that area which I have in a previous work” designated the ‘* Pacific section,” which includes the Pacific slope north of Mexico and all of Mexico and Central America. This fact and the additional fact that the system prevails in northeastern Asia, while it is rare in other parts of that grand division, except an area in the Caucasus region, and is wanting in the Atlantic slope of North America, are interesting and of considerable importance in the study of the ethnology of our continent. It would be interesting in this connection to inquire into the rang of this numeral system in South America, but we have not the data at hand necessary for this purpose. Conant says in general terms that it prevailed in the northern and western portions of the continent, thougk it is known that on the Pacific slope it did not extend south- ward farther than the borders of Peru, where the decimal system prevailed. It appears to have been in use among the Chibchas or Muyscas, a group extending both north and south of the Isthmus. It is or was in use among some of the tribes on the Orinoco, in eastern Brazil, and in Paraguay. However, the range of the system in South America is as yet unascertained.* 1Number Concept, p. 191. 2Twelfth Ann. Rep. Bur. Ethn., pp. 723-24. 3 Professor W J McGee suggests that it may possibly hold true in a general sense that the barefoot or sandal-wearing habit accompanied the use of this system of counting. 926 NUMERAL SYSTEMS (ETH. ANN. 19 Before proceeding I wish to quote some remarks by Conant in regard to the origin and spread of the vigesimal system, which I will then refer to.’ In its ordinary development the quinary system is almost sure to merge into either the decimal or the yigesimal system, and to form, with one or the other or both of these, a mixed system of counting. In Africa, Oceanica, and parts of North America, the union is almost always with the decimal scale; while in other parts of the world the quinary and the vigesimal systems have shown a decided affinity for each other. It is not to be understood that any geographical law of distribution has ever been observed which governs this, but merely that certain families of races have shown a preference for the one or the other method of counting. These families, disseminat- ing their characteristics through their various branches, have produced certain groups of races which exhibit a well-marked tendency, here toward the decimal and there toward the vigesimal form of numeration. As far as can be ascertained, the choice of the one or the other scale is determined by no external circumstances, but depends solely on the mental characteristics of the tribes themselves. Environment does not exert any appreciable influence either. Both decimal and yvigesimal numeration are found indifferently in warm and in cold countries; in fruitful and in barren lands; in maritime and in inland regions; and among highly civilized or deeply degraded peoples. Whether or not the principal number base of any tribe is to be 20 seems to depend entirely upon a single consideration; are the fingers alone used as an aid to counting, or are both fingers and toes used? If only the fingers are employed, the resulting scale must become decimal if sufficiently extended. If use is made of the toes in addition to the fingers, the outcome must inevitably be a vigesimal system. Subor- dinate to either one of these the quinary may and often does appear. It is never the principal base in any extended system. To the statement just made respecting the origin of vigesimal counting, exception may, of course, be taken. In the case of numeral scales like the Welsh, the Nahuatl, and many others where the exact meanings of the numerals can not be ascertained, no proof exists that the ancestors of these peoples ever used either finger or toe counting; and the sweeping statement that any vigesimal scale is the outgrowth of the use of these natural counters is not susceptible of proof. Butso many examples are met with in which the origin is clearly of this nature that no hesitation is felt in putting the above forward as a general explanation for the existence of this kind of counting. Any other origin is difficult to reconcile with observed facts, and still more difficult to reconcile with any rational theory of number system development. I note some facts, taken in part from the work quoted, in order that the reader may see the bearing they have on the opinions expressed in this quotation. According to the data furnished by this writer it seems that this system occurred in Europe only along the western sea- coast and that almost exclusively among the Celts, the only group of the Aryan stock which seems to have used it. In Asia it has been found toany extent only in the Caucasic group and in the northeastern part of of the continent, that is, in what Brinton terms the **Arctic Group” of his Siberic branch. Notasingle example is noted from the Sinitic group or from the Semitic branch. In Africa none have been reported from the Hamitic group, and but few from the negro dialects, but the latter field has been only superticially examined in this respect. Nota single 1 Number Concept, p. 176-8. THOMAS] DISCUSSION AND COMPARISONS 927 exuunple is noted from Polynesia or from any of the Malayan dialects. So far the data seem to agree with Conant’s conclusion, but more detailed examination presents at least some exceptions. We see the Nahuatlan family divided into two groups in this respect, the Aztecan and part of the Sonoran branches using the vigesi- mal system, while the Shoshonean and other divisions of the Sonoran branch follow the decimal method. Among the multiplicity of small linguistic families in California and Oregon examples of the vigesimal system occur sporadically, so far as is indicated by the still incomplete data, even occurring in one or two small tribes of a family while other tribes of the same family use the decimal system. But it is necessary to bear in mind that here, as in the Sboshonean group, the lists have been obtained after there has been long intercourse with the whites, which may have materially modified original systems. These facts are sufficient to show that ethnic lines do not always govern the range of the system. That there is a very general agreement among students in the opin- ion that as a general rule the adoption of the vigesimal system results from bringing the toes as well as the fingers into the count is admitted, yet it is possible that there are more exceptions to the rule than is supposed. That every vigesimal as well as decimal system has 5 at the base, or in other words, started with the hand, may be safely assumed, and that whenever 20 is expressly or impliedly understood as the equivalent of ‘one man” the toes are considered in the count may, perhaps, also be assumed. However, there are reasons for believing that in some instances the hands alone were used in actual count, being doubled to make the whole man; yet in such cases the toes were prob- ably originally used. It is possible and even probable that in some cases where the numeral terms have no reference to the toes or mana change from the original name has taken place. Such a change seems to be shown in the name for 20 in the Mayan dialects. In the Huasteca, Pokonchi, Pokomam, Cakchiquel, Quiche, Uspanteca, [xil, Aguacateca, and Mam the name for 20 is **man,” while in the Maya, Tzotzil, Chanabal, Chol, and Kekchi other terms are used, but even in these (except the Maya and Chol) awz/n7k, or **man,” is introduced into the terms for the mul- tiples of 20. Even in the Mexican (Aztec), which Conant looks upon us an exception, cempoalli (=one 20), which signifies ‘*1 counting,” evidently refers to something so well known and so generally under- stood as to require no explanatory term. What else could this, the thing counted, have been than one man—the fingers and_ toes? Although it must be admitted that there are some systems which can not be explained in this way, yet the explanation may be accepted as generally, in fact, almost universally, xpplicable. Even among the Greenland Eskimo, where we would suppose Protessor McGee’s sug- 928 NUMERAL SYSTEMS [ETH. ANN. 19 gestion, given in a note above, would fail, the toes were brought into the count, as shown by the following terms: 11 achqaneq-atauseq—first foot 1. 16 achfechsanea-atauseq—other foot 1. 20 inuk navdlucho—a man ended. Why tribes belonging to the same well-defined, limited linguistic group and living geographically in close relation—as, for example, in the Cahita group of northwestern Mexico and one or two of the Cali- fornia groups—should adopt different systems, some the vigesimal and others the decimal, we are unable to answer with our present information. Before answer can be made it will be necessary to elimi- nate what has been derived from contact with the whites. In concluding this topic it may be added that Conant appears to be fully justified by the data in infering that environment exerts no appreciable influence in determining the system. In the regions occupied by the Semitic, Hamitic, and Polynesian races, where we should most expect to find the vigesimal system, it is entirely unknown, while, on the contrary, it is found in the frozen regions of the north, where it would be least of all expected. As yet we are unable to assign any general influencing cause for its development. While the chief object of this paper is an examination and discus- sion of the numeral systems of the Mexican and Central American tribes with special reference to their relation to the Nahuatlan and Mayan systems, another object is to bring together the data which seem to have a bearing on the questions of the origin, development, and relations of these systems. In accordance, therefore, with this object, a comparison of the names used in counting (1 to 5, 10, and 20) in a number of dialects is herewith presented. It is true that nearly all of these can be found in the preceding lists. The object of reintro- ducing them here is to bring the corresponding names into close con- trast for convenience in comparison. They are brought together in the order of the groups, the Nahuatlan, which is the most extensive, coming first. The names in the Mayan series are so uniform that it is unnecessary to reintroduce them here. i. Nahuatl 2. Pipil 5. Alaguilae 1, Cahita es : SS _ aes | 1 | ce ce se | senu 2 | ome ume umi | uol 3 | yei yei | hei | vahi, or bei’ bey $ | naui navui nagul | naequi 5 | macuilli macuil makuil | mamni 10 matlaetli mahtlati matakti | uo-mamni 20 | cem-poalli cempual sempual | taeahua THOMAS COMPARISONS 929 | 5. Opata 6. Tarahumari 7. Tepehuan 8. Kern River 1 | se, or seni bire, or sinepi uma chich 2 | gode oea, or guoca gokado, or gaok | wah 3 | veide beica veicado pai nago naguo maukao na-nau 4 | marizi mariki chetam mahaichinga 10 | makoi makoe umhaichinga 20 | seuri bosamacoi zm (eae ; 9. Pima 10. Gaitchaim | TCanReer a? conten bel 1) humak 1 | so-pul 1 | shoui shui 2) houak 2 | vue 2 | wail vay 3 | vaik 3 | pahe 3 | pahi pay 4) kiik 4 | vosa 4 | wachoui vatchue 5 | huitas 5 | mahaar 5 | manek manigi 10 | wistima 7 | se-ula 10 | matshoui mashu 20 | ku’ko-wisti- 20 | wai-matsho- | yoyha-mashu ma ul 13. Chemehuevi 14. Capote Uta a rary ums 16. Comanche 1 | shooy soois simitich semmus 2 | vay Wwy-une hwat, or wat waha pay pi-une pite pahu 4 | vatchue watssu-une watsuet hagar-sowa? 5 | manuy manegin managet mawaka 10 | mashu towumsu-une shimmer shurmun 20 | yvoyha-mushu wah-massee wam-i-no 8 nahua-wachota =4X2 pace ealtornia TE 18. Kauyuya 19. Kechi (San Luis) | 20. Cahuillo 1 | shumuue sople suploh supli 2 | voahay vuy whii me-wi 3 | pahi pa paa me-pai 4 | voatsagve vuitehiu witcho me-wittsu 5 | manegi namu-kuanon nummu-quano nome-kadnun 10 | shuyan nami-tchumi nomat-sumi | 20 | voaha-vanoy vuys-namitchumi 19 ETH, Pr 2 24 930 NUMERAL SYSTEMS [ETH. ANN. 19 21. Takhtam 22. Tobikhar 23. Kij 24. Kechi (S. Diego) 1 | aukpeya pugu puku tehoumou 2 | vurm? vehe wehe echyou 3 | pahe pahi pahe micha 4 | yoatcham vateha watsa paski 5 | ma-hatcham mahar maharr tiyerva 10 | yoa-hamateh vehes-mahar touymili 20 | yoa-va-hamatech | hurura-vehe | 25, Hopi! 26. Millerton 27. Tejon Pass 28. Cora 1 sukia si-muh pau-kup ceaut 2 | luen wohattuh wah huapoa 3 payam pait pahai huaeica 4+ naleem watsukit watsa moacoa 5 | teivo malokit mahats amauri 10 pakte se-wanu we-mahat tamoamata 20 shuna-tu 29. Zapotec 30. Mixtec 31. Chuchon 31. Popoloca 1 | tobi, or chaga ec (ce?) ngu gou 2 | topa, or cato wui yuu yuu 3 | chona, or cayo | uni ni, or nyl nii 4 | tapa, or taa gmi, or kmi fuu noo 5 | caayo, or gayo hoho nau nag-hou 10 | chii usi te’ tie 20 | cal le kaa, 11 usi-ce j 32: Trike 33. Mazateca 34. Zoque 35. Mixe t= 1 | ngo gu tuma tuue 2 | nghui ho metza metsk 3 | guandnha ha tucay tukok 4 | kaha ni-ku macscuy maktash 5 | huhtha w masay, or mosay | mo’koshk { 10} chia te macay makh, or mahe 20 | hikoo, or kooha | ka yps, or ips ypx 1Furnished by Dr J. W. Fewkes. THOMAS] COMPARISONS 931 36. ees (Te- | 37. Othomi 38. Pirinda 39, Tarasco 1 | tuub n/nra, or ra yndahhuy ma 2 | mesko yoho ynahuy tziman 3 | tuo hiu | ynyuhu tanimu 4 | maktaxko gooho yneunohuy tamu 5 | mokoxko kuta, or qyta. yneuthaa yumu 10 | mako reta yndahatta temben 20 | ipxe n-rahte yndohonta macquatze 40. Totonaca 41. Sinacanta 42. Jutiapa 43. Cabecar = z tum | ica | ical estaba 2 | tuyun | ti piar bocteba 3 | tutu | uala guarar manhalegui 4 | tati hiria iriar quetovo 5 | kitsiz | puh puhar exquetegu 10 | kau, or cauh | pakil paquilar dope 20 ——— ynste | 44. Viceyta 45. Lean y mulia 46. Terrava 47. Mosquito 1 | etabageme pani krara kumi 2 | butteba matiaa krowtt wal 3 | manac contias krommia niupa 4 | quiet chiquitia krobking walwal 5 | exquetegu cumasopni kraschkingde matasip 10 | dop comassopnas dwowdeh matawalsip 20 | ynste comascoapssub zac-vbu Although the first twenty-eight lists in this series, which are from idioms of the Nahuatlan stock, might possibly be arranged in a more systematic order as to terms, yet a careful study will suffice to detect the links by which they appear to be connected, thus agreeing with the conclusion of the linguists in regard to the relationship of the different groups of this great family. The terms for 2 and 3 appear to be the most persistent, especially the latter term, which shows but slight variation, except in the Kechi (San Diego) and Cora dialects. While the differences between the names in this family and the others represented in the series is too clearly marked to be overlooked, corre- sponding in this respect with the decision of the linguists in regard to 932 NUMERAL SYSTEMS (ETH. ANN.19 the family distinctions, we notice here and there slight indications of the influence of intercourse. Numbers 44 to 48, which pertain to the extreme southern dialects, are added merely for the purpose of comparison. The first four (44 to 47), are classed with the Chibcha stock, among which the vigesimal system prevailed. In the tribes from the Mexican boundary northward, with the excep- tion of those pertaining to the Nahuatlan group, most of which have been noticed, we find nothing in the numerals, so far as the data at hand show, to indicate any relationship other than that in accordance with the linguistic classification proposed by Major J.W. Powell. An appar- ent approach to the names in some of the Shoshonean dialects can be noticed in the Konkau, Nishinam, and Nakum dialects heretofore given. The count in two of these idioms is, as has been already mentioned, in part, at least, vigesimal. Compare the Nakum list with that of Shoshone (number 5). These tribes are included in Major Powell’s classification in his Pujunan family. The determination whether such resemblances are real or only apparent must be left to the linguists; I haye included them merely as material for comparison. Before closing this chapter attention is called to one point which, so far as I am aware, has not been discussed, but in regard to which I must acknowledge inability to offer an entirely satisfactory expla- nation. As hes been shown in my paper on the calendar systems, and by the evidence presented by Dr Férstemann and Mr Goodman, the Mayan priests, or at least the authors of the Dresden codex and the Mayan inscriptions, did actually perform computations reaching into the mil- lions, where the primary unit had necessarily to be retained, that is, could not be lost in higher units considered as measures. To illustrate: Take the following time count actually found in one of the Central American inscriptions: 8 cycles+14 katuns+3 ahaus-+-1 month+12 days, to the day 1 Eb, the 5th day of the month Zac. As 1 cycle equals 20 katuns, 1 katun equals 20 ahaus, 1 ahau equals 18 months, and 1 month equals 20 days, we can find by calculation that 1 cycle=144,000 days, 1 katun=7,200 days, and 1 ahau=360 days, and that the 8 cycles, 14 katuns, 3 ahaus, 1 month, and 12 days added together equal 1,253,912 days. The reader is familiar with the methods necessary to make this and all such computations. How did the Maya scribe or priest accom- plish it? As a particular day was to be reached and there were num- bers in each order of units, and the total had to be transferred into years of 365 days each, and the surplus months and days ascertained, it is apparent that it was necessary to reduce the whole to primary units— that is, to days—and then ascertain by division or in some other way, how many even years were contained therein, and how many months and days would be contained in the overplus. THOMAS] METHOD OF COMPUTATION 933 That they had time tables by which they could compute intervals of moderate length, as the day series in the Codex Cortesianus, which could be used as the Mexican Tonalamatl, is well known; we can use them to-day for that purpose. It would seem also from the four plates in the Dresden codex, and four in the Troano codex, showing the four year series, that they also had tables by which to count year intervals, but there are no indications of tables to aid in the reduction of the higher orders of units—cycles, katuns, etc. In the Mexican manuscripts, as will be seen in the following chapter, the number of tzontli (400 each) and aiguipillé (8,000 each)—the highest counts dis- covered therein—were indicated simply by repeating the symbols, but the Maya had reached the art of numbering their symbols. Now, it is apparent that the latter must have had some method of computa- tion where such high numbers as those indicated were involved. This was necessary even to ascertain the number of days in a cycle or katur, and when several of these and of each of the lower units were to be reduced to primary units, or days, and these to be changed into years, months, and days, and the commencing and ending dates determined, the count would seem to transcend the power of simple mental compu- tation. How then was this accomplished? It would seem, therefore, that they must have had some way of making these lengthy calcula- tions other than counting ‘‘in the head;” but what it was we have no means of determining. There would seem to be no doubt that they had a way of *‘cipher- ing”—to use a schoolboy term—and this appears to be confirmed by Landa, who, speaking of their method of counting, says: Que su cuenta es de vy en v, hasta xx, y de xx en xx, hasta c, y de c en c hasta 400, y de cece en ccce hasta yiir mil. Y desta cuenta se servian mucho para la con- tratacion de cacao. Tienen otras cuentas muy largas, y que las protienden in infinitum, contandolas yt mil xx yezes que son c y Lx mil, y tornando a xx duplican estas ciento y Lx mil, y despues yrlo assi xx duplicando hasta que hazen un incontable numero: cuentan en el suelo o cosa Ilana. ‘ The last phrase, ‘‘cuentan en el suelo o cosa Ilana,” indicates the manner in which they made their calculations, to wit, on the ground or on some flat or smooth thing. Brassuer translates the sentence thus: ‘*Leurs comptes se font sur le sol, ou une chose plane.” This certainly indicates ‘‘figuring” or performing calculations by marking on a smooth surface. Although multiplication and division seem impos- sible with their symbols, it is possible, as Professor McGee suggests to me, that they reached the desired result by repeated additions and subtractions. These operations may be readily performed with the ordinary number symbols (dots and short lines), the orders of units being indicated by position, as in the Dresden codex. The chief dif- ficulty would be to change the sum of units into years. This, when the number was large, must have been accomplished by means of what Goodman calls the ‘‘calendar round” or 52-year period, for which 934 NUMERAL SYSTEMS [FTH. ANN. 19 they had a specific symbol, though not of the ordinary form, The sum (18,980) could be expressed thus: - - =14,400 ——= 4,320 suche) — 260 S= 0 18, 980 By using this form and subtracting until the given sum should be reduced below 18,980 the number of subtractions would indicate the number of 52-year periods. The years could be obtained in the same way by repeated subtractions from the overplus with the ordinary symbols, thus: 7) 360 Q= —_ >= oO 365 Whether this was the method followed I can not say, but it is cer- tain that the desired result could be obtained in this way. Nevyerthe- less, this method of changing high series, reaching into millions of years, must have been very tedious, unless there was some way of shortening the process. I may, however, have more to say on this subject in a subsequent paper, in which I propose to discuss the Quirigua inscriptions. NUMBERS IN THE MEXICAN CODICES The data relating to the use of numbers in the Mexican codices, so far as we are as yet able to interpret the symbols, are meager com- pared with those relating tonumbers in the Mayan codices and inscrip- tions. We lack also in this investigation the means of demonstration in regard to the higher numbers, being limited in this respect to the statements of historians and the interpreters of the Mendoza and Vatican codices. However before proceeding with the examination of the codices, it is necessary to refer briefly to certain facts in regard to the Mexican time system. This system is, as is well known and as I have shown in a previous paper,’ like that of the Maya, except in the names of the days and months and in the symbols used to represent them. As there will be occasion to refer to these in discussing the numbers in the Mexican codices they are for the convenience of the reader given here. A condensed calendar like that used in discussing Mayan dates in our previous paper is also given. 1 Notes on certain Mayan and Mexican Manuscripts, in Third Ann. Rep. Bur. Eth. THOMAS] NUMBERS IN THE MEXICAN CODICES 935 The days as represented in the codices when placed in regular succes- sion are as shown in table 1. TABLE | 1 Cipactli. 11 Ozomatli. 2 Ehecatl). 12 Malinalli. 3 Calli. 13 Acatl. 4 Cuetzpallin. 14 Ocelotl. 5 Coatl. 15 Quauhtli. 6 Miquiztli. 16 Cozcaquauhtli. 7 Mazatl. 17 Olin. 8 Tochtli. 18 Tecpatl. 9 Atl. 19 Quiahiutl. 10 Itzecuintli. 20 Xochitl. In attempting to form a condensed calendar for the Mexican system difficulties are met with which do not arise in forming one for the Mayan system. There can be no question that the year-bearers or dominical days were Tochtli, the rabbit; Acatl, the reed; Tecpatl, the flint or flint knife, and Calli, the house; but were these the first days of the years? Gemelli Carreri' says that the year Tochtli began with the day Cipactli, Acatl with Miquiztli, Tecpatl with Ozomatli, and Calli with Cozeaquauhtli, in which he is supported by Clavigero,? while Boturini and Veytia declare that they began with the dominical days. As the latter method appears to be the natural one, and is that adopted by Miss Nuttall* after a somewhat careful examination of the subject, I shall follow it. My condensed calendar will therefore be as shown in table 2. 1Churchill’s Voyages, vol. Iv, p. 492. * Hist. Mexico, Cullen’s Transl., yol. 1, p. 292. 3 Notes on the Ancient Mexican Calendar System, p. 5. TH. ANN. 19 E [ N SMSTEMS NUMERAL ZL tH 169 oD nN (AEM (GE rgovdip GMOX Bmyene pedoay, UNO, Tyynenbeozoy THEN?) HO[P9O, peoy T[BUr BIA T]}BUL0ZO, TyumMoz}y DV THQOL eze Tazmbipy pe) ulpedzjanp TRO. sivas 18D unto TaYynenheazo—p Ty qneney 0290 Roy T[BULTRI 1p}VUIOzZ_) YQuimoz}] VY ToL Bze TZzmbIAL EL tere) urpedzjong ize) [eooygy qqoediy pIUpox mye?) pedoay, sivok [yrdoay, T[BALLS TAL T]VRULOzZEO, tury DY THY9OL eze razmbiyy peo) urpedzjany THRO [}B090 OL tondry yupox rayeme) Qedoay, unlO, Taynenbeozoy Tynenty BOlP220 eoy sivas [ROY eLLZAD AV 1yZta bi Leo urypedzjany THRO [Roayyy toedyy HIqo0X myer?) pedoay, UunlO, TBYynenbwoz09 Tynenty GO12290 Roy T[BULLBIA TyBUI0zZE—, 1yUMoz}] GY TQQooyp sino TOOT, 936 Z WIV y, THOMAS] NUMBERS IN THE MEXICAN CODICES 937 The symbols of the days are shown in figure 23, which is a photo-en- graved copy from plates 51-52 of the Vatican codex B. The names in English of those in the four col- umns 8-11 as they stand in the fig- ure are as follow: Column 8 Column 9/ Column 10) Column 11 Water Dog Monkey) Grass Movement) Flint Rain Flower Snake Death | Deer Rabbit Cane Tiger | Eagle Vulture Dragon Wind | House Lizard The symbol for water is oftener in the form shown in figure 24, and that for house in the form shown in figure 25. As the numerous plates of the codices to which reference will be made can not be copied here, these will enable the reader who is not already familiar with the sub- ject, but who has the codices (at least as given in Kingsborough) before him, to follow my references. As the names of the Mexican months will not be used in this paper, it is not necessary to give them here. We shall have occasion to note par- ticularly the direction in which the plates of the codices referred to are to be read, as the determination of this is the most important result obtained by an examination of the numerals, especially in cases where the order of the days fails us in this respect. As a rule which has few if any exceptions, numbers which refer to time counts in the Mexican codices are expressed by dots, or sometimes small circles, usually colored, and “‘sABPUBOIXAI OY JO SpoquiAg—¢Ez “Oly abit ~ IL £1 938 NUMERAL SYSTEMS (ETH. ANN. 19 never running higher, so far as has yet been determined, than 26. Their use is seen on plates 17-56 of the Vatican Codex number 3738 eB i Color scheme used in figures 24-40, 1, yellow and white; 2, brown; 3, drab; 4, green; 5, blue; 6, red. and in other similar counts. Here they are used to number the days in regular succession, beginning with 1 Cipactli, 2 Ehecatl, 3 Calli, etc., counting to 13, and then commencing again with 1, etc., as was the rule in the Mayan day-count. As the series on the pages referred to (the order being from left to right) runs through two hundred and sixty days, or twenty thirteens, the Mexican Fic. 24—Symbol for method of numbering days is clearly and distinetly pat shown. In this series two plates are allowed to each thirteen days, five days on the first (plate 17) and eight on the second (plate 18), five on the third, eight on the fourth, etc. Why this division into 5 and 8, when 6 and 7 is the usual method, is not apparent unless it was best adapted to the size of the original page, or was to introduce the 5. It is possible the latter explanation is the correct one, as Fie. 5—Sym- the eight days are arranged in a line of 5 and column of teas 8. and the numerals above 5 are, with but two or three apparently accidental exceptions, arranged with reference to 5, thus: C} Too oO 0 OP rier “e! cell ote t levieire) felve Vives, ws 'ej)s ete os se LT eine de: © con Pepramie oho mae CCM OPO Or aa IVER Aro Oeoe SOLO OC OOo CG) OPO Oo OND 0 G44 [Sib total Copel (etfe\Jaweniey tenella This arrangement, which would seem to be merely for convenience in counting rather than for any mystic purpose, is not found in the Borgian or Bodleian codices, which are undoubtedly pre-Columbian, while the Vatican (3738) is, in part at least, post-Columbian. The numerals are, as is general in the codices, of different Rallis Fic. 20— colors; for example, 1, the first of the series oe Symbol pa eee CLOELECMLOS is green, the next (2) is yellow, the quintli next (8) blue, the next (4) red, the fifth green, Fie. 27 — (aR) the sixth, seventh, and eighth red, the ninth pik apes § #5 vellow. the tenth red, the eleventh blue, the twelfth red, (tiger): the thirteenth green, ete. The color no doubt had a sig- nification understood at least by the priests, but which there is, so far as is known, no way of determining at this day. In the same codex, on plates 91, 92, and 93 and those which follow, THOMAS] NUMBERS IN THE MEXICAN CODICES 939 we see the years indicated by the symbols for Tochtli, Acatl, Teepatl, and Calli, and numbered in regular succession. Here, as in case of the days, the numbering is from 1 to 13, this order being repeated throughout. There is in this series one continuous stretch of 208 (=4 52) years without a single break in the order of the years or of the numbers. We have in this fact proof not only that the years were numbered as in the Mayan calendar, and were of the same length, the 365 being completed by the addition of five days at the end, as was stated by the early writers (for only in this way can this succession be accounted for), but also presumptive evidence, although not positive proof, that there was no provision for bissextile years, unless it was made by counting unnumbered and unnamed days. As the years are numbered from the day numbers as they come in regular succession, there could be no additional numbered and named days without mak- ing a jog in the numbering of the years. The assumption that there were added days which were neither named nor numbered is a mere supposition based on the seeming need of them; there appears to be no proof of it in the codices. On plates 59-62 of the Mendoza codex we find numerals used to state the different ages of youth from 3 to 15. These are given by the little circles already described, all of them in this instance being blue. From 3 to 6 they are placed in single straight lines. The other numbers are given thus: WY oo 660 5000 IW 5G ooo 9 O; .ehre, ie UW S66 O06 Wee Goo ob Mm SG eo60 UW) so boo While there are indications of the tendency to count by fives, it seems a little strange that the arrangement of the dots in 7 and 8 should have varied from this rule. Attention is called to these seem- ingly unimportant points in view of what has been said in the preced- ing part of this paper in reference to the Mexican method of counting as indicated by the names of their numerals. In the lists of years on the first seven plates of this codex the numbers above 5 are arranged in almost every instance by fives or with regard to 5. However, it is necessary to bear in mind that most, if not all, of this codex is 940 NUMERAL SYSTEMS [erH. ANN. 19 post-Columbian, an explanation of it haying been made by native priests and turned into Spanish for the use of the Emperor Charles V. It must be admitted, however, that very slight, if any, indications of European contact are to be found in it. Turning now to the Fejervary codex, to plates 22, 21, 20, etc., to 13 (taking them backward as paged), we find the method of counting from day to day, and thereby the order in which the days are to be taken. As the colored figures can not be introduced here, Arabic numbers are substituted for the dots or little circles, and the day names, for the symbols. The relation one to another in which they stand on the plates is maintained. The pages are given in the order of the num- bering, but are to be read in the opposite direction, beginning with 22. PLATE 13 Upper line: Xochitl, Quiahuitl, 3 Ocelotl. Tecpatl. Lower line: 23 Tochtli. 13 Ocelotl. Puate 14 Upper line: 3 Itzquintli. 3 Miquiztli. Lower line: 12 Cipactli. 9 Ozomatli. PuatTeE 15 Upper line: 2 Calli. 1 Cipaetli. Lower line: 10 Xochitl. 7 Malinalli. PLATE 16 Upper line: 3 Ollin. 3 Acatl. Lower line: th XQ) 10 (?) PLATE 17 Upper line: 3 Atl. 3 Coatl. 3 Cipaetli. Lower line: Sui (is) 9 (?) PuatTe 18 Upper line: 3 Ollin. 3 Acatl. 3 Atl. Lower line: 6 (?) 5 (?) PLATE 19 Upper line: 3 Coatl. 3 Cipactli. 3 Ollin. Lower line: 6 Atl, Coatl, Ollin, Acatl, Cipactli. PLATE 20 Upper line: 3 Acatl. 3 Atl. 3 Coatl. Lower line: (?) 7 Acati. PLATE 21 Upper line: 3 Cipactli. 3 Ollin. 3 Acatl. Lower line: 4 Tochtli. 2 Coatl 4 Xochitl. 2 Ollin. THOMAS] NUMBERS IN THE MEXICAN CODICES 941 PLATE 22 Upper line: 3 , Atl. 3 Coatl. 3 Cipactli. Lower line: 4 Malinalli. 2 Atl. 4 Cuetzpallin. 2 Cipactli. In counting in this case the numbers are to be understood as indi- cating the intervening days, and do not include either the day counted from or the day reached. The ‘‘lower lines” are throughout inde- pendent and not connected with the ‘‘upper lines.” Commencing with Cipactli at the right of the lower line of plate. 22, and referring to table 1 for the list of the days, we see that counting forward—that is, passing over—two days we reach Cuetzpallin; passing over four more we come to Atl; passing over two more brings us to Malinalli, and four more to Ollin, which is found at the right of the lower line of plate 21; and so we reach Acatl, the right of the lower line of plate 20. Counting 7 from the last brings us to Cipactli. As the count here ends with Xochitl, the last of the twenty days, this series may end here, or may pass to Cipactli. However, as there are no day sym- bols to guide us until we get back to plate 15, where we find 7 Mali- nalli at the right, we begin again with this day. Passing over seven days from Malinalli we reach Xochitl; passing over ten more we reach Ozomatli, at the right of the lower line of plate 14. Passing over nine more we come to Cipactli; twelve more bring us to Ocelotl, at the right of the lower line of plate 13; thirteen more to Tochtli; twenty-three more would bring us to Malinalli, but the day is not found, as the series appears to end here. Possibly we go back, as is a common rule in the Troano codex, to the first date; if so, Malinalli, on plate 15, begins a second series. This is prob- ably the true method, as adding together the counters and the days represented by symbols gives eighty, just four twenties. It is prob- able that the same rule applies to the first series, beginning with Cipactli (plate 22) and ending with 7 Acatl (plate 20), as the counters and days added together make forty, or two twenties. Taking now the upper line, beginning with 3 Cipactli at the right (plate 22), we pass over three days, which brings us to Coatl, three more to Atl, and so on by threes to Ollin at the left of plate 16; three days more bring us to Cipactli, but whether to the beginning or to 1 Cipactli at the right of the upper line of plate 15 is a question. How- ever, as the number of days counted up to this point is 80, or four twenties, and a new series begins in the lower line with Malinalli at the right of plate 15, it is most likely a new series begins here with Cipactli in the upper line. This supposition appears to be confirmed by the fact that to Xochitl at the left of the upper line of plate 13 1s just twenty days. No attempt will be made at this point to explain the figures con- nected with these day and numeral series, the only object in view at present being to illustrate the use of the numerals and thereby to show 949 NUMERAL SYSTEMS [ETH. ANN. 19 the direction in which the plates are to be read. It is clear that in this vase they are to be read from right to left; that is,in a reverse order to the paging. We turn next to plates 11 and 12 of the same codex. Here, as in the preceding illustrations, the series of counters and days are placed in two lines, an upper anda lower; however, the numbers in the lower, apparently because of the want of space, are not placed in connection with the day symbols, but by the side of the larger figures. In each section of the lower line are five day symbols; for convenience I have placed the names in columns, the top one corresponding with the symbol at the left in the plate. PuaTeE 11 Upper line: 4 Malinalli. 4 Mazatl. Tochthi. Quauhtli. | cozeagonunth er Lower line: 12) Cuetzpallin. 12; Ozomatli. |satna |guiahin, Xochitl. Mazatl. PLATE 12 Upper line: 4 Ehecatl. 4 Ollin. Ehecatl. Atl. cena [one Lower line: 12) Tecpatl. 12) Coatl. [Mia [eat Ocelotl. Cipactli. Commencing with Cipactli at the right of the lower line of plate 12, we go backward (upward as given in the list above) to Atl, then to Ocelotl and pack (up) to Ehecatl, thence to Mazatl, right of lower line, plate 11, and so on to Tochtli. We begin the upper line with 4 Ollin, at the right of plate 12. Passing over four days we reach Ehecatl; four days more bring us to Mazatl, upper line, plate 11; four more to Mal- inalli, and four more back to Ollin, thus covering twenty days. The Ollin symbol of this series (plate 12) is immediately under the blue sit- ting figure; Mazatl, or Deer (plate 9, upper line) is represented by the foot or lower portion of the leg of a deer. This proves that the read- ing is from right to left and from the bottom upward as in the preced- ing plates. It also enables us to determine positively the unusual Mazatl symbol. The days in the lower line are arranged five to a section, after the manner explained in a previous paper.’ Commencing with Cipactli, at the right (bottom in our list) of plate 12, we count or pass over twelve days and reach Ocelotl, the day at the right (bottom) of the le ent series of the same plate; twelve more bring us to Mazatl, right 1Notes on Certain Maya and Mexican Manuscripts, in the Third Annual Report of the Bureau of Ethnology. THOMAS] NUMBERS IN THE MEXICAN CODICES 943 of plate 11; and twelve more to Xochitl, right of the left series, same plate; counting twelve more brings us to Acatl. As this makes no connection, let us try another method: Counting from Atl, the left (upper) name of the right series of plate 12, we reach Ehecatl, left (upper) name of the left series,same plate; twelve more to Quauhtli, left (upper) name of the right series of plate 11; twelve more to Tochtli, left (upper) name of the left series, same plate; and twelve more to Cipacth, the beginning. This proves that the reading is to the left and upward, and that from a day in one section to the corre- sponding day in the next section an interval of twelve days is to be reckoned. The arrangement on plates 5 to 10 (inclusive) is the same, except that the days in the upper line follow one another in regular order without any interval and that the counters belonging to the lower line vary. The movement here is backward,as before. By this series, counting as indicated, we are enabled to determine that the unusual symbol (figure +) on plate 6 is that of the day Itzcuintli, and the symbol (figure 5), same plate, is that for the day Ocelotl. Plate 5 appears to be connected backward with plates +, 3, and 2 by the lower series, column to the right. The counter in the lower half of plate 5 is 9, and the lowest day of the column at the right is Cipactli. Counting nine inter- mediate days from this brings us to Ozomatli, the first or lowest day of the column in the lower half of plate 4; the counter here is 3, and passing over this number of days brings us to Quauhtli, lowest day of plate 3; here the counter is 16, which carries us to Malinalli, lowest day in plate 2, and eight days more to Cipactli, the commencement. This lower series of plates 10 to 2 (inclusive) if to be considered as one, embraces one hundred and four days, not an even twenty, but exactly eight thirteens. The upper series of plates 4 and 3 has five days to each section arranged in the same manner as the column in the lower half. The counters here are small black dots, 12 to each section. Counting this number from Cipactli, the day at the right of the right-hand section of plate 4, brings us to Ocelotl, right of left section; twelve more to Mazatl, ete. The dots or little circles used as counters in this codex are, with the exception just named, colored blue, red, green, and yellow, those of different colors being found in almost every number. There is no tendency shown to arrange by fives, though plates 23 to 40 (inclusive) are largely filled with number symbols, short black lines (fives) and dots, as in the Mayan writings. So far I have been unable to determine the use of these numbers in the connection they are found. Vatican codex— Plates 81 to 90 of this codex (Kingsborough, vol. 1m) are, as is shown by the numbers and day symbols, to be read as follow: The upper line, containing day symbols each followed by the counter 3, 944 NUMERAL SYSTEMS [ETH. ANN. 19 in regular succession from left to right throughout; the lower, where the numbers are unaccompanied by day symbols, from right to left, beginning on plate 90 with the number 2, to plate 81, where the number is 26. The upper line issimple and easily followed, and, counting the days, embraces four twenties. To what the numbers in the lower line—which follow in regular succession, 2, 3, 4, etc.—refer is as yet unknown, though it seems they have some relation to 13; and why they begin with 2 is also without satisfactory explanation. Plates 91 to 96 are to be taken from left to right, according to the paging. The counters in the middle express the intervals between the left-hand day of the lower line of one plate and the left-hand day of the lower line of the next plate, etc. The same is true also of plates 72 to 75. Borgian codec—As the only object in view at present is to illus- trate the use of numbers in the Mexican codices, and not to introduce attempted explanations of the figures, I give a few illustrations from the Borgian codex, which is probably the oldest of the existing Na- huatl manuscripts. Neither in this nor in the two last codices to which I have referred does there appear to be any indication of a tendency to arrange the counters in groups of 5. Where it is practi- ‘able—that is, where the number is not too great—they are placed in a single straight row, but the arrangement is governed by the space. We turn to plates 18 to 21. Here the pages are arranged in two divisions, an upper and lower, each having a row of day symbols run- ning along its lower edge; in the upper division the large red counters are placed in a column at the right of each page, and in the lower at the left. With two exceptions (upper divisions of plates 20 and 21) there are six counters in each column; in the exceptions there are 4 in acolumn. Starting with Cipactli, right of lower division plate 21, passing over six days we reach Tochtli, at the right of the lower divi- sion of plate 20, and so on to Ehecatl, at the right of the lower division of plate 18. Counting six more takes us to Atl, at the left of the upper division of plate 18; six more to Cozcaquauhtli, left of the upper divi- sion, plate 19; six more to Calli, plate 20, and four more to Tochtli, left of the upper division of plate 21. Counting four days from Coz- caquaubtli to the last day of the upper division of this plate brings us back to Cipactli, the beginning, the sum of the days being 52, or 4X13. The 12 large red counters in the upper division of plate 17 express the number of intervening days between a day of the right section and a corresponding day of the left section, the counting being always for- ward in the calendar. The red counters on plate 58 indicate the interval between the corresponding days of the different sections in the order in which they follow one another. Commencing with the right section THOMAS] NUMBERS IN THE MEXICAN CODICES 945 of the lowest division, the movement is to the left up to the middle division, then to the right up to the upper division, and then to the left. The 12 large red counters of plate 59 denote the interval between the days of the two columns, commencing with Cipactli in the lower right-hand cor- ner, and passing to the lower day in the left column, to the second (next to the lower) in the right column, to the second in the left, and so on throughout. The 12 red counters (plates 63 to 65) denote the intervals between the corresponding days in the lower line of the pages in the order in which they follow one another; that is, from right to left, beginning with plate 65. But in this instance the count 4, 28—Symbol for 400. includes the beginning or ending day. Mendoza codex, plate 20, a Oe : ; : figure 16. This will suffice to illustrate the use of the jeunes counters in the Mexican codices in connection with days, so far as it has been ascertained. NR mo The higher numbers are rep- SN y N i resented in the Mexican codices AN Z SUZ bya different class of symbols BQe Z BZ from those which have been SX rd noticed, but for the explanation KK YI li Wy of these we have to rely wholly YAY LX : ae = SZ ZieN Z upon the interpretations made NAN Z = by early Spanish authorities WA — and based upon the statements Fic. 29—Symbol for 4,000. Mendoza codex, plate 28, figure 24. of native priests. The first to which reference will be made are found in the Mendoza codex, in Kingsborough, vol. 1, the original Spanish explanations being given in volume 5 of the same work. As the different symbols for these higher numbers are not numerous, it will only be necessary to present a sufficient number of examples to illustrate the forms of the symbols and their use. Mendoza codex—Plate 20, figure 16, shown in our figure 28, is interpreted 400 loads of great mantles, the number symbol being the fringed spike or leaf on top. Fig. 30—Sym- Plate 28, figure 24, shown in our figure 29, is inter- a none preted 4,000. This is correct, counting each spike as 400, Mendoza co- Plate 38, figure 21 (our figure 30), is interpreted 20 jars aoa a of honey. Plate 39, figure 20 (our figure 31), is interpreted 100 (that is, 5 20) hatchets of copper. 19 ETH, PT 2 25 946 NUMERAL SYSTEMS [ETH. ANN. 19 Plate 19, figure 2 (our figure 32), is interpreted 20 baskets of ground cacao (‘‘cestos de cacao molido”); but it is evident that the number indicated by the symbols is 204004 or 32,000. The reference therefore is to the grains or beans, each basket con- taining, or supposed to contain, 4400 or 1,600 y/; i grains or beans. y V7 Plate 19, figures 10, 11, Li NZ Fic. 31—Symbol for100hatch- 12, 13 is our figure 33: REPS ORCA, 7 of in the interpretation as flowers or as flower ‘ like, denote 80 days, each circle indicating 20 days. ‘i Plate 25, figure 11 (our figure 34) is inter- 5, c=) ets. Mendoza codex, plate These four vari-colored 39, figure 20. : 3 ; circles, which are spoken 32—Symbol for 20 preted 8,000 sheets of paper of the country _ baskets. Mendoza codex, z is 99) . late 19, fig. 2. (‘‘pliegos de papal de tierra”). The reticulee PP" ™" shaped figure is the number symbol; this is evident from the next example. O S) A dx Aan IS » CTs Fic. 33—Symbols for 20 days. Mendoza codex, plate 19, figures 10, 11, 12, 18. Plate 38, figure 35 (our figure 35) is interpreted 8,000 pellets of copal for refining, wrapped in palm leaves. Plate +4, figure 34 (our figure 36) is interpreted 200 cacaxtles (**sorte de crochet en bois pour porter des fardeaux,” Siméon); I would explain it as a hand barrow! It is doubtful whether there is any numer- ical symbol here. Codex Telleriano-Remensis plate 25 (Kingsborough, vol. 1; explanation, vol. v). The figure in the lower left-hand 8,000 sheets paper, DPOrtion of this plate repre- Mendoza codex, sents a mass of people over- plate 25, figure 11. Fic. 34—Symbol for Fic. 35—Symbol for 8,000 pel- whelmed by a flood; the ex- lets copal. Mendoza codex, plate 38, fignre 35 planation says in consequence of an earth- quake. The number symbol is reproduced in our figure 37. It THOMAS] NUMBERS IN THE MEXICAN CODICES 947 ; A 400, 400 : naga ata denotes 1800, that is 4x 40( +—5-. The -5— or 200 is indicated by the half leaf or spike at the right. Vatican codex, number 3738 (Kingsborough, vol. 11; explanation, vol. v)—On plate 7, figures 2 and 3, are the symbols shown in our figure 38, interpreted 4008 and sup- posed to refer to the years of the second age of the world. Each one of the crossed and fringed circles (blue in the original) represents 400 and is an equiva- lent and perhaps a mere variation of the fringed spike-like leaf. The 8 is represented by the upper engeome rc cae OU of smaller circles (also blue). ireise—symoll for 900 1800. Codex Teller. ¥Ve add one more of this type cacaxtles. Mendoza iano-Remensis, plate from plate 10 (see our figure 39). DEO rae a This is interpreted 5042; this, however, is a mistake; the correct number according to the sym- bol is 5206=13x400+6. Attention is called to this mistake in a note to the English translation of the explanationin Kingsborough, vol. vi, but the correct number is not stated. We find on plate 123 the combi- Oo0Cce 00 Be nation shown in our figure 40. Although no interpretation of this page is given, the symbols clearly yj Fic. 88—Symbol for 4,008. Vatican codex 3738, plate 7, figures 2, 3. signify 28,000+9x400 or 19,600. To what the numbers refer is uncertain, but probably to warriors. These are all the types of numeral symbols, except the combined short lines and dots found in the codices, which are known as such and have been determined, and are all that Clavigero gives. There are reasons for believing that there are some others, but there are no means known by which to determine the point. Although the value of the various groups of short (black) lines and dots can easily be Fic. 39—Symbol for 5,206. Vatican codex 3738, plate 10. 948 NUMERAL SYSTEMS [ETH. ANN. 19 determined, their application and use in the connections in which they are found has not been ascertained. It is apparent from the data presented that the Aztec or Mexican Fic. 40—Symbol for 19,600. Vatican codex 3738, plate 123. tribes by whom the codices were made were not so well advanced in mathematics and time count, or in the symbolic designation of num- bers, as the Mayan tribes. THE MYSTIC AND CEREMONIAL USE OF NUMBERS In taking up this branch of the subject we enter upon a field where the evidence must be drawn very largely from the early (chiefly Span- ish) authorities; their testimony is, however, corroborated to some extent by the codices and inscriptions. As there is no intention of entering at this time upon a general discussion of the subject of the mystic and ceremonial use of numbers among the Mexican and Central American tribes, but simply of presenting the data so far as they may seem to have relation to the subject treated in this paper, this part will be brief. As 2 is a number connected in some way with almost every action of life, and necessarily referred to in almost every ceremonial and mystie rite, it is difficult to determine where it is specially referred to because of its numeral value. I therefore omit it from considera- tion in this respect. Three is a number so seldom brought anto use in the customs of the natives of the regions mentioned that it may be passed over. Reference to the number + in myths and ceremonials as well as in other relations by savage tribes, as also by peoples of more advanced ‘ture, is so general and so well known that it requires no proof here. This, as is well understood, arises to a large extent from the universal custom of considering the horizontal expanse with reference to four cardinal points, governed primarily by the rising and setting of the sun—east and west—the midway points on the cirele being the north and south. The number, even outside of any process of count- ing, would become apparent in any figure or structure in the form of - a square, the four sides and the four corners; and in the personal rela- tions, front and back, right and left, as is suggested by Professor THOMAS] MYSTIC USE OF NUMBERS 949 McGee. And this would be true even in advance of a number system. The number 4 was therefore one which would naturally become promi- nent, and would necessarily become connected with the recognition of the cardinal points. The ‘*Cult of the Quarters” in mystic and cere- monial rites was therefore a natural outgrowth of the recognition of these points. This Cult of the Quarters and recognition of the number 4+ appears to have been carried almost to the extreme limit among the Mexican and Central American tribes. Reference to the cardinal points appears hundreds of times in the Mexican and Mayan codices, and reference to the number 4 is scarcely less frequent. In the latter, as in the Troano codex, on plate after plate the symbols of the cardinal points are placed in the four corners of the sections around the main central figure, indicating, as we may reasonably presume, that reference to these points is made in the ceremony to which the figure relates. In the Mexican codices they are referred to in several ways, sometimes, it would seem, almost unconsciously, from the mere force of habit. Sey- eral plates of the Borgian codex—which is probably the oldest of the series—are crowded with figures referring to the quarters and with symbolic representations of them, some plates being devoted entirely thereto. For example, three out of the four chief figures of plate 4 are evidently drawn with direct'reference to these points, and the lurge figure on plate 7 is devoted to the same cult, this being indi- rated in the figure in different ways, as by colors, figures, four-day symbols, ete. Reference to this cult, or to the number 4, is also dis- tinctly seen in plates 9,10, 11, 12, 13, 14, 48, 61, 71, 72, 73, 74, and 75. Four isa prominent number in the time systems of the Mexican and Central American tribes. The years are arranged in four series, each with its dominical day. The Mexican cycle of fifty-two years consisted of four thirteens or four weeks of years, and according to the mythol- ogy of the same people the world has passed through four ages. In both Mexican and Mayan mythology the culture heroes appear as four brothers. This number also occurs so frequently in other connections as to show that it had with the native population a mystic significance. For example, it was believed by the Mexicans that the end of the world would happen on the day 4 Ollin, and in accordance with this belief the ‘* Feast of the Lords” lasted four days, beginning with 1 Ocelotl and ending with 4 Ollin; and other great feasts usually continued four days. The cross appears also to relate to the cult of the quarters, espe- ciaily such as the four-colored St Andrew’s cross on plate 70 of the Borgian codex. The Mexicans also assigned four gods as rulers over the inferno. It is stated in the Maya Chronicles, where they speak of the coming of the Tutulxiu, that there were four. The Cakchiquels, according to their Annals, consisted of four subtribes or clans, though 950 NUMERAL SYSTEMS [ETH. ANN.19 there were thirteen divisions. The same Annals, alluding to the ori- gin of the people, speak of four men (leaders), four Tulans or tradi- tional homes, and four rulers. The great Mexican festivals occurred on the fourth, thirteenth, and fifty-second years. Four arrows were placed in the hand of their great deity, Huitzilopochtli. At the great feast symbolizing the death of this deity four of the chief priests ofti- ciated and four youths were chosen as attendants. The Guatemalans recognized four culture heroes; at Cholula, four disciples of Quetzalcoatl were charged with the government; in Tlax- calla, four princes formed the supreme council; and finally, according to Brasseur, almost all the villages or tribes of Mexico were divided into four clans or quarters. According to the Popol Vuh, in the descent to Xibalba (Inferno?) four roads were encountered; one of these was red, one black, one white, and one yellow. And Gucumatz, in his ascent to heaven and descent to Xibalba every seven days, under- went four changes in form, becoming first, a serpent; next, an eagle; next a tiger, and last, coagulated blood. This number and 5, together with the product of 4+ and 5, 20, form the base and scaffolding of the Mexican and Mayan numeral and time systems, though two other factors,13 and 18, were brought into the latter. y Although the number 5 does not appear to have entered so exten- sively into the mythology and ceremonials—that is to say, in so many different relations—as the 4, yet in some respects it was more promi- nent. For example, there is scarcely a page of the Troano, Dresden, or Cortesian codices without from one to four groups (usually columns) of five days, arranged in some regular order, which bear some rela- tion to the accompanying symbolic figures and numerals. Similar groups of five days frequently occur in the Mexican codices, where they also bear some relation to the accompanying symbolic figures. The day symbols in the Tonalamatl, as found in three of these codices, are arranged in 5 lines of 4 times 13 days each. The use of this number with a mystic or mythological significance appears to be shown on several plates of the Mexican codices, as for example, on plates 11 and 12 of the Borgian codex. On each of these plates are five scenes or groups of figures in five sections, placed as is shown in the diagram (figure 41). The fact that the chief symbolic figure in each is the Rain god, Tlaloc, and that the lower portion of each section apparently denotes earth and vegetation growing therefrom, renders it probable that there is some reference here to the seasons or the vicissitudes of cultivated plant life. Be this as it may, the reference to five is apparent, not only from the number and position of the sections, but also from the colors of the Tlalocs on plate 12, one of the outer four being red, another blue, another yellow, and another black, while that in the center is striped with red and white. THOMAS] MYSTIC USE OF NUMBERS 951 One thing worthy of notice in this diagram (figure 41) is that one of the five figures is placed centrally, at the expense of the four outer squares. We have in this, it seems, evidence of reference to the four quarters and the center. What is to be understood in these figures by the ‘‘center” is somewhat uncertain. It may be simply a conyen- ient way of locating the fifth symbol, which is in all probability the correct explanation in some cases, but even here it may have arisen, as is suggested by Professor McGee, through reference to the Ego in considering the quarters, giving rise to the quincunx. The same con- cept is symbolized on plate 4 of the Borgian codex, where we see four outer colored squares and a central colored circle, the Cipactli figure over which the latter is placed symbolizing the earth, and the dark outer border surrounding the whole figure denoting the clouds or sky. The central circle may in this case indicate the sun, which we find clearly represented on plate 43 of the same codex, though what seems to be the corresponding figure on plate 24 of the Vatican codex is without any central symbol. In some of the figures indicating the quarters, as one on plate 4 of the Borgian codex, where the four winds are represented, the center is occupied by a human form. In another place where wind symbols occupy the corners a death’s-head is placed in the center. It is proper, however, to bear in mind the fact that the arrangement of the days by fours and fives would follow as a necessary consequence of the time system. The year being divided into eighteen months of twenty days each, and five days being added at the end to complete the 365, each year would be five days in advance of that which preceded, Fie. 41—Diagram of figures on plates 11 and 12 of the Borgian Codex. and the years necessarily began on the same four days. The division of the twenty days of the month into four periods of five days would be a natural result. Why the five days of the columns in the codices are not in regular order according to this division, but are selected by skipping over regular intervals, is not so easily determined, though as has been shown in a previous paper, they usually have some reference the 260-day period. The number 7, though playing a less important role than 4 and 5, seems to have had some significance in the mysteries and ceremonies of the Mexicans and Maya. Dr Brinton, in his Native Calendar says that the Tzental appear to have developed the number 7 as an arithmetic element in their astronomic system, as they had in their 952 NUMERAL SYSTEMS (ETH. ANN. 19 calendars seven days painted with black figures, the first beginning with a Friday. This period was, however, probably based on the European week. That 7 would appear in the adjustment of the thirteen series to the twenty days of the month is evident; it is also noticeable that in some of the Mexican codices where the space is not sufficient to place thirteen day-symbols in a single series, where series of this length are referred to, the division is usually, though not always, into seven and six. However, the necessity of referring to seven in these instances does not appear to have brought it into use as a counter. Its appear- ance, therefore, in the time system and time count may be considered as accidental, or at least without significance. Nevertheless it does appear occasionally in relations where its use seems to be mystical. From the earliest times, the Cakchiquel, with perhaps others with whom they were related, are mentioned in their annals as ‘*seven tribes” or seyen villages arranged in thirteen divisions. Their sacred days were the seventh and the thirteenth. Tradition brings the ancestors of the Mexicans from seven caves; they come as seven tribes, the descendants of seven brothers. Among their gods was a deess named Centeocihuatl, also called Chicomecohuatl or the ‘‘Seven Serpents,” who, it is said, nourished the seven gods who survived the flood. It is said in the Quiche legend (Popul Vuh) that Gucumatz, their great culture hero, ascended each seven days to heaven, and in seven days descended into Xibalba; that for seven days he took the form of a ser- pent; seven others that of an eagle; seven others that of a tiger, and seven others that of coagulated blood, as has been already mentioned. Among their mythical heroes was Vukub-Cahix (**Seven Aras”), and the ruler of Nibalba was Vukub-Came (‘‘Seven Deaths”). The number 9, though seldom referred to in the ceremonials and mysteries, was not without a place therein among the Mexicans. They recognized nine ‘‘ Lords of the Night.” These are evidently referred to in the Borgian codex, as in the Tonalamatl, plates 31 to 38, where they are marked by footprints, and on plate 75, where the night is symbolized by the large black figure and the nine lords by nine star-like figures. It is stated in the Explanation of the Codex Tel- leriano-Remensis that he who was born on the day 9 Ehecatl would be prosperous as a merchant, while he who was born on the day 9 Itzeuintli would be a great magician. The Mexicans also recognized nine heavens. This number appears also to have had some significance among the Quiche, as they held that in each month there would be nine good and nine bad days, and two indifferent. Next to 20, 13 was the most important number in the time systems of Mexico and Central America. Not only was it the number of days in their so-called week, but it was that by which the days were num- bered. Although it did not form one of the regular time periods, as THOMAS] MYSTIC USE OF NUMBERS 953 the month, ahau, year or katun, the so-called week not being recog- nized as a regular period in their systems, it entered into almost every time count and every time series in the codices and inscriptions. It was one of the factors on which the so-called ‘‘sacred year” of 260 days and the cycle of fifty-two years were based. eing so important in the time systems, it would be expected to enter more or less into the activities of life; nevertheless it appears to have played a comparatively unimportant réle as a mystic or cere- monial number. It was the custom of several Mayan tribes to arrange their armies in thirteen divisions. It appears in the Votan myth among the Tzental, where ‘‘thirteen serpents” are referred to; and among the Cakchiquel the day numbered 13 was considered sacred. The number 20 is the base of the numeral system of the Mexican and Central American tribes, and it may perhaps also be correctly considered the base of their calendar system, although there are other necessary factors. Nevertheless 20 does not appear to have been used as a mystic number in rites and ceremonies, except so far as the calendar was made to serve divinatory purposes. Why twenty days were adopted as a time period and a division of the year has as yet received no entirely satisfactory explanation, though it is generally supposed that it was chosen because the arithmetical system of these tribes was vigesimal. That there is some connection between the two is quite likely, especially as this would seem to correspond with the probable order of the steps in the formation of the two systems. That the formation of the yigesimal system preceded that of the time sys- tem appears to be an absolute requisite, but the steps in the forma- tion of the latter can not be assumed with the certainty which we may have with regard to the former. That the custom of grouping the days by fives did not begin until 26 had come into use is clear. Did the introduction of 13 as a factor precede or follow the adoption of 20% Dr Brinton states in his Native Calendar that he is persuaded that this period was posterior and secondary to the twenty-day period. Although this opinion may be, and probably is, correct, the evidence on which to base it is not so apparent as to leave no doubt. It seems probable, as Dr Brinton suggests, that the twenty-day period was derived from the vigesimal number system, but this does not explain the origin of the peculiarities of the unusual time system, which seems to have reference to no natural phenomena save the earth’s annual revolution. There are other peoples than those of Mexico and Central America who use the vigesimal system, but no others, so far as known, who adopt the twenty-day month or eighteen-month year. The moon’s reyo- lution is the factor on which the month in most of the world’s time systems is based, and the name for month in most, or at least several 954 NUMERAL SYSTEMS [ETH. ANN.19 of the Mayan tongues, is the same as that for moon. This is also true of the Zapotec language, and Cordova (Arte Idioma Zapoteco) says that the people of this tribe even count by moons; however, the latter statement may apply to post-Columbian times. The names for month and moon are the same in Cahita, Othomi, and Zoque. This fact, and the further fact that substantially the same term has passed oyer, in some instances, from one linguistic family to another, as the Zapo- tec, peo or beo; Loque, poya; Kakchi (Mayan), po or poo, would seem to indicate an original lunar month. It is also true that the oldest inscriptions and the Dresden codex refer to a year of 365 days. How- ever, against this evidence must be placed the fact.that all the inserip- tions and codices base the time count on the twenty-day month, and the day numbering on 13, the latter also being a factor in other counts of the inscriptions and codices. The oldest evidence, therefore, to which we can appeal where numbers are used, agrees with the time system of the ‘‘native calendar.” That a change from a lunar count to a twenty-day period could have been made otherwise than arbitrarily seems impossible; we can not con- ceive how the one could have grown out of the other. This must have been true or the system must have developed with the growth of the number system; at least no other supposition seems possible unless we assume that two time systems, a secular and a sacred one, were in use at the same time, and that the latter finally obscured the former. This seems to have been the case with some tribes. If the supposition that the time system developed with the number system be correct, then the lunar period could never have been a factor. It is somewhat strangely in accordance with this supposition that the moon, so far as the aboriginal records and early authorities show, is almost wholly absent from the codices, and does not appear, so far as is known, in the inscriptions. Notwithstanding this negative evidence, I can not believe that a time system without reference to the lunar periods could have devel- oped among the tribes of the region of which we are treating. My conclusion is, therefore, that the priests at an early date adopted a method of counting time for their ceremonial and divinatory purposes which would fit most easily into their numeral system, and that this system, in consequence of the overwhelming influence of the priest- hood, caused the lunar count to drop into disuse. Moreover, the only native records which are available are those made by the priests for their purposes. This will probably account for the introduction of the twenty-day period, but does not account for the introduction of the 13. Dr Forstemann suggests that at one time the Mayas arranged the days of the solar year in four groups of seven weeks each, the week consisting of 13 days, the year being then counted as 364 days (4x 13 THOMAS] MYSTIC USE OF NUMBERS 955 x 7=364), and that each of the four groups was assigned to a particu- lar cardinal point. Although it is true that the Tonalamatl, as given in some of the Mexican codices, seems to show, by the upper and lower border Jines, which contain 52 figures each, some indications of a year of 364 days, this does not account for the introduction of the 13; moreover, Dr Férstemann’s explanation introduces the factors 7 and 91 (7X13), and 7 and 28 (47), which are not found in the time counts of the codices or inscriptions. However, it is possible that the 28 (4x7) may be supposed to indicate the true lunar period, and the 4 times 7 the four changes of the moon. Mr Cushing suggests another explanation based on his observations among the Zuni. In the cere- monies of this people the complete terrestrial sphere is symbolized by pointing or blowing smoke toward the four cardinal points, to the zenith and nadir, the individual making the seventh number. When the celestial sphere was symbolized only the six directions were added to the seven, no further reference to the individual being made. Thus 13 typifies the whole universe. While this explanation seems plausi- ble, we lack the evidence that such a custom was 1n vogue among the people using the native calendar, nothing suggesting it being stated in the authorities or indicated in the codices, unless in the so-called title- pages of the Troano codex and Codex Cortesianus, which are sup- posed by most investigators to be parts of one plate or series. There we find the four cardinal point symbols taken in one direction fol- lowed by two symbols, which Seler believes indicate the zenith and nadir; these are followed by the cardinal point symbols taken in the opposite direction, and these by three other symbols, two of which appear to be the same as the supposed zenith and nadir symbols. Unfortunately the third, which makes the thirteenth, is too nearly obliterated to determine its form. The number symbols 1 to 13 stand above these. Other suggestions as to the reason of the use of this number as a factor in the time system have been offered, but, like those mentioned, they are not entirely satisfactory. That 13 was considered important by most of the tribes is true, and that it was used by some otherwise than in time counts is true, but why is as yet an unsolved mystery, nor is there any satisfactory evidence that it was preceded by the twenty- day period, though this is probable. Clayvigero asserts that the Mexi- ‘ans, in their computations of time, disregarded months and years, counting by thirteens, but he evidently means by this that 13 was used as the multiplier, and, like Goodman, evidently confounds the system of numeration with the time system. However, this will be discussed more fully in a subsequent paper relating to the native time system. 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