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THE ART OF COUNTING.

with words for 'hand,' &c., as when the Omagua uses pua, 'hand,' for 5, and reduplicates this into upapua for 10. In some South American languages a man is reckoned by fingers and toes up to 20, while in contrast to this, there are two languages which display a miserably low mental state, the man counting only one hand, thus stopping short at 5; the Juri ghomen apa 'one man,' stands for 5; the Cayriri ibichó is used to mean both 'person' and 5. Digit-numerals are not confined to tribes standing, like these, low or high within the limits of savagery. The Muyscas of Bogota were among the more civilized native races of America, ranking with the Peruvians in their culture, yet the same method of formation which appears in the language of the rude Tamanacs is to be traced in that of the Muyscas, who, when they came to 11, 12, 13, counted quihicha ata, bosa, mica, i.e., 'foot one, two, three,'[1] To turn to North America, Cranz, the Moravian missionary, thus describes about a century ago the numeration of the Greenlanders. 'Their numerals,' he says, 'go not far, and with them the proverb holds that they can scarce count five, for they reckon by the five fingers and then get the help of the toes on their feet, and so with labour bring out twenty.' The modern Greenland grammar gives the numerals much as Cranz does, but more fully. The word for 5 is tatdlimat, which there is some ground for supposing to have once meant 'hand;' 6 is arfinek-attausek, 'on the other hand one,' or more shortly arfinigdlit, 'those which have on the other hand;' 7 is arfinek-mardluk, 'on the other hand two;' 13 is arkanek-pingasut, 'on the first foot three;' 18 is arfersanek-pingasut, 'on the other foot three;' when they reach 20, they can say inuk nâvdlugo, 'a man ended,' or inûp avatai nâvdlugit, 'the man's outer members ended;' in this way by counting several men they reach higher

  1. Gilij; 'Saggio di Storia Americana,' vol. ii. p. 332 (Tamanac, Maypure). Martius, 'Gloss, Brasil,' (Cayriri, Tupi, Carib, Omagua, Juri, Guachi, Coretu, Cherentes, Maxuruna, Caripuna, Cauixana, Carajás, Coroado, &c.); Dobrizhoffer, 'Abipones,' vol. ii. p. 168; Humboldt, 'Monumens,' pl. xliv. (Muysca).