From some minor details in numeration, ethnological hints may be gained. Among rude tribes with scanty series of numerals, combination to make out new numbers is very soon resorted to. Among Australian tribes addition makes 'two-one,' 'two-two,' express 3 and 4; in Guachi 'two-two' is 4; in San Antonio 'four and two-one' is 7. The plan of making numerals by subtraction is known in North America, and is well shown in the Aino language of Yesso, where the words for 8 and 9 obviously mean 'two from ten,' 'one from ten.' Multiplication appears, as in San Antonio, 'two-and-one-two,' and in a Tupi dialect 'two-three,' to express 6. Division seems not known for such purposes among the lower races, and quite exceptional among the higher. Facts of this class show variety in the inventive devices of mankind, and independence in their formation of language. They are consistent at the same time with the general principles of hand-counting. The traces of what might be called binary, ternary, quaternary, senary reckoning, which turn on 2, 3, 4, 6, are mere varieties, leading up to, or lapsing into, quinary and decimal methods.
The contrast is a striking one between the educated European, with his easy use of his boundless numeral series, and the Tasmanian, who reckons 3, or anything beyond 2, as 'many,' and makes shift by his whole hand to reach the limit of 'man,' that is to say, 5. This contrast is due to arrest of development in the savage, whose mind remains in the childish state which the beginning of one of our nur- sery number-rhymes illustrates curiously. It runs —
'One's none, Two's some, Three's a many, Four's a penny, Five's a little hundred.'
by twenties. Shaw, l.c. The use of a 'score' as an indefinite number in England, and similarly of 20 in France, of 40 in the Hebrew of the Old Testament and the Arabic of the Thousand and One Nights, may be among other traces of vigesimal reckoning.
