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262 reason that a set of independent numerals to 20 would be inconvenient; but it takes on from quinary, as in Aztec, which may be analyzed as 1, 2 ... 5, 5⋅1 ... 10, 10⋅1 ... 10⋅5, 10⋅5⋅1 ... 20, 20⋅1 ... 20⋅10, 20⋅10⋅1 ... 40, &c.; or from decimal, as in Basque, 1 ... 10, 10⋅1 ... 20, 20⋅1 ... 20⋅10, 20⋅10⋅1 ... 40 &c. It seems unnecessary to! bring forward here the mass of linguistic details required for any general demonstration of these principles of numeration among the races of the world. Prof. Pott, of Halle, has treated the subject on elaborate philological evidence, in a special monograph, which is incidentally the most extensive collec- tion of details relating to numerals, indispensable to students occupied with such enquiries. For the present purpose the following rough generalization may suffice, that the quinary system is frequent among the lower races, among whom also the vigesimal system is considerably developed, but the ten- dency of the higher nations has been to avoid the one as too scanty, and the other as too cumbrous, and to use the in- termediate decimal system. These differences in the usage of various tribes and nations do not interfere with, but rather confirm, the general principle which is their common cause, that man originally learnt to reckon from his fingers and toes, and in various ways stereotyped in language the result of this primitive method.

Some curious points as to the relation of these systems may be noticed in Europe. It was observed of a certain deaf-and-dumb boy, Oliver Caswell, that he learnt to count as high as 50 on his fingers, but always 'fived,' reckoning, for instance, 18 objects as 'both hands, one hand, three fingers.' The suggestion has been made that the Greek use

1 The actual word-numerals of the two quinary series are given as examples. Triton's Bay, 1, samosi; 2, roëeti; 3, touwroe; 4, faat; 5, rimi; 6, rim-samos; 7, rim-roëeti; 8, rim-touwroe; 9, rim-faat; 10, woetsja. Lifu, 1, pacha; 2, lo; 3, kun; 4, thack; 5, thabumb; 6, lo-acha; 7, lo-a-lo; 8, lo-kunn; 9, lo-thack; 10, te-bennete.

2 A. F. Pott, 'Die Quinäre und Vigesimale Zählmethode bei Völkern aller Welttheile,' Halle, 1847; supplemented in 'Festgabe zur xxv. Versammlung Deutscher Philologen, &c., in Halle' (1867).

3 'Account of Laura Bridgman,' London, 1845, p. 159.