590 PRIMITIVE NUMBER SYSTEMS. 



in our own laugiiage we fliid an occasioual hint of the same thing in 

 tlie words ''pair," •'l)ra(*e,'' '•coui)le," etc; obscure traces of a binary 

 uuniber system api)ear on some of the early Chinese monuments, but 

 w'C have no real evidence that such a system was ever definitely and 

 exckisively used by the Chinese. Certain savage tribes, however, 

 count exclusively or in part by twos. The Baccaraaibi, n, South 

 American tribe of the Xingn region, count only to 0. But they call 4, 

 2 and 2, 5, 2 and 2 and 1, and (>, 2 and 2 and 2. The least developed 

 of the Australian tribes are in many cases found to reckon in the same 

 way.* The structure of the Arikara numerals would indicate that this 

 people counted at first exclusively by pairs, the odd numbers being in- 

 terpolated afterwards.! The lowest of the native tribes of the East 

 Indian Archipelago count upon a binary scale, if indeed they can prop- 

 erly be said to use any.f Examples of this kind might be multiplied 

 to a very considerable extent. But it should not be overlooked that 

 these are hardly to be considered as tair examples of the use of cuiy 

 system. The tribes mentioned have no form of noration other than re- 

 peating scratches or piling pebbles: and their numeration is of the 

 rudest kind. All that can be said is that, as far as any system is used 

 among them, that system is the binary. Making the same (jualifica- 

 tion, we may note that the Cuchaus of Colorado count Avith a mixed 

 ternary and quaternary scale, expressing by the phrase "2 3's," 9 

 by "3 3's," and S by '"2 4's;"§ and that the Lulos of South America, 

 the Triton Bay and the Ende Polynesians count with a quaternary 

 scale, expressing numbers as far as 4 by simple words, and then 

 counting 4-1, 4-2, et<'. The last-named tribe gives a further indication 

 of the use of the quaternary scale by using for 8 a word signifying 

 "2 4"s.'''|| Occasionally we come, in the midst of some other well-de- 

 fined system, upon sporadic traces of reckoning upon 4, 6, 8, or 9 as a 

 base. The Wallachians, for example, say "den-maw," 2-9 for 18. The 

 Bretagnes call 18 "trionche," 3-G. But otherwise these languages 

 contain no trace of the senary or octonary scales. Pott states** that 

 the Bolans of West Africa appear to use 6 as their number base; but 

 aside from this solitary instance we know of no tribe w^hich employs 0, 

 7, 8, or 9 for that purpose. The most remarkable example of tribal ec- 

 centricity in this particular is that of the Maoris, of New Zealand, 

 whose number base is 11. To that number they count by means of 

 simple words; 12, 13, 14, etc., are with them 11-1, 11-2, 11-3, etc.; the 

 multiples of 11, as 22 and 33, are formed directly on the word for 11; 

 and the square and cube of 11, or 121 and 1331, are expressed by 

 simple w^ords having no connection with the names of smaller num- 

 bers.tt Occasionally a rude number system occurs which shows no 



* LetourneauSj Bull. Soc. AnUiropol., Paris, 1886, p. 91. 



i Trumbull, J. H., Proc. Am. Antq. Soc. 1875, p. 76. 



J Marre, A. De V arlthmetique dans VarcMpel Indien, }•. 7. 



^ Trumbull, J. H., Trans. Am. Phil. Ass'n, 1874, p. 46. 



II Marre, A., oj). cil.. p. 7. ** Die Spi-achvershiedenhcit, p. 30. 



tl^Neumayer, oj). cit. B. ii, p, 229. 



