PRIMITIVE Nl'MBKR SYSTEMS. 587 



lents found that they are recojiiiized by competent aiitliority as under- 

 lying- one of the most common of the methods of numeral formation.* 



Tn a (ionsideration of the subject of primitive number one thought 

 must be kei)t prominently in mind. Savage races may have numerals 

 hy means of which they count to 5, 10,20, 100, or even 1,000, beyond 

 which they rarely venture. I>ut it by no means follows that, after 

 passing" beyond the very smallest, they have any exact notions of the 

 numbers they are using. As long as they can check off on the fingers, 

 or by meansof i)ebbles, sticks or shells, they und<mbtedly have a fairly 

 distinct idea of the totals they name. But want of familiarity with 

 the use of numl)ers, and lack of any convenient means of comparison, 

 nnist rt^sult in extreme indeliniteness of mental conception, and must, 

 when recourse can not l>e hjid to counters of some kiml, inevitably 

 give rise to great vagueness in the use of numbers. This has been 

 noted and commented on by many observers, Hund)oldt among them, 

 who remarks t that he never met an Indian who on being asked his 

 age would not answer indiiferently 10 or UO. 



The statement has been made above that tiu', numbei' systems of 

 savage races rarely, if ever, extend beyond 1,000. A single observa- 

 tion respecting the development of the systems of civilized races may 

 not here be out of place as showing of how universal api)lication is this 

 statement. The number systems of tlie civilized world to-day are of 

 unlimited «^xtent. But we need go back but a few centuries to tind a 

 time when our owil systems were as diminutive as are those to which 

 reference has just been made. Although in response to the demands 

 of crmimerce and science our English system has been brought to its 

 l)resent elastic condition, the evidence of language shows conclusively 

 that our Teut(mic ancestors stopped at the same limit that has been 

 named as the maxinmm for ?avage tribes. The higher numeral words 

 of our language, million, hillion^ frill ion, etc., are all borrowed words; 

 while the word thousand is pure Saxon, like the words one, two, three, 

 ten, hundred, etc. The German, the Scandinavian ami other languages 

 have borrowed their higher numeral words, and the same statement 

 is probably true of the French. Other languages, like tlie (Chinese, 

 Sanskrit, Aztec, etc., contain only native numeral words; but however 

 higli these systems may be found to extend, there can be no doubt that 

 they were at one time limited to a single tliousand, and perhaps less. 

 In this connection it is instructive to obserAC the number limits of tlie 

 half civilized nations of the ]n'esent day. The tribes of Arabia, the 

 Persians, the Abyssinians, and most of theXorth Al'rican peoi>les imve 

 number .systems terminating with eleph or alph (1,000). Tlie Lapland- 

 ers and the Erse have no words higher than zhioette and <-iad, respec- 

 tively, each of these words signifying 100. In ancient times the Latins 

 were content with mille (1,000), and the Greeks with /j.np'.a- (10,000), as 

 their number limits, and the Malays of to-day with ribou, also meaning 



* Chase, Proc. Am. Phil. Soc. ISfif), p. 23. 

 tPers. Narrative, vol. v, p. 165. 



