PRIMITIVE NUMBER SYSTEMS. 593 



prise that either 5 or 10 should in jieiieial be jnefeiTed for th;it purpose. 

 It i.s a matter of some surprise, however, that the quinary should in so 

 many cases merge into the vigesiuial rather than the decimal system. 



The vigesimal system is never found entirely pure. Examination 

 always sliows some trace either of the quinary or the decimal system 

 subordinate to it. Among tlu' native races of Anu^rica it is almost as 

 common as the quinary and is more common than the decimal, l)ut it 

 is there always found mixed with either the one or the other. The 

 same commingling is ob.serve<l among Asiatic and Afric^an tribes. The 

 elaborate Aztec system is the most i)erfect known example of the vig- 

 esimal-number system, but it contained both the (piinary and the deci- 

 mal scales subordinate to the vigesimal. The Muyscas of Bogota 

 possessed an exceedingly elaborate and extended vigesimal system, but 

 the decinml is used to supi>lenient it. The same is true of the Bas- 

 ques of northern Spain. 



For some unexplained reason vigesimal-number systems are lare in 

 the Old World. The only European example I am able t(> cite is tlie 

 Bas(]ue system. The Ainus of northern Siberia reckon by twenties, 

 and a number of the tribes of the Caucasus do tlie sanie. Tn Africa 

 this mode of counting is almost unknown, only two or three examples 

 of it being on record. It is oidy in America that vigesimal-number 

 systems have flourished and h<dd their own. But it is a noteworthy 

 fact that in ancient times 20 was the number base used in many ])arts 

 of Europe, as is attested by abundant traces in the modern European 

 languages. The lMi(enicians, and presumably the Carthagenians, also 

 used this method of reckoning, and thnuigh contact with them the 

 Celtic nations of western Europe gradually became familiarized with 

 it. From using it in commercial intercourse with these traders from 

 the Mediterranean they may have adopted it as their own scale. Cer- 

 tain it is that the vigesimal-number system was a, strongly marked 

 characteristic of all the Celtic i-aces, as their languages uneciui vocally 

 prove. The liretons still say " unnek ha tringeut,"' 11 and ."> liO's, for 

 71. The French say "(juatre vignt" for 80, and from that ]»oint to 100 

 count u])on a ])ure vigesimal scale, as far as the names of their nund)ers 

 are coiu'crned. The Welsh, the Erse, the Giclic, the Manx, and other 

 Celtic races sliow in their languages similar traces of a forinei' use of 

 the vigesimal base. Singularly (Miough. like traces ar<> to some slight 

 extent found among Teutonic languages also, ])ut they are so infrequent 

 as to indicate but little and to prove nothing. A hundred consisting 

 of 120, and known as ''the great hundred" or " long hundred, " was 

 formerly in use in England, and was legal for eggs, spars, an<l certain 

 other articles. That this was a common use would appear troni the 

 poi)ular old distich (pioted by Peacock:* 



Five score of men, iiioijcn. .'iikI pins, 

 Six score of all other thinjrs. 



* Encyclopedia Mciropolitana, vol. i, \}. 381. 



n. Mis. 114 — -38 



