PRIMITIVE NUMBER SYSTEMS. 591 



trace of a base, the numhers, as lar as tliey extend, beiii<i' iiidepeiKleut 

 of each other. Such cases are, liowexcr, necessarily rare. 



The only remaining example that need l)e mentioned of the use of 

 an unusual iiuudjci' as the base of a system, is the Babylonians. As 

 is well known, the base of their number system was (JO, the largest 

 nund)er ever used for such a purpose. To the modern world, the fact 

 that the Babylonians nse<l GO as their unit of reckonini;- is most im 

 portant, for that fact has entailed upon us a sexagesimal system of 

 astronomical com[)utation, 



^Vith the exception of a small number of isolated cases, such as 

 those mentioned above, it may be laid down as a universal law that 

 every language containing a number system extemling beyond 5 

 reveals the use of one of tlie three numbers, o, 10, or 20, as the base of 

 that system. Each of three numbers reipiires extended mention. 



One of the most niteresting j)oints to be met with in connection 

 with the study of numeral words, is the resemblam-e found to exist 

 in nuiny languages between thB words for ''hand'' and "'live.'' Count 

 ing as they do, by means of their tiugers, savage races naturally use 

 for tiA'e some expressicm like "one hand," or -'a hand linislied," or 

 simply "'hand." Then, ])roceeding with their count, they begin to 

 build on this as a base, using for ('», 7, S, etc., the ex])ressions, "hand 

 one," "hand two,"' "hand three," et<-. In such a system, 10 is, of 

 C(mrse. "two hands.*' Counting above 10, we find tMo common meth 

 ods ])iactised. The tbigers being finished by the count uj) to 10, re- 

 course may be liad either to the toes or to the fingers of a second man. 

 In the former ease, 11 would be "one on the foot." Twenty, complet- 

 ing the tale of l)oth lingers and toes, is called '-one man." ik'yond 

 this i)oint there is less uniformity in the metluxl of counting than be- 

 fore, ])iit examples are numerous of tribes which use exactly this 

 method up to 100, calling 40, (50, so, and 100, '-two men," '-three men," 

 "four men," and "five men," resi)ectively. Ibit, as will l)c noted later, 

 the use of the pure (piinary scale above L'O is rarely il' ever found. 

 A\'ith ti'ibes having a limited ninnl)er sense, !iowe\'er, tribes whosesys- 

 tem.'< do not extend Ix'yoiid 10 or 15 or 20, this scale is almost as com- 

 mon as the decinuil. The naturalness of this scale is \ cry evident, 

 and, as compan'd with the decimal, the wonder is, not thai I lie (luinaiy 

 scale is s(» very common, but rather that it is not more comnion than 

 the decimal. The reason for this will apjx-ar when we come to con- 

 sider the latter. 



lOxamples of the use of the (punary scale :\n- conunoii in all parts of 

 the world.* it is the scale of many of the nati\ e North Siberian tribes, 

 of the Aleuts, the Kamtschatkans, and at least three of the tribes of 

 the New Hebrides. In Africa we note tlu^ Wolofs and Sbillorns, 

 which were visited by iMnngo Tark, the Kaiuiris, the Temues, the 



The nmiicrals of the liil»os licre iiieutioiied, Imt for wliicli no sjn-eilic reference 

 is made, are fouii<l in Miiller, op. cit.. or in Pott. Die (Jiiinuic itinl riycaiuialii zahl- 

 nwthodchci \'oJkeni uUrr ll'clttlicile. 



