THE ORIGIN OF NUMBER SYSTEMS. 531 



pute whether all numeral systems were not originally quinary, 

 and the adoption of a larger base came as, with the lapse of time, 

 its superior advantages were recognized. I think that not only 

 is the evidence in favor of the opposite view, but also that from 

 a priori considerations we might expect to see the adoption of 

 10 as a base as readily as 5. It depends, I think, entirely upon 

 whether 6 is called "five-one" or is designated in some other 

 way. In speaking upon this point Prof. Conant says (pages 170, 

 171): "From the fact that the quinary is that one of the three 

 natural scales with the smallest base, it has been conjectured that 

 all tribes possess at some time in their history a quinary numera- 

 tion, which at a later period merges into either the decimal or the 

 vigesimal, and thus disappears, or forms with one of the latter a 

 mixed system.* In support of this theory it is urged that exten- 

 sive regions which now show nothing but decimal counting were, 

 beyond all reasonable doubt, quinary. It is well known, for 

 example, that the decimal system of the Malays has spread over 

 almost the entire Polynesian region, displacing whatever native 

 scales it encountered. The same phenomenon has been observed 

 in Africa, where the Arab traders have disseminated their own 

 numeral system very widely, the native tribes adopting it, or 

 modifying their own scales in such a manner that the Arab influ- 

 ence is detected without difficulty. 



"In view of these facts and of the extreme readiness with 

 which a tribe would through its finger-counting fall into the use 

 of the quinary method, it does not at first seem improbable that 

 the quinary was the original system. But an extended study of 

 the methods of counting in vogue among the uncivilized races of 

 all parts of the world has shown that this theory is entirely 

 untenable. The decimal scale is no less simple in its structure 

 than the quinary, and the savage, as he extends the limits of his 

 scale from 5 to 6, may call his new number 5-1, or, with equal 

 probability, give it an entirely new name, independent in all 

 respects of any that have preceded it. With the use of this new 

 name there may be associated the conception of ' 5 and 1 more ' ; 

 but in such multitudes of instances the words employed show no 

 trace of any such meaning, that it is impossible for any one to 

 draw with any degree of safety the inference that the signifi- 

 cance was originally there, but that the changes of time had 

 wrought changes in verbal form so great as to bury it past the 

 power of recovery." 



In support of this argument it may be said that at least in the 

 languages of the most cultivated races to-day those elements of 



* An elaborate argument in support of this theory is to be found in Hervas's celebrated 

 work, Arithrnetica di quasi tutte le nazioni conosciute. 



