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 numeration, 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.[1] In support of this theory it is urged that extensive 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 influence 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 significance 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, Arithmetica di quasi tutte Ie nazioni conosciute.
