Page:Popular Science Monthly Volume 51.djvu/544

 Before leaving this part of the subject the writer wishes merely to add that the etymologies suggested above for six, seven, and eight appear to be quite plausible; for navan, or nine, however, it appears to him that the association with the idea of "last" is the more reasonable, and would fit in with the finger interpretation of the others just as well as the one suggested.

We return now to the general question of the development of number systems, which we left at the point where men were supposed to have learned to use their fingers and toes as a natural abacus, and to have reached, therefore, the number 20. Before any further progress can be made a scale of notation must be adopted. Of course, this is not done consciously. Within certain limits it is probably entirely a matter of chance what number will be selected as a base. I had better say what number will become the base; for the use of the word "selected" unconsciously implies that the savage exercises a choice, while in fact, as already stated, he is simply led by circumstances. In most cases he has adopted some kind of a base before he has counted as far as 20. We have already seen that one of the commonest forms for "6" is "hand-one" or five-one. When the savage expresses 6 in this way he is committed to a quinary scale. The chances are, however, overwhelmingly against his carrying out this system consistently in all higher numbers, and for very obvious reasons. A pure quinary system of numeration is therefore extremely rare. Nevertheless, at least one such exists, one that is purely quinary as far as it seems to be known; this is the scale of one of the Betoya dialects of South America. In this scale

(Conant, pages 57 and 140.) It would be interesting to know whether this scale is carried on consistently—that is, whether 25, the square of the base, is recognized as a new starting point, or whether they call it simply "five hands," without any sign to mark it off distinctly from other multiples of the base.

What is generally found in these scales that introduce the quinary element at 6 is that "10" is designated by some expression other than "two fives"; and eleven then becomes 10 + 1; twelve, 10 + 2, etc.—that is, the quinary scale here merges into the decimal; and either we see no more of it, or it continues with the other in a subsidiary place. The latter is the more usual. Thus sixteen is 10 + 5 + 1; seventeen, 10 + 5 + 2, etc. Thus is formed a mixed decimal and quinary scale.

It is a question over which there has been considerable