It is impossible that any such change can ever meet with general or even partial favour, so firmly has the decimal scale become intrenched in its position.  But it is more than probable that a large part of the world of trade and commerce will continue to buy and sell by the dozen, the gross, or some multiple or fraction of the one or the other, as long as buying and selling shall continue.  Such has been its custom for centuries, and such will doubtless be its custom for centuries to come.  The duodecimal is not a natural scale in the same sense as are the quinary, the decimal, and the vigesimal; but it is a system which is called into being long after the complete development of one of the natural systems, solely because of the simple and familiar fractions into which its base is divided.  It is the scale of civilization, just as the three common scales are the scales of nature.  But an example of its use was long sought for in vain among the primitive races of the world.  Humboldt, in commenting on the number systems of the various peoples he had visited during his travels, remarked that no race had ever used exclusively that best of bases, 12.  But it has recently been announced[226] that the discovery of such a tribe had actually been made, and that the Aphos of Benue, an African tribe, count to 12 by simple words, and then for 13 say 12-1, for 14, 12-2, etc.  This report has yet to be verified, but if true it will constitute a most interesting addition to anthropological knowledge.

CHAPTER VI.

THE QUINARY SYSTEM.

The origin of the quinary mode of counting has been discussed with some fulness in a preceding chapter, and upon that question but little more need be said.  It is the first of the natural systems.  When the savage has finished his count of the fingers of a single hand, he has reached this natural number base.  At this point he ceases to use simple numbers, and begins the process of compounding.  By some one of the numerous methods illustrated in earlier chapters, he passes from 5 to 10, using here the fingers of his second hand.  He now has two fives; and, just as we say “twenty,” i.e. two tens, he says “two hands,” “the second hand finished,” “all the fingers,” “the fingers of both hands,” “all the fingers come to an end,” or, much more rarely, “one man.”  That is, he is, in one of the many ways at his command, saying “two fives.”  At 15 he has “three hands” or “one foot”; and at 20 he pauses with “four hands,” “hands and feet,” “both feet,” “all the fingers of hands and feet,” “hands and feet finished,” or, more probably, “one man.”  All these modes of expression are strictly natural, and all have been found in the number scales which were, and in many cases still are, in daily use among the uncivilized races of mankind.