its stead. It is said that
Charles XII. of Sweden was actually contemplating such a change in his
dominions at the time of his death. In pursuance of this idea, some writers
have gone so far as to suggest symbols for 10 and 11, and to recast our
entire numeral nomenclature to conform to the duodecimal base.[225] Were
such a change made, we should express the first nine numbers as at present,
10 and 11 by new, single symbols, and 12 by 10. From this point the
progression would be regular, as in the decimal scale--only the same
combination of figures in the different scales would mean very different
things. Thus, 17 in the decimal scale would become 15 in the duodecimal;
144 in the decimal would become 100 in the duodecimal; and 1728, the cube
of the new base, would of course be represented by the figures 1000.

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 pre