e quinary, the decimal, and the vigesimal. The number of
fingers on one hand is, excluding the thumb, four. Possibly there have been
tribes among which counting by fours arose as a legitimate, though unusual,
result of finger counting; just as there are, now and then, individuals who
count on their fingers with the forefinger as a starting-point. But no such
practice has ever been observed among savages, and such theorizing is the
merest guess-work. Still a definite tendency to count by fours is sometimes
met with, whatever be its origin. Quaternary traces are repeatedly to be
found among the Indian languages of British Columbia. In describing the
Columbians, Bancroft says: "Systems of numeration are simple, proceeding by
fours, fives, or tens, according to the different languages...."[198] The
same preference for four is said to have existed in primitive times in the
languages of Central Asia, and that this form of numeration, resulting in
scores of 16 and 64, was a development of finger counting.[199]

In the Hawaiian and a few other languages of the islands of the central
Pacific, where in general the number systems employed are decimal, we find
a most interesting case of the development, within number scales already
well established, of both binary and quaternary systems. Their origin seems
to have been perfectly natural, but the systems themselves must have been
perfected very slowly. In Tahitian, Rarotongan, Mangarevan, and other
dialects found in the neighbouring islands of those southern latitudes,
certain of the higher units, _tekau_, _rau_, _mano_, which originally
signified 10, 100, 1000, have become doubled in value, and now stand for
20, 200, 2000. In Hawaiian and other dialects they have again been doubled,
and there they stand for 40, 400, 4000.[200] In the Marquesas group both
forms are found, the former in the southern, the latter in the northern,
part of the archipelago; and it seems probable that one or both of these
methods of numeration are scattered somewhat widely throughout that region.
The origin of these methods is probably to be found in the fact that, after
the migration from the west toward the east, nearly all the objects the
natives would ever count in any great numbers were small,--as yams,
cocoanuts, fish, etc.,--and would be most conveniently counted by pairs.
Hence the native, as he counted one pair, two pairs, etc., might readily
say _one_, _two_, and so on, omitting the word "pair" alto