a real bar to the extension of the system. The same thing is true, to an
even greater degree, of tribes whose number sense is so defective that they
begin almost from the outset to use combinations. If a savage expresses the
number 3 by the combination 2-1, it will at once be suspected that his
numerals will, by the time he reaches 10 or 20, become so complex and
confused that numbers as high as these will be expressed by finger
pantomime rather than by words. Such is often the case; and the comment is
frequently made by explorers that the tribes they have visited have no
words for numbers higher than 3, 4, 5, 10, or 20, but that counting is
carried beyond that point by the aid of fingers or other objects. So
reluctant, in many cases, are savages to count by words, that limits have
been assigned for spoken numerals, which subsequent investigation proved to
fall far short of the real extent of the number systems to which they
belonged. One of the south-western Indian tribes of the United States, the
Comanches, was for a time supposed to have no numeral words below 10, but
to count solely by the use of fingers. But the entire scale of this
taciturn tribe was afterward discovered and published.

To illustrate the awkward and inconvenient forms of expression which
abound in primitive numeral nomenclature, one has only to draw from such
scales as those of the Zuñi, or the Point Barrow Eskimos, given in the
last chapter. Terms such as are found there may readily be duplicated
from almost any quarter of the globe. The Soussous of Sierra Leone[126]
call 99 _tongo solo manani nun solo manani_, _i.e._ to take (10
understood) 5 + 4 times and 5 + 4. The Malagasy expression for 1832
is[127] _roambistelo polo amby valonjato amby arivo_, 2 + 30 + 800 + 1000.
The Aztec equivalent for 399 is[128] _caxtolli onnauh poalli ipan caxtolli
onnaui_, (15 + 4) × 20 + 15 + 4; and the Sioux require for 29 the
ponderous combination[129] _wick a chimen ne nompah sam pah nep e chu wink
a._ These terms, long and awkward as they seem, are only the legitimate