20, and not infrequently to 100. Again, we find 1000
as the limit; or perhaps 10,000; and sometimes the savage carries his
number system on into the hundreds of thousands or millions. Indeed, the
high limit to which some savage races carry their numeration is far more
worthy of remark than the entire absence of the number sense exhibited by
others of apparently equal intelligence. If the life of any tribe is such
as to induce trade and barter with their neighbours, a considerable
quickness in reckoning will be developed among them. Otherwise this power
will remain dormant because there is but little in the ordinary life of
primitive man to call for its exercise.

In giving 1, 2, 3, 5, 10, or any other small number as a system limit, it
must not be overlooked that this limit mentioned is in all cases the limit
of the spoken numerals at the savage's command. The actual ability to count
is almost always, and one is tempted to say always, somewhat greater than
their vocabularies would indicate. The Bushman has no number word that will
express for him anything higher than 2; but with the assistance of his
fingers he gropes his way on as far as 10. The Veddas, the Andamans, the
Guachi, the Botocudos, the Eskimos, and the thousand and one other tribes
which furnish such scanty numeral systems, almost all proceed with more or
less readiness as far as their fingers will carry them. As a matter of
fact, this limit is frequently extended to 20; the toes, the fingers of a
second man, or a recount of the savage's own fingers, serving as a tale for
the second 10. Allusion is again made to this in a later chapter, where the
subject of counting on the fingers and toes is examined more in detail.

In saying that a savage can count to 10, to 20, or to 100, but little idea
is given of his real mental conception of any except the smallest numbers.
Want of familiarity with the use of numbers, and lack of convenient means
of comparison, must result in extreme indefiniteness of mental conception
and almost entire absence of exactness. The experience of Captain
Parry,[47] who found that the Eskimos made mistakes before they reached 7,
and of Humboldt,[48] who says that a Chayma might be made to say that his
age was either 18 or 60, has been duplicated by all investigators who have
had actual experience among savage races. Nor, on the other hand, is the
development of a numeral system an infallible index of mental power, or of
any real approach