magnitude than this.  But as Dr. Boas was engaged in active work among them for three years, we may conclude that the Eskimo has an arithmetic but little more extended than that which sufficed for the Australians and the forest tribes of Brazil.  Early Russian explorers among the northern tribes of Siberia noticed the same difficulty in ordinary, every-day reckoning among the natives.  At first thought we might, then, state it as a general law that those races which are lowest in the scale of civilization, have the feeblest number sense also; or in other words, the least possible power of grasping the abstract idea of number.

But to this law there are many and important exceptions.  The concurrent testimony of explorers seems to be that savage races possess, in the great majority of cases, the ability to count at least as high as 10.  This limit is often extended to 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