in want of a term with which to describe the 5, 10, or any other number of the numeral scale they were unconsciously forming.  That the first numbers of a numeral scale are usually derived from other sources, we have some reason to believe; but that all above 2, 3, or at most 4, are almost universally of digital origin we must admit.  Exception should properly be made of higher units, say 1000 or anything greater, which could not be expected to conform to any law of derivation governing the first few units of a system.

Collecting together and comparing with one another the great mass of terms by which we find any number expressed in different languages, and, while admitting the great diversity of method practised by different tribes, we observe certain resemblances which were not at first supposed to exist.  The various meanings of 1, where they can be traced at all, cluster into a little group of significations with which at last we come to associate the idea of unity.  Similarly of 2, or 5, or 10, or any one of the little band which does picket duty for the advance guard of the great host of number words which are to follow.  A careful examination of the first decade warrants the assertion that the probable meaning of any one of the units will be found in the list given below.  The words selected are intended merely to serve as indications of the thought underlying the savage’s choice, and not necessarily as the exact term by means of which he describes his number.  Only the commonest meanings are included in the tabulation here given.

1   = existence, piece, group, beginning.
2   = repetition, division, natural pair.
3   = collection, many, two-one.
4   = two twos.
5   = hand, group, division,
6   = five-one, two threes, second one.
7   = five-two, second two, three from ten.
8   = five-three, second three, two fours, two from ten.
9   = five-four, three threes, one from ten.
10   = one (group), two fives (hands), half a man, one man.
15   = ten-five, one foot, three fives.
20   = two tens, one man, two feet.[165]

CHAPTER V.

MISCELLANEOUS NUMBER BASES.

In the development and extension of any series of numbers into a systematic arrangement to which the term system may be applied, the first and most indispensable step is the selection of some number which is to serve as a base.  When the savage begins the process of counting he invents, one after another, names with which to designate the successive steps of his numerical journey.  At first there is no attempt at definiteness in the description he gives of any considerable number.  If he cannot show what he means by the use of his fingers, or perhaps by the fingers of a single hand, he unhesitatingly passes it by, calling it many, heap, innumerable, as many as the leaves on the trees, or something else equally expressive and equally indefinite.  But the time comes at last when a greater degree of exactness