as an indefinite term for a great many. Spix and Martins say of the low tribes of Brazil: ‘They count commonly by their finger joints, and so up to three only. Any larger number they express by the word many.’ In a Puri vocabulary the numerals are given as—1, omi; 2, curiri; 3, prica, ‘many’: in a Botocudo vocabulary—1, mokenam; 2, uruhú, ‘many.’" It is needless to multiply these examples.
The next step in advance in the development of a number system is taken when the fingers and toes are brought in as aids in the art of counting. The advance is now comparatively rapid up to the point where, these means being exhausted, there is no further natural aid conveniently at hand. It is popularly believed that finger-counting represents the very earliest stage of the art, but the existence of tribes who can not count as far as five, as already cited, would seem to be conclusive evidence of a stage which antedates this. The etymological character of the numeral words in most of the known languages points to the same conclusion. Prof. Levi Leonard Conant, in a book recently published under the title The Number Concept, has collected and analyzed a great number of the numeral systems of savage and semicivilized tribes. He says (pages 98 and 99): "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 practiced 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 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 terms 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. |
