lopment, among savage tribes to whom some writers on civilization have rashly denied the very faculty of self-improvement. The original meaning of a great part of the stock of numerals of the lower races, especially of those from 1 to 4, not suited to be named as hand-numerals, is obscure. They may have been named from comparison with objects, in a way which is shown actually to happen in such forms as 'together' for 2, 'throw' for 3, 'knot' for 4; but any concrete meaning we may guess them to have once had seems now by modification and mutilation to have passed out of knowledge.
Remembering how ordinary words change and lose their traces of original meaning in the course of ages, and that in numerals such breaking down of meaning is actually desirable, to make them fit for pure arithmetical symbols, we cannot wonder that so large a proportion of existing numerals should have no discernible etymology. This is especially true of the 1, 2, 3, 4, among low and high races alike, the earliest to be made, and therefore the earliest to lose their primary significance. Beyond these low numbers the languages of the higher and lower races show a remarkable difference. The hand-and-foot numerals, so prevalent and unmistakable in savage tongues like Esquimaux and Zulu, are scarcely if at all traceable in the great languages of civilization, such as Sanskrit and Greek, Hebrew and Arabic. This state of things is quite conformable to the development-theory of language. We may argue that it was in comparatively recent times that savages arrived at the invention of hand-numerals, and that therefore the etymology of such numerals remains obvious. But it by no means follows from the non-appearance of such primitive forms in cultured Asia and Europe, that they did not exist there in remote ages; they may since have been rolled and battered like pebbles by the stream of time, till their original shapes can no longer be made out. Lastly, among savage and civilized races alike, the general framework of numeration stands throughout the world as an
