and 10,000 persons were to pass him in single file without his counting them as they passed, what sort of an estimate would he make of their number?  The truth seems to be that our mental conception of number is much more limited than is commonly thought, and that we unconsciously adopt some new unit as a standard of comparison when we wish to render intelligible to our minds any number of considerable magnitude.  For example, we say that A has a fortune of $1,000,000.  The impression is at once conveyed of a considerable degree of wealth, but it is rather from the fact that that fortune represents an annual income of $40,000 than, from the actual magnitude of the fortune itself.  The number 1,000,000 is, in itself, so greatly in excess of anything that enters into our daily experience that we have but a vague conception of it, except as something very great.  We are not, after all, so very much better off than the child who, with his arms about his mother’s neck, informs her with perfect gravity and sincerity that he “loves her a million bushels.”  His idea is merely of some very great amount, and our own is often but little clearer when we use the expressions which are so easily represented by a few digits.  Among the uneducated portions of civilized communities the limit of clear comprehension of number is not only relatively, but absolutely, very low.  Travellers in Russia have informed the writer that the peasants of that country have no distinct idea of a number consisting of but a few hundred even.  There is no reason to doubt this testimony.  The entire life of a peasant might be passed without his ever having occasion to use a number as great as 500, and as a result he might have respecting that number an idea less distinct than a trained mathematician would have of the distance from the earth to the sun.  De Quincey[50] incidentally mentions this characteristic in narrating a conversation which occurred while he was at Carnarvon, a little town in Wales.  “It was on this occasion,” he says, “that I learned how vague are the ideas of number in unpractised minds.  ’What number of people do you think,’ I said to an elderly person, ’will be assembled this day at Carnarvon?’ ‘What number?’ rejoined the person addressed; ’what number?  Well, really, now, I should reckon—­perhaps a matter of four million.’  Four millions of extra people in little Carnarvon, that could barely find accommodation (I should calculate) for an extra four hundred!” So the Eskimo and the South American Indian are, after all, not so very far behind the “elderly person” of Carnarvon, in the distinct perception of a number which familiarity renders to us absurdly small.

CHAPTER III.

THE ORIGIN OF NUMBER WORDS.