at some time, in some prehistoric language, have had definite meanings entirely apart from those which they now convey to our minds.  In savage languages it is sometimes possible to detect these meanings, and thus to obtain possession of the clue that leads to the development, in the barbarian’s rude mind, of a count scale—­a number system.  But in languages like those of modern Europe, the pedigree claimed by numerals is so long that, in the successive changes through which they have passed, all trace of their origin seems to have been lost.

The actual number of such words is, however, surprisingly small in any language.  In English we count by simple words only to 10.  From this point onward all our numerals except “hundred” and “thousand” are compounds and combinations of the names of smaller numbers.  The words we employ to designate the higher orders of units, as million, billion, trillion, etc., are appropriated bodily from the Italian; and the native words pair, tale, brace, dozen, gross, and score, can hardly be classed as numerals in the strict sense of the word.  German possesses exactly the same number of native words in its numeral scale as English; and the same may be said of the Teutonic languages generally, as well as of the Celtic, the Latin, the Slavonic, and the Basque.  This is, in fact, the universal method observed in the formation of any numeral scale, though the actual number of simple words may vary.  The Chiquito language has but one numeral of any kind whatever; English contains twelve simple terms; Sanskrit has twenty-seven, while Japanese possesses twenty-four, and the Chinese a number almost equally great.  Very many languages, as might be expected, contain special numeral expressions, such as the German dutzend and the French dizaine; but these, like the English dozen and score, are not to be regarded as numerals proper.

The formation of numeral words shows at a glance the general method in which any number scale has been built up.  The primitive savage counts on his fingers until he has reached the end of one, or more probably of both, hands.  Then, if he wishes to proceed farther, some mark is made, a pebble is laid aside, a knot tied, or some similar device employed to signify that all the counters at his disposal have been used.  Then the count begins anew, and to avoid multiplication of words, as well as to assist the memory, the terms already used are again resorted to; and the name by which the first halting-place was designated is repeated with each new numeral.  Hence the thirteen, fourteen, fifteen, etc., which are contractions of the fuller expressions three-and-ten, four-and-ten, five-and-ten, etc.  The specific method of combination may not always be the same, as witness the eighteen, or eight-ten, in English, and dix-huit, or ten-eight, in French; forty-five, or four-tens-five, in English, and fuenf und vierzig,