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258 three, four, five. But among the very low ones there is to be seen evidence of independent formation quite uncon- nected with a conventional system of numerals already existing. Thus the Greenlander did not use his 'one' to make 'first,' but calls it sujugdlek, 'foremost,' nor 'two' to make 'second,' which he calls aipâ, 'his companion;' it is only at 'third' that he takes to his cardinals, and forms pingajuat in connexion with pingasut, 3. So, in Indo-European languages, the ordinal prathamas, πρῶτος, primus, first, has nothing to do with a numerical 'one,' but with the preposition pra, 'before,' as meaning simply 'foremost;' and although Greeks and Germans call the next ordinal δεύτερος, zweite, from δύο, zwei, we call it second, Latin secundus, 'the following' (sequi), which is again a descriptive sense-word.

If we allow ourselves to mix for a moment what is with what might be, we can see how unlimited is the field of possible growth of numerals by mere adoption of the names of familiar things. Following the example of the Sleswigers we might make shilling a numeral for 12, and go on to ex- press 4 by groat; week would provide us with a name for 7, and clover for 3. But this simple method of description is not the only available one for the purpose of making numerals. The moment any series of names is arranged in regular order in our minds, it becomes a counting-machine. I have read of a little girl who was set to count cards, and she counted them accordingly, January, February, March, April. She might, of course, have reckoned them as Monday, Tuesday, Wednesday. It is interesting to find a case coming under the same class in the language of grown people. We know that the numerical value of the Hebrew letters is given with reference to their place in the alphabet, which was arranged for reasons that can hardly have had anything to do with arithmetic. The Greek alphabet is modi- fied from a Semitic one, but instead of letting the numeral value of their letters follow throughout their newly-arranged alphabet, they reckon α, β, γ, δ, ε, properly, as 1, 2, 3, 4, 5,