Decimal numeration grew out of the fact that each person has ten fingers and thumbs, without reference to science, art, or commerce. Ultimately scientific men discovered that it was not the best for certain purposes, consequently that a change might be desirable; but as they were not disposed to accommodate themselves to popular practices, which they erroneously viewed, not as necessary consequences, but simply as bad habits, they suggested a base with reference not so much to commerce as to science. The suggestion was never acted on, however; indeed, it would have been in vain, as Delambre remarks, for the French commission to have made the attempt, not only for the reason he presents, but also because it does not agree with natural division, and is therefore not suited to commerce; neither is it suited to the average capacity of mankind for numbers; for, though some may be able to use duodecimal numeration and notation with ease, the great majority find themselves equal to decimal only, and some come short even of that, except in its simplest use. Theoretically, twelve should be preferred to ten, because it agrees with circle measure at least, and ten agrees with nothing; besides, it affords a more comprehensive notation, and is divisible by 6, 4, 3, and 2 without a fraction, qualities that are theoretically valuable. At first sight, the universal use of decimal numeration seems to be an argument in its favor. It appears as though Nature had pointed directly to it, on account of some peculiar fitness. It is assumed, indeed, that this is the case, and habit confirms the assumption; yet, when reflection has overcome habit, it will be seen that its adoption was due to accident alone,--that it took place before any attention was paid to a general system, in short, without reflection,--and that its supposed perfection is a mere delusion; for, as a member of such a system, it presents disagreements on every hand; as has been said, it has no agreement with anything, unless it be allowable to say that it agrees with the Arabic mode of notation. This kind of agreement it has, in common with every other base. It is this that gives it character. On this account alone it is believed by many to be the perfection of harmony. They get the base of numeration and the mode of notation so mingled together, that they cannot separate them sufficiently to obtain a distinct idea of either; and some are not conscious that they are distinct, but see in the Arabic mode nothing save decimal notation, and attribute to it all those high qualities that belong to the mode only. The Arabic mode is an invention of the highest merit, not surpassed by any other; but the admiration that belongs to it is thus bestowed upon a quite commonplace idea, a misapplication, which, in this as in many other cases, arises from the fact, that it is much easier to admire than to investigate. This result of carelessness, if isolated, might be