mon 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
excused; but all errors are productive, and it should be remembered that
this one has produced that extraordinary perversion of truth to be found
in the reply to the question, How is all this confusion to be brought
into harmony? It has produced it not only in words, but in deed. Was it
not this reply that led the French commission to extend the use of the
present base from numeration to gradation also, under the delusive hope
of producing a perfectly homogeneous system, that would be practical
also? Was it not under its influence, that, adhering to the base to
which the world had been so long accustomed, instead of attempting to
regulate ideal division by real, which might have led to the adoption of
the true base and a practical system, they committed the one great error
of endeavoring to reverse true order, by forcing real division into
conformity with a preconceived ideal? This attempt was made at a time
supposed by many to be peculiarly suited to the purpose, a time of
changes. It was a time of changes, truly; but these were the result of
high excitement, not of quiet thought, such as the subject requires,--a
time for rushing forward, not for retracing misguided steps.
Accordingly, a system was produced which from its magnitude and
importance was truly imposing, and which, to the present day, is highly
applauded by all those who, under the influence of the error alluded to,
conceive decimal numeration to be a sacred truth: applauded, not because
of its adaptation to commerce, but simply because of its beautiful
proportions, its elegant symmetry, to say nothing of the array of
learning and power en