e practices of the
governors and the governed, neither of whom pursued a legitimate
course, confusion reigned supreme. Indeed, a system of weights,
measures, and coins, with a constant and real standard, and
corresponding multiples and divisions, though indulged in as a day-dream
by a few, has never yet been presented to the world in a definite form;
and as, in the absence of such a system, a corresponding system of
numeration and notation can be of no real use, the probability is, that
neither the one nor the other has ever been fully idealized. On the
contrary, the present base is taken to be a fixed fact, of the order of
the laws of the Medes and Persians; so much so, that, when the great
question is asked, one of the leading questions of the age,--How is this
mass of confusion to be brought into harmony?--the reply is,--It is only
necessary to adopt one constant and real standard, with decimal
multiples and divisions, and a corresponding nomenclature, and the work
is done: a reply that is still persisted in, though the proposition has
been fairly tried, and clearly proved to be impracticable.

Ever since commerce began, merchants, and governments for them, have,
from time to time, established multiples and divisions of given
standards; yet, for some reason, they have seldom chosen the number ten
as a base. From the long-continued and intimate connection of decimal
numeration and notation with the quantities commerce requires, may not
the fact, that it has not been so used more frequently, be considered as
sufficient evidence that this use is not proper to it? That it is not
may be shown thus:--A thing may be divided directly into equal parts
only by first dividing it into two, then dividing each of the parts into
two, etc., producing 2, 4, 8, 16, etc., equal parts, but ten never. This
results from the fact, that doubling or folding is the only direct mode
of dividing real quantities into equal parts, and that balancing is the
nearest indirect mode,--two facts that go far to prove binary division
to be proper to weights, measures, and coins. Moreover, use evidently
requires things to be divided by two more frequently than by any other
number,--a fact apparently due to a natural agreement between men and
things. Thus it appears the binary division of things is not only most
readily obtained, but also most frequently required. Indeed, it is to
some extent necessary; and though it may be set aside in part, with
proporti