gaged in its production and inauguration: imposing,
truly, and alike on its authors and admirers; for the qualities they so
much admire are not peculiar to the decimal base, but to the use of one
and the same base for numeration, notation, and gradation. But if the
base ten agrees with nothing, over, on, or under the earth, can it be
the best for scientific use? can it be at all suited to commercial
purposes? If true order is the object to be attained, and that for the
sake of its utility, then agreement between real and ideal division is
the one thing needful, the one essential change without which all other
changes are vain, the only change that will yield the greatest good to
the greatest number,--a change, which, as volition is with the ideal,
and inertia with the real, can be attained only by adaptation of the
ideal to the real.

A full investigation of the existing heterogeneous or fragmentary system
will lead to the discovery that it contains two elements which are at
variance with natural division and with each other, and that the
unsuccessful issue of every attempt at regulation hitherto made has been
the proper result of the mistake of supposing agreement between those
elements to be a possible thing.

The first element of discord to be considered is the division of things
by personal proportion, as by fathom, yard, cubit, foot, etc. It is
obvious at a glance, that these do not agree with binary division, nor
with decimal, nor yet with each other. It is this element that has
suggested the duodecimal base, to which some adhere so tenaciously,
apparently because they have not ascertained the essential quality of a
base.

The second is the numeration of things by personal parts, as fingers,
hands, etc.,--suggesting a base of numeration that has no agreement
with the binary, nor with personal proportion, neither can it have with
any proper general system. Are there any things in Nature that exist by
tens, that associate by tens, that separate into tenths? Are there any
things that are sold by tens, or by tenths? Even the fingers number
eight, and, had there been any reflection used in the adoption of a base
of numeration, the thumbs would not have been included. The ease with
which the simplest arithmetical series may be continued led our fathers
quietly to the adoption, first, of the quinary, and second, of the
decimal group; and we have continued its use so quietly, that its
propriety has rarely been question