from this cause, like the destructive effect of
the constant dropping of water, though too slow in its progress to be
distinctly traced, is not the less certain. The economic value of binary
gradation is, in the aggregate, immense; yet its moral value is not to
be overlooked, when a full estimate of its worth is required.

Admitting binary gradation to be proper to weights, measures, and coins,
it follows that a corresponding base of numeration and notation must be
provided, as that best suited to commerce. For this purpose, the number
two immediately presents itself; but binary numeration and notation
being too prolix for arithmetical practice, it becomes necessary to
select for a base a power of two that will afford a more comprehensive
notation: a power of two, because no other number will agree with binary
gradation. It is scarcely proper to say the third power has been
selected, for there was no alternative,--the second power being too
small, and the fourth too large. Happily, the third is admirably suited
to the purpose, combining, as it does, the comprehensiveness of eight
with the simplicity of two.

It may be asked, how a number, hitherto almost entirely overlooked as a
base of numeration, is suddenly found to be so well suited to the
purpose. The fact is, the present base being accepted as proper for
numeration, however erroneously, it is assumed to be proper for
gradation also; and a very flattering assumption it is, promising a
perfectly homogeneous system of weights, measures, coins, and numbers,
than which nothing can be more desirable; but, siren-like, it draws the
mind away from a proper investigation of the subject, and the basic
qualities of numbers, being unquestioned, remain unknown. When the
natural order is adopted, and the base of gradation is ascertained by
its adaptation to things, and the base of numeration by its agreement
with that of gradation, then, the basic qualities of numbers being
questioned, two is found to be proper to the first use, and eight to the
second.

The idea of changing the base of numeration will appear to most persons
as absurd, and its realization as impossible; yet the probability is, it
will be done. The question is one of time rather than of fact, and there
is plenty of time. The diffusion of education will ultimately cause it
to be demanded. A change of notation is not an impossible thing. The
Greeks changed theirs, first for the alphabetic, and afterwards, with
t