l accepted. Those of
the present base are accepted with the mode, but those proper to a base
remain to be determined. In attempting to ascertain these, it will be
necessary to consider the uses of numeration and of notation.

These may be arranged in three divisions,--scientific, mechanical, and
commercial. The first is limited, being confined to a few; the second is
general, being common to many; the third is universal, being necessary
to all. Commercial use, therefore, will govern the present inquiry.

Commerce, being the exchange of property, requires real quantity to be
determined, and this in such proportions as are most readily obtained
and most frequently required. This can be done only by the adoption of a
unit of quantity that is both real and constant, and such multiples and
divisions of it as are consistent with the nature of things and the
requirements of use: real, because property, being real, can be measured
by real measures only; constant, because the determination of quantity
requires a standard of comparison that is invariable; conveniently
proportioned, because both time and labor are precious. These rules
being acted on, the result will be a system of real, constant, and
convenient weights, measures, and coins. Consequently, the numeration
and notation best suited to commerce will be those which agree best with
such a system.

From the earliest periods, special attention has been paid to units of
quantity, and, in the ignorance of more constant quantities, the
governors of men have offered their own persons as measures; hence the
fathom, yard, pace, cubit, foot, span, hand, digit, pound, and pint. It
is quite probable that the Egyptians first gave to such measures the
permanent form of government standards, and that copies of them were
carried by commerce, and otherwise, to surrounding nations. In time,
these became vitiated, and should have been verified by their originals;
but for distant nations this was not convenient; moreover, the governors
of those nations had a variety of reasons for preferring to verify them
by their own persons. Thus they became doubly vitiated; yet, as they
were not duly enforced, the people pleased themselves, so that almost
every market-town and fair had its own weights and measures; and as, in
the regulation of coins, governments, like the people, pleased
themselves, so that almost every nation had a peculiar currency, the
general result was, that with the laws and th