al series
of numbers, we shall probably be able to find no other source to
which it can be referred than a comparison of the solar and lunar
periods. Still more than the double hand of ten fingers did the
solar cycle of nearly twelve lunar periods first suggest to man
the profound conception of an unit composed of equal units, and
thereby originate the idea of a system of numbers, the first step
towards mathematical thought. The consistent duodecimal development
of this idea appears to have belonged to the Italian nation, and
to have preceded the first contact with the Greeks.

Hellenic Measures in Italy

But when at length the Hellenic trader had opened up the route to
the west coast of Italy, the measures of surface remained unaffected,
but the measures of length, of weight, and above all of capacity--in
other words those definite standards without which barter and traffic
are impossible--experienced the effects of the new international
intercourse. The oldest Roman foot has disappeared; that which we
know, and which was in use at a very early period among the Romans,
was borrowed from Greece, and was, in addition to its new Roman
subdivision into twelfths, divided after the Greek fashion into four
hand-breadths (-palmus-) and sixteen finger-breadths (-digitus-).
Further, the Roman weights were brought into a fixed proportional
relation to the Attic system, which prevailed throughout Sicily
but not in Cumae--another significant proof that the Latin traffic
was chiefly directed to the island; four Roman pounds were assumed as
equal to three Attic -minae-, or rather the Roman pound was assumed
as equal to one and a half of the Sicilian -litrae- or half-minae.(7)
But the most singular and chequered aspect is presented by the
Roman measures of capacity, as regards both their names and their
proportions. Their names have come from the Greek terms either by
corruption (-amphora-, -modius- after --medimnos--, -congius- from
--choeus--, -hemina-, -cyathus-) or by translation (-acetabulum-from
--ozubaphon--); while conversely --zesteis-- is a corruption of
-sextarius-. All the measures are not identical, but those in most
common use are so; among liquid measures the -congius- or -chus-,
the -sextarius-, and the -cyathus-, the two last also for dry
goods; the Roman -amphora- was equalized in water-weight to the
Attic talent, and at the same time stood to the Greek --metretes--
in the fixed ratio of 3:2, and to the G