If we inquire into the basis of the duodecimal system and consider how it can have happened that, in addition to ten, twelve should have been so early and universally singled out from the equal 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 Greek —­medimnos—­ of 2:1.  To one who can decipher the significance of such records, these names and numerical proportions fully reveal the activity and importance of the intercourse between the Sicilians and the Latins.  The Greek numeral signs were not adopted; but the Roman probably