The development of astronomy implies considerable progress in mathematics; it is not surprising, therefore, that the Babylonians should have invented an extremely simple method of ciphering or have discovered the convenience of the **duodecimal** system.

Calculations involving feet and inches are sometimes performed by means of **duodecimal** arithmetic; i.e., in effect, the tables of square measure and of cubic measure are amplified by the insertion of intermediate units.

The value of 7r for **duodecimal** arithmetic is 3+1/12+8/122+ 4/12 3 +8/12 4 +..

.; so that, marking off **duodecimal** fractions by commas, the area in the above case is 4 of 3, I, 8, 4, 8 X15, 3 X15, 3 sq.

Hence we see that it probably passed from the East through Greece to Etruria, and thence became the standard foot of Rome; there, though divided by the Italian **duodecimal** system into 12 unciae, it always maintained its original 16 digits, which are found marked on some of the foot-measures.

-- 100 feet, 66 feet or a chain of 100 links, rod, pole, or perch, measures from 10 feet to 1 foot; 18 inches; yard of 36 inches, 1/2, 1/4, 18, 1/16 yard, nail, inch, and **duodecimal**, decimal, and binary parts of an inch.