On Agriculture (De Re Rustica)

...contain four equinoctial hours. In like manner, the fourth is the same as the thirteenth with one-third of the fourteenth; the fifth is the remainder of the fourteenth with two-thirds of the fifteenth; the sixth is the remainder of the fifteenth with a full sixteenth, and it is noon. Likewise, the three temporal hours of the seventh, eighth, and ninth are the same as four equinoctial hours, namely the seventeenth, eighteenth, nineteenth, and twentieth. Similarly, the tenth, eleventh, and twelfth are the same as the twenty-first, twenty-second, twenty-third, and twenty-fourth. It did not seem out of place here to append the epigram of Martial to Euphemus, the steward of Domitian, where he mentions these temporal hours. It is as follows:

The first hour detains those paying respects, and the second as well.

Rome exercises its various labors until the fifth:

The eighth suffices for the shining games until the ninth.

The tenth hour, Euphemus, is for my little books,

And good Caesar is relaxed by the ethereal nectar,

Then admit the jests. My Thalia fears to go with a licentious step

The hours about which Palladius treats are those that divide the day from sunrise to sunset into twelve parts, which are detected by shadows in this way. Make a square plane according to a ruler and level in an open place that is illuminated by the sun all day, and let one side face north, another south, another east, and another west. Then, in the middle of the square, place the shadow-seeker, which in Greek is called γνώμων gnomon or σκιαθήρας shadow-catcher. Observe the first day of any month—for example, January—under a clear sky. Then, when the gnomon is touched by the sun's rays, the shadow of the gnomon at the first hour of the day will be 29 feet long; the second, 19; the third, 15; the fourth, 12; the fifth, 10; the sixth, 9. At this hour, as I said, it is always noon, for then the sun is at its highest and makes the shortest shadows. Then it begins to decline and descend toward sunset, and the shadows grow by the same measure they had decreased. Thus, at the seventh hour—which is the first after noon—the gnomon's shadow is 10 feet long and corresponds to the fifth hour before noon (for hours before the sixth are called antemeridian, and those after the sixth are called pomeridian). The eighth is 12 feet long...