On Agriculture (De Re Rustica)

...and corresponds to the fourth. The ninth is as long as the third had been; the tenth, 19, just as the second had been; the eleventh, 29, just as the first. And since January coincides with the month of December in the span of its hours, the shadows at each hour in this month will be the same as they are in January. The same is to be done in the other months, specifically by counting them in pairs: February agrees in the measure of its hours with November; March with October; April with September; May with August; June with July, as may be seen at the end of each month in Palladius. That passage in the same author at the end of the last month in these words: "Different cause joined December to January in hours, for the former increases with a similar line, while the latter decreases," should be understood as applying to the shadows—that they are equal and the same in individual paired months both before and after noon—and it is for a different reason also regarding the days, which are known to increase for six months and decrease for six. For even if the hours in the month of January are of the same quantity as in December, and the same in February as in November, and so on in the other pairs as the author shows, yet from each pair, as much as one increases, the other diminishes. For as the sun ascends from Capricorn to Cancer (as we said above), the days always increase; conversely, they decrease as it descends from Cancer to Capricorn. It should also be noted that as the days increase, the shadows of the gnomon always decrease; conversely, as the days decrease, these always increase. Hence, in the month of January, when the days are shortest and are increasing, the shadow of the gnomon at the first hour of the day is at its longest, at 29 feet. In February, which is the longest, 27; March, 25; April, 24; May, 23; June, 22. But in the month of July, when the days are longest and are decreasing, the shadow of the gnomon at the first hour of the day is 22 feet long, which is the shortest. August, 23; September, 24; October, 25; November, 27; December, 29. In order that this may be better known, we have also subjoined those months in which the days increase and shadows decrease, and those in which the days decrease and shadows increase. We began with January and July, in one of which the days are shortest and always increase until the summer solstice, and the shadows are longest but decrease as long as the days increase. In the other, the days are longest and always decrease until the winter solstice, and the shadows are shortest but increase as long as the days decrease. And although we should have begun from the solstices, which occur in December and June, and at that time the days begin to either increase or decrease...