Romans split the daylight from sunrise to sunset into twelve equal horae, and the night into twelve more, grouped into four military watches (vigiliae), so an hour stretched in summer and shrank in winter. Amusingly, Marcus Terentius Varro writes that Rome's first public sundial, brought from Catania, was laid out for the wrong latitude and told the wrong time for 99 years.
By day this page draws a hemicyclium, the hollow cut into a squared stone block that Vitruvius credits to Berosus the Chaldean, laid out for your latitude. A metal gnomon sits at the center-top of the hemispherical cutout so its shadow falls opposite the sun. Facing south, it starts high on the west (left) side at sunrise, sinks to the bottom at noon, and climbs to the east (right) side by sunset. Eleven hour lines divide the hemisphere into twelve sections, and three horizontal curves are drawn like on surviving dials: the winter solstice (bruma), the equinox (aequinoctium) and the summer solstice (solstitium). The dashed line is today's path, with sunrise and sunset worked out using the NOAA solar formulas.
By night, when a sundial is useless, the page switches to the water clock of Ctesibius. Water drips at a steady rate through a hole precisely bored in to gold or gemstone. It flows into a cylinder, and a float lifts a figure whose wand points to the hour on a display column. Nights lengthen and shorten through the year, so Ctesibius marks "the lines of the months" on the column and makes it turn appropriately, resulting in curved hour-lines wrapping around.