The Prosciutto di Portici Sundial, more often called the Portici Ham Sundial, dates from the first century somewhere between  8 BCE to 79 CE.  This small silvered bronze dial was uncovered on 11 June, 1755 in the ruins of Herculaneum (current day Portici) in the "Villa of the Papyri", buried in volcanic ash and charred papyri from the eruption of Mount Vesuvius in 79 CE. The form of the sundial, which resembles a ham, has been extensively studied.  It is an altitude dial with similarities to the cylindrical sundial. 

Live Science reporter Kristina Killgrove writes, "Historians have long assumed that the owner of the Villa of the Papyri was L. Calpurnius Piso Caesoninus, the father-in-law of Julius Caesar."  https://www.livescience.com/archaeology/romans/prosciutto-di-portici-a-portable-sundial-that-looks-like-a-pork-leg-and-it-was-likely-owned-by-julius-caesars-father-in-law-before-mount-vesuvius-erupted

Calpurnius likely commissioned the Epicurean philospher Philodemus to drave the numerous charred scrolls at Villa of the Papyri.  Killgrove commented that "This may explain why the Roman pocketwatch was shaped like a ham. For adherents of Epicurean thought, the lowly pig was often used as a metaphor, as it was seen as a naturally pleasure-seeking creature.

To clarify the use of the dial and the drawn lines attributed in the article as "hours before or after sunset" were actually temporal hours. The lines measuried the hours from sunrise to sunset. Temporary (ancient) hours go across the dial face and vertical lines represent the boundary between the zodiac signs representing the twelve months of the year.  In this dial the twelve months have been “folded” and the month pair labeled between the lines: IUN-IU (June-July), MA-AU (May-August), AP-SE (April-September), MA-OC (March-October), FE-NO (February-November) and JA-DE (January-December).  Notice that both July and August are used and the longest shadows occuring at the end of June while the shortest occur at the end of December.  Further, since July and August are named, the dial was created after the reign of Julius and Augustus Caesar, and in particular when Augustus renamed the month Sextilis to August in 8 BCE.

The Ham dial has a fixed gnomon, the flattened piece at middle-left in the photo.  When properly working, the gnomon is actually much longer and the tip set a specific distance above the dial face and at the upper left corner of the hour-date lines.  To read the time, the dial is rotated from a string at top of the dial until the shadow falls on the vertical date line (or distance between) corresponding to the date. Like the cylindrical sundial, time is read from the downward shadow of the tip crossing the temporary hour line.

The Ham dial also has “folded” hour lines that run across the dial to tell temporary (ancient) hours.  The lines are from top to bottom are for sunrise, 1^st/11^th, 2^nd/10^th, 3^rd/9^th, 4^th/8^th, 5^th/7^th, and at bottom, the 6^th hour line for mid-day.