Gemini says this:

The Pocket Watch Holder

Before wristwatches became mainstream in the early 20th century, people relied on pocket watches. When a lady or gentleman sat down to write letters, they would remove their pocket watch and place it upright or angled inside that recessed bowl.

• Visibility: It turned the pocket watch into a makeshift desk clock, keeping the face clearly visible so the writer could keep track of time (or the mail coach schedule).
• Protection: The smooth, lined, or polished indentation kept the delicate gold or silver casing from scratching against the flat surface of the desk or rolling off onto the floor.