I found this in a box along with some battery rests. Is it actually a battery rest? I can't find a reference or drawing or anything that matches it. 3¾" diameter, just over 1" tall.

Answer: Nick Bergkessel thought it might be the bottom half of a British or French battery rest, so I compared it to one of my two-piece British rests (the kind with the perforated sheet lead cushion between the halves) and it's a match. Wish I had thought of that myself.