The Answer

to the question about what is the pot.  Ann, with utmost speed, sent a link to the description of the Nippon Porcelain Condensed Milk Set.  Apparently in the late Victorian era and early 1900’s condensed milk was  popular and this particular set was manufactured in Japan.  The can of milk drops into the jar, and the hole enables one to push the can out again with the index and middle finger, to pour.  When finished, drop the can back into the porcelain container and reapply the lid. It was selling for $8.  Now, knowing what to look for, I see them advertised for around $200.