What you describe is definitely NOT a pencil sharpener.  It is an opium
bowl, or a fragment thereof.  The opening that is about 1 cm in diameter
is where the bowl would screw on to the actual pipe, which is generally a
long shaft through which the smoke is inhaled.
 
I worked on a Gold Rush era site in San Francisco's Chinatown several
years ago and we found lots of these opium bowls, in many different
designs.  I seem to recall that the cone shape was fairly prevalent, as
was the bronze patina and the Chinese characters.  I don't recall what
kind of literature we found on these artifacts, but museums often have
good books and catalogs from exhibits -- try the DeYoung in San Francisco
or the Sackler in D.C.  Also any "gray literature" from CRM reports of
Chinese sites in the west.
 
Good luck!
 
Julie Abell
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