Possible battery? What is this?

[east texas terry]

The core is what i find the most

 

[east texas terry]

 

[Bohdan]

Terry's got it right -- eg Columbia Dry Cell Battery -- see....

Columbia Dry Cell Battery - Landmark - American Chemical Society

American Chemical Society: Chemistry for Life.

www.acs.org

I suppose the shiny black material is an insulating/sealing glassy / ceramic material, or something tarry? Copper in the center electrode, corroding green -- perhaps you will find the location of the other electrode under the adhering muck on the other side?
Pretty cool. 1 1/2 volts - I wonder what it might have powered back then -- might be interesting to better establish age --- that type top seems, on quick internet search, to date from as early as the 1890s.
View attachment 238578

Probably used in a telephone.