I always wondered what this structure originally looked like. Finally, thanks to an article written by Post and Courier writer, Robert Behre, on Sunday, August 26th, titled "Preservation Remains Big Business Here," I have a better idea.
It seems that a woman named Frances Benjamin Johnston traveled to Charleston during the mid-1930s to photograph "endangered Southern architecture." Ms. Johnston's pictures are now part of the Library of Congress archives, and the old museum is included in this collection.
My favorite photo is posted below. It's taken facing west from across the street on Rutledge Avenue.
Frances Benjamin Johnston
I usually shoot from the opposite direction, or from the western edge of the park, looking east.