Philip Mead was online late one night in May, looking for possible artifacts from the American Revolution, when a painting up for auction caught his eye and got his heart racing. The chief historian at the Museum of the American Revolution, in Philadelphia, Pennsylvania, had spied an unsigned watercolor from 1782. It was a panorama of an army encampment, and to his expert eye seemed to feature the only known wartime depiction of the tent George Washington used as his command center during the Revolutionary War. The tent is the marquee exhibit at the museum, which opened in April. And,...