Belmont was a surgeon specializing in heart and lungs.

From http://www.nytimes.com/books/first/s/sperber-bogart.html

Even in that well-off community, the Bogarts were accorded a certain deference. Dr. Bogart ran a flourishing downstate practice and was known to have inherited wealth. His wife was the renowned illustrator and children's artist Maud Humphrey. It was said in hushed tones that they were DeForests--socially well connected and linked in some indefinable way with one of the oldest and most distinguished names in New York.