War Department records for the US Civil War show that he enlisted 22 Aug 1862 with Company "H", 137th Pennsylvania Volunteer Infantry. By the end of the War he reached the rank of 2nd lieutenant. He received a pension as an Army Invalid.
Edmund was graduated from Columbia Law School, New York City, in 1865 and was practising his profession at 133 Nassau Street, New York, in October 1875.
From the New York Times, 22 Jan 1921: Edmund Bragdon Barnum, lawyer and prominent in the Democratic Party in the 80s and 90s, died on Thursday at his home, 437 Prospect Place, Brooklyn. He was in his seventy-seventh year. Mr. Barnum was born in Bethel, Conn., but removed to Brooklyn with his parents during his infancy. When 18 years old, he enlisted as a private in the 137th Regiment of Pennsylvania Volunteers and later became a Second Lieutenant. He was graduated from the Columbia Law School, and for years was a leading patent lawyer with offices in Manhattan and Brooklyn.