He was a Lieutenant Commander in the US Navy during World War II and there is a bay named after him on the South Pacific island of Peleliu, in the Palau Group. (N.B., this statement could not be confirmed in 2003, but there is a wall dive called Barnum's Wall near Peleliu that is well known to scuba divers). He remained in the Naval Reserve after the war and was a Rear Admiral at the time of his death. His parents were music professors at a college in Indianapolis.
From the New York Times, February 1, 1989: H. James Barnum, 68, Ad Agency Founder. Dr. H. James Barnum Jr., the founder, chairman and chief executive officer of Barnum Communications, Inc., an advertising and public relations agency that represents medical and pharmaceutical companies, died of cancer Sunday at Columbia-Presbyterian Medical Center. he was 68 years old and lived in Manhattan.
Dr. Barnum founded the Manhattan agency in 1975 after a 10-year career at the J. Walter Thompson Company, where he rose to group executive vice president and president of J. W. T. Affiliated Companies. Thompson sued Dr. Barnum amid assertions of client-luring, but the dispute was settled out of court.
Dr. Barnum, a collateral descendant of the showman P. T. Barnum, was born in Indianapolis and grew up in Lakeland, Fla. He was a graduate of the United States Naval Academy, commanded a task group in the Pacific in World War II and rose to Rear Admiral in the Naval Reserve. In 1964, he received a medical degree from Columbia University.
Surviving are his wife, Barbara; two daughters, Elizabeth, of Manhattan, and Shauna, of Greenwich, Conn.; a son David, of Manhattan, and four grandchildren.