'The Barnum Family, 1350-1907' calls him Hurlbert Eugene Barnum. When he was 19 years old (in 1870) he worked as a hostler for Sol Royce's hotel, in Thompson, New York. In 1900 he was the census enumerator for the town of Thompson, District No. 99.
The 1910 US Census for Thompson, Sullivan, New York shows: Eugene H. Barnum, head of house, M, W, 53, married 28 years Lillian J. Barnum, wife, F, W, 44, married 28 years, four children, three living Weston G. Barnum, son, M, W, 24, single Leon S. Barnum, son, M, W, 16, single Neal Dow Barnum, son, M, W, 11, single The place of birth for all family members and all their parents was given as New York; all of them spoke English.
From the Middletown (NY) Times Herald, Wednesday, May 16, 1934: Deaths and Funerals. Bridgeville- Herbert Eugene Barnum, a life resident of this community and son of two other life residents, died yesterday at the age of seventy-seven. He was a farmer, justice of the peace and member of the election board for many years. He and his wife, the former Miss Lillian Stratton of Thompsonville, passed the fifty-second wedding anniversary last December. Son of the late Lewis Henry and Maria Dewey Barnum, Mr. Barnum was born June twentieth, 1856. Besides his wife, he leaves two sons, Weston of Middletown, and Leon of Bridgeville; also a brother, Dr. H. W. Barnum of Pasadena, Calif. and six grandchildren. Funeral services will take place at the home at 2:30 p. m. Thursday and interment will be in Bridgeville cemetery. Heart trouble had kept Mr. Barnum in ill health several years.