His middle initial, on his nearly-illegible gravestone, could be H., N. or W.
In the 1860 US Census for Bangor, Franklin County, New York the family of Harvey Barnum was enumerated as follows:
Dwelling #1167; Family #1167
Harvey Barnum, 39, M, Farmer, Real property $3,000, Personal property $800, b. New York
Malinda Barnum, 31, F, Farmer, b. New York
Solon W. Barnum, 5, M, b. New York, Attended school within the year
Earla J. Barnum, 1, F, b. New York
His father and mother and his brother Carlos lived next door and several distant cousins lived nearby.
without issue.