In The Genealogical Record of the Barnum Family (1912) he is called Bardsley Barnum.
In the 1850 US Census for Defiance, Defiance County, Ohio the family of Samuel B. Barnum was enumerated as follows:
Dwelling #164; Family #164
Samuel Barnum, 52, M, Carder and Fuller, Real property $700, b. Vermont
Maria Barnum, 45, F, b. Vermont
Jeduthan Barnum, 16, M, Carder, b. New York
John Barnum, 7, M, b. New York, Attended school within the year