In the 1850 US Census for Lima, Livingston County, New York Jonathan Barnum was enumerated as follows;
Dwelling #166; Family #185
Jono. T. Barnhum [sic], 22, M, W, Student, b. New York, Attended school within the year
The "dwelling" where Jonathan was enumerated was apparently a school or university, within which a total of 214 persons were enumerated, including professors, teachers, clergymen, administrators and support staff.
Jonathan Barnum and his family appear in the 1880 US Census for Shandaken, Ulster County, New York. The census taker spelled their surname as Barnun and the wife of the family is Jonathan's second wife, Clara (Clarissa) Griffin.