There are some similarities between this Abel Barnum and Abel J. Barnum (1804-1896). However, both appear in the 1870 US Census.
In the 1860 US Census for Hagar, Berrien County, Michigan the family of Abel Barnum was enumerated as follows:
Dwelling #228; Family #214
Abel Barnum, 57, M, W, Farmer, Real property $2,400, Personal property $408, b. New York
Sarah A. Barnum, 46, F, W, b. New York
Abel T. Barnum, 19, M, W, Farmer, b. New York, Attended school within the year
Andrew D. Barnum, 14, M, W, b. New York, Attended school within the year
Daniel Barnum, 9, M, W, b. Michigan, Attended school within the year
Ai Barnum, 2, M, W, b. Michigan
In the 1870 US Census for Hagar, Berrien County, Michigan the family of Abel Barnum was enumerated as follows:
Dwelling #136; Family #136
Barnum, Abel; 62; M; W; Farmer; Real property $3,000; Personal property $500; b. New York; Male citizen of the US of 21 years of age and upwards
Barnum, Sarah; 54; F; W; Keeps house; b. New York
Barnum, Daniel; 19; M; W; b. New York
Barnum, Ai; 12; M; W; b. Michigan; Attended school during the census year
Note: the family of Theodore Barnum, b. abt. 1848, lived four houses away.
In the 1880 US Census for District 8, Hagar, Berrien County, Michigan the family of Abel Barnum was enumerated as follows:
Dwelling #185; Family #206
Barnum, Abel J.; W; M; 62; Married; Farmer; b. New York; Both parents b. Connecticut
Barnum, Sarah A.; W; F; 58; Married; Keeping house; b. New York; Father b. New York; Mother b. Massachusetts
Note: living next door was the family of Ai Barnum, b. abt. 1858.