Could you be more specific about the William Barnett you are looking for? The two choices you have given do not appear to be the same person, and I could find neither in the 1870 census. 1860 Person Cp., NC...William was born in NC, is a mechanic, wife's name Nancy A. 1880 Benton Co., AR...William was born in TN, is a tenant (farmer?), wife's name Dolla B. Nancy in MO