I found Jacob in the 1880 Census of Walton, Labette Co., KS. Jacob is a farmer, age 46, born in NY. Both parents are born in NY, too. No wife is listed. His three children are listed (and a niece): Estella (17, MI, NY, NY); Eugene (16, MI, NY, NY); and Mary (15, MI, NY, NY). The niece is Ella Kitchel (15, MI, MI, MI).
I later found him in the 1870 Census of Dover, Lenawee Co., MI: Jacob Burdine (40, NY), Lucy A. (36, NY), Alonza B. (female, 12, MI), Estella (8, MI), Eugene (6, MI), Mary (4, MI), and Charles (1, MI).