After further research, the Burton Moore living in Jefferson County, TN in 1870 may not be the same Burton Moore that I am looking for. The Burton Moore I am looking for lived in Sullivan County, TN in 1860, and 1880. He then moved to Benton County, AR. He is listed on the 1900 Census in Benton County, AR., and he is listed in the Carroll County, AR. census in 1910 and 1920.