"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MX7J-VF1 : accessed 20 September 2015), Thomas F Hamilton in household of Thomas Hamilton, Kentucky, United States; citing p. 25, family 160, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 545,945.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCCM-DDP : accessed 20 September 2015), Thomas H Hamilton in household of Thos B Hamilton, Owingsville, Bath, Kentucky, United States; citing enumeration district 3, sheet 292A, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 0402; FHL microfilm 1,254,402.
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DNA Connections
It may be possible to confirm family relationships with Thomas by comparing test results with other carriers of his ancestors' Y-chromosome or mitochondrial DNA.
However, there are no known yDNA or mtDNA test-takers in his direct paternal or maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Thomas: