"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M6LP-CM7 : 12 April 2016), William Smith in household of Wm C Smith, Ohio, United States; citing p. 36, family 265, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 552,763.
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M8S2-XPM : 16 July 2017), William Smith in household of William C Smith, York, Sandusky, Ohio, United States; citing enumeration district ED 71, sheet 16C, NARA microfilm publication T9 (Washington D.C.: National Archives and Records Administration, n.d.), roll 1063; FHL microfilm 1,255,063.
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DNA Connections
It may be possible to confirm family relationships with William 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 William: