"United States Census, 1920," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MV95-F86 : accessed 16 June 2017), William F Walsh, Hoosick, Rensselaer, New York, United States; citing ED 15, sheet 1B, line 59, family 17, NARA microfilm publication T625 (Washington D.C.: National Archives and Records Administration, 1992), roll 1256; FHL microfilm 1,821,256.
"United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:X4TZ-FGR : accessed 16 June 2017), William F Walsh, Hoosick, Rensselaer, New York, United States; citing enumeration district (ED) ED 11, sheet 8A, line 8, family 202, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 1637; FHL microfilm 2,341,371.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K3BY-H19 : accessed 16 June 2017), William Walsh, Ward 4, Hoosick Falls, Hoosick Town, Rensselaer, New York, United States; citing enumeration district (ED) 42-15, sheet 2A, line 20, family 30, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 2756.
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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 Y-chromosome or his mother's 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: