Paternal relationship is confirmed through Y-chromosome DNA testing. William Farrar and James Farrar match on 67 of 67 markers (see YSearch IDs FRXP4 and F8AKZ) thereby confirming their direct paternal lines back to the MRCA William Farrar III.
↑ ["United States Census, 1930," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:HX52-2N2 : accessed 30 August 2017), James E Farrar, Precinct 3, Madison, Texas, United States; citing enumeration district (ED) ED 9, sheet 12A, line 49, family 268, NARA microfilm publication T626 (Washington D.C.: National Archives and Records Administration, 2002), roll 2375; FHL microfilm 2,342,109.]
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DNA Connections
It may be possible to confirm family relationships with James by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: