"United States Census, 1900," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/M3F3-N81 : accessed 11 March 2015), Gertrude Williams in household of W F Williams, Bodcaw Township Sardis village, Hempstead, Arkansas, United States; citing sheet 8A, family 127, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,240,060.
"United States Census, 1910," index and images, FamilySearch (https://familysearch.org/pal:/MM9.1.1/MKJ1-QYL : accessed 11 March 2015), Gertrude Williams in household of William F Williams, Bodcaw, Hempstead, Arkansas, United States; citing enumeration district (ED) 72, sheet 2B, family 24, NARA microfilm publication T624 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,374,065.
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DNA Connections
It may be possible to confirm family relationships with Gertrude by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.