Mother's obituary names all living children, which did not include William.
Sources
"United States Census, 1880," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:MXJ5-CH6 : 13 January 2022), Willie Langridge in household of Richard Langridge, Kewanee, Henry, Illinois, United States; citing enumeration district , sheet , NARA microfilm publication T9 (Washington, D.C.: National Archives and Records Administration, n.d.), FHL microfilm .
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DNA Connections
It may be possible to confirm family relationships with William Barge 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 Barge: