In the 1870 census Francis is listed as 6 mos old and living with Andrew Cornelius who has no wife with him, only a 24 year old housekeeper named Marta Cornelius.
"United States Census, 1870," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MXWC-Y77 : accessed 20 April 2016), Frances Cornelius in household of Andrew Cornelius, Kentucky, United States; citing p. 5, family 37, NARA microfilm publication M593 (Washington D.C.: National Archives and Records Administration, n.d.); FHL microfilm 545,970.
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M26D-ZY9 : accessed 17 April 2016), Hugh Isaacs in household of Andrew Isaacs, Berea, Madison, Kentucky, United States; citing enumeration district (ED) ED 73, sheet 14A, NARA microfilm publication T624 (Washington, D.C.: National Archives and Records Administration, n.d.); FHL microfilm 1,374,507.
Note: May be the sister of Lafayette Cornelius (Sept 1871) and Finley Cornelius (Jan 1879) who were registered as borders with Andrew and Francis in the 1900 census. District: 58 , Sheet Number and Letter: 3A , Household ID: 45 , Line Number: 34 , Affiliate Name: The U.S. National Archives and Records Administration (NARA) , Affiliate Publication Number: T623 , GS Film Number: 1240527 , Digital Folder Number: 004118915 , Image Number: 00807 . familysearch: https://familysearch.org/pal:/MM9.1.1/M94N-D58
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DNA Connections
It may be possible to confirm family relationships with Frances by comparing test results with other carriers of her mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Frances:
Cornelius-1034 and Cornelius-951 appear to represent the same person because: They have the same husband and children, but I think the correct spelling of her name is Frances, not Francis -- at least, Frances is how it is spelled on her tombstone