In the 1850 census she is called Jane, whereas in the 1860 census she is called Eliza, hence her name is Eliza Jane Conner.
Eliza Jane Conner Married A.J. Phipps https://www.myheritage.com/research/record-1-380923-2-4154/eliza-jane-phipps-born-conner-in-myheritage-family-trees
1850
Jane Conner: United States Census, 1850
Household Role Sex Age Birthplace Abner Conner M 46 Pennsylvania Winifried Conner M 33 Pennsylvania Abner Conner M 22 Pennsylvania Mary Conner F 7 Pennsylvania Amos Conner M 6 Pennsylvania Jane Conner F 3 Pennsylvania Margery Conner F 0 Pennsylvania John Worner M 60 Pennsylvania
Citing this Record:
1860
Eliza Conner: United States Census, 1860
Household Role Sex Age Birthplace Abner Conner M 56 Pennsylvania Winefred Conner F 45 Pennsylvania Mary Conner F 21 Pennsylvania Amos Conner M 17 Pennsylvania Eliza Conner F 13 Pennsylvania Margard Conner F 11 Pennsylvania Aaron Conner M 7 Pennsylvania James Conner M 6 Pennsylvania Molinda Conner F 3 Pennsylvania
Citing this Record:
1874
Jane E. Phipps: mentioned in the Death Record of Charles G. Phipps Name: Charles G. Phipps Event Type: Death Event Date: 28 Jun 1883 Event Place: Pittsburgh, Allegheny, Pennsylvania Gender: Male Age: 9 Birth Year (Estimated): 1874 Father's Name: Albert J. Phipps Mother's Name: Jane E. Phipps Spouse's Name: Reference ID: v 34 p 366 GS Film number: 505833 Digital Folder Number: 004672708 Image Number: 00216
Citing this Record: "Pennsylvania, Pittsburgh City Deaths, 1870-1905," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XZ7F-NQS : 8 December 2014), Jane E. Phipps in entry for Charles G. Phipps, 28 Jun 1883; citing v 34 p 366, Allegheny County Courthouse, Pittsburgh; FHL microfilm 505,833.
1877 --- Death Conner, Eliza J. 1848 -1877 29
http://files.usgwarchives.net/pa/westmoreland/cemeteries/sardis01.txt
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