Her death is inferred by the fact she does not appear with her siblings in the 1875 census when she would have been only 5 years old. Also her father names another daughter with his second wife 'Edith M', presumably in her memory.
Name: Emma A Peterson Event Type: Census Event Date: 1870 Event Place: Ballston, Saratoga, New York, United States Event Place (Original): Ballston, Saratoga, New York, United States Gender: Female Age: 3 Race: White Birth Year (Estimated): 1867 Birthplace: New York Page Number: 14
Household Role Sex Age Birthplace Almon R Peterson M 31 New York Eliza Peterson F 29 New York Emma A Peterson F 3 New York Edna M Peterson F 2 New York Edith M Peterson F 1 New York Abraham Hogeboom M 49 New York
Household ID: 109 Line Number: 9 Affiliate Name: The U.S. National Archives and Records Administration (NARA) Affiliate Publication Number: M593 GS Film Number: 000552587 Digital Folder Number: 004277081 Image Number: 00019
Citing this Record "United States Census, 1870", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M8K4-ZNF : 14 June 2019), Abraham Hogeboom in entry for Almon R Peterson, 1870.
Name: Almon Peterson Event Type: Census Event Date: 1875 Event Place: Corinth, Saratoga, New York, United States Gender: Male Age: 38 Birth Year (Estimated): 1837
Household Role Sex Age Birthplace Almon Peterson M 38 Emma Peterson Daughter F 8 Edna Peterson Daughter F 6 Gardner Peterson Son M 4 William Peterson Son M 2 Julia L Peterson Niece F 22 Peter A Payne Boarder M 37
Family Number: 92 Page: 8 Line Number: 43 GS Film number: 559005 Digital Folder Number: 004327093 Image Number: 00154
Citing this Record "New York State Census, 1875," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:VNV6-396 : 11 March 2018), Peter A Payne in household of Almon Peterson, Corinth, Saratoga, New York, United States; citing p. 9, line 4, State Library, Albany; FHL microfilm 559,005.
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