Two children Nancy Hamilton and Nathanial Hamilton do not appear in any records associated with David or his wife. David's will only mentions sons Levi and Josiah and adopted daughter Harriet. In the 1830 census he only has one child, a male under 5, who is Levi. In 1840 there are two sons, Levi 10-15 and Josiah 5-10. There is also a 15-20 year old female but she is likely associated with the 20-30 year old male living with them who is too old to be their child. The records for Nancy and Nathaniel appear to be associated with a different David Hamilton. I have disconnected them from these parents.
Sources
"United States Census, 1830," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHP3-WBJ : 19 August 2017), David H Hamilton, Sterling, Cayuga, New York, United States; citing 420, NARA microfilm publication M19, (Washington D.C.: National Archives and Records Administration, n.d.), roll 88; FHL microfilm 17,148.
"United States Census, 1840," database with images, FamilySearch (https://www.familysearch.org/ark:/61903/1:1:XHY4-CCC : 19 May 2020), D Hamilton, Brutus, Cayuga, New York, United States; citing p. 184, NARA microfilm publication , (Washington D.C.: National Archives and Records Administration, n.d.), roll ; FHL microfilm .
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCTL-GG7 : 4 April 2020), David H Hamilton, Brutus, Cayuga, New York, United States; citing family 243, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"New York State Census, 1865," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVNJ-HZC3 : 10 March 2018), David H Hamilton, , Barton, Cayuga, New York, United States; citing Census, p. 26, citing multiple county Clerks; Warren and Lewis County Board of Supervisors; multiple counties in New York; Utica and East Hampton Public Libraries, New York.
"New York State Census, 1875," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:VTD4-BG7 : 3 April 2020), David Hamilton, Brutus, Cayuga, New York, United States; citing p. 20, line 15, State Library, Albany; FHL microfilm 853,204.
New York, Wills and Probate Records, 1659-1999, Cayuga, Record of Wills, Vol 0027-0028, 1878-1881, David H. Hamilton (ancestry.com)
Find a Grave, database and images (https://www.findagrave.com/memorial/31884629), memorial page for David H. Hamilton (1802–1879), Find a Grave Memorial no. 31884629, citing Weedsport Rural Cemetery, Weedsport, Cayuga County, New York, USA ; Maintained by Dorothy Baker (contributor 46914541).
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