I think this might be your 'Nathan Woodhull' Smith, by connecting the dots of Sarah (Smith) Durbrow and James B. Smith - likely some of Nathans' siblings.. So much for transcriptions!!!
Sarah's Death: "New York, New York City Municipal Deaths, 1795-1949," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:2W53-71L : 10 February 2018), Benjamin E. Smith in entry for Sarah Elizabeth Durbrow, 02 Jun 1911; citing Death, New York City, Richmond, New York, United States, New York Municipal Archives, New York; FHL microfilm 1,322,807.
Name Sarah Elizabeth Durbrow
Death 02 Jun 1911 New York City, Richmond, New York, United States
Female Age 80 Marital Status Widowed
Birth (Est) 1831 Birthplace N. Y.
Burial Date 06 Jun 1911
Father Benjamin E. Smith Birthplace N. Y.
Mother Harriett Tier Birthplace N. Y.
James B. Smith, son of Benjamin and Harriet Tier Smith marriage
Source: "New York Marriages, 1686-1980," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F6QT-DL7 : 10 February 2018), Benjamin E. Smith in entry for James B. Smith and Sarah E. Underwood Greaton, 26 Oct 1892; citing reference ; FHL microfilm 1,452,333.
New York Marriages
James B. Smith
Father Benjamin E. Smith Mother Harriet Tier
Spouse Sarah E. Underwood Greaton
Marriage 26 Oct 1892 Manhattan, New York, New York
Father William N. Underwood Mother Mary Raynolds
Source: "United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MCBX-YFM : 12 April 2016), Benjamin E Smith, New York City, ward 17, New York, New York, United States; citing family 1310, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
United States Census, 1850 New York City, ward 17, New York, New York, United States
Benjamin E Smith M 51 New York
Harriet Smith F 50 New York
Nicholas E Smith M 22 New York
Daniel P Smith M 20 New York
William H Smith M 17 New York
Jeremiah F Smith M 15 New York
James B Smith M 13 New York
Woodhul C Smith M 10 New York
Charles Smith M 9 New York
Julia B Indlum F 29 New York
William Durbrow M 25 New York
Sarah E Durbrow F 23 New York
William H Indlum M 30 New York
Eugene E Indlum M 5 New York
Source: "New York State Census, 1855," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:K67B-NJC : 13 March 2018), Benjamin E Smith in household of Wifhair Dubrow, E.D. 2, Ward 4, Brooklyn City, Kings, New York, United States; citing p. , line #21, family #575, county clerk offices, New York; FHL microfilm 1,930,197.
New York State Census, 1855 E.D. 2, Ward 4, Brooklyn City, Kings, New York, United States
Wifhair Dubrow Head M 30
Sarah E Durbrow Wife F 30
Lucretia Durbrow Child F 3
Benjamin E Smith Father M 60
Daniel P Smith Brother M 24
Nathan Smith Brother M 16
Charles J Smith Brother M 12