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1. Martha Mattie (b.Nov 1858 NY)
2. Charles (b.~1864 NY)
3. Fanny (b.~1866 NY)
4. Olive (b.Sept 1870 NY)
5. Richard (b.~1873 NY)

research of Kevin Everingham of MI, 2008-2009:

1870 CENSUS Troy, Rensselaer, NY ... Alexander Everingham 39, b.ENG,.. Emiline 40, b.NY,.. Mattie 12, b.NY,.. Aleck 9, b.NY,.. Charles 6, b.NY,.. Fanny 4, b.NY.

1880 CENSUS Troy, Rensselaer, NY (pg 474D #5726) ... Alex Everingham 49, b.ENG, occ: boiler maker,.. Emma 50, wife,.. Martha 21, school teacher,.. Aleck H. 19, printer,.. Charles 16,.. Fanney 13,.. Olive 9,.. Richard 7. (children born NY).

1900 CENSUS Brooklyn, Kings, NY (Page 7B, fam#159) ... Martha Evans 64, b.May 1886 NY, parents b.Ireland, occ: dress maker,.. Jane Brower 67, b. Dec 1833 NY, sister, parents b.Ireland,.. Elec H. Everingham 38, nephew, b.March 1862, parents b.NY. occ; music teacher.
1905 STATE CENSUS Brooklyn, Kings, NY (Page 2, Fam#362) ... Martha Evans 68, dressmaker,.. Jane Brower 70, sister,.. Aleck Everingham 40, nephew, musician

1910 CENSUS Brooklyn, Kings, NY (Page 7, fam#144) ... Martha Evans 73, b.NY, single, parents b.Ireland,... Aleck H. Everingham 49, b.NY, nephew, married, father b.ENG, mother b.NY.

1930 CENSUS Queens, Queens, New York (Sheet 14B, line 76)... Aleck H. Everingham 69, b.NY, father b.ENG, mother b.NY, married.

Are Martha and Jane sisters of his mom Emiline? Why does Alek show up in 1910 and 1930 listed as married but not living with a wife?

1936 Brooklyn, NY death record (cn 12956).. "Aleck H. Everingham age 75, died 10 June 1936 at Brooklyn, Kings County, New York,.. address: 15 Arlington Place, single, male, occupation; Musician, born 10 March 1861.. Burial 12 June 1936 Oakwood cemetery, Troy, NY. father; Alexander Everingham, mother Emiline Evans... Note: In NYC 40 yrs."