Eugene is not living with his family in 1900, he would have been 6 yrs old. Eugene is not living with his family in 1905, he would have been 11 yrs old. Maybe he died. Also noted is his father is not in the home either.
"New York, Births and Christenings, 1640-1962," index, FamilySearch (https://familysearch.org/pal:/MM9.1.1/FD2G-6LY : accessed 08 Jun 2013), Florine Tatu in entry for Eugenius Arthur Steinmetz, 03 Sep 1894.
"New York, State Census, 1905
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