I checked the Ellis Island web site and, as far as I can tell, Joseph and
Ruth Parkinson did not travel through Ellis Island in 1910. There was nobody
of the right ages anywhere near the year 1910.
Ancestry has a 1920 census index for some major US cities, which I would
check but Ancestry appears to be having technical problems right now. If
nobody else comes up with the goods I'll check it tomorrow.