You can find ship arrivals in 1884 and much more at you local Mormon
Library. There are also indexed passenger lists for Philadelphia,
Boston, Baltimore, Galveston, and more. It is genealogist's heaven.
Please be aware, though, that NYC passenger lists are not indexed for
that time period, so you will have to look through lots of ships if
you don't know which one they came on. I would suggest checking
things like Hamburg Passenger List indexes first-they may save you
some time and give you information which is lacking on early NYC
You might not find a person on the ship and year you were told for
several reasons. First, many ships went back and forth between Europe
and NYC. The Darmstadt might have arrived in NY 12 times that year,
did you check all 12 lists? Of course, the information you have could
be wrong-they might have been off by a year or something.