Early Train Telegraphy - Scientific American Issue, 21 February 1885
In 1885 the New Haven Railroad experimented on its Harlem River Branch with "The
Phelps system of Telegraphing from a railway train while in motion."  The inventor
worked on the principle that if two wires are extended parallel to each other, a 
current sent through one will excite a momentary current in the other, in the
opposite direction.  ... Messages sent from a moving train were taken up
by induction by the track wire.  ... The Phelps Company grew through several
consolidations, but eventually train telegraphy died out.  Possibly the equipment
required to pick up the comparatively weak signal was too sensitive to stand
continuous service without the aid of electronic devices to amplify currents.

[Note: The Northern Railway of Canada experimented with train telephony about the
same time and found it successful but like the New Haven above, it too, was not
expanded even after much success.]