The Electromotograph

 One of the earliest references to trains and  radio transmission I can find comes from the labs of Thomas Edison. In the mid-1880s, he patented an induction powered system on December 29, 1891. He called the receiving machine an "electromotograph" and the technique "grasshopper telegraphy." Rather than rehashing the patent, I'll just quote it.

"A cylinder of chalk, moistened with solution of caustic soda, is mounted so as to be rotated by a handle. A diaphragm has an arm connected to its center. This arm is pressed against the surface of the cylinder by a spring. When the cylinder is rotated, a constant tension is exerted on the diaphragm. If a current is passed through the junction of arm and cylinder the electrolytic action alters the friction so as to change the stress upon the diaphragm. If the current producing this effect is of the type produced by the human voice through a microphone the successive variations in strain upon the diaphragm will cause it to emit articulate sounds."

Edison had already sold his telephone patent to the Bell company, who also had bought several other phone related patents. So Edison needed to effectively reinvent the entire telephone. This sort of instance happened a lot in his career, today it's called NIH. Edison restarted with a good carbon-pencil transmitter invented by Frederic Gower.Then he began working on the new receiver. he filed for a patent in 1886 and it was granted in 1891. You can read it here. More on the electromotograph here.

Different systems used electrostatic and electromagnetic induction.  Let's define those quickly to save you from looking those up.  Nobody does that anyway.

• Electrostatic induction:  The redistribution of electrical charge in an object, caused by the influence of nearby charges. This is the principle under which the Van de Graaff generator functions.

• Electromagnetic induction:  The production of an electric current across a conductor moving through a magnetic field. This effect governs the function of a solenoid among other things.

Here's where we get to radio.  Edison's system used electromagnetic induction which gave it some unusual features. It allowed telegraphic signals to jump the short distance between a running train and telegraph wires running parallel to the tracks. You still see old wires like these running along old lines today. During the Great Blizzard of 1888, this system was used to send and receive wireless messages from trains buried in snowdrifts, perhaps the first successful use of wireless telegraphy to send distress calls.

Beyond that kind of emergency use, it had very little commercial appeal. Edison sold the system to Marconi in 1903. It was never used again to my knowledge.