How did stations share lines? Sending signals from New York to Sacramento wouldn’t be on a line used only by two stations. Several along the way would surely use it too.
IIRC, what would happen is that the messages couldn’t travel very far, so that the stations had to be fairly close together, and the whole thing operated like an electronic pony express. If you wanted to send a message to Sacramento from NYC, it would have to go through every telegraph operator between the two cities. Before each message was sent, the operator would signal the next operator down the line that a message was coming. That operator would signal back that he was ready, or that he was occupied with sending another message, in which case the operator wanting to send the message could query other operators to see if they were free or had a working line. This process would continue until the message got all the way to it’s destination. Thomas Edison got his start working on the telegraph and his first inventions were a repeater (to elminate all the substations), and a paper recorder (so if the operator was out of the office, the message could still get delivered).
My understanding is that you had one line that (in theory) ran from New York to Sacramento with stations along the way also connected to the same single line. Telegrams would be preceded by the station code that was to receive it, and the operators at each station wouldn’t transcribe the message unless it was actually intended for their station.
The “sharing” was done by using destination station coding on messages and a policy that you waited for a clear line before sending.
However, telegraph cables were only good for about 300 to 500 miles; the signal got too weak after that. So to send a message from New York to Sacramento, you’d probably actually send it to Pittsburgh, who would send it on to Cincinnati, then St. Louis, then Kansas City, then Denver, then Salt Lake City, then finally Sacramento. The “telegraphic repeater” was a class of devices created to “automate” this process.
The inability to use repeaters in underwater cable (at least until recently), incidentially, is why the Transatlantic Cable was such a remarkable feat originally. Modern underwater cables, of course, have imbedded repeaters, but that wasn’t really possible until the invention of the solid state amplifier, which came over a century after the invention of the telegraph.
This page may be of some tangential interest.
I also think that that is how the electromagnetic relay got its name. I don’t think the system was automated all the way across the courntry but for shorter distances there were relay stations. The incoming dot-dash code, weakened by having traveld some distance from the source, actuated the mechanism of the relay which is just a magnetically operated switch. The incoming and weak signal generated a magnetic field via a coil with an iron core. This field closed the relay contacts which connected a dc power supply to the outgoing telegraph lines making a duplicate of the incoming signal with its original amplitude restored to send on to the next relay station.