What method of communication became extremely important by the end of the nineteenth century because of its use in coordinating rail travel?

Telegraph

Explanation: Telegraph was a device that was discovered in 1844 for the long distance communication. This device functioned by transmitting a message through electrical signal from source to destination and then receive back a message as a response.

Telegraph operator ,also known as telegrapher was the main worker for operating and processing the task of telegraphy in the field of rail . Morse code were used for creating the message communication for maintaining the coordination rail field.