Railway's use of telegraph

From: kathy@kbowenmysteries.com

I'm writing a work of fiction set aboard a train that's traveling between Chicago and San Francisco in the summer of 1898. If there was an emergency aboard the train that necessitated alerting the police at the next major station, were they capable of sending a telegram while still en route, or would they have to wait until the train reached the closest station with a telegraph? ...

—Kathy Owen