This refers to the governor on a steam engine. Two heavy balls are attached to the engine so that as engine speed increases, the centrifigal force of the flywheel causes the balls to rise. As the balls top out, they govern (limit) the engine, thereby controlling maximum engine speed. "Balls out," then, refers to running the engine at maximum speed.
The engineer was running the train at a "balls out" pace while trying to make up time.
Old timey terminology: on steam engines, they had steel balls in there that resricted steam flow. When the conductor was ready to pick up speed, he'd yell "Balls out!", signaling the help to do just that, thereby letting them haul some ass.
"Balls out! We got to mow down those hobos!"
Dutch Grosseによって 2003年09月29日(月)