On the morning of the grand opening, eight coal wagons were assembled into a train. They were pulled up the first hill on a rope driven by a stationary engine at the top of the hill, then lowered down the other side.
horses pulled them over a bridge, then they were pulled up the next hill with a rope and another stationary engine, and lowered down the other side.
A later run that day used a locomotive and carried passengers.
it was the Stockton & Darlington Railway (corrected)
When I worked there (at the original station) it still had trains but I believe is now closed.
There is an absolutely huge station on the hill at the top end of the town, now called "Darlington Station" but then known by railway folk as "Bank Top" or "High Level" because ours was much lower.
many years later I discovered my grandfather had been born in Darlington, though from a Fife family.