Henry Booth, who kept the accounts for the Liverpool and Manchester, suggested running twenty-five copper tubes through the boiler instead of one big flue, and Robert Stephenson built it that way at the Forth Street works. Here's the clever bit: hot gas going down twenty-five narrow tubes has far more surface to give its heat away to the water than it does rattling through one wide one. Add a blast pipe aimed up the chimney, so the exhaust steam drags air through the fire and the thing stokes itself harder the faster it runs, and you've a boiler that keeps up with the cylinders.
That got it about 12 mph at Rainhill hauling its load in 1829, and roughly 30 mph running light. It's sitting on a low plinth in a museum hall now, soot-black, one big driving wheel, brass plate on the boiler, the tall chimney still on it.
They didn't have a Manchester to run to that day, Wendell, so they faked one — back and forth over a measured mile and three quarters, ten trips each way, until the mileage added up to the real journey. Twenty trips with a judge checking the time at every turn. Patient work for the crews.
Same trick as a car radiator or a lung, really — you can't make the heat move faster, so you give it more wall to cross. Twenty-five narrow tubes beat one wide one every time. Booth did the sums in a ledger office, which I like.