There was a waterwheel in the hole that powered a linked rod that went all the way up the Thriddle Incline to power the pumps.
Here's what it looked like. I can see that the mechanism at the bottom turns rotary motion into backwards and forwards motion. There is a film of one working here.I was wondering how a backwards and forwards motion did the pumping but that is exactly what happens with an old-fashioned bicycle pump! This article was very useful.