This pump was designed in the 1800's by John Ericsson, designer of the Civil War battleship Monitor. A fascinating series of linkages sequences all the events. The pump works by continuously heating and cooling the same air.
Water circulating around the cylinder cools the air, causing it to contract.
The water that cools the air was just brought up from the well. The Air Piston pushes the cooled, contracted air down past the Transfer Piston and the cycle repeats. It consists of 36 frames.