Yes, Its a water well pump for a well deeper than 50 feet. Water wells ran 3/8 diameter rods all the way to the bottom of the well pipe which was usually 1 & 1/4" diameter. The bottom 3 foot section of pipe was a machined tube with a Ball Check Valve in the bottom with the ball sitting on top of a seat. Attached to the rods was a Cylinder shaped Ball Check Valve with the ball sitting on top of the seat with Leather Cups on the cylinder part (think piston). The up and down motion created a suction opening the bottom valve to let water into the cylinder. On the down stroke, the bottom ball seated and the "working" ball valve opened to travel thru the water in the cylinder displacing it to its top. On the next stroke, the whole process repeated. This is the same way oil is pumped out of the ground on a larger scale.
My Grandfather used to service water wells like this in the upper New York State area.