This configuration, with the engine directly driving a pump, was first used by Thomas Newcomen around 1705 to remove water from mines in Cornwall.
The Newcomen atmospheric engine was adopted by many mines in Cornwall and elsewhere, but it was relatively inefficient and consumed a large quantity of fuel.
Technically this was still an atmospheric engine until (under subsequent patents) he enclosed the upper part of the cylinder, introducing steam to also push the piston down.
However, in reality development had been ongoing by others and at the end of the patent period there was an explosion of new ideas and improvements.
Watt's beam engines were used commercially in much larger numbers and many continued to run for 100 years or more.
The beam engine went on to be considerably improved and enlarged in the tin- and copper-rich areas of south west England, which enabled the draining of the deep mines that existed there.
This is the compound effect; the waste steam from this can produce further work if it is then passed into a condenser in the normal way.
The early engines showed little performance gain: the steam pressure was too low, interconnecting pipes were of small diameter and the condenser ineffective.
In particular, their valve gear was cutting-in at the wrong position in the stroke, not allowing for expansive working in the cylinder.
This had two important effects: it massively reduced the pressure on the beam, and the connecting steam pipe, being long, acted as an expansive receiver – the element missing in the Woolf design.