A compound steam engine unit is a type of steam engine where steam is expanded in two or more stages. A typical arrangement for a compound engine is that the steam is first expanded in a high-pressure (HP) cylinder, then having given up heat and losing pressure, it exhausts directly into one or more larger-volume low-pressure (LP) cylinders. Multiple-expansion engines employ additional cylinders, of progressively lower pressure, to extract further energy from the steam. Invented in 1781, this technique was first employed on a Cornish beam engine in 1804. Around 1850, compound engines were first introduced into Lancashire textile mills. Compound systems There are many compound systems and configurations, but there are two basic types, according to how HP and LP piston strokes are phased and hence whether the HP exhaust is able to pass directly from HP to LP (Woolf compounds) or whether pressure fluctuation necessitates an intermediate "buffer" space in the form of a steam chest or pipe known as a receiver (receiver compounds). In a single-expansion (or 'simple') steam engine, the high-pressure steam enters the cylinder at boiler pressure through an inlet valve. The steam pressure forces the piston down the cylinder, until the valve shuts (e.g. after 25% of the piston's stroke). After the steam supply is cut off the trapped steam continues to expand, pushing the piston to the end of its stroke, where the exhaust valve opens and expels the partially depleted steam to the atmosphere, or to a condenser. This "cut-off" allows much more work to be extracted, since the expansion of the steam is doing additional work beyond that done by the steam at boiler pressure. An earlier cut-off increases the expansion ratio, which in principle allows more energy to be extracted and increases efficiency. Ideally, the steam would expand adiabatically, and the temperature would drop corresponding to the volume increase. However, in practice the material of the surrounding cylinder acts as a heat reservoir, cooling the steam in the earlier part of the expansion and heating it in the later part. These irreversible heat flows decrease the efficiency of the process, so that beyond a certain point, further increasing the expansion ratio would actually decrease efficiency, in addition to decreasing the mean effective pressure and thus the power of the engine. Compounding engines A solution to the dilemma was invented in 1804 by British engineer Arthur Woolf, who patented his Woolf