phase with each other (quartered). When the double-expansion group is duplicated, producing a four-cylinder compound, the individual pistons within the group are usually balanced at 180°, the groups being set at 90° to each other. In one case (the first type of Vauclain compound), the pistons worked in the same phase driving a common crosshead and crank, again set at 90° as for a two-cylinder engine. With the three-cylinder compound arrangement, the LP cranks were either set at 90° with the HP one at 135° to the other two, or in some cases, all three cranks were set at 120°. The adoption of compounding was common for industrial units, for road engines and almost universal for marine engines after 1880; it was not universally popular in railway locomotives where it was often perceived as complicated. This is partly due to the harsh railway operating environment and limited space afforded by the loading gauge (particularly in Britain, where compounding was never common and not employed after 1930). However, although never in the majority, it was popular in many other countries. Multiple-expansion engines It is a logical extension of the compound engine (described above) to split the expansion into yet more stages to increase efficiency. The result is the multiple-expansion engine. Such engines use either three or four expansion stages and are known as triple- and quadruple-expansion engines respectively. These engines use a series of cylinders of progressively increasing diameter. These cylinders are designed to divide the work into equal shares for each expansion stage. As with the double-expansion engine, if space is at a premium, then two smaller cylinders may be used for the low-pressure stage. Multiple-expansion engines typically had the cylinders arranged inline, but various other formations were used. In the late 19th century, the Yarrow-Schlick-Tweedy balancing "system" was used on some marine triple-expansion engines. Y-S-T engines divided the low-pressure expansion stages between two cylinders, one at each end of the engine. This allowed the crankshaft to be better balanced, resulting in a smoother, faster-responding engine which ran with less vibration. This made the four-cylinder triple-expansion engine popular with large passenger liners (such as the Olympic class), but this was ultimately replaced by the virtually vibration-free turbine engine. It is noted, however, that triple-expansion reciprocating steam engines were used to drive the World War II Liberty ships, by far the largest number of identical ships ever built. Over 2700 ships