Other equivalent classifications are:
UIC classification: 2A (also known as German classification and Italian classification)
French classification: 210
Turkish classification: 13
Swiss classification: 1/3
A few examples of Stephenson locomotives were already in operation in America, so engineers did not have to travel too far to get their initial ideas.
In America, the design was a modification of the 0-4-0 design then in common use. The 0-4-0 proved to be too rigid for the railroads of the day, often derailing on the tight curves and quick elevation changes of American railroads. For the 4-2-0, Jervis designed a four-wheel leading truck under the locomotive's smoke box that swiveled independently from the main frame of the locomotive. The pistons powered a single driving axle at the rear of the locomotive, just behind the firebox. This design resulted in a much more stable locomotive that was able to guide itself into curves more easily than the 0-4-0.
In England, it had developed from the 2-2-2 design of Stephenson's first Long Boiler locomotive, around 1840, which he had altered to place two pairs wheels at the front with the outside cylinders between them to improve stability.
This design proved so effective on American railroads that many of the early 0-4-0s were rebuilt as 4-2-0s. The 4-2-0 excelled in its ability to stay on the track. But with only one driving axle, the locomotive's weight was spread over a small proportion of the powered wheels, which meant its total power was substantially reduced.
One possible solution, patented in 1835 by Charles and George E. Sellers, caused the locomotive to tip upward while it was ascending a grade. This plan placed more of the locomotive's weight on the driving axle, but by reducing the weight on the leading truck, also made it more prone to derailments.
A more practical solution, first put into production by Norris, moved the driving axle to a location on the frame in front of the locomotive's firebox. Cantilevering the weight of the firebox and the locomotive crew behind the driving axle placed more weight on the driving axle without substantially reducing the weight on the leading truck. However, Norris's design led to a shorter wheelbase, which tended to offset any gains in the tractive force on the driving axle by reducing the locomotive's overall stability.
As the 1840s approached, and more American railroads were experimenting with the new 4-4-0 locomotive type, the 4-2-0 fell out of favor as it was not as able to pull a paying load on the railroad as the 4-4-0.
4-2-0s were built into the 1850s, but their use was restricted to light-duty trains as most railroads by this time had found them unsuitable for regular work.
In England, for freight work, four-coupled and six-coupled engines were performing well. However, for passenger work, the aim was greater speed. Because of the fragility of cast-iron connecting rods, "singles" continued to be used, with the largest driving wheels possible.
For some reason, British manufacturers did not take up the idea of mounting the forward wheels on a bogie for some years. Possibly there were fears about their stability, but with a long rigid frame, greater speed was achieved at the cost of a very rough ride and damage to the track.
The culmination of this approach was seen in the Crampton locomotive where, to make the drivers as large as possible, they were mounted behind the firebox.
Once steel became available, greater rotational speeds became possible with multiple, smaller coupled wheels.