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The Prussian Class S 3s were saturated steam locomotives developed by Hanomag for the Prussian state railways and were built from 1893.
They were a further development of the S 2 and used the same boiler. The "S" stood for Schnellzuglokomotive, or express locomotive, of which the S 3 was a large and powerful type. Because larger turntables with a 16-metre diameter were then being built, the wheelbase could be longer, which gave it better riding qualities. The locomotive had one high-pressure and one low-pressure cylinder, coupled to four driving wheels in a 4-4-0 configuration.
They were the first class of locomotives to use superheating, a process in which the steam leaving the boiler is re-heated, resulting in better efficiency.
The railway procured a total of 1,027 locomotives of this class up to 1904, and they were stabled at almost all locomotive depots ( Betriebswerk or Bw), making them the most numerous German express train locomotives. In addition, several hundred units were manufactured with smaller driving wheels - dubbed the P4 class.
Another 40 examples went to the Imperial Railways in Alsace-Lorraine (see Alsace-Lorraine S 3) and six units, with a modified axle base, to the Grand Duchy of Oldenburg State Railways (see Oldenburg S 3).
Whilst the Deutsche Reichsbahn still listed 451 Prussian S 3 engines in its 1923 renumbering plan (as 13 008 - 458), only 27 of them were left in 1925. They were grouped as DRG Class 13.0 with operating numbers 13 002–028. Locomotive 13 001 was not an S 3, but a Prussian S 2 converted into an Erfurt-type compound locomotive. The machines were retired by 1927.
The Oldenburg State Railway locomotives were allocated numbers 13 1801–1806 in 1925, but were retired only a year later.
After the First World War over 100 engines were left with the Polish ( PKP) and Lithuanian Railways where some were still in service in the 1940s. Some were incorporated into the Reichsbahn fleet during the Second World War as 13 010, 301, 302, 305 - 337, 339 and 340. Several of these locomotives were in the East German Deutsche Reichsbahn until 1955 and were then returned to Poland.
The locomotives were equipped with Prussian 3 T 15, 2'2' T 16, 2'2' T 20 and 2'2' T 21.5 tenders.