RMS = Royal Merchant Ship.
The RMS Mauretania and th RMS Aquitania
RMS stands for Royal Mail Steamer.
RMS in this context stands for Royal Mail Ship. Please see the related link.
Since 1840, ships which carried mail under contract to Royal Mail have been granted the designation Royal Mail Ship (RMS). A famous example is the RMS Carpathia, which rescued the survivors of the RMS Titanic and was later sunk by a German U-Boat in 1918.
The first ships were RMS Tayleur, Blue jacket and White Star. These were chartered sailing ships.
Royal Mail Steamer
There were two sister ships - the RMS Olympic and the HMHS Britannic.
RMS stands for Royal Mail Ship. Large British shipping companies won contracts to carry mail to the far extremes of the British Empire. These ships names were prefixed with RMS instead of SV (Sailing Vessel) as in the first mails ships and later SS (steamship). Both the Titanic and the Lousitania of the White Star Line were RMS ships.
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There were two sister ships - the RMS Olympic and the HMHS Britannic.
The RMS Carpathia
The RMS on Titanic stood for "Royal Mail Ship".